From e7ccf2e72a07fa1e7da2c5ddfa1f786ccca07699 Mon Sep 17 00:00:00 2001 From: Calascibetta Romain Date: Fri, 20 Dec 2024 23:45:12 +0100 Subject: [PATCH] First commit --- GNUmakefile | 120 + armstub8.S | 213 + clock.c | 41 + configure.sh | 456 ++ crt.c | 44 + doc.txt | 58 + exception_handler.c | 6 + exception_stub.S | 298 + gen-headers.sh | 104 + gilbraltar.ld | 52 + include/bcm.h | 23 + include/clock.h | 6 + include/exception_handler.h | 32 + include/exception_stub.h | 8 + include/gpio.h | 6 + include/led.h | 8 + include/log.h | 19 + include/mbox.h | 21 + include/mem.h | 23 + include/memory_map.h | 57 + include/serial.h | 29 + include/sysconfig.h | 44 + include/tag.h | 10 + include/timer.h | 13 + interrupt_handler.c | 9 + kernel.c | 3 + led.c | 14 + log.c | 32 + mbox.c | 18 + nolibc/GNUmakefile | 58 + nolibc/assert.c | 18 + nolibc/ctype.c | 26 + nolibc/dlmalloc.i | 6339 ++++++++++++++++++ nolibc/dtoa.c | 6234 +++++++++++++++++ nolibc/errlist.c | 64 + nolibc/fprintf.c | 12 + nolibc/include/_gilbraltar/byteorder.h | 16 + nolibc/include/_gilbraltar/overrides.h | 13 + nolibc/include/assert.h | 20 + nolibc/include/ctype.h | 12 + nolibc/include/dirent.h | 12 + nolibc/include/endian.h | 45 + nolibc/include/errno.h | 26 + nolibc/include/fcntl.h | 18 + nolibc/include/features.h | 6 + nolibc/include/inttypes.h | 122 + nolibc/include/limits.h | 23 + nolibc/include/math.h | 1 + nolibc/include/pthread.h | 57 + nolibc/include/sched.h | 8 + nolibc/include/setjmp.h | 5 + nolibc/include/signal.h | 27 + nolibc/include/stdio.h | 42 + nolibc/include/stdlib.h | 39 + nolibc/include/string.h | 29 + nolibc/include/sys/ioctl.h | 4 + nolibc/include/sys/mman.h | 26 + nolibc/include/sys/param.h | 6 + nolibc/include/sys/stat.h | 20 + nolibc/include/sys/time.h | 16 + nolibc/include/sys/times.h | 13 + nolibc/include/sys/types.h | 13 + nolibc/include/sys/wait.h | 4 + nolibc/include/time.h | 1 + nolibc/include/unistd.h | 26 + nolibc/memchr.c | 23 + nolibc/memcmp.c | 8 + nolibc/memcpy.c | 124 + nolibc/memmove.c | 36 + nolibc/memset.c | 86 + nolibc/mmap.c | 77 + nolibc/printf.c | 12 + nolibc/puts.c | 17 + nolibc/snprintf.c | 13 + nolibc/stpncpy.c | 27 + nolibc/strchr.c | 9 + nolibc/strchrnul.c | 23 + nolibc/strcmp.c | 7 + nolibc/strerror_r.c | 19 + nolibc/strlen.c | 18 + nolibc/strncmp.c | 9 + nolibc/strncpy.c | 9 + nolibc/strnlen.c | 20 + nolibc/strstr.c | 155 + nolibc/strtol.c | 150 + nolibc/stubs.c | 152 + nolibc/sysconf.c | 11 + nolibc/sysdeps.c | 47 + nolibc/vfprintf.c | 650 ++ nolibc/vsnprintf.c | 41 + openlibm/.gitignore | 7 + openlibm/.mailmap | 61 + openlibm/.travis.yml | 73 + openlibm/CMakeLists.txt | 576 ++ openlibm/LICENSE.md | 115 + openlibm/Make.inc | 190 + openlibm/Makefile | 137 + openlibm/README.md | 71 + openlibm/aarch64/Make.files | 1 + openlibm/aarch64/fenv.c | 51 + openlibm/amd64/Make.files | 7 + openlibm/amd64/bsd_asm.h | 110 + openlibm/amd64/bsd_fpu.h | 218 + openlibm/amd64/bsd_ieeefp.h | 272 + openlibm/amd64/e_fmod.S | 56 + openlibm/amd64/e_fmodf.S | 26 + openlibm/amd64/e_fmodl.S | 52 + openlibm/amd64/e_remainder.S | 30 + openlibm/amd64/e_remainderf.S | 29 + openlibm/amd64/e_remainderl.S | 35 + openlibm/amd64/e_sqrt.S | 40 + openlibm/amd64/e_sqrtf.S | 39 + openlibm/amd64/e_sqrtl.S | 46 + openlibm/amd64/fenv.c | 162 + openlibm/amd64/s_llrint.S | 12 + openlibm/amd64/s_llrintf.S | 12 + openlibm/amd64/s_llrintl.S | 45 + openlibm/amd64/s_logbl.S | 29 + openlibm/amd64/s_lrint.S | 44 + openlibm/amd64/s_lrintf.S | 44 + openlibm/amd64/s_lrintl.S | 45 + openlibm/amd64/s_remquo.S | 76 + openlibm/amd64/s_remquof.S | 76 + openlibm/amd64/s_remquol.S | 81 + openlibm/amd64/s_rintl.S | 26 + openlibm/amd64/s_scalbn.S | 55 + openlibm/amd64/s_scalbnf.S | 55 + openlibm/amd64/s_scalbnl.S | 40 + openlibm/arm/Make.files | 1 + openlibm/arm/fenv.c | 52 + openlibm/bsdsrc/Make.files | 1 + openlibm/bsdsrc/b_exp.c | 172 + openlibm/bsdsrc/b_log.c | 466 ++ openlibm/bsdsrc/b_tgamma.c | 319 + openlibm/bsdsrc/mathimpl.h | 70 + openlibm/docs/CNAME | 1 + openlibm/docs/images/arrow-down.png | Bin 0 -> 216 bytes openlibm/docs/images/octocat-small.png | Bin 0 -> 357 bytes openlibm/docs/index.html | 93 + openlibm/docs/javascripts/scale.fix.js | 20 + openlibm/docs/params.json | 1 + openlibm/docs/stylesheets/pygment_trac.css | 69 + openlibm/docs/stylesheets/styles.css | 423 ++ openlibm/i387/Make.files | 21 + openlibm/i387/bsd_asm.h | 118 + openlibm/i387/bsd_ieeefp.h | 265 + openlibm/i387/bsd_npx.h | 160 + openlibm/i387/e_exp.S | 76 + openlibm/i387/e_fmod.S | 25 + openlibm/i387/e_log.S | 21 + openlibm/i387/e_log10.S | 21 + openlibm/i387/e_log10f.S | 22 + openlibm/i387/e_logf.S | 21 + openlibm/i387/e_remainder.S | 25 + openlibm/i387/e_remainderf.S | 26 + openlibm/i387/e_remainderl.S | 25 + openlibm/i387/e_sqrt.S | 37 + openlibm/i387/e_sqrtf.S | 21 + openlibm/i387/e_sqrtl.S | 19 + openlibm/i387/fenv.c | 226 + openlibm/i387/invtrig.c | 86 + openlibm/i387/osx_asm.h | 408 ++ openlibm/i387/s_ceil.S | 34 + openlibm/i387/s_ceilf.S | 36 + openlibm/i387/s_ceill.S | 34 + openlibm/i387/s_copysign.S | 25 + openlibm/i387/s_copysignf.S | 26 + openlibm/i387/s_copysignl.S | 24 + openlibm/i387/s_cos.S | 33 + openlibm/i387/s_floor.S | 35 + openlibm/i387/s_floorf.S | 36 + openlibm/i387/s_floorl.S | 34 + openlibm/i387/s_llrint.S | 43 + openlibm/i387/s_llrintf.S | 43 + openlibm/i387/s_llrintl.S | 42 + openlibm/i387/s_logb.S | 21 + openlibm/i387/s_logbf.S | 22 + openlibm/i387/s_logbl.S | 20 + openlibm/i387/s_lrint.S | 42 + openlibm/i387/s_lrintf.S | 42 + openlibm/i387/s_lrintl.S | 41 + openlibm/i387/s_remquo.S | 69 + openlibm/i387/s_remquof.S | 69 + openlibm/i387/s_remquol.S | 69 + openlibm/i387/s_rint.S | 20 + openlibm/i387/s_rintf.S | 21 + openlibm/i387/s_rintl.S | 19 + openlibm/i387/s_scalbn.S | 23 + openlibm/i387/s_scalbnf.S | 26 + openlibm/i387/s_scalbnl.S | 26 + openlibm/i387/s_sin.S | 33 + openlibm/i387/s_tan.S | 35 + openlibm/i387/s_trunc.S | 33 + openlibm/i387/s_truncf.S | 33 + openlibm/i387/s_truncl.S | 33 + openlibm/include/openlibm.h | 8 + openlibm/include/openlibm_complex.h | 179 + openlibm/include/openlibm_defs.h | 14 + openlibm/include/openlibm_fenv.h | 25 + openlibm/include/openlibm_fenv_amd64.h | 223 + openlibm/include/openlibm_fenv_arm.h | 230 + openlibm/include/openlibm_fenv_i387.h | 260 + openlibm/include/openlibm_fenv_loongarch64.h | 226 + openlibm/include/openlibm_fenv_mips.h | 278 + openlibm/include/openlibm_fenv_powerpc.h | 279 + openlibm/include/openlibm_fenv_riscv.h | 261 + openlibm/include/openlibm_fenv_s390.h | 235 + openlibm/include/openlibm_math.h | 493 ++ openlibm/ld128/Make.files | 13 + openlibm/ld128/e_acoshl.c | 58 + openlibm/ld128/e_atanhl.c | 65 + openlibm/ld128/e_coshl.c | 105 + openlibm/ld128/e_expl.c | 145 + openlibm/ld128/e_fmodl.c | 129 + openlibm/ld128/e_hypotl.c | 122 + openlibm/ld128/e_lgammal_r.c | 1037 +++ openlibm/ld128/e_log10l.c | 255 + openlibm/ld128/e_log2l.c | 248 + openlibm/ld128/e_logl.c | 283 + openlibm/ld128/e_powl.c | 439 ++ openlibm/ld128/e_rem_pio2l.h | 144 + openlibm/ld128/e_sinhl.c | 104 + openlibm/ld128/e_tgammal.c | 39 + openlibm/ld128/invtrig.c | 100 + openlibm/ld128/invtrig.h | 113 + openlibm/ld128/k_cosl.c | 61 + openlibm/ld128/k_sinl.c | 59 + openlibm/ld128/k_tanl.c | 120 + openlibm/ld128/s_asinhl.c | 69 + openlibm/ld128/s_ceill.c | 69 + openlibm/ld128/s_erfl.c | 926 +++ openlibm/ld128/s_exp2l.c | 431 ++ openlibm/ld128/s_expm1l.c | 162 + openlibm/ld128/s_floorl.c | 71 + openlibm/ld128/s_log1pl.c | 247 + openlibm/ld128/s_modfl.c | 73 + openlibm/ld128/s_nanl.c | 46 + openlibm/ld128/s_nextafterl.c | 72 + openlibm/ld128/s_nexttoward.c | 85 + openlibm/ld128/s_nexttowardf.c | 65 + openlibm/ld128/s_remquol.c | 168 + openlibm/ld128/s_tanhl.c | 105 + openlibm/ld128/s_truncl.c | 72 + openlibm/ld80/Make.files | 13 + openlibm/ld80/e_acoshl.c | 57 + openlibm/ld80/e_atanhl.c | 60 + openlibm/ld80/e_coshl.c | 83 + openlibm/ld80/e_expl.c | 131 + openlibm/ld80/e_fmodl.c | 142 + openlibm/ld80/e_hypotl.c | 122 + openlibm/ld80/e_lgammal_r.c | 425 ++ openlibm/ld80/e_log10l.c | 205 + openlibm/ld80/e_log2l.c | 199 + openlibm/ld80/e_logl.c | 190 + openlibm/ld80/e_powl.c | 615 ++ openlibm/ld80/e_rem_pio2l.h | 152 + openlibm/ld80/e_sinhl.c | 76 + openlibm/ld80/e_tgammal.c | 313 + openlibm/ld80/invtrig.c | 82 + openlibm/ld80/invtrig.h | 114 + openlibm/ld80/k_cosl.c | 78 + openlibm/ld80/k_sinl.c | 62 + openlibm/ld80/k_tanl.c | 125 + openlibm/ld80/s_asinhl.c | 54 + openlibm/ld80/s_ceill.c | 78 + openlibm/ld80/s_erfl.c | 430 ++ openlibm/ld80/s_exp2l.c | 295 + openlibm/ld80/s_expm1l.c | 138 + openlibm/ld80/s_floorl.c | 80 + openlibm/ld80/s_log1pl.c | 191 + openlibm/ld80/s_modfl.c | 69 + openlibm/ld80/s_nanl.c | 45 + openlibm/ld80/s_nextafterl.c | 90 + openlibm/ld80/s_nexttoward.c | 86 + openlibm/ld80/s_nexttowardf.c | 67 + openlibm/ld80/s_remquol.c | 166 + openlibm/ld80/s_tanhl.c | 79 + openlibm/ld80/s_truncl.c | 72 + openlibm/loongarch64/Make.files | 1 + openlibm/loongarch64/fenv.c | 27 + openlibm/mips/Make.files | 1 + openlibm/mips/fenv-softfloat.h | 184 + openlibm/mips/fenv.c | 67 + openlibm/openlibm.pc.in | 6 + openlibm/powerpc/Make.files | 1 + openlibm/powerpc/fenv.c | 47 + openlibm/riscv64/Make.files | 1 + openlibm/riscv64/fenv.c | 63 + openlibm/s390/Make.files | 1 + openlibm/s390/fenv.c | 50 + openlibm/src/Make.files | 78 + openlibm/src/aarch64_fpmath.h | 60 + openlibm/src/amd64_fpmath.h | 55 + openlibm/src/bsd_cdefs.h | 102 + openlibm/src/cdefs-compat.h | 105 + openlibm/src/common.c | 7 + openlibm/src/e_acos.c | 111 + openlibm/src/e_acosf.c | 78 + openlibm/src/e_acosh.c | 68 + openlibm/src/e_acoshf.c | 49 + openlibm/src/e_acosl.c | 87 + openlibm/src/e_asin.c | 117 + openlibm/src/e_asinf.c | 66 + openlibm/src/e_asinl.c | 77 + openlibm/src/e_atan2.c | 129 + openlibm/src/e_atan2f.c | 97 + openlibm/src/e_atan2l.c | 120 + openlibm/src/e_atanh.c | 68 + openlibm/src/e_atanhf.c | 46 + openlibm/src/e_cosh.c | 85 + openlibm/src/e_coshf.c | 60 + openlibm/src/e_exp.c | 171 + openlibm/src/e_expf.c | 97 + openlibm/src/e_fmod.c | 133 + openlibm/src/e_fmodf.c | 105 + openlibm/src/e_fmodl.c | 150 + openlibm/src/e_hypot.c | 131 + openlibm/src/e_hypotf.c | 84 + openlibm/src/e_hypotl.c | 124 + openlibm/src/e_j0.c | 388 ++ openlibm/src/e_j0f.c | 337 + openlibm/src/e_j1.c | 383 ++ openlibm/src/e_j1f.c | 332 + openlibm/src/e_jn.c | 271 + openlibm/src/e_jnf.c | 200 + openlibm/src/e_lgamma.c | 36 + openlibm/src/e_lgamma_r.c | 298 + openlibm/src/e_lgammaf.c | 37 + openlibm/src/e_lgammaf_r.c | 231 + openlibm/src/e_lgammal.c | 15 + openlibm/src/e_log.c | 146 + openlibm/src/e_log10.c | 93 + openlibm/src/e_log10f.c | 75 + openlibm/src/e_log2.c | 116 + openlibm/src/e_log2f.c | 85 + openlibm/src/e_logf.c | 89 + openlibm/src/e_pow.c | 317 + openlibm/src/e_powf.c | 253 + openlibm/src/e_rem_pio2.c | 183 + openlibm/src/e_rem_pio2f.c | 81 + openlibm/src/e_remainder.c | 79 + openlibm/src/e_remainderf.c | 66 + openlibm/src/e_remainderl.c | 39 + openlibm/src/e_sinh.c | 79 + openlibm/src/e_sinhf.c | 57 + openlibm/src/e_sqrt.c | 451 ++ openlibm/src/e_sqrtf.c | 86 + openlibm/src/e_sqrtl.c | 162 + openlibm/src/fpmath.h | 124 + openlibm/src/i386_fpmath.h | 54 + openlibm/src/k_cos.c | 80 + openlibm/src/k_cosf.c | 48 + openlibm/src/k_exp.c | 108 + openlibm/src/k_expf.c | 87 + openlibm/src/k_log.h | 100 + openlibm/src/k_logf.h | 39 + openlibm/src/k_rem_pio2.c | 444 ++ openlibm/src/k_sin.c | 71 + openlibm/src/k_sinf.c | 48 + openlibm/src/k_tan.c | 134 + openlibm/src/k_tanf.c | 68 + openlibm/src/loongarch64_fpmath.h | 56 + openlibm/src/math_private.h | 375 ++ openlibm/src/math_private_openbsd.h | 218 + openlibm/src/mips_fpmath.h | 57 + openlibm/src/polevll.c | 104 + openlibm/src/powerpc_fpmath.h | 49 + openlibm/src/riscv_fpmath.h | 58 + openlibm/src/s390_fpmath.h | 51 + openlibm/src/s_asinh.c | 62 + openlibm/src/s_asinhf.c | 49 + openlibm/src/s_atan.c | 124 + openlibm/src/s_atanf.c | 93 + openlibm/src/s_atanl.c | 85 + openlibm/src/s_cabs.c | 32 + openlibm/src/s_cabsf.c | 25 + openlibm/src/s_cabsl.c | 26 + openlibm/src/s_cacos.c | 67 + openlibm/src/s_cacosf.c | 60 + openlibm/src/s_cacosh.c | 62 + openlibm/src/s_cacoshf.c | 55 + openlibm/src/s_cacoshl.c | 56 + openlibm/src/s_cacosl.c | 63 + openlibm/src/s_carg.c | 40 + openlibm/src/s_cargf.c | 40 + openlibm/src/s_cargl.c | 40 + openlibm/src/s_casin.c | 136 + openlibm/src/s_casinf.c | 132 + openlibm/src/s_casinh.c | 62 + openlibm/src/s_casinhf.c | 55 + openlibm/src/s_casinhl.c | 56 + openlibm/src/s_casinl.c | 130 + openlibm/src/s_catan.c | 133 + openlibm/src/s_catanf.c | 124 + openlibm/src/s_catanh.c | 62 + openlibm/src/s_catanhf.c | 55 + openlibm/src/s_catanhl.c | 56 + openlibm/src/s_catanl.c | 127 + openlibm/src/s_cbrt.c | 118 + openlibm/src/s_cbrtf.c | 74 + openlibm/src/s_cbrtl.c | 161 + openlibm/src/s_ccos.c | 91 + openlibm/src/s_ccosf.c | 84 + openlibm/src/s_ccosh.c | 155 + openlibm/src/s_ccoshf.c | 104 + openlibm/src/s_ccoshl.c | 59 + openlibm/src/s_ccosl.c | 82 + openlibm/src/s_ceil.c | 77 + openlibm/src/s_ceilf.c | 53 + openlibm/src/s_ceill.c | 102 + openlibm/src/s_cexp.c | 89 + openlibm/src/s_cexpf.c | 89 + openlibm/src/s_cexpl.c | 69 + openlibm/src/s_cimag.c | 37 + openlibm/src/s_cimagf.c | 37 + openlibm/src/s_cimagl.c | 37 + openlibm/src/s_clog.c | 79 + openlibm/src/s_clogf.c | 72 + openlibm/src/s_clogl.c | 73 + openlibm/src/s_conj.c | 38 + openlibm/src/s_conjf.c | 38 + openlibm/src/s_conjl.c | 38 + openlibm/src/s_copysign.c | 34 + openlibm/src/s_copysignf.c | 37 + openlibm/src/s_copysignl.c | 43 + openlibm/src/s_cos.c | 89 + openlibm/src/s_cosf.c | 85 + openlibm/src/s_cosl.c | 90 + openlibm/src/s_cpow.c | 78 + openlibm/src/s_cpowf.c | 73 + openlibm/src/s_cpowl.c | 74 + openlibm/src/s_cproj.c | 47 + openlibm/src/s_cprojf.c | 43 + openlibm/src/s_cprojl.c | 43 + openlibm/src/s_creal.c | 37 + openlibm/src/s_crealf.c | 37 + openlibm/src/s_creall.c | 37 + openlibm/src/s_csin.c | 93 + openlibm/src/s_csinf.c | 85 + openlibm/src/s_csinh.c | 157 + openlibm/src/s_csinhf.c | 105 + openlibm/src/s_csinhl.c | 58 + openlibm/src/s_csinl.c | 84 + openlibm/src/s_csqrt.c | 114 + openlibm/src/s_csqrtf.c | 90 + openlibm/src/s_csqrtl.c | 109 + openlibm/src/s_ctan.c | 159 + openlibm/src/s_ctanf.c | 148 + openlibm/src/s_ctanh.c | 144 + openlibm/src/s_ctanhf.c | 84 + openlibm/src/s_ctanhl.c | 60 + openlibm/src/s_ctanl.c | 157 + openlibm/src/s_erf.c | 307 + openlibm/src/s_erff.c | 184 + openlibm/src/s_exp2.c | 396 ++ openlibm/src/s_exp2f.c | 136 + openlibm/src/s_expm1.c | 221 + openlibm/src/s_expm1f.c | 123 + openlibm/src/s_fabs.c | 28 + openlibm/src/s_fabsf.c | 34 + openlibm/src/s_fabsl.c | 43 + openlibm/src/s_fdim.c | 48 + openlibm/src/s_floor.c | 78 + openlibm/src/s_floorf.c | 62 + openlibm/src/s_floorl.c | 102 + openlibm/src/s_fma.c | 284 + openlibm/src/s_fmaf.c | 69 + openlibm/src/s_fmal.c | 269 + openlibm/src/s_fmax.c | 54 + openlibm/src/s_fmaxf.c | 54 + openlibm/src/s_fmaxl.c | 56 + openlibm/src/s_fmin.c | 54 + openlibm/src/s_fminf.c | 54 + openlibm/src/s_fminl.c | 56 + openlibm/src/s_fpclassify.c | 98 + openlibm/src/s_frexp.c | 56 + openlibm/src/s_frexpf.c | 44 + openlibm/src/s_frexpl.c | 63 + openlibm/src/s_ilogb.c | 49 + openlibm/src/s_ilogbf.c | 41 + openlibm/src/s_ilogbl.c | 54 + openlibm/src/s_isfinite.c | 61 + openlibm/src/s_isinf.c | 66 + openlibm/src/s_isnan.c | 67 + openlibm/src/s_isnormal.c | 61 + openlibm/src/s_llrint.c | 9 + openlibm/src/s_llrintf.c | 9 + openlibm/src/s_llrintl.c | 9 + openlibm/src/s_llround.c | 11 + openlibm/src/s_llroundf.c | 11 + openlibm/src/s_llroundl.c | 11 + openlibm/src/s_log1p.c | 179 + openlibm/src/s_log1pf.c | 114 + openlibm/src/s_logb.c | 49 + openlibm/src/s_logbf.c | 41 + openlibm/src/s_logbl.c | 52 + openlibm/src/s_lrint.c | 61 + openlibm/src/s_lrintf.c | 9 + openlibm/src/s_lrintl.c | 9 + openlibm/src/s_lround.c | 69 + openlibm/src/s_lroundf.c | 11 + openlibm/src/s_lroundl.c | 11 + openlibm/src/s_modf.c | 76 + openlibm/src/s_modff.c | 58 + openlibm/src/s_modfl.c | 101 + openlibm/src/s_nan.c | 124 + openlibm/src/s_nearbyint.c | 56 + openlibm/src/s_nextafter.c | 83 + openlibm/src/s_nextafterf.c | 67 + openlibm/src/s_nextafterl.c | 80 + openlibm/src/s_nexttoward.c | 72 + openlibm/src/s_nexttowardf.c | 61 + openlibm/src/s_remquo.c | 158 + openlibm/src/s_remquof.c | 122 + openlibm/src/s_remquol.c | 177 + openlibm/src/s_rint.c | 92 + openlibm/src/s_rintf.c | 53 + openlibm/src/s_rintl.c | 116 + openlibm/src/s_round.c | 55 + openlibm/src/s_roundf.c | 53 + openlibm/src/s_roundl.c | 53 + openlibm/src/s_scalbln.c | 80 + openlibm/src/s_scalbn.c | 66 + openlibm/src/s_scalbnf.c | 57 + openlibm/src/s_scalbnl.c | 70 + openlibm/src/s_signbit.c | 61 + openlibm/src/s_signgam.c | 7 + openlibm/src/s_sin.c | 89 + openlibm/src/s_sincos.c | 159 + openlibm/src/s_sincosf.c | 172 + openlibm/src/s_sincosl.c | 31 + openlibm/src/s_sinf.c | 85 + openlibm/src/s_sinl.c | 88 + openlibm/src/s_tan.c | 83 + openlibm/src/s_tanf.c | 72 + openlibm/src/s_tanh.c | 83 + openlibm/src/s_tanhf.c | 56 + openlibm/src/s_tanl.c | 90 + openlibm/src/s_tgammaf.c | 45 + openlibm/src/s_trunc.c | 67 + openlibm/src/s_truncf.c | 54 + openlibm/src/s_truncl.c | 69 + openlibm/src/types-compat.h | 13 + openlibm/src/w_cabs.c | 25 + openlibm/src/w_cabsf.c | 19 + openlibm/src/w_cabsl.c | 22 + openlibm/test/.gitignore | 9 + openlibm/test/Makefile | 37 + openlibm/test/inf_torture.c | 76 + openlibm/test/libm-bench.cpp | 144 + openlibm/test/libm-test-ulps.h | 254 + openlibm/test/libm-test.c | 4537 +++++++++++++ openlibm/test/test-211.c | 12 + openlibm/test/test-double.c | 34 + openlibm/test/test-float.c | 34 + openlibm/wasm32/Make.files | 0 openlibm/wasm32/assert.h | 1 + openlibm/wasm32/float.h | 33 + openlibm/wasm32/limits.h | 9 + openlibm/wasm32/stdint.h | 43 + printf.c | 12 + serial.c | 47 + startup.S | 105 + test/test01.c | 15 + test/test02.c | 9 + test/test03.c | 28 + timer.c | 25 + 567 files changed, 68348 insertions(+) create mode 100644 GNUmakefile create mode 100644 armstub8.S create mode 100644 clock.c create mode 100755 configure.sh create mode 100644 crt.c create mode 100644 doc.txt create mode 100644 exception_handler.c create mode 100644 exception_stub.S create mode 100755 gen-headers.sh create mode 100644 gilbraltar.ld create mode 100644 include/bcm.h create mode 100644 include/clock.h create mode 100644 include/exception_handler.h create mode 100644 include/exception_stub.h create mode 100644 include/gpio.h create mode 100644 include/led.h create mode 100644 include/log.h create mode 100644 include/mbox.h create mode 100644 include/mem.h create mode 100644 include/memory_map.h create mode 100644 include/serial.h create mode 100644 include/sysconfig.h create mode 100644 include/tag.h create mode 100644 include/timer.h create mode 100644 interrupt_handler.c create mode 100644 kernel.c create mode 100644 led.c create mode 100644 log.c create mode 100644 mbox.c create mode 100644 nolibc/GNUmakefile create mode 100644 nolibc/assert.c create mode 100644 nolibc/ctype.c create mode 100644 nolibc/dlmalloc.i create mode 100644 nolibc/dtoa.c create mode 100644 nolibc/errlist.c create mode 100644 nolibc/fprintf.c create mode 100644 nolibc/include/_gilbraltar/byteorder.h create mode 100644 nolibc/include/_gilbraltar/overrides.h create mode 100644 nolibc/include/assert.h create mode 100644 nolibc/include/ctype.h create mode 100644 nolibc/include/dirent.h create mode 100644 nolibc/include/endian.h create mode 100644 nolibc/include/errno.h create mode 100644 nolibc/include/fcntl.h create mode 100644 nolibc/include/features.h create mode 100644 nolibc/include/inttypes.h create mode 100644 nolibc/include/limits.h create mode 100644 nolibc/include/math.h create mode 100644 nolibc/include/pthread.h create mode 100644 nolibc/include/sched.h create mode 100644 nolibc/include/setjmp.h create mode 100644 nolibc/include/signal.h create mode 100644 nolibc/include/stdio.h create mode 100644 nolibc/include/stdlib.h create mode 100644 nolibc/include/string.h create mode 100644 nolibc/include/sys/ioctl.h create mode 100644 nolibc/include/sys/mman.h create mode 100644 nolibc/include/sys/param.h create mode 100644 nolibc/include/sys/stat.h create mode 100644 nolibc/include/sys/time.h create mode 100644 nolibc/include/sys/times.h create mode 100644 nolibc/include/sys/types.h create mode 100644 nolibc/include/sys/wait.h create mode 120000 nolibc/include/time.h create mode 100644 nolibc/include/unistd.h create mode 100644 nolibc/memchr.c create mode 100644 nolibc/memcmp.c create mode 100644 nolibc/memcpy.c create mode 100644 nolibc/memmove.c create mode 100644 nolibc/memset.c create mode 100644 nolibc/mmap.c create mode 100644 nolibc/printf.c create mode 100644 nolibc/puts.c create mode 100644 nolibc/snprintf.c create mode 100644 nolibc/stpncpy.c create mode 100644 nolibc/strchr.c create mode 100644 nolibc/strchrnul.c create mode 100644 nolibc/strcmp.c create mode 100644 nolibc/strerror_r.c create mode 100644 nolibc/strlen.c create mode 100644 nolibc/strncmp.c create mode 100644 nolibc/strncpy.c create mode 100644 nolibc/strnlen.c create mode 100644 nolibc/strstr.c create mode 100644 nolibc/strtol.c create mode 100644 nolibc/stubs.c create mode 100644 nolibc/sysconf.c create mode 100644 nolibc/sysdeps.c create mode 100644 nolibc/vfprintf.c create mode 100644 nolibc/vsnprintf.c create mode 100644 openlibm/.gitignore create mode 100644 openlibm/.mailmap create mode 100644 openlibm/.travis.yml create mode 100755 openlibm/CMakeLists.txt create mode 100644 openlibm/LICENSE.md create mode 100644 openlibm/Make.inc create mode 100644 openlibm/Makefile create mode 100644 openlibm/README.md create mode 100644 openlibm/aarch64/Make.files create mode 100644 openlibm/aarch64/fenv.c create mode 100644 openlibm/amd64/Make.files create mode 100644 openlibm/amd64/bsd_asm.h create mode 100644 openlibm/amd64/bsd_fpu.h create mode 100644 openlibm/amd64/bsd_ieeefp.h create mode 100644 openlibm/amd64/e_fmod.S create mode 100644 openlibm/amd64/e_fmodf.S create mode 100644 openlibm/amd64/e_fmodl.S create mode 100644 openlibm/amd64/e_remainder.S create mode 100644 openlibm/amd64/e_remainderf.S create mode 100644 openlibm/amd64/e_remainderl.S create mode 100644 openlibm/amd64/e_sqrt.S create mode 100644 openlibm/amd64/e_sqrtf.S create mode 100644 openlibm/amd64/e_sqrtl.S create mode 100644 openlibm/amd64/fenv.c create mode 100644 openlibm/amd64/s_llrint.S create mode 100644 openlibm/amd64/s_llrintf.S create mode 100644 openlibm/amd64/s_llrintl.S create mode 100644 openlibm/amd64/s_logbl.S create mode 100644 openlibm/amd64/s_lrint.S create mode 100644 openlibm/amd64/s_lrintf.S create mode 100644 openlibm/amd64/s_lrintl.S create mode 100644 openlibm/amd64/s_remquo.S create mode 100644 openlibm/amd64/s_remquof.S create mode 100644 openlibm/amd64/s_remquol.S create mode 100644 openlibm/amd64/s_rintl.S create mode 100644 openlibm/amd64/s_scalbn.S create mode 100644 openlibm/amd64/s_scalbnf.S create mode 100644 openlibm/amd64/s_scalbnl.S create mode 100644 openlibm/arm/Make.files create mode 100644 openlibm/arm/fenv.c create mode 100644 openlibm/bsdsrc/Make.files create mode 100644 openlibm/bsdsrc/b_exp.c create mode 100644 openlibm/bsdsrc/b_log.c create mode 100644 openlibm/bsdsrc/b_tgamma.c create mode 100644 openlibm/bsdsrc/mathimpl.h create mode 100644 openlibm/docs/CNAME create mode 100644 openlibm/docs/images/arrow-down.png create mode 100644 openlibm/docs/images/octocat-small.png create mode 100644 openlibm/docs/index.html create mode 100644 openlibm/docs/javascripts/scale.fix.js create mode 100644 openlibm/docs/params.json create mode 100644 openlibm/docs/stylesheets/pygment_trac.css create mode 100644 openlibm/docs/stylesheets/styles.css create mode 100644 openlibm/i387/Make.files create mode 100644 openlibm/i387/bsd_asm.h create mode 100644 openlibm/i387/bsd_ieeefp.h create mode 100644 openlibm/i387/bsd_npx.h create mode 100644 openlibm/i387/e_exp.S create mode 100644 openlibm/i387/e_fmod.S create mode 100644 openlibm/i387/e_log.S create mode 100644 openlibm/i387/e_log10.S create mode 100644 openlibm/i387/e_log10f.S create mode 100644 openlibm/i387/e_logf.S create mode 100644 openlibm/i387/e_remainder.S create mode 100644 openlibm/i387/e_remainderf.S create mode 100644 openlibm/i387/e_remainderl.S create mode 100644 openlibm/i387/e_sqrt.S create mode 100644 openlibm/i387/e_sqrtf.S create mode 100644 openlibm/i387/e_sqrtl.S create mode 100644 openlibm/i387/fenv.c create mode 100644 openlibm/i387/invtrig.c create mode 100644 openlibm/i387/osx_asm.h create mode 100644 openlibm/i387/s_ceil.S create mode 100644 openlibm/i387/s_ceilf.S create mode 100644 openlibm/i387/s_ceill.S create mode 100644 openlibm/i387/s_copysign.S create mode 100644 openlibm/i387/s_copysignf.S create mode 100644 openlibm/i387/s_copysignl.S create mode 100644 openlibm/i387/s_cos.S create mode 100644 openlibm/i387/s_floor.S create mode 100644 openlibm/i387/s_floorf.S create mode 100644 openlibm/i387/s_floorl.S create mode 100644 openlibm/i387/s_llrint.S create mode 100644 openlibm/i387/s_llrintf.S create mode 100644 openlibm/i387/s_llrintl.S create mode 100644 openlibm/i387/s_logb.S create mode 100644 openlibm/i387/s_logbf.S create mode 100644 openlibm/i387/s_logbl.S create mode 100644 openlibm/i387/s_lrint.S create mode 100644 openlibm/i387/s_lrintf.S create mode 100644 openlibm/i387/s_lrintl.S create mode 100644 openlibm/i387/s_remquo.S create mode 100644 openlibm/i387/s_remquof.S create mode 100644 openlibm/i387/s_remquol.S create mode 100644 openlibm/i387/s_rint.S create mode 100644 openlibm/i387/s_rintf.S create mode 100644 openlibm/i387/s_rintl.S create mode 100644 openlibm/i387/s_scalbn.S create mode 100644 openlibm/i387/s_scalbnf.S create mode 100644 openlibm/i387/s_scalbnl.S create mode 100644 openlibm/i387/s_sin.S create mode 100644 openlibm/i387/s_tan.S create mode 100644 openlibm/i387/s_trunc.S create mode 100644 openlibm/i387/s_truncf.S create mode 100644 openlibm/i387/s_truncl.S create mode 100644 openlibm/include/openlibm.h create mode 100644 openlibm/include/openlibm_complex.h create mode 100644 openlibm/include/openlibm_defs.h create mode 100644 openlibm/include/openlibm_fenv.h create mode 100644 openlibm/include/openlibm_fenv_amd64.h create mode 100644 openlibm/include/openlibm_fenv_arm.h create mode 100644 openlibm/include/openlibm_fenv_i387.h create mode 100644 openlibm/include/openlibm_fenv_loongarch64.h create mode 100644 openlibm/include/openlibm_fenv_mips.h create mode 100644 openlibm/include/openlibm_fenv_powerpc.h create mode 100644 openlibm/include/openlibm_fenv_riscv.h create mode 100644 openlibm/include/openlibm_fenv_s390.h create mode 100644 openlibm/include/openlibm_math.h create mode 100644 openlibm/ld128/Make.files create mode 100644 openlibm/ld128/e_acoshl.c create mode 100644 openlibm/ld128/e_atanhl.c create mode 100644 openlibm/ld128/e_coshl.c create mode 100644 openlibm/ld128/e_expl.c create mode 100644 openlibm/ld128/e_fmodl.c create mode 100644 openlibm/ld128/e_hypotl.c create mode 100644 openlibm/ld128/e_lgammal_r.c create mode 100644 openlibm/ld128/e_log10l.c create mode 100644 openlibm/ld128/e_log2l.c create mode 100644 openlibm/ld128/e_logl.c create mode 100644 openlibm/ld128/e_powl.c create mode 100644 openlibm/ld128/e_rem_pio2l.h create mode 100644 openlibm/ld128/e_sinhl.c create mode 100644 openlibm/ld128/e_tgammal.c create mode 100644 openlibm/ld128/invtrig.c create mode 100644 openlibm/ld128/invtrig.h create mode 100644 openlibm/ld128/k_cosl.c create mode 100644 openlibm/ld128/k_sinl.c create mode 100644 openlibm/ld128/k_tanl.c create mode 100644 openlibm/ld128/s_asinhl.c create mode 100644 openlibm/ld128/s_ceill.c create mode 100644 openlibm/ld128/s_erfl.c create mode 100644 openlibm/ld128/s_exp2l.c create mode 100644 openlibm/ld128/s_expm1l.c create mode 100644 openlibm/ld128/s_floorl.c create mode 100644 openlibm/ld128/s_log1pl.c create mode 100644 openlibm/ld128/s_modfl.c create mode 100644 openlibm/ld128/s_nanl.c create mode 100644 openlibm/ld128/s_nextafterl.c create mode 100644 openlibm/ld128/s_nexttoward.c create mode 100644 openlibm/ld128/s_nexttowardf.c create mode 100644 openlibm/ld128/s_remquol.c create mode 100644 openlibm/ld128/s_tanhl.c create mode 100644 openlibm/ld128/s_truncl.c create mode 100644 openlibm/ld80/Make.files create mode 100644 openlibm/ld80/e_acoshl.c create mode 100644 openlibm/ld80/e_atanhl.c create mode 100644 openlibm/ld80/e_coshl.c create mode 100644 openlibm/ld80/e_expl.c create mode 100644 openlibm/ld80/e_fmodl.c create mode 100644 openlibm/ld80/e_hypotl.c create mode 100644 openlibm/ld80/e_lgammal_r.c create mode 100644 openlibm/ld80/e_log10l.c create mode 100644 openlibm/ld80/e_log2l.c create mode 100644 openlibm/ld80/e_logl.c create mode 100644 openlibm/ld80/e_powl.c create mode 100644 openlibm/ld80/e_rem_pio2l.h create mode 100644 openlibm/ld80/e_sinhl.c create mode 100644 openlibm/ld80/e_tgammal.c create mode 100644 openlibm/ld80/invtrig.c create mode 100644 openlibm/ld80/invtrig.h create mode 100644 openlibm/ld80/k_cosl.c create mode 100644 openlibm/ld80/k_sinl.c create mode 100644 openlibm/ld80/k_tanl.c create mode 100644 openlibm/ld80/s_asinhl.c create mode 100644 openlibm/ld80/s_ceill.c create mode 100644 openlibm/ld80/s_erfl.c create mode 100644 openlibm/ld80/s_exp2l.c create mode 100644 openlibm/ld80/s_expm1l.c create mode 100644 openlibm/ld80/s_floorl.c create mode 100644 openlibm/ld80/s_log1pl.c create mode 100644 openlibm/ld80/s_modfl.c create mode 100644 openlibm/ld80/s_nanl.c create mode 100644 openlibm/ld80/s_nextafterl.c create mode 100644 openlibm/ld80/s_nexttoward.c create mode 100644 openlibm/ld80/s_nexttowardf.c create mode 100644 openlibm/ld80/s_remquol.c create mode 100644 openlibm/ld80/s_tanhl.c create mode 100644 openlibm/ld80/s_truncl.c create mode 100644 openlibm/loongarch64/Make.files create mode 100644 openlibm/loongarch64/fenv.c create mode 100644 openlibm/mips/Make.files create mode 100644 openlibm/mips/fenv-softfloat.h create mode 100644 openlibm/mips/fenv.c create mode 100644 openlibm/openlibm.pc.in create mode 100644 openlibm/powerpc/Make.files create mode 100644 openlibm/powerpc/fenv.c create mode 100644 openlibm/riscv64/Make.files create mode 100644 openlibm/riscv64/fenv.c create mode 100644 openlibm/s390/Make.files create mode 100644 openlibm/s390/fenv.c create mode 100644 openlibm/src/Make.files create mode 100644 openlibm/src/aarch64_fpmath.h create mode 100644 openlibm/src/amd64_fpmath.h create mode 100644 openlibm/src/bsd_cdefs.h create mode 100644 openlibm/src/cdefs-compat.h create mode 100644 openlibm/src/common.c create mode 100644 openlibm/src/e_acos.c create mode 100644 openlibm/src/e_acosf.c create mode 100644 openlibm/src/e_acosh.c create mode 100644 openlibm/src/e_acoshf.c create mode 100644 openlibm/src/e_acosl.c create mode 100644 openlibm/src/e_asin.c create mode 100644 openlibm/src/e_asinf.c create mode 100644 openlibm/src/e_asinl.c create mode 100644 openlibm/src/e_atan2.c create mode 100644 openlibm/src/e_atan2f.c create mode 100644 openlibm/src/e_atan2l.c create mode 100644 openlibm/src/e_atanh.c create mode 100644 openlibm/src/e_atanhf.c create mode 100644 openlibm/src/e_cosh.c create mode 100644 openlibm/src/e_coshf.c create mode 100644 openlibm/src/e_exp.c create mode 100644 openlibm/src/e_expf.c create mode 100644 openlibm/src/e_fmod.c create mode 100644 openlibm/src/e_fmodf.c create mode 100644 openlibm/src/e_fmodl.c create mode 100644 openlibm/src/e_hypot.c create mode 100644 openlibm/src/e_hypotf.c create mode 100644 openlibm/src/e_hypotl.c create mode 100644 openlibm/src/e_j0.c create mode 100644 openlibm/src/e_j0f.c create mode 100644 openlibm/src/e_j1.c create mode 100644 openlibm/src/e_j1f.c create mode 100644 openlibm/src/e_jn.c create mode 100644 openlibm/src/e_jnf.c create mode 100644 openlibm/src/e_lgamma.c create mode 100644 openlibm/src/e_lgamma_r.c create mode 100644 openlibm/src/e_lgammaf.c create mode 100644 openlibm/src/e_lgammaf_r.c create mode 100644 openlibm/src/e_lgammal.c create mode 100644 openlibm/src/e_log.c create mode 100644 openlibm/src/e_log10.c create mode 100644 openlibm/src/e_log10f.c create mode 100644 openlibm/src/e_log2.c create mode 100644 openlibm/src/e_log2f.c create mode 100644 openlibm/src/e_logf.c create mode 100644 openlibm/src/e_pow.c create mode 100644 openlibm/src/e_powf.c create mode 100644 openlibm/src/e_rem_pio2.c create mode 100644 openlibm/src/e_rem_pio2f.c create mode 100644 openlibm/src/e_remainder.c create mode 100644 openlibm/src/e_remainderf.c create mode 100644 openlibm/src/e_remainderl.c create mode 100644 openlibm/src/e_sinh.c create mode 100644 openlibm/src/e_sinhf.c create mode 100644 openlibm/src/e_sqrt.c create mode 100644 openlibm/src/e_sqrtf.c create mode 100644 openlibm/src/e_sqrtl.c create mode 100644 openlibm/src/fpmath.h create mode 100644 openlibm/src/i386_fpmath.h create mode 100644 openlibm/src/k_cos.c create mode 100644 openlibm/src/k_cosf.c create mode 100644 openlibm/src/k_exp.c create mode 100644 openlibm/src/k_expf.c create mode 100644 openlibm/src/k_log.h create mode 100644 openlibm/src/k_logf.h create mode 100644 openlibm/src/k_rem_pio2.c create mode 100644 openlibm/src/k_sin.c create mode 100644 openlibm/src/k_sinf.c create mode 100644 openlibm/src/k_tan.c create mode 100644 openlibm/src/k_tanf.c create mode 100644 openlibm/src/loongarch64_fpmath.h create mode 100644 openlibm/src/math_private.h create mode 100644 openlibm/src/math_private_openbsd.h create mode 100644 openlibm/src/mips_fpmath.h create mode 100644 openlibm/src/polevll.c create mode 100644 openlibm/src/powerpc_fpmath.h create mode 100644 openlibm/src/riscv_fpmath.h create mode 100644 openlibm/src/s390_fpmath.h create mode 100644 openlibm/src/s_asinh.c create mode 100644 openlibm/src/s_asinhf.c create mode 100644 openlibm/src/s_atan.c create mode 100644 openlibm/src/s_atanf.c create mode 100644 openlibm/src/s_atanl.c create mode 100644 openlibm/src/s_cabs.c create mode 100644 openlibm/src/s_cabsf.c create mode 100644 openlibm/src/s_cabsl.c create mode 100644 openlibm/src/s_cacos.c create mode 100644 openlibm/src/s_cacosf.c create mode 100644 openlibm/src/s_cacosh.c create mode 100644 openlibm/src/s_cacoshf.c create mode 100644 openlibm/src/s_cacoshl.c create mode 100644 openlibm/src/s_cacosl.c create mode 100644 openlibm/src/s_carg.c create mode 100644 openlibm/src/s_cargf.c create mode 100644 openlibm/src/s_cargl.c create mode 100644 openlibm/src/s_casin.c create mode 100644 openlibm/src/s_casinf.c create mode 100644 openlibm/src/s_casinh.c create mode 100644 openlibm/src/s_casinhf.c create mode 100644 openlibm/src/s_casinhl.c create mode 100644 openlibm/src/s_casinl.c create mode 100644 openlibm/src/s_catan.c create mode 100644 openlibm/src/s_catanf.c create mode 100644 openlibm/src/s_catanh.c create mode 100644 openlibm/src/s_catanhf.c create mode 100644 openlibm/src/s_catanhl.c create mode 100644 openlibm/src/s_catanl.c create mode 100644 openlibm/src/s_cbrt.c create mode 100644 openlibm/src/s_cbrtf.c create mode 100644 openlibm/src/s_cbrtl.c create mode 100644 openlibm/src/s_ccos.c create mode 100644 openlibm/src/s_ccosf.c create mode 100644 openlibm/src/s_ccosh.c create mode 100644 openlibm/src/s_ccoshf.c create mode 100644 openlibm/src/s_ccoshl.c create mode 100644 openlibm/src/s_ccosl.c create mode 100644 openlibm/src/s_ceil.c create mode 100644 openlibm/src/s_ceilf.c create mode 100644 openlibm/src/s_ceill.c create mode 100644 openlibm/src/s_cexp.c create mode 100644 openlibm/src/s_cexpf.c create mode 100644 openlibm/src/s_cexpl.c create mode 100644 openlibm/src/s_cimag.c create mode 100644 openlibm/src/s_cimagf.c create mode 100644 openlibm/src/s_cimagl.c create mode 100644 openlibm/src/s_clog.c create mode 100644 openlibm/src/s_clogf.c create mode 100644 openlibm/src/s_clogl.c create mode 100644 openlibm/src/s_conj.c create mode 100644 openlibm/src/s_conjf.c create mode 100644 openlibm/src/s_conjl.c create mode 100644 openlibm/src/s_copysign.c create mode 100644 openlibm/src/s_copysignf.c create mode 100644 openlibm/src/s_copysignl.c create mode 100644 openlibm/src/s_cos.c create mode 100644 openlibm/src/s_cosf.c create mode 100644 openlibm/src/s_cosl.c create mode 100644 openlibm/src/s_cpow.c create mode 100644 openlibm/src/s_cpowf.c create mode 100644 openlibm/src/s_cpowl.c create mode 100644 openlibm/src/s_cproj.c create mode 100644 openlibm/src/s_cprojf.c create mode 100644 openlibm/src/s_cprojl.c create mode 100644 openlibm/src/s_creal.c create mode 100644 openlibm/src/s_crealf.c create mode 100644 openlibm/src/s_creall.c create mode 100644 openlibm/src/s_csin.c create mode 100644 openlibm/src/s_csinf.c create mode 100644 openlibm/src/s_csinh.c create mode 100644 openlibm/src/s_csinhf.c create mode 100644 openlibm/src/s_csinhl.c create mode 100644 openlibm/src/s_csinl.c create mode 100644 openlibm/src/s_csqrt.c create mode 100644 openlibm/src/s_csqrtf.c create mode 100644 openlibm/src/s_csqrtl.c create mode 100644 openlibm/src/s_ctan.c create mode 100644 openlibm/src/s_ctanf.c create mode 100644 openlibm/src/s_ctanh.c create mode 100644 openlibm/src/s_ctanhf.c create mode 100644 openlibm/src/s_ctanhl.c create mode 100644 openlibm/src/s_ctanl.c create mode 100644 openlibm/src/s_erf.c create mode 100644 openlibm/src/s_erff.c create mode 100644 openlibm/src/s_exp2.c create mode 100644 openlibm/src/s_exp2f.c create mode 100644 openlibm/src/s_expm1.c create mode 100644 openlibm/src/s_expm1f.c create mode 100644 openlibm/src/s_fabs.c create mode 100644 openlibm/src/s_fabsf.c create mode 100644 openlibm/src/s_fabsl.c create mode 100644 openlibm/src/s_fdim.c create mode 100644 openlibm/src/s_floor.c create mode 100644 openlibm/src/s_floorf.c create mode 100644 openlibm/src/s_floorl.c create mode 100644 openlibm/src/s_fma.c create mode 100644 openlibm/src/s_fmaf.c create mode 100644 openlibm/src/s_fmal.c create mode 100644 openlibm/src/s_fmax.c create mode 100644 openlibm/src/s_fmaxf.c create mode 100644 openlibm/src/s_fmaxl.c create mode 100644 openlibm/src/s_fmin.c create mode 100644 openlibm/src/s_fminf.c create mode 100644 openlibm/src/s_fminl.c create mode 100644 openlibm/src/s_fpclassify.c create mode 100644 openlibm/src/s_frexp.c create mode 100644 openlibm/src/s_frexpf.c create mode 100644 openlibm/src/s_frexpl.c create mode 100644 openlibm/src/s_ilogb.c create mode 100644 openlibm/src/s_ilogbf.c create mode 100644 openlibm/src/s_ilogbl.c create mode 100644 openlibm/src/s_isfinite.c create mode 100644 openlibm/src/s_isinf.c create mode 100644 openlibm/src/s_isnan.c create mode 100644 openlibm/src/s_isnormal.c create mode 100644 openlibm/src/s_llrint.c create mode 100644 openlibm/src/s_llrintf.c create mode 100644 openlibm/src/s_llrintl.c create mode 100644 openlibm/src/s_llround.c create mode 100644 openlibm/src/s_llroundf.c create mode 100644 openlibm/src/s_llroundl.c create mode 100644 openlibm/src/s_log1p.c create mode 100644 openlibm/src/s_log1pf.c create mode 100644 openlibm/src/s_logb.c create mode 100644 openlibm/src/s_logbf.c create mode 100644 openlibm/src/s_logbl.c create mode 100644 openlibm/src/s_lrint.c create mode 100644 openlibm/src/s_lrintf.c create mode 100644 openlibm/src/s_lrintl.c create mode 100644 openlibm/src/s_lround.c create mode 100644 openlibm/src/s_lroundf.c create mode 100644 openlibm/src/s_lroundl.c create mode 100644 openlibm/src/s_modf.c create mode 100644 openlibm/src/s_modff.c create mode 100644 openlibm/src/s_modfl.c create mode 100644 openlibm/src/s_nan.c create mode 100644 openlibm/src/s_nearbyint.c create mode 100644 openlibm/src/s_nextafter.c create mode 100644 openlibm/src/s_nextafterf.c create mode 100644 openlibm/src/s_nextafterl.c create mode 100644 openlibm/src/s_nexttoward.c create mode 100644 openlibm/src/s_nexttowardf.c create mode 100644 openlibm/src/s_remquo.c create mode 100644 openlibm/src/s_remquof.c create mode 100644 openlibm/src/s_remquol.c create mode 100644 openlibm/src/s_rint.c create mode 100644 openlibm/src/s_rintf.c create mode 100644 openlibm/src/s_rintl.c create mode 100644 openlibm/src/s_round.c create mode 100644 openlibm/src/s_roundf.c create mode 100644 openlibm/src/s_roundl.c create mode 100644 openlibm/src/s_scalbln.c create mode 100644 openlibm/src/s_scalbn.c create mode 100644 openlibm/src/s_scalbnf.c create mode 100644 openlibm/src/s_scalbnl.c create mode 100644 openlibm/src/s_signbit.c create mode 100644 openlibm/src/s_signgam.c create mode 100644 openlibm/src/s_sin.c create mode 100644 openlibm/src/s_sincos.c create mode 100644 openlibm/src/s_sincosf.c create mode 100644 openlibm/src/s_sincosl.c create mode 100644 openlibm/src/s_sinf.c create mode 100644 openlibm/src/s_sinl.c create mode 100644 openlibm/src/s_tan.c create mode 100644 openlibm/src/s_tanf.c create mode 100644 openlibm/src/s_tanh.c create mode 100644 openlibm/src/s_tanhf.c create mode 100644 openlibm/src/s_tanl.c create mode 100644 openlibm/src/s_tgammaf.c create mode 100644 openlibm/src/s_trunc.c create mode 100644 openlibm/src/s_truncf.c create mode 100644 openlibm/src/s_truncl.c create mode 100644 openlibm/src/types-compat.h create mode 100644 openlibm/src/w_cabs.c create mode 100644 openlibm/src/w_cabsf.c create mode 100644 openlibm/src/w_cabsl.c create mode 100644 openlibm/test/.gitignore create mode 100644 openlibm/test/Makefile create mode 100644 openlibm/test/inf_torture.c create mode 100644 openlibm/test/libm-bench.cpp create mode 100644 openlibm/test/libm-test-ulps.h create mode 100644 openlibm/test/libm-test.c create mode 100644 openlibm/test/test-211.c create mode 100644 openlibm/test/test-double.c create mode 100644 openlibm/test/test-float.c create mode 100644 openlibm/wasm32/Make.files create mode 100644 openlibm/wasm32/assert.h create mode 100644 openlibm/wasm32/float.h create mode 100644 openlibm/wasm32/limits.h create mode 100644 openlibm/wasm32/stdint.h create mode 100644 printf.c create mode 100644 serial.c create mode 100644 startup.S create mode 100644 test/test01.c create mode 100644 test/test02.c create mode 100644 test/test03.c create mode 100644 timer.c diff --git a/GNUmakefile b/GNUmakefile new file mode 100644 index 0000000..7ee13be --- /dev/null +++ b/GNUmakefile @@ -0,0 +1,120 @@ +RM= rm +CC= $(CONFIG_TARGET_CC) +AS= $(CONFIG_TARGET_CC) +# NOTE(dinosaure): we must use [aarch64-none-elf-gcc] to compile assembly code +# to be able to include some files and define some macros. +LD= $(CONFIG_TARGET_LD) +AR= aarch64-none-elf-ar # TODO +OBJDUMP= aarch64-none-elf-objdump # TODO +OBJCOPY= $(CONFIG_TARGET_OBJCOPY) + +export TOPDIR := $(abspath .) + +$(TOPDIR)/Makeconf: + $(error Makeconf not found, please run ./configure.sh) + +include $(TOPDIR)/Makeconf + +# armstub8.bin: armstub8.S +# @echo "CC -DGIC=1 $<" +# @$(CC) -DGIC=1 -o ${<:S=o} -c $< +# @echo "LD --section-start=.text=0 ${<:S=o}" +# @$(LD) --section-start=.text=0 -o ${<:S=elf} ${<:S=o} +# @echo "DUMP ${<:S=elf}" +# @$(OBJDUMP) -D ${<:S=elf} > ${<:S=lst} +# @echo "COPY ${<:S=elf}" +# @$(OBJCOPY) ${<:S=elf} -O binary $@ + +include/$(CONFIG_TARGET_TRIPLE): + @echo "GEN $@" + @./gen-headers.sh $@ + +CPU ?= -mcpu=cortex-a76 -mlittle-endian +ARCH += -DAARCH=64 $(CPU) +TARGET ?= kernel_2712 + +DEFINE += -DSSP_GUARD_SYMBOL=__stack_chk_guard \ + -DSSP_FAIL_SYMBOL=__stack_chk_fail + +INCLUDE += -I $(TOPDIR)/include -I $(TOPDIR)/include/$(CONFIG_TARGET_TRIPLE) \ + -I $(TOPDIR)/nolibc/include + +AFLAGS += $(ARCH) $(DEFINE) $(INCLUDE) + +CFLAGS += -std=c11 -ffreestanding -fstack-protector-strong -nostdlib \ + -nostartfiles -mstrict-align -Wall \ + $(ARCH) $(DEFINE) $(INCLUDE) $(CONFIG_TARGET_CC_CFLAGS) + +LDFLAGS += -nostdlib -static -Wl,--no-warn-rwx-segments \ + -Wl,--section-start=.init=0x80000 -Wl,--build-id=none \ + -Wl,--start-group -L . -lgilbraltar -L nolibc -lnolibc -L openlibm -lopenlibm -lgcc -Wl,--end-group + +SRCS= kernel.c timer.c led.c interrupt_handler.c exception_handler.c \ + mbox.c clock.c crt.c serial.c log.c + +ASMS= startup.S exception_stub.S + +OBJS= $(SRCS:c=o) $(ASMS:S=o) + +%.o: %.S + @echo "AS $@" + @$(AS) $(AFLAGS) -c -o $@ $< + +%.o: %.c include/$(CONFIG_TARGET_TRIPLE) + @echo "CC $@" + @$(CC) $(CFLAGS) -c -o $@ $< + +libgilbraltar.a: $(OBJS) + @echo "AR $@" + @rm -f $@ + @$(AR) cr $@ $^ + +.PHONY: phony-openlibm +phony-openlibm: include/$(CONFIG_TARGET_TRIPLE) + @$(MAKE) -C openlibm \ + "CC=$(CC)" "CPPFLAGS=$(CFLAGS)" libopenlibm.a + +openlibm/libopenlibm.a: phony-openlibm + +NOLIBC_CFLAGS= $(CFLAGS) -I $(TOPDIR)/nolibc/include -I $(TOPDIR)/openlibm/src -I $(TOPDIR)/openlibm/include + +.PHONY: phony-nolibc +phony-nolibc: include/$(CONFIG_TARGET_TRIPLE) + $(MAKE) -C nolibc libnolibc.a \ + "CC=$(CC)" "FREESTANDING_CFLAGS=$(NOLIBC_CFLAGS)" + +nolibc/libnolibc.a: phony-nolibc + +.PHONY: all +all: libgilbraltar.a + +.PHONY: clean +clean: + $(RM) -f *.o *.a *.elf *.bin *.lst *.img + $(RM) -rf include/$(CONFIG_TARGET_TRIPLE) + $(RM) -f test/*.o + $(MAKE) -C openlibm clean + $(MAKE) -C nolibc clean FREESTANDING_CFLAGS=_ + +.PHONY: distclean +distclean: clean + $(RM) -f Makeconf + +test/%.o: test/%.c + @echo "CC $@" + @$(CC) $(CFLAGS) -c -o $@ $< + +test01.img: libgilbraltar.a nolibc/libnolibc.a openlibm/libopenlibm.a test/test01.o + @echo "LD ${@:img=elf}" + @$(LD) test/${@:img=o} -o ${@:img=elf} $(LDFLAGS) -Wl,-T gilbraltar.ld + @$(OBJCOPY) ${@:img=elf} -O binary $@ + +test02.img: libgilbraltar.a nolibc/libnolibc.a openlibm/libopenlibm.a test/test02.o + @echo "LD ${@:img=elf}" + @$(LD) test/${@:img=o} -o ${@:img=elf} $(LDFLAGS) -Wl,-T gilbraltar.ld + @$(OBJCOPY) ${@:img=elf} -O binary $@ + +test03.img: libgilbraltar.a nolibc/libnolibc.a openlibm/libopenlibm.a test/test03.o + @echo "LD ${@:img=elf}" + @$(LD) test/${@:img=o} -o ${@:img=elf} $(LDFLAGS) -Wl,-T gilbraltar.ld + @$(OBJCOPY) ${@:img=elf} -O binary $@ diff --git a/armstub8.S b/armstub8.S new file mode 100644 index 0000000..84ea1e1 --- /dev/null +++ b/armstub8.S @@ -0,0 +1,213 @@ +/* + * Copyright (c) 2024 Romain Calascibetta + * Copyright (c) 2016-2019 Raspberry Pi (Trading) Ltd. + * Copyright (c) 2016 Stephen Warren + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions are met: + * * Redistributions of source code must retain the above copyright notice, + * this list of conditions and the following disclaimer. + * * Redistributions in binary form must reproduce the above copyright notice, + * this list of conditions and the following disclaimer in the documentation + * and/or other materials provided with the distribution. + * * Neither the name of the copyright holder nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" + * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE + * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#define BIT(x) (1 << (x)) + +#define LOCAL_CONTROL 0xff800000 +#define LOCAL_PRESCALER 0xff800008 +#define GIC_DISTB 0xff841000 +#define GIC_CPUB 0xff842000 +#define OSC_FREQ 54000000 + +#define SCR_RW BIT(10) +#define SCR_HCE BIT(8) +#define SCR_SMD BIT(7) +#define SCR_RES1_5 BIT(5) +#define SCR_RES1_4 BIT(4) +#define SCR_NS BIT(0) +#define SCR_VAL \ + (SCR_RW | SCR_HCE | SCR_SMD | SCR_RES1_5 | SCR_RES1_4 | SCR_NS) + +#define ACTLR_VAL \ + (BIT(0) | BIT(1) | BIT(4) | BIT(5) | BIT(6)) + +#define CPUECTLR_EL1 S3_1_C15_C2_1 +#define CPUECTLR_EL1_SMPEN BIT(6) + +#define SPSR_EL3_D BIT(9) +#define SPSR_EL3_A BIT(8) +#define SPSR_EL3_I BIT(7) +#define SPSR_EL3_F BIT(6) +#define SPSR_EL3_MODE_EL2H 9 +#define SPSR_EL3_VAL \ + (SPSR_EL3_D | SPSR_EL3_A | SPSR_EL3_I | SPSR_EL3_F | SPSR_EL3_MODE_EL2H) + +#define L2CTLR_EL1 S3_1_C11_C0_2 +#define GICC_CTRLR 0x0 +#define GICC_PMR 0x4 +#define IT_NR 0x8 // Number of interrupt enable registers (256 total irqs) +#define GICD_CTRLR 0x0 +#define GICD_IGROUPR 0x80 + +.globl _start +_start: + // LOCAL_CONTROL: + // Bit 9 clear: Increment by 1 (vs. 2). + // Bit 8 clear: Timer source is 19.2MHz crystal (vs. APB). + ldr x0, =LOCAL_CONTROL + str wzr, [x0] + // LOCAL_PRESCALER; divide-by (0x80000000 / register_val) == 1 + mov w1, 0x80000000 + str w1, [x0, #(LOCAL_PRESCALER - LOCAL_CONTROL)] + + // Set L2 read/write cache latency to 3 + mrs x0, L2CTLR_EL1 + mov x1, #0x22 + orr x0, x0, x1 + msr L2CTLR_EL1, x0 + + // Set up CNTFRQ_EL0 + ldr x0, =OSC_FREQ + msr CNTFRQ_EL0, x0 + + // Set up CNTVOFF_EL2 + msr CNTVOFF_EL2, xzr + + // Enable FP/SIMD + // Bit 10 (TFP) is set to 0 + msr CPTR_EL3, xzr + + // Set up SCR + mov x0, #SCR_VAL + msr SCR_EL3, x0 + + // Set up ACTLR + mov x0, #ACTLR_VAL + msr ACTLR_EL3, x0 + + // Set SMPEN + mov x0, #CPUECTLR_EL1_SMPEN + msr CPUECTLR_EL1, x0 + +#ifdef GIC + bl setup_gic +#endif + // Set up SCTLR_EL2 + // All set bits below are res1. LE, no WXN/I/SA/C/A/M + ldr x0, =0x30c50830 + msr SCTLR_EL2, x0 + + // Switch to EL2 + mov x0, #SPSR_EL3_VAL + msr spsr_el3, x0 + adr x0, in_el2 + msr elr_el3, x0 + eret +in_el2: + mrs x6, MPIDR_EL1 + and x6, x6, #0x3 + cbz x6, primary_cpu + + adr x5, spin_cpu0 +secondary_spin: + wfe + ldr x4, [x5, x6, lsl #3] + cbz x4, secondary_spin + mov x0, #0 + b boot_kernel + +primary_cpu: + ldr w4, kernel_entry32 + ldr w0, dtb_ptr32 + +boot_kernel: + mov x1, #0 + mov x2, #0 + mov x3, #0 + br x4 + +.ltorg + +.org 0xd8 +.globl spin_cpu0 +spin_cpu0: + .quad 0 +.org 0xe0 +.globl spin_cpu1 +spin_cpu1: + .quad 0 +.org 0xe8 +.globl spin_cpu2 +spin_cpu2: + .quad 0 +.org 0xf0 +.globl spin_cpu3 +spin_cpu3: +# Shared with next two symbols/.word +# FW clears the next 8 bytes after reading the initial value, leaving +# the location suitable for use as spin_cpu3 +.org 0xf0 +.globl stub_magic +stub_magic: + .word 0x5afe570b +.org 0xf4 +.globl stub_version +stub_version: + .word 0 +.org 0xf8 +.globl dtb_ptr32 +dtb_ptr32: + .word 0x0 +.org 0xfc +.globl kernel_entry32 +kernel_entry32: + .word 0x0 + +.org 0x100 + +#ifdef GIC + +setup_gic: // Called from secure mode - set all interrupts to group 1 and enable. + mrs x0, MPIDR_EL1 + ldr x2, =GIC_DISTB + tst x0, #0x3 + b.eq 2f // primary core + + mov w0, #3 // Enable group 0 and 1 IRQs from distributor + str w0, [x2, #GICD_CTRLR] +2: + add x1, x2, #(GIC_CPUB - GIC_DISTB) + mov w0, #0x1e7 + str w0, [x1, #GICC_CTRLR] // Enable group 1 IRQs from CPU interface + mov w0, #0xff + str w0, [x1, #GICC_PMR] // priority mask + add x2, x2, #GICD_IGROUPR + mov x0, #(IT_NR * 4) + mov w1, #~0 // group 1 all the things +3: + subs x0, x0, #4 + str w1, [x2, x0] + b.ne 3b + ret + +#endif + +.globl dtb_space +dtb_space: diff --git a/clock.c b/clock.c new file mode 100644 index 0000000..8ef2996 --- /dev/null +++ b/clock.c @@ -0,0 +1,41 @@ +#include +#include +#include + +#define PROPTAG_GET_CLOCK_RATE 0x00030002 +#define PROPTAG_GET_CLOCK_RATE_MEASURED 0x00030047 + +uint32_t gilbraltar_get_clock(uint32_t cid) { + uint32_t proptag0[] __attribute__ ((aligned(16))) = + { + 8.4, + CODE_REQUEST, + PROPTAG_GET_CLOCK_RATE, + 4*4, + 1*4, + cid, + 0, + PROPTAG_END + }; + + gilbraltar_mbox_write_read((uintptr_t) &proptag0); + + if (proptag0[6] != 0) + return proptag0[6]; + + uint32_t proptag1[] __attribute__ ((aligned(16))) = + { + 8*4, + CODE_REQUEST, + PROPTAG_GET_CLOCK_RATE_MEASURED, + 4*4, + 1*4, + cid, + 0, + PROPTAG_END + }; + + gilbraltar_mbox_write_read((uintptr_t) &proptag1); + + return proptag1[6]; +} diff --git a/configure.sh b/configure.sh new file mode 100755 index 0000000..0f6a0eb --- /dev/null +++ b/configure.sh @@ -0,0 +1,456 @@ +#!/bin/sh +# Copyright (c) 2015-2020 Solo5 Contributors +# Copyright (c) 2024 Romain Calascibetta +# +# This file is part of Gilbraltar, a bare-metal OS for Raspberry Pi. +# +# Permission to use, copy, modify, and/or distribute this software +# for any purpose with or without fee is hereby granted, provided +# that the above copyright notice and this permission notice appear +# in all copies. +# +# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL +# WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED +# WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE +# AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR +# CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS +# OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, +# NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN +# CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + +TARGET_CC="${TARGET_CC:-aarch64-none-elf-gcc}" +TARGET_LD="${TARGET_LD:-aarch64-none-elf-gcc}" +TARGET_OBJCOPY="${TARGET_OBJCOPY:-aarch64-none-elf-objcopy}" + +prog_NAME="$(basename $0)" + +cleanup() +{ + rm -f conftmp.c conftmp.d conftmp*.o +} + +err() +{ + echo "${prog_NAME}: ERROR: $@" 1>&2 +} + +die() +{ + echo "${prog_NAME}: ERROR: $@" 1>&2 + cleanup + exit 1 +} + +warn() +{ + echo "${prog_NAME}: WARNING: $@" 1>&2 +} + +usage() +{ + cat <&2 +usage: ${prog_NAME} [ OPTIONS ] + +Configures the Gilbraltar build system. + +Options: + --prefix=DIR + Installation prefix (default: /usr/local). + +Environment variables affecting the build system configuration: + HOST_CC + C compiler used for host tools. + + TARGET_CC (= $TARGET_CC) + TARGET_LD (= $TARGET_LD) + TARGET_OBJCOPY (= $TARGET_OBJCOPY) + C compiler, linker and objcopy used for target toolchain. + + Experimental: If a cross-toolchain is specified here, the resulting + target toolchain and bindings will be cross-compiled to its + architecture. +EOM + exit 1 +} + +cc_maybe_gcc() +{ + ${CC} -dM -E - /dev/null 2>&1 +int main(int argc, char *argv[]) +{ + return 0; +} +EOM +} + +cc_check_header() +{ + ${CC} ${PKG_CFLAGS} -x c -o /dev/null - </dev/null 2>&1 +#include <$@> + +int main(int argc, char *argv[]) +{ + return 0; +} +EOM +} + +cc_check_lib() +{ + ${CC} -x c -o /dev/null - "$@" ${PKG_LIBS} </dev/null 2>&1 +int main(int argc, char *argv[]) +{ + return 0; +} +EOM +} + +ld_is_lld() +{ + ${LD} --version 2>&1 | grep -q '^LLD' +} + +# Check that the linker ${LD} is available and suitable for our purposes. +check_ld() +{ + echo -n "${prog_NAME}: Checking if ${LD} is available: " + if [ -x "$(command -v ${LD})" ]; then + echo "yes" + else + echo "no" + return 1 + fi + echo -n "${prog_NAME}: Checking if ${LD} is LLD: " + if ld_is_lld; then + echo "yes" + # LLD < 8 chokes on the Xen ldscript, so refuse to use it. + echo -n "${prog_NAME}: Checking if LLD ${LD} is LLVM 8 or newer: " + if ${LD} --version 2>&1 | grep -q '^LLD [1-7]\.'; then + echo "no" + return 1 + else + echo "yes" + fi + else + echo "no" + fi + + cat >conftmp.c </dev/null 2>&1; then + echo "no" + return 1 + else + echo "yes" + fi + return 0 +} + +# Check that the objcopy ${OBJCOPY} is available and suitable for our purposes. +check_objcopy() +{ + echo -n "${prog_NAME}: Checking if ${OBJCOPY} is available: " + if [ -x "$(command -v ${OBJCOPY})" ]; then + echo "yes" + else + echo "no" + return 1 + fi + + cat >conftmp.c </dev/null 2>&1; then + echo "no" + return 1 + else + echo "yes" + fi + # [Clang] For LLVM objcopy, -w was introduced in + # https://reviews.llvm.org/D66613 (release/12.x) and -G was introduced in + # https://reviews.llvm.org/D50589 (release/8.x). + echo -n "${prog_NAME}: Checking if ${OBJCOPY} understands -w -G: " + if ! ${OBJCOPY} -w -G KEEP\* conftmp.o conftmp.o >/dev/null 2>&1; then + echo "no" + return 1 + else + echo "yes" + fi + return 0 +} + +OPT_PREFIX=/usr/local +while [ $# -gt 0 ]; do + OPT="$1" + + case "${OPT}" in + --prefix=*) + OPT_PREFIX="${OPT##*=}" + ;; + --help) + usage + ;; + *) + err "Unknown option: '${OPT}'" + usage + ;; + esac + + shift +done + +# +# Configure host tools based on HOST_CC. +# +HOST_CC=${HOST_CC:-cc} +HOST_CC_MACHINE=$(${HOST_CC} -dumpmachine) +[ $? -ne 0 ] && + die "Could not run '${HOST_CC} -dumpmachine', is your compiler working?" +echo "${prog_NAME}: Using ${HOST_CC} for host compiler (${HOST_CC_MACHINE})" + +case ${HOST_CC_MACHINE} in + x86_64-*linux*) + CONFIG_HOST_ARCH=x86_64 CONFIG_HOST=Linux + ;; + aarch64-*linux*) + CONFIG_HOST_ARCH=aarch64 CONFIG_HOST=Linux + ;; + powerpc64le-*linux*|ppc64le-*linux*) + CONFIG_HOST_ARCH=ppc64le CONFIG_HOST=Linux + ;; + x86_64-*freebsd*) + CONFIG_HOST_ARCH=x86_64 CONFIG_HOST=FreeBSD + ;; + amd64-*openbsd*) + CONFIG_HOST_ARCH=x86_64 CONFIG_HOST=OpenBSD + ;; + *) + die "Unsupported host toolchain: ${HOST_CC_MACHINE}" + ;; +esac + +# If no toolchain was requested, stop here. +# XXX De-duplicate the generation of Makeconf*? +if [ -n "${OPT_DISABLE_TOOLCHAIN}" ]; then + cat <Makeconf +# Generated by configure.sh +CONFIG_PREFIX=${OPT_PREFIX} +CONFIG_HOST_ARCH=${CONFIG_HOST_ARCH} +CONFIG_HOST=${CONFIG_HOST} +CONFIG_HOST_CC=${HOST_CC} +EOM + sed -Ee 's/^([A-Z_]+)=(.*)$/\1="\2"/' Makeconf >Makeconf.sh + cleanup + exit 0 +fi + +# +# Configure target toolchain and bindings based on TARGET_{CC,LD,OBJCOPY}. +# +TARGET_CC="${TARGET_CC:-cc}" + +echo -n "${prog_NAME}: Checking that ${TARGET_CC} works: " +cat >conftmp.c </dev/null 2>&1; then + echo "no" + die "Could not find a working compiler for target toolchain" +else + echo "yes" +fi +TARGET_CC_MACHINE=$(${TARGET_CC} -dumpmachine) + +CONFIG_HVT= CONFIG_SPT= CONFIG_VIRTIO= CONFIG_MUEN= CONFIG_XEN= +case ${TARGET_CC_MACHINE} in + x86_64-*|amd64-*) + TARGET_ARCH=x86_64 + TARGET_LD_MAX_PAGE_SIZE=0x1000 + ;; + aarch64-*) + TARGET_ARCH=aarch64 + TARGET_LD_MAX_PAGE_SIZE=0x1000 + ;; + powerpc64le-*|ppc64le-*) + TARGET_ARCH=ppc64le + TARGET_LD_MAX_PAGE_SIZE=0x10000 + ;; + *) + die "Unsupported target toolchain: ${TARGET_CC_MACHINE}" + ;; +esac + +TARGET_CC_CFLAGS= +TARGET_CC_IS_OPENBSD= +if CC="${TARGET_CC}" cc_is_clang; then + TARGET_CC_CFLAGS=-nostdlibinc + # XXX Clang warns for no good reason if -nostdlibinc is used and no + # compliation is performed. We could work around this by using --config + # which "claims" all command line arguments as "used", but this is easier + # for now. + TARGET_CC_CFLAGS="${TARGET_CC_CFLAGS} -Wno-unused-command-line-argument" +else + TARGET_CC_CFLAGS=-nostdinc +fi +case ${TARGET_CC_MACHINE} in + x86_64-*linux*|powerpc64le-*linux*|ppc64le-*linux*) + # On x86_64 and PPC we need to ensure that TLS is not used for the + # stack protector: + # [GCC] -mstack-protector-guard=global is available from GCC 4.9.0. + # [Clang] -mstack-protector-guard=global was introduced in + # https://reviews.llvm.org/D88631 (release/12.x). + CC="${TARGET_CC}" cc_check_option -mstack-protector-guard=global || \ + die "${TARGET_CC} does not support -mstack-protector-guard=" + TARGET_CC_CFLAGS="${TARGET_CC_CFLAGS} -mstack-protector-guard=global" + ;; + *openbsd*) + # [Clang] OpenBSD's Clang needs to be told to switch off mitigations. + TARGET_CC_CFLAGS="${TARGET_CC_CFLAGS} -mno-retpoline -fno-ret-protector" + # [Clang] OpenBSD's LLVM/Clang uses a global stack protector guard, but + # different symbols; see bindings/GNUmakefile. + TARGET_CC_IS_OPENBSD=1 + ;; +esac + +echo "${prog_NAME}:" \ + "Using ${TARGET_CC} for target compiler (${TARGET_CC_MACHINE})" + +# TARGET_CC_LDFLAGS are used by "cc as linker"; TARGET_LD_LDFLAGS are used by +# the plain "ld" wrapper. +# TODO: Are there Linux distributions with toolchains configured to force PIE +# even if -static is used? If yes, these will need treatment similar to OpenBSD +# below, and/or disabling PIE in "cc". +TARGET_CC_LDFLAGS= +TARGET_LD_LDFLAGS= +case ${CONFIG_HOST} in + Linux) + # The "--build-id=none" nonsense is needed for "cc as a linker" to suppress any + # generation of a .note.gnu.build-id, since our linker scripts don't + # support it and Linux "cc" toolchains insist on adding it by default + # which leads to linkers warning if it is enabled but the input section + # is subsequently discarded. + TARGET_LD="${TARGET_LD:-ld}" + TARGET_OBJCOPY="${TARGET_OBJCOPY:-objcopy}" + TARGET_CC_LDFLAGS="-Wl,--build-id=none" + ;; + FreeBSD) + TARGET_LD="${TARGET_LD:-ld.lld}" + TARGET_OBJCOPY="${TARGET_OBJCOPY:-objcopy}" + # FreeBSD's GNU ld is old and broken, refuse to use it. + if ! LD="${TARGET_LD}" ld_is_lld; then + err "${TARGET_LD} is not LLVM LLD" + die "Using GNU LD is not supported on FreeBSD" + fi + ;; + OpenBSD) + TARGET_LD="${TARGET_LD:-ld.lld}" + TARGET_OBJCOPY="${TARGET_OBJCOPY:-objcopy}" + # OpenBSD's GNU ld is old and broken, refuse to use it. + if ! LD="${TARGET_LD}" ld_is_lld; then + err "${TARGET_LD} is not LLVM LLD" + die "Using GNU LD is not supported on OpenBSD" + fi + # [LLD] OpenBSD's LLD needs to be explicitly told not to produce PIE + # executables. + TARGET_CC_LDFLAGS="-Wl,-nopie" + TARGET_LD_LDFLAGS="-nopie" + ;; + *) + die "Unsupported host system: ${CONFIG_HOST}" + ;; +esac +# [Clang] Force Clang to use the right TARGET_LD when run as "cc as linker". +# -fuse-ld= is braindead and accepts either a "flavour" (e.g. "lld") or an +# absolute path; we try with the latter. +# TODO XXX: This is fragile, but works for the default cases for now. +# TODO document: This won't work with clang "bare metal" targets. +if CC="${TARGET_CC}" cc_is_clang; then + REAL_TARGET_LD="$(command -v ${TARGET_LD})" + [ ! -x "${REAL_TARGET_LD}" ] && \ + die "Cannot determine absolute path for ${TARGET_LD}" + TARGET_CC_LDFLAGS="${TARGET_CC_LDFLAGS} -fuse-ld=${REAL_TARGET_LD}" +fi +if ! CC="${TARGET_CC}" LD="${TARGET_LD}" check_ld; then + die "Could not find a working target linker" +fi +if ! CC="${TARGET_CC}" OBJCOPY="${TARGET_OBJCOPY}" check_objcopy; then + die "Could not find a working target objcopy" +fi + +echo "${prog_NAME}: Using ${TARGET_LD} for target linker" +echo "${prog_NAME}: Using ${TARGET_OBJCOPY} for target objcopy" + +TARGET_TRIPLE="${TARGET_ARCH}-gilbraltar-none-static" +echo "${prog_NAME}: Target toolchain triple is ${TARGET_TRIPLE}" + +# +# Generate Makeconf, to be included by Makefiles. +# +cat <Makeconf +# Generated by configure.sh +CONFIG_PREFIX=${OPT_PREFIX} +CONFIG_HOST_ARCH=${CONFIG_HOST_ARCH} +CONFIG_HOST=${CONFIG_HOST} +CONFIG_HOST_CC=${HOST_CC} +CONFIG_TARGET_ARCH=${TARGET_ARCH} +CONFIG_TARGET_TRIPLE=${TARGET_TRIPLE} +CONFIG_TARGET_CC=${TARGET_CC} +CONFIG_TARGET_CC_CFLAGS=${TARGET_CC_CFLAGS} +CONFIG_TARGET_CC_LDFLAGS=${TARGET_CC_LDFLAGS} +CONFIG_TARGET_CC_IS_OPENBSD=${TARGET_CC_IS_OPENBSD} +CONFIG_TARGET_LD=${TARGET_LD} +CONFIG_TARGET_LD_LDFLAGS=${TARGET_LD_LDFLAGS} +CONFIG_TARGET_LD_MAX_PAGE_SIZE=${TARGET_LD_MAX_PAGE_SIZE} +CONFIG_TARGET_OBJCOPY=${TARGET_OBJCOPY} +EOM + +# +# Generate Makeconf.sh, to be included by shell scripts. +# +sed -Ee 's/^([A-Z_]+)=(.*)$/\1="\2"/' Makeconf >Makeconf.sh + +cleanup diff --git a/crt.c b/crt.c new file mode 100644 index 0000000..22eab7d --- /dev/null +++ b/crt.c @@ -0,0 +1,44 @@ +/* + * Copyright (c) 2015-2019 Contributors as noted in the AUTHORS file + * + * This file is part of Gilbraltar, a bare-metal OS for RPi4. + * + * Permission to use, copy, modify, and/or distribute this software + * for any purpose with or without fee is hereby granted, provided + * that the above copyright notice and this permission notice appear + * in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL + * WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED + * WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE + * AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR + * CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS + * OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, + * NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN + * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#include +#include + +/* + * The stack canary value will be initialised to a pseudo-random value by + * crt_init_early(), keep an easily recognisable "terminator" value here to + * flag if that did not happen as expected. + */ +uintptr_t SSP_GUARD_SYMBOL = 0x00deadbeef0d0a00; + +/* + * Called by compiler-generated code when corruption of the canary value is + * detected. There is very little we can do here safely, so just print a + * message and abort, taking care to make minimal use of the stack. + */ +static const char stack_chk_fail_message[] = + "ABORT: Stack corruption detected\n"; + +extern void uart_puts(const char *str); + +__attribute__((noreturn)) void SSP_FAIL_SYMBOL(void) { + for (;;) + ; +} diff --git a/doc.txt b/doc.txt new file mode 100644 index 0000000..73f95f2 --- /dev/null +++ b/doc.txt @@ -0,0 +1,58 @@ +# How to make a simple unikernel on RBPi + +File required on Raspberry Pi 5: +- bcm2712-rpi-5-b.dtb +- overlays/bcm2712d0.dtdo +- config.txt + +CPU used by Raspberry Pi 5: Cortex-A76 +BCM2712 is the Broadcom chip used by Raspberry Pi 5 + +# Memory layout + +| Base | Size | Contents | Remarks | +|------------|----------------------|----------------------------|---------| +| 00000000 | 32 KByte | ARM Trusted Firmware | BL31 | +| 0006F000 | 4 KByte | EL3 Stack | +| 00070000 | 2 KByte | Exception vector table EL3 | +| ... +| 00080000 | max. 6 MByte | Kernel image | +| | .init | startup code | +| | .text | | +| | .rodata | | +| | .data | | +| | .bss | | +| ... +| | Kernel stacks | | +| 00280000 | 128 KByte | for Core 0 | +| 002A0000 | 128 KByte | for Core 1 | +| 002C0000 | 128 KByte | for Core 2 | +| 002E0000 | 128 KByte | for Core 3 | +| 00300000 | | End of stacks | +| | Exception stacks | | +| 00300000 | 32 KByte | for Core 0 | +| 00308000 | 32 KByte | for Core 1 | +| 00310000 | 32 KByte | for Core 2 | +| 00318000 | 32 KByte | for Core 3 | +| 00320000 | | End of exception stacks | +| | IRQ stack | | +| 00320000 | 32 KByte | for Core 0 | +| 00328000 | 32 KByte | for Core 1 | +| 00330000 | 32 KByte | for Core 2 | +| 00338000 | 32 KByte | for Core 3 | +| 00340000 | | End of IRQ stacks | +| | FIQ stack | | +| 00340000 | 32 KByte | for Core 0 | +| 00348000 | 32 KByte | for Core 1 | +| 00350000 | 32 KByte | for Core 2 | +| 00358000 | 32 KByte | for Core 3 | +| 00360000 | | End of FIQ stacks | +| | Page Table | | +| 00360000 | 16 KByte | | +| 00364000 | | End of page table | +| 00500000 | 4 MByte | Coherent region | +| 00900000 | | | +| 40000000 | | Heap | +| ... +| 1FFFFFFFF | 8192 MB | Heap | +| 1000000000 | 16 MByte | AXI peripherals | diff --git a/exception_handler.c b/exception_handler.c new file mode 100644 index 0000000..ef8824d --- /dev/null +++ b/exception_handler.c @@ -0,0 +1,6 @@ +#include + +void gilbraltar_exception_handler(uint64_t exn, struct frame *frame) { + while (1) + __asm__ __volatile("wfi"); +} diff --git a/exception_stub.S b/exception_stub.S new file mode 100644 index 0000000..b966cea --- /dev/null +++ b/exception_stub.S @@ -0,0 +1,298 @@ +/* + * exceptionstub.S + * + * Copyright (C) 2014-2020 R. Stange + * Copyright (C) 2024 Romain Calascibetta + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see . + */ +#include "exception_stub.h" +#include "bcm.h" + +.macro vector handler +.align 7 + b \handler +.endm + +.macro stub name, exception +.globl \name +\name: + mrs x0, esr_el1 + mrs x1, spsr_el1 + mov x2, x30 // lr + mrs x3, elr_el1 + mrs x4, sp_el0 + mov x5, sp + mrs x6, far_el1 + + str x6, [sp, #-16]! + stp x4, x5, [sp, #-16]! + stp x2, x3, [sp, #-16]! + stp x0, x1, [sp, #-16]! + + mov x0, #\exception + mov x1, sp + b gilbraltar_exception_handler // never returns +.endm + +.text +.align 11 +.globl VectorTable +VectorTable: + // from current EL with sp_el0 + vector synchronous_stub + vector IRQ_stub + vector FIQ_stub + vector system_error_stub + + // from current EL with sp_elx, x != 0 + vector synchronous_stub + vector IRQ_stub + vector FIQ_stub + vector system_error_stub + + // from lower EL, target EL minus 1 is AArch64 + vector HVC_stub + vector unexpected_stub + vector unexpected_stub + vector unexpected_stub + + // from lower EL, target EL minus 1 is AArch32 + vector unexpected_stub + vector unexpected_stub + vector unexpected_stub + vector unexpected_stub + + // Abort stubs + stub unexpected_stub, EXCEPTION_UNEXPECTED + stub synchronous_stub, EXCEPTION_SYNCHRONOUS + stub system_error_stub,EXCEPTION_SYSTEM_ERROR + +// IRQ stub +.globl IRQ_stub +IRQ_stub: + stp x29, x30, [sp, #-16]! // save x29, x30 onto stack + + mrs x29, elr_el1 // save elr_el1, spsr_el1 onto stack + mrs x30, spsr_el1 + stp x29, x30, [sp, #-16]! + msr DAIFClr, #1 // enable FIQ + +#ifdef SAVE_VFP_REGS_ON_IRQ + stp q30, q31, [sp, #-32]! // save q0-q31 onto stack + stp q28, q29, [sp, #-32]! + stp q26, q27, [sp, #-32]! + stp q24, q25, [sp, #-32]! + stp q22, q23, [sp, #-32]! + stp q20, q21, [sp, #-32]! + stp q18, q19, [sp, #-32]! + stp q16, q17, [sp, #-32]! + stp q14, q15, [sp, #-32]! + stp q12, q13, [sp, #-32]! + stp q10, q11, [sp, #-32]! + stp q8, q9, [sp, #-32]! + stp q6, q7, [sp, #-32]! + stp q4, q5, [sp, #-32]! + stp q2, q3, [sp, #-32]! + stp q0, q1, [sp, #-32]! +#endif + stp x27, x28, [sp, #-16]! // save x0-x28 onto stack + stp x25, x26, [sp, #-16]! + stp x23, x24, [sp, #-16]! + stp x21, x22, [sp, #-16]! + stp x19, x20, [sp, #-16]! + stp x17, x18, [sp, #-16]! + stp x15, x16, [sp, #-16]! + stp x13, x14, [sp, #-16]! + stp x11, x12, [sp, #-16]! + stp x9, x10, [sp, #-16]! + stp x7, x8, [sp, #-16]! + stp x5, x6, [sp, #-16]! + stp x3, x4, [sp, #-16]! + stp x1, x2, [sp, #-16]! + str x0, [sp, #-16]! + + ldr x0, =IRQ_return_address // store return address for profiling + str x29, [x0] + + bl gilbraltar_interrupt_handler + + ldr x0, [sp], #16 // restore x0-x28 from stack + ldp x1, x2, [sp], #16 + ldp x3, x4, [sp], #16 + ldp x5, x6, [sp], #16 + ldp x7, x8, [sp], #16 + ldp x9, x10, [sp], #16 + ldp x11, x12, [sp], #16 + ldp x13, x14, [sp], #16 + ldp x15, x16, [sp], #16 + ldp x17, x18, [sp], #16 + ldp x19, x20, [sp], #16 + ldp x21, x22, [sp], #16 + ldp x23, x24, [sp], #16 + ldp x25, x26, [sp], #16 + ldp x27, x28, [sp], #16 +#ifdef SAVE_VFP_REGS_ON_IRQ + ldp q0, q1, [sp], #32 // restore q0-q31 from stack + ldp q2, q3, [sp], #32 + ldp q4, q5, [sp], #32 + ldp q6, q7, [sp], #32 + ldp q8, q9, [sp], #32 + ldp q10, q11, [sp], #32 + ldp q12, q13, [sp], #32 + ldp q14, q15, [sp], #32 + ldp q16, q17, [sp], #32 + ldp q18, q19, [sp], #32 + ldp q20, q21, [sp], #32 + ldp q22, q23, [sp], #32 + ldp q24, q25, [sp], #32 + ldp q26, q27, [sp], #32 + ldp q28, q29, [sp], #32 + ldp q30, q31, [sp], #32 +#endif + + msr DAIFSet, #1 // disable FIQ + ldp x29, x30, [sp], #16 // restore elr_el1, spsr_el1 from stack + msr elr_el1, x29 + msr spsr_el1, x30 + + ldp x29, x30, [sp], #16 // restore x29, x30 from stack + + eret + +// FIQ stub +.globl FIQ_stub +FIQ_stub: +#ifdef SAVE_VFP_REGS_ON_FIQ + stp q30, q31, [sp, #-32]! + stp q28, q29, [sp, #-32]! + stp q26, q27, [sp, #-32]! + stp q24, q25, [sp, #-32]! + stp q22, q23, [sp, #-32]! + stp q20, q21, [sp, #-32]! + stp q18, q19, [sp, #-32]! + stp q16, q17, [sp, #-32]! + stp q14, q15, [sp, #-32]! + stp q12, q13, [sp, #-32]! + stp q10, q11, [sp, #-32]! + stp q8, q9, [sp, #-32]! + stp q6, q7, [sp, #-32]! + stp q4, q5, [sp, #-32]! + stp q2, q3, [sp, #-32]! + stp q0, q1, [sp, #-32]! +#endif + stp x29, x30, [sp, #-16]! + stp x27, x28, [sp, #-16]! + stp x25, x26, [sp, #-16]! + stp x23, x24, [sp, #-16]! + stp x21, x22, [sp, #-16]! + stp x19, x20, [sp, #-16]! + stp x17, x18, [sp, #-16]! + stp x15, x16, [sp, #-16]! + stp x13, x14, [sp, #-16]! + stp x11, x12, [sp, #-16]! + stp x9, x10, [sp, #-16]! + stp x7, x8, [sp, #-16]! + stp x5, x6, [sp, #-16]! + stp x3, x4, [sp, #-16]! + stp x1, x2, [sp, #-16]! + str x0, [sp, #-16]! + + ldr x2, =FIQ_data + ldr x1, [x2] // get FIQ_data.pHandler + cmp x1, #0 // is handler set? + b.eq 2f + ldr x0, [x2, #8] // get FIQ_data.pParam + blr x1 // call handler + +1: + ldr x0, [sp], #16 + ldp x1, x2, [sp], #16 + ldp x3, x4, [sp], #16 + ldp x5, x6, [sp], #16 + ldp x7, x8, [sp], #16 + ldp x9, x10, [sp], #16 + ldp x11, x12, [sp], #16 + ldp x13, x14, [sp], #16 + ldp x15, x16, [sp], #16 + ldp x17, x18, [sp], #16 + ldp x19, x20, [sp], #16 + ldp x21, x22, [sp], #16 + ldp x23, x24, [sp], #16 + ldp x25, x26, [sp], #16 + ldp x27, x28, [sp], #16 + ldp x29, x30, [sp], #16 +#ifdef SAVE_VFP_REGS_ON_FIQ + ldp q0, q1, [sp], #32 + ldp q2, q3, [sp], #32 + ldp q4, q5, [sp], #32 + ldp q6, q7, [sp], #32 + ldp q8, q9, [sp], #32 + ldp q10, q11, [sp], #32 + ldp q12, q13, [sp], #32 + ldp q14, q15, [sp], #32 + ldp q16, q17, [sp], #32 + ldp q18, q19, [sp], #32 + ldp q20, q21, [sp], #32 + ldp q22, q23, [sp], #32 + ldp q24, q25, [sp], #32 + ldp q26, q27, [sp], #32 + ldp q28, q29, [sp], #32 + ldp q30, q31, [sp], #32 +#endif + + eret + +2: + ldr x1, =ARM_IC_FIQ_CONTROL // disable FIQ (if handler is not set) + mov w0, #0 + str w0, [x1] + b 1b + +// SMC stub +.globl SMC_stub +SMC_stub: + ldr x2, =SMC_stack + mov sp, x2 + str x30, [sp, #-16]! + bl gilbraltar_secure_monitor_handler + ldr x30, [sp], #16 + eret + +// HVC stub +HVC_stub: // return to EL2h mode + mrs x0, spsr_el2 + bic x0, x0, #0xF + mov x1, #9 + orr x0, x0, x1 + msr spsr_el2, x0 + eret + +.data +.align 3 +.globl FIQ_data +FIQ_data: +.quad 0 // handler +.quad 0 // param +.word 0 // FIQ_number (unused) + +.align 3 +.globl IRQ_return_address +IRQ_return_address: +.quad 0 + +.bss +.align 4 +.space 128 +SMC_stack: diff --git a/gen-headers.sh b/gen-headers.sh new file mode 100755 index 0000000..1d62fec --- /dev/null +++ b/gen-headers.sh @@ -0,0 +1,104 @@ +#!/bin/sh +# Copyright (c) 2015-2021 Contributors as noted in the AUTHORS file +# +# This file is part of Gilbraltar, a bare-metal OS for RPi4. +# +# Permission to use, copy, modify, and/or distribute this software +# for any purpose with or without fee is hereby granted, provided +# that the above copyright notice and this permission notice appear +# in all copies. +# +# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL +# WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED +# WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE +# AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR +# CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS +# OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, +# NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN +# CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + +# gen-headers.sh: Appropriate internal "C runtime" header files needed for the +# target toolchain from the origin compiler. + +prog_NAME="$(basename $0)" + +cleanup() +{ + rm -f conftmp.c conftmp.d conftmp*.o +} + +die() +{ + echo "${prog_NAME}: ERROR: $@" 1>&2 + cleanup + exit 1 +} + +cc_is_clang() +{ + ${CC} -dM -E - ${temp} || return 1 + sed -e 's!.*\.o:!!g' -e "s!${path}/!!g" ${temp} \ + | tr ' \\' '\n' \ + | sort \ + | uniq + rm ${temp} + ) +} + +[ "$#" -ne 1 ] && die "Missing DESTDIR" +DESTDIR=$1 +. ./Makeconf.sh || die "Can't find . ./Makeconf.sh" + +mkdir -p ${DESTDIR} || die "mkdir failed" + +if CC=${CONFIG_TARGET_CC} cc_is_clang; then + case ${CONFIG_HOST} in + # The BSDs don't ship some standard headers that we need in Clang's + # resource directory. Appropriate these from the host system. + FreeBSD|OpenBSD) + SRCDIR=/usr/include + SRCS="float.h stddef.h stdint.h stdbool.h stdarg.h" + DEPS="$(mktemp)" + CC=${CONFIG_TARGET_CC} cc_get_header_deps ${SRCDIR} ${SRCS} \ + >${DEPS} || \ + die "Failure getting dependencies of host headers" + # cpio will fail if CRT_INCDIR is below a symlink, so squash that + DESTDIR="$(readlink -f ${DESTDIR})" + Q= + [ "${CONFIG_HOST}" = "FreeBSD" ] && Q="--quiet" + (cd ${SRCDIR} && cpio ${Q} -Lpdm ${DESTDIR} <${DEPS}) || \ + die "Failure copying host headers" + rm ${DEPS} + ;; + # Other known Clang toolchains don't require anything special here as + # -nostdlibinc will pick up all we need from the compiler's resource + # directory. + *) + ;; + esac +else + # For GCC there isn't an equivalent of -nostdlibinc, so we need to + # appropriate all of its internal headers. + SRCDIR="$(${CONFIG_TARGET_CC} -print-file-name=include)" + [ -d "${SRCDIR}" ] || die "Cannot determine gcc include directory" + cp -R "${SRCDIR}/." ${DESTDIR} || \ + die "Failure copying host headers" +fi + +echo "uint64_t tscclock_monotonic(void);" > ${DESTDIR}/rpi4.h + +cleanup diff --git a/gilbraltar.ld b/gilbraltar.ld new file mode 100644 index 0000000..dcdba50 --- /dev/null +++ b/gilbraltar.ld @@ -0,0 +1,52 @@ +ENTRY(_start) + +PHDRS { + tdata PT_LOAD FLAGS(4); +} + +SECTIONS +{ + .init : { + *(.init) + } + + .text : { + *(.text*) + _etext = .; + } + + .rodata : { + *(.rodata*) + } + + .ARM.exidx : { + __exidx_start = .; + *(.ARM.exidx*) + __exidx_end = .; + } + + .eh_frame : { + *(.eh_frame*) + } + + .data : { + *(.data*) + } + + .tdata : { + _stdata = .; + *(.tdata) + } :tdata + _edata = .; + + .tbss : { + *(.tbss) + } : tbss + + .bss : { + __bss_start = .; + *(.bss*) + *(COMMON) + _end = .; + } +} diff --git a/include/bcm.h b/include/bcm.h new file mode 100644 index 0000000..d2121a5 --- /dev/null +++ b/include/bcm.h @@ -0,0 +1,23 @@ +#ifndef __GILBRALTAR_BCM__ +#define __GILBRALTAR_BCM__ + +#define ARM_IO_BASE 0x107c000000UL + +// System timers +#define ARM_SYSTIMER_BASE (ARM_IO_BASE + 0x3000) +#define ARM_SYSTIMER_CS (ARM_SYSTIMER_BASE + 0x00) +#define ARM_SYSTIMER_CLO (ARM_SYSTIMER_BASE + 0x04) +#define ARM_SYSTIMER_CHI (ARM_SYSTIMER_BASE + 0x08) + +// Interrupt Controller +#define ARM_IC_BASE (ARM_IO_BASE + 0xb000) + +#define ARM_IC_FIQ_CONTROL (ARM_IO_BASE + 0x20c) + +// General Purpose I/O #2 +#define ARM_GPIO2_BASE (ARM_IO_BASE + 0x1517c00) + +#define ARM_GPIO2_DATA0 (ARM_GPIO2_BASE + 0x04) +#define ARM_GPIO2_IODIR0 (ARM_GPIO2_BASE + 0x08) + +#endif diff --git a/include/clock.h b/include/clock.h new file mode 100644 index 0000000..b1c570a --- /dev/null +++ b/include/clock.h @@ -0,0 +1,6 @@ +#ifndef __GILBRALTAR_CLOCK__ +#define __GILBRALTAR_CLOCK__ + +uint32_t gilbraltar_get_clock(uint32_t); + +#endif diff --git a/include/exception_handler.h b/include/exception_handler.h new file mode 100644 index 0000000..7fb4968 --- /dev/null +++ b/include/exception_handler.h @@ -0,0 +1,32 @@ +#ifndef __GILBRALTAR_EXCEPTION_HANDLER__ +#define __GILBRALTAR_EXCEPTION_HANDLER__ + +#include + +struct frame { + uint32_t sp_irq; + uint32_t lr_irq; + uint32_t sp_fiq; + uint32_t lr_fiq; + uint32_t r0; + uint32_t r1; + uint32_t r2; + uint32_t r3; + uint32_t r4; + uint32_t r5; + uint32_t r6; + uint32_t r7; + uint32_t r8; + uint32_t r9; + uint32_t r10; + uint32_t r11; + uint32_t r12; + uint32_t sp; + uint32_t lr; + uint32_t spsr; + uint32_t pc; +}; + +void gilbraltar_exception_handler(uint64_t, struct frame *); + +#endif diff --git a/include/exception_stub.h b/include/exception_stub.h new file mode 100644 index 0000000..e3b8787 --- /dev/null +++ b/include/exception_stub.h @@ -0,0 +1,8 @@ +#ifndef __GILBRALTAR_EXCEPTION_STUB__ +#define __GILBRALTAR_EXCEPTION_STUB__ + +#define EXCEPTION_UNEXPECTED 0 +#define EXCEPTION_SYNCHRONOUS 1 +#define EXCEPTION_SYSTEM_ERROR 2 + +#endif diff --git a/include/gpio.h b/include/gpio.h new file mode 100644 index 0000000..306b737 --- /dev/null +++ b/include/gpio.h @@ -0,0 +1,6 @@ +#ifndef __GILBRALTAR_GPIO__ +#define __GILBRALTAR_GPIO__ + +#include + +#endif diff --git a/include/led.h b/include/led.h new file mode 100644 index 0000000..f8918b5 --- /dev/null +++ b/include/led.h @@ -0,0 +1,8 @@ +#ifndef __GILBRALTAR_LED__ +#define __GILBRALTAR_LED__ + +#include + +void gilbraltar_led(bool); + +#endif diff --git a/include/log.h b/include/log.h new file mode 100644 index 0000000..6829ac3 --- /dev/null +++ b/include/log.h @@ -0,0 +1,19 @@ +#ifndef __GILBRALTAR_LOG__ +#define __GILBRALTAR_LOG__ + +#include +#include +#include + +enum log_level { + ERROR= 0, + WARN, + INFO, + DEBUG +}; + +size_t gilbraltar_log(enum log_level, const char *fmt, ...) + __attribute__((format (printf, 2, 3))); +void gilbraltar_log_set(enum log_level); + +#endif diff --git a/include/mbox.h b/include/mbox.h new file mode 100644 index 0000000..a984b88 --- /dev/null +++ b/include/mbox.h @@ -0,0 +1,21 @@ +#ifndef __GILBRALTAR_MBOX__ +#define __GILBRALTAR_MBOX__ + +#include +#include + +#define MAILBOX_BASE (ARM_IO_BASE + 0x13880) + +#define MAILBOX0_READ (MAILBOX_BASE + 0x00) +#define MAILBOX0_STATUS (MAILBOX_BASE + 0x18) +#define MAILBOX1_WRITE (MAILBOX_BASE + 0x20) +#define MAILBOX1_STATUS (MAILBOX_BASE + 0x38) + +#define MAILBOX_STATUS_EMPTY 0x40000000 +#define MAILBOX_STATUS_FULL 0x80000000 + +#define BCM_MAILBOX_PROP_OUT 8 + +uint32_t gilbraltar_mbox_write_read(uintptr_t data); + +#endif diff --git a/include/mem.h b/include/mem.h new file mode 100644 index 0000000..6f4d133 --- /dev/null +++ b/include/mem.h @@ -0,0 +1,23 @@ +#ifndef __GILBRALTAR_MEM__ +#define __GILBRALTAR_MEM__ + +#include +#include + +static inline uint8_t read8(uintptr_t addr) { + return *(uint8_t volatile *)addr; +} + +static inline void write8(uintptr_t addr, uint8_t v) { + *(uint8_t volatile *)addr = v; +} + +static inline uint32_t read32(uintptr_t addr) { + return *(uint32_t volatile *)addr; +} + +static inline void write32(uintptr_t addr, uint32_t v) { + *(uint32_t volatile *)addr = v; +} + +#endif diff --git a/include/memory_map.h b/include/memory_map.h new file mode 100644 index 0000000..42770fc --- /dev/null +++ b/include/memory_map.h @@ -0,0 +1,57 @@ +#ifndef __GILBRALTAR_MEMORY_MAP__ +#define __GILBRALTAR_MEMORY_MAP__ + +#ifndef __GILBRALTAR_MEMORY_MAP__ +#error Do not include memory_map.h file directly! +#endif + +#ifndef MEGABYTE +#define MEGABYTE 0x100000 +#endif + +#ifndef GIGABYTE +#define GIGABYTE 0x40000000UL +#endif + +#define CORES 4 // must be a power of 2 +#define MEM_SIZE (512 * MEGABYTE) // default size +#define GPU_MEM_SIZE (64 * MEGABYTE) // set in config.txt +#define ARM_MEM_SIZE (MEM_SIZE - GPU_MEM_SIZE) // normally overwritten +#define PAGE_SIZE 0x10000 // page size used by us +#define PAGE_SHIFT 16 +#define PAGE_MASK ~(0xffff) +#define EXCEPTION_STACK_SIZE 0x8000 +#define PAGE_RESERVE (16 * MEGABYTE) + +// Kernel +#define MEM_KERNEL_START 0x80000 // main code starts here +#define MEM_KERNEL_END (MEM_KERNEL_START + KERNEL_MAX_SIZE) +#define MEM_KERNEL_STACK (MEM_KERNEL_END + KERNEL_STACK_SIZE) // expands down + +#define MEM_EXCEPTION_STACK \ + (MEM_KERNEL_STACK + KERNEL_STACK_SIZE * (CORES - 1) + EXCEPTION_STACK_SIZE) +#define MEM_EXCEPTION_STACK_END \ + (MEM_EXCEPTION_STACK + EXCEPTION_STACK_SIZE * (CORES - 1)) + +// Coherent Memory Region (4 MB) +#define MEM_COHERENT_REGION \ + ((MEM_EXCEPTION_STACK_END + 2 * MEGABYTE) & ~(MEGABYTE - 1)) + +// Heap +#define MEM_HEAP_START GIGABYTE +#define MEM_HEAP_END (8 * GIGABYTE - 1) + +// IRQ & FIC stacks +#define MEM_ABORT_STACK (MEM_KERNEL_STACK + KERNEL_STACK_SIZE * (CORES - 1)) +#define MEM_IRQ_STACK (MEM_EXCEPTION_STACK_END + EXCEPTION_STACK_SIZE) +#define MEM_FIQ_STACK \ + (MEM_IRQ_STACK + EXCEPTION_STACK_SIZE * (CORES - 1) + EXCEPTION_STACK_SIZE) + +// Page table +#define MEM_PAGE_TABLE1 \ + (MEM_FIQ_STACK + EXCEPTION_STACK_SIZE * (CORES - 1)) + +#define PAGE_TABLE1_SIZE 0x4000 +#define MEM_PAGE_TABLE1_END (MEM_PAGE_TABLE1 + PAGE_TABLE1_SIZE) + +#endif diff --git a/include/serial.h b/include/serial.h new file mode 100644 index 0000000..1292bfb --- /dev/null +++ b/include/serial.h @@ -0,0 +1,29 @@ +#ifndef __GILBRALTAR_SERIAL__ +#define __GILBRALTAR_SERIAL__ + +#include +#include +#include + +#define ARM_UART0_BASE (ARM_IO_BASE + 0x1001000) + +#define ARM_UART0_DR (ARM_UART0_BASE + 0x00) +#define ARM_UART0_FR (ARM_UART0_BASE + 0x18) +#define ARM_UART0_IBRD (ARM_UART0_BASE + 0x24) +#define ARM_UART0_FBRD (ARM_UART0_BASE + 0x28) +#define ARM_UART0_LCRH (ARM_UART0_BASE + 0x2c) +#define ARM_UART0_CR (ARM_UART0_BASE + 0x30) +#define ARM_UART0_IFLS (ARM_UART0_BASE + 0x34) +#define ARM_UART0_IMSC (ARM_UART0_BASE + 0x38) +#define ARM_UART0_RIS (ARM_UART0_BASE + 0x3c) +#define ARM_UART0_MIS (ARM_UART0_BASE + 0x40) +#define ARM_UART0_ICR (ARM_UART0_BASE + 0x44) + +void gilbraltar_serial_init(void); +void gilbraltar_serial_send(uint8_t); +uint8_t gilbraltar_serial_recv(void); +void gilbraltar_serial_puts(const char *); +void gilbraltar_serial_putchar(int); +void gilbraltar_serial_write(const char *, size_t); + +#endif diff --git a/include/sysconfig.h b/include/sysconfig.h new file mode 100644 index 0000000..de1d6e2 --- /dev/null +++ b/include/sysconfig.h @@ -0,0 +1,44 @@ +#ifndef __GILBRALTAR_SYSCONFIG__ +#define __GILBRALTAR_SYSCONFIG__ + +#define MEGABYTE 0x100000 + +/* KERNEL_MAX_SIZE is the maximum allowed size of a built kernel image. If your + * kernel image contains big data areas it may be required to increase this + * value. This value must be a multiple of 16 KByte. + */ +#ifndef KERNEL_MAX_SIZE +#define KERNEL_MAX_SIZE (6 * MEGABYTE) +#endif + +/* KERNEL_STACK_SIZE is the size of the stack set on startup for the main + * thread. This must be a multiple of 16 KByte. + */ +#ifndef KERNEL_STACK_SIZE +#define KERNEL_STACK_SIZE 0x20000 +#endif + +#define USE_PHYSICAL_COUNTER +#define SERIAL_GPIO_SELECT 14 // and 15 + +#if __GNUC__ >= 12 +// GNU-C 12.x uses floating point registers for optimizations. This may occur +// anywhere in the code, even in IRQ and FIQ handlers. + +#ifndef SAVE_VFP_REGS_ON_IRQ +#define SAVE_VFP_REGS_ON_IRQ +#endif + +#ifndef SAVE_VFP_REGS_ON_FIQ +#define SAVE_VFP_REGS_ON_FIQ +#endif + +#ifndef __FAST_MATH__ +#define __FAST_MATH__ +#endif + +#endif + +#include "memory_map.h" + +#endif diff --git a/include/tag.h b/include/tag.h new file mode 100644 index 0000000..bad0137 --- /dev/null +++ b/include/tag.h @@ -0,0 +1,10 @@ +#ifndef __GILBRALTAR_TAG__ +#define __GILBRALTAR_TAG__ + +#define CODE_REQUEST 0x00000000 +#define CODE_RESPONSE_SUCCESS 0x80000000 +#define CODE_RESPONSE_FAILURE 0x80000001 + +#define PROPTAG_END 0x00000000 + +#endif diff --git a/include/timer.h b/include/timer.h new file mode 100644 index 0000000..b3921a6 --- /dev/null +++ b/include/timer.h @@ -0,0 +1,13 @@ +#ifndef __GILBRALTAR_TIMER__ +#define __GILBRALTAR_TIMER__ + +#include +#include + +#define CLOCKHZ 1000000 + +void gilbraltar_delay_hot_loop(uint32_t); +void gilbraltar_delay_us(uint32_t); +void gilbraltar_delay_ms(uint32_t); + +#endif diff --git a/interrupt_handler.c b/interrupt_handler.c new file mode 100644 index 0000000..4bc28c3 --- /dev/null +++ b/interrupt_handler.c @@ -0,0 +1,9 @@ +void gilbraltar_interrupt_handler(void) { + while (1) + __asm__ __volatile("wfi"); +} + +void gilbraltar_secure_monitor_handler(void) { + while (1) + __asm__ __volatile("wfi"); +} diff --git a/kernel.c b/kernel.c new file mode 100644 index 0000000..7bc35df --- /dev/null +++ b/kernel.c @@ -0,0 +1,3 @@ +extern void main(void); + +void gilbraltar_sysinit(void) { main(); } diff --git a/led.c b/led.c new file mode 100644 index 0000000..2955724 --- /dev/null +++ b/led.c @@ -0,0 +1,14 @@ +#include +#include +#include + +void gilbraltar_led(bool s) { + uint32_t reg = read32(ARM_GPIO2_DATA0); + + if (s) + reg |= 0x200; // set bit 9 to 1 + else + reg &= ~0x200; // set bit 9 to 0 + + write32(ARM_GPIO2_DATA0, reg); +} diff --git a/log.c b/log.c new file mode 100644 index 0000000..a9b4652 --- /dev/null +++ b/log.c @@ -0,0 +1,32 @@ +#include +#include +#include + +static enum log_level actual_level = INFO; + +size_t gilbraltar_log(enum log_level level, const char *fmt, ...) { + if (actual_level < level) + return 0; + + va_list args; + size_t size; + char buffer[320]; + + va_start(args, fmt); + size = vsnprintf(buffer, sizeof buffer, fmt, args); + va_end(args); + + if (size >= sizeof buffer) { + const char trunc[] = "(truncated)\n"; + gilbraltar_serial_write(buffer, sizeof buffer - 1); + gilbraltar_serial_write(trunc, sizeof buffer - 1); + return (sizeof buffer - 1); + } else { + gilbraltar_serial_write(buffer, size); + return size; + } +} + +void gilbraltar_log_set(enum log_level level) { + actual_level = level; +} diff --git a/mbox.c b/mbox.c new file mode 100644 index 0000000..b425ca5 --- /dev/null +++ b/mbox.c @@ -0,0 +1,18 @@ +#include +#include + +uint32_t gilbraltar_mbox_write_read(uintptr_t dma) { + dma |= 0xc0000000U; + + while (read32(MAILBOX1_STATUS) & MAILBOX_STATUS_FULL); + write32(MAILBOX1_WRITE, BCM_MAILBOX_PROP_OUT | dma); + + uint32_t result; + + do { + while (read32(MAILBOX0_STATUS) & MAILBOX_STATUS_EMPTY); + result = read32(MAILBOX0_READ); + } while ((result & 0xf) != BCM_MAILBOX_PROP_OUT); + + return (result & ~0xf); +} diff --git a/nolibc/GNUmakefile b/nolibc/GNUmakefile new file mode 100644 index 0000000..6e13859 --- /dev/null +++ b/nolibc/GNUmakefile @@ -0,0 +1,58 @@ +ifeq ($(FREESTANDING_CFLAGS),) + $(error FREESTANDING_CFLAGS not set) +endif + +all: libnolibc.a test-headers + +.PHONY: all test-headers clean + +clean: + $(RM) libnolibc.a *.o test-include/*.[co] test-include/sys/*.[co] + +CC=cc +CFLAGS=-O2 -std=c99 -Wall -Wno-parentheses -Werror +CFLAGS+=$(FREESTANDING_CFLAGS) + +OBJS=assert.o \ + ctype.o \ + dtoa.o \ + errlist.o strerror_r.o \ + memchr.o memcmp.o memcpy.o memmove.o memset.o \ + strcmp.o strlen.o strnlen.o strtol.o strchr.o strchrnul.o strncpy.o stpncpy.o \ + strstr.o strncmp.o puts.o \ + stubs.o \ + vfprintf.o vsnprintf.o snprintf.o fprintf.o printf.o \ + sysconf.o \ + mmap.o + +SYSOBJS=sysdeps.o + +dtoa.o: CFLAGS+=-fno-strict-aliasing + +libnolibc.a: $(OBJS) $(SYSOBJS) + $(AR) rcs $@ $(OBJS) $(SYSOBJS) + +# The following test ensures that each header file provided by nolibc is both +# self-contained and compile-tested. Note that headers in include/_freestanding +# are not intended to be included directly, thus are exempt from this check. + +HEADERS=$(wildcard include/*.h include/sys/*.h) + +# For each HEADER we want to test, produce test-include/HEADER.o. Note that +# HEADER will include subdirectories, if matched. +TEST_H_OBJS=$(patsubst %.h,test-%.o,$(HEADERS)) + +# For each HEADER we want to test, generate a C source file including only +# that HEADER. As above, HEADER may include subdirectories. +test-include/%.c: include/%.h | test-include/sys/ + echo "#include \"../$<\"" >$@ + +.PRECIOUS: test-include/%.c + +test-include/: + mkdir -p $@ + +test-include/sys/: test-include/ + mkdir -p $@ + +test-headers: $(TEST_H_OBJS) | test-include/sys/ diff --git a/nolibc/assert.c b/nolibc/assert.c new file mode 100644 index 0000000..ae89be3 --- /dev/null +++ b/nolibc/assert.c @@ -0,0 +1,18 @@ +#include +#include + +/* + * These functions deliberately do not call printf() or malloc() in order to + * abort as quickly as possible without triggering further errors. + */ + +void _assert_fail(const char *file, const char *line, const char *e) +{ + puts(file); + puts(":"); + puts(line); + puts(": Assertion `"); + puts(e); + puts("' failed\n"); + abort(); +} diff --git a/nolibc/ctype.c b/nolibc/ctype.c new file mode 100644 index 0000000..cfa203c --- /dev/null +++ b/nolibc/ctype.c @@ -0,0 +1,26 @@ +#include + +int isalpha(int c) +{ + return ((unsigned)c|32)-'a' < 26; +} + +int isdigit(int c) +{ + return (unsigned)c-'0' < 10; +} + +int isprint(int c) +{ + return (unsigned)c-0x20 < 0x5f; +} + +int isspace(int c) +{ + return c == ' ' || (unsigned)c-'\t' < 5; +} + +int isupper(int c) +{ + return (unsigned)c-'A' < 26; +} diff --git a/nolibc/dlmalloc.i b/nolibc/dlmalloc.i new file mode 100644 index 0000000..5eceeee --- /dev/null +++ b/nolibc/dlmalloc.i @@ -0,0 +1,6339 @@ +/* + Note: that this is a slightly modified version of dlmalloc to add + the internal_memory_usage field to the malloc_state structure. This + field is used with the gm variable to keep track of the amount of + memory allocated in the heap. + The results of this fast estimation are returned by the + dlmalloc_memory_usage function exported as malloc_memory_usage. + See lines 993, 2629 and in dlmalloc(), dlfree(), internal_memalign() + and dlrealloc*() +*/ + +/* + This is a version (aka dlmalloc) of malloc/free/realloc written by + Doug Lea and released to the public domain, as explained at + http://creativecommons.org/publicdomain/zero/1.0/ Send questions, + comments, complaints, performance data, etc to dl@cs.oswego.edu + +* Version 2.8.6 Wed Aug 29 06:57:58 2012 Doug Lea + Note: There may be an updated version of this malloc obtainable at + ftp://gee.cs.oswego.edu/pub/misc/malloc.c + Check before installing! + +* Quickstart + + This library is all in one file to simplify the most common usage: + ftp it, compile it (-O3), and link it into another program. All of + the compile-time options default to reasonable values for use on + most platforms. You might later want to step through various + compile-time and dynamic tuning options. + + For convenience, an include file for code using this malloc is at: + ftp://gee.cs.oswego.edu/pub/misc/malloc-2.8.6.h + You don't really need this .h file unless you call functions not + defined in your system include files. The .h file contains only the + excerpts from this file needed for using this malloc on ANSI C/C++ + systems, so long as you haven't changed compile-time options about + naming and tuning parameters. If you do, then you can create your + own malloc.h that does include all settings by cutting at the point + indicated below. Note that you may already by default be using a C + library containing a malloc that is based on some version of this + malloc (for example in linux). You might still want to use the one + in this file to customize settings or to avoid overheads associated + with library versions. + +* Vital statistics: + + Supported pointer/size_t representation: 4 or 8 bytes + size_t MUST be an unsigned type of the same width as + pointers. (If you are using an ancient system that declares + size_t as a signed type, or need it to be a different width + than pointers, you can use a previous release of this malloc + (e.g. 2.7.2) supporting these.) + + Alignment: 8 bytes (minimum) + This suffices for nearly all current machines and C compilers. + However, you can define MALLOC_ALIGNMENT to be wider than this + if necessary (up to 128bytes), at the expense of using more space. + + Minimum overhead per allocated chunk: 4 or 8 bytes (if 4byte sizes) + 8 or 16 bytes (if 8byte sizes) + Each malloced chunk has a hidden word of overhead holding size + and status information, and additional cross-check word + if FOOTERS is defined. + + Minimum allocated size: 4-byte ptrs: 16 bytes (including overhead) + 8-byte ptrs: 32 bytes (including overhead) + + Even a request for zero bytes (i.e., malloc(0)) returns a + pointer to something of the minimum allocatable size. + The maximum overhead wastage (i.e., number of extra bytes + allocated than were requested in malloc) is less than or equal + to the minimum size, except for requests >= mmap_threshold that + are serviced via mmap(), where the worst case wastage is about + 32 bytes plus the remainder from a system page (the minimal + mmap unit); typically 4096 or 8192 bytes. + + Security: static-safe; optionally more or less + The "security" of malloc refers to the ability of malicious + code to accentuate the effects of errors (for example, freeing + space that is not currently malloc'ed or overwriting past the + ends of chunks) in code that calls malloc. This malloc + guarantees not to modify any memory locations below the base of + heap, i.e., static variables, even in the presence of usage + errors. The routines additionally detect most improper frees + and reallocs. All this holds as long as the static bookkeeping + for malloc itself is not corrupted by some other means. This + is only one aspect of security -- these checks do not, and + cannot, detect all possible programming errors. + + If FOOTERS is defined nonzero, then each allocated chunk + carries an additional check word to verify that it was malloced + from its space. These check words are the same within each + execution of a program using malloc, but differ across + executions, so externally crafted fake chunks cannot be + freed. This improves security by rejecting frees/reallocs that + could corrupt heap memory, in addition to the checks preventing + writes to statics that are always on. This may further improve + security at the expense of time and space overhead. (Note that + FOOTERS may also be worth using with MSPACES.) + + By default detected errors cause the program to abort (calling + "abort()"). You can override this to instead proceed past + errors by defining PROCEED_ON_ERROR. In this case, a bad free + has no effect, and a malloc that encounters a bad address + caused by user overwrites will ignore the bad address by + dropping pointers and indices to all known memory. This may + be appropriate for programs that should continue if at all + possible in the face of programming errors, although they may + run out of memory because dropped memory is never reclaimed. + + If you don't like either of these options, you can define + CORRUPTION_ERROR_ACTION and USAGE_ERROR_ACTION to do anything + else. And if if you are sure that your program using malloc has + no errors or vulnerabilities, you can define INSECURE to 1, + which might (or might not) provide a small performance improvement. + + It is also possible to limit the maximum total allocatable + space, using malloc_set_footprint_limit. This is not + designed as a security feature in itself (calls to set limits + are not screened or privileged), but may be useful as one + aspect of a secure implementation. + + Thread-safety: NOT thread-safe unless USE_LOCKS defined non-zero + When USE_LOCKS is defined, each public call to malloc, free, + etc is surrounded with a lock. By default, this uses a plain + pthread mutex, win32 critical section, or a spin-lock if if + available for the platform and not disabled by setting + USE_SPIN_LOCKS=0. However, if USE_RECURSIVE_LOCKS is defined, + recursive versions are used instead (which are not required for + base functionality but may be needed in layered extensions). + Using a global lock is not especially fast, and can be a major + bottleneck. It is designed only to provide minimal protection + in concurrent environments, and to provide a basis for + extensions. If you are using malloc in a concurrent program, + consider instead using nedmalloc + (http://www.nedprod.com/programs/portable/nedmalloc/) or + ptmalloc (See http://www.malloc.de), which are derived from + versions of this malloc. + + System requirements: Any combination of MORECORE and/or MMAP/MUNMAP + This malloc can use unix sbrk or any emulation (invoked using + the CALL_MORECORE macro) and/or mmap/munmap or any emulation + (invoked using CALL_MMAP/CALL_MUNMAP) to get and release system + memory. On most unix systems, it tends to work best if both + MORECORE and MMAP are enabled. On Win32, it uses emulations + based on VirtualAlloc. It also uses common C library functions + like memset. + + Compliance: I believe it is compliant with the Single Unix Specification + (See http://www.unix.org). Also SVID/XPG, ANSI C, and probably + others as well. + +* Overview of algorithms + + This is not the fastest, most space-conserving, most portable, or + most tunable malloc ever written. However it is among the fastest + while also being among the most space-conserving, portable and + tunable. Consistent balance across these factors results in a good + general-purpose allocator for malloc-intensive programs. + + In most ways, this malloc is a best-fit allocator. Generally, it + chooses the best-fitting existing chunk for a request, with ties + broken in approximately least-recently-used order. (This strategy + normally maintains low fragmentation.) However, for requests less + than 256bytes, it deviates from best-fit when there is not an + exactly fitting available chunk by preferring to use space adjacent + to that used for the previous small request, as well as by breaking + ties in approximately most-recently-used order. (These enhance + locality of series of small allocations.) And for very large requests + (>= 256Kb by default), it relies on system memory mapping + facilities, if supported. (This helps avoid carrying around and + possibly fragmenting memory used only for large chunks.) + + All operations (except malloc_stats and mallinfo) have execution + times that are bounded by a constant factor of the number of bits in + a size_t, not counting any clearing in calloc or copying in realloc, + or actions surrounding MORECORE and MMAP that have times + proportional to the number of non-contiguous regions returned by + system allocation routines, which is often just 1. In real-time + applications, you can optionally suppress segment traversals using + NO_SEGMENT_TRAVERSAL, which assures bounded execution even when + system allocators return non-contiguous spaces, at the typical + expense of carrying around more memory and increased fragmentation. + + The implementation is not very modular and seriously overuses + macros. Perhaps someday all C compilers will do as good a job + inlining modular code as can now be done by brute-force expansion, + but now, enough of them seem not to. + + Some compilers issue a lot of warnings about code that is + dead/unreachable only on some platforms, and also about intentional + uses of negation on unsigned types. All known cases of each can be + ignored. + + For a longer but out of date high-level description, see + http://gee.cs.oswego.edu/dl/html/malloc.html + +* MSPACES + If MSPACES is defined, then in addition to malloc, free, etc., + this file also defines mspace_malloc, mspace_free, etc. These + are versions of malloc routines that take an "mspace" argument + obtained using create_mspace, to control all internal bookkeeping. + If ONLY_MSPACES is defined, only these versions are compiled. + So if you would like to use this allocator for only some allocations, + and your system malloc for others, you can compile with + ONLY_MSPACES and then do something like... + static mspace mymspace = create_mspace(0,0); // for example + #define mymalloc(bytes) mspace_malloc(mymspace, bytes) + + (Note: If you only need one instance of an mspace, you can instead + use "USE_DL_PREFIX" to relabel the global malloc.) + + You can similarly create thread-local allocators by storing + mspaces as thread-locals. For example: + static __thread mspace tlms = 0; + void* tlmalloc(size_t bytes) { + if (tlms == 0) tlms = create_mspace(0, 0); + return mspace_malloc(tlms, bytes); + } + void tlfree(void* mem) { mspace_free(tlms, mem); } + + Unless FOOTERS is defined, each mspace is completely independent. + You cannot allocate from one and free to another (although + conformance is only weakly checked, so usage errors are not always + caught). If FOOTERS is defined, then each chunk carries around a tag + indicating its originating mspace, and frees are directed to their + originating spaces. Normally, this requires use of locks. + + ------------------------- Compile-time options --------------------------- + +Be careful in setting #define values for numerical constants of type +size_t. On some systems, literal values are not automatically extended +to size_t precision unless they are explicitly casted. You can also +use the symbolic values MAX_SIZE_T, SIZE_T_ONE, etc below. + +WIN32 default: defined if _WIN32 defined + Defining WIN32 sets up defaults for MS environment and compilers. + Otherwise defaults are for unix. Beware that there seem to be some + cases where this malloc might not be a pure drop-in replacement for + Win32 malloc: Random-looking failures from Win32 GDI API's (eg; + SetDIBits()) may be due to bugs in some video driver implementations + when pixel buffers are malloc()ed, and the region spans more than + one VirtualAlloc()ed region. Because dlmalloc uses a small (64Kb) + default granularity, pixel buffers may straddle virtual allocation + regions more often than when using the Microsoft allocator. You can + avoid this by using VirtualAlloc() and VirtualFree() for all pixel + buffers rather than using malloc(). If this is not possible, + recompile this malloc with a larger DEFAULT_GRANULARITY. Note: + in cases where MSC and gcc (cygwin) are known to differ on WIN32, + conditions use _MSC_VER to distinguish them. + +DLMALLOC_EXPORT default: extern + Defines how public APIs are declared. If you want to export via a + Windows DLL, you might define this as + #define DLMALLOC_EXPORT extern __declspec(dllexport) + If you want a POSIX ELF shared object, you might use + #define DLMALLOC_EXPORT extern __attribute__((visibility("default"))) + +MALLOC_ALIGNMENT default: (size_t)(2 * sizeof(void *)) + Controls the minimum alignment for malloc'ed chunks. It must be a + power of two and at least 8, even on machines for which smaller + alignments would suffice. It may be defined as larger than this + though. Note however that code and data structures are optimized for + the case of 8-byte alignment. + +MSPACES default: 0 (false) + If true, compile in support for independent allocation spaces. + This is only supported if HAVE_MMAP is true. + +ONLY_MSPACES default: 0 (false) + If true, only compile in mspace versions, not regular versions. + +USE_LOCKS default: 0 (false) + Causes each call to each public routine to be surrounded with + pthread or WIN32 mutex lock/unlock. (If set true, this can be + overridden on a per-mspace basis for mspace versions.) If set to a + non-zero value other than 1, locks are used, but their + implementation is left out, so lock functions must be supplied manually, + as described below. + +USE_SPIN_LOCKS default: 1 iff USE_LOCKS and spin locks available + If true, uses custom spin locks for locking. This is currently + supported only gcc >= 4.1, older gccs on x86 platforms, and recent + MS compilers. Otherwise, posix locks or win32 critical sections are + used. + +USE_RECURSIVE_LOCKS default: not defined + If defined nonzero, uses recursive (aka reentrant) locks, otherwise + uses plain mutexes. This is not required for malloc proper, but may + be needed for layered allocators such as nedmalloc. + +LOCK_AT_FORK default: not defined + If defined nonzero, performs pthread_atfork upon initialization + to initialize child lock while holding parent lock. The implementation + assumes that pthread locks (not custom locks) are being used. In other + cases, you may need to customize the implementation. + +FOOTERS default: 0 + If true, provide extra checking and dispatching by placing + information in the footers of allocated chunks. This adds + space and time overhead. + +INSECURE default: 0 + If true, omit checks for usage errors and heap space overwrites. + +USE_DL_PREFIX default: NOT defined + Causes compiler to prefix all public routines with the string 'dl'. + This can be useful when you only want to use this malloc in one part + of a program, using your regular system malloc elsewhere. + +MALLOC_INSPECT_ALL default: NOT defined + If defined, compiles malloc_inspect_all and mspace_inspect_all, that + perform traversal of all heap space. Unless access to these + functions is otherwise restricted, you probably do not want to + include them in secure implementations. + +ABORT default: defined as abort() + Defines how to abort on failed checks. On most systems, a failed + check cannot die with an "assert" or even print an informative + message, because the underlying print routines in turn call malloc, + which will fail again. Generally, the best policy is to simply call + abort(). It's not very useful to do more than this because many + errors due to overwriting will show up as address faults (null, odd + addresses etc) rather than malloc-triggered checks, so will also + abort. Also, most compilers know that abort() does not return, so + can better optimize code conditionally calling it. + +PROCEED_ON_ERROR default: defined as 0 (false) + Controls whether detected bad addresses cause them to bypassed + rather than aborting. If set, detected bad arguments to free and + realloc are ignored. And all bookkeeping information is zeroed out + upon a detected overwrite of freed heap space, thus losing the + ability to ever return it from malloc again, but enabling the + application to proceed. If PROCEED_ON_ERROR is defined, the + static variable malloc_corruption_error_count is compiled in + and can be examined to see if errors have occurred. This option + generates slower code than the default abort policy. + +DEBUG default: NOT defined + The DEBUG setting is mainly intended for people trying to modify + this code or diagnose problems when porting to new platforms. + However, it may also be able to better isolate user errors than just + using runtime checks. The assertions in the check routines spell + out in more detail the assumptions and invariants underlying the + algorithms. The checking is fairly extensive, and will slow down + execution noticeably. Calling malloc_stats or mallinfo with DEBUG + set will attempt to check every non-mmapped allocated and free chunk + in the course of computing the summaries. + +ABORT_ON_ASSERT_FAILURE default: defined as 1 (true) + Debugging assertion failures can be nearly impossible if your + version of the assert macro causes malloc to be called, which will + lead to a cascade of further failures, blowing the runtime stack. + ABORT_ON_ASSERT_FAILURE cause assertions failures to call abort(), + which will usually make debugging easier. + +MALLOC_FAILURE_ACTION default: sets errno to ENOMEM, or no-op on win32 + The action to take before "return 0" when malloc fails to be able to + return memory because there is none available. + +HAVE_MORECORE default: 1 (true) unless win32 or ONLY_MSPACES + True if this system supports sbrk or an emulation of it. + +MORECORE default: sbrk + The name of the sbrk-style system routine to call to obtain more + memory. See below for guidance on writing custom MORECORE + functions. The type of the argument to sbrk/MORECORE varies across + systems. It cannot be size_t, because it supports negative + arguments, so it is normally the signed type of the same width as + size_t (sometimes declared as "intptr_t"). It doesn't much matter + though. Internally, we only call it with arguments less than half + the max value of a size_t, which should work across all reasonable + possibilities, although sometimes generating compiler warnings. + +MORECORE_CONTIGUOUS default: 1 (true) if HAVE_MORECORE + If true, take advantage of fact that consecutive calls to MORECORE + with positive arguments always return contiguous increasing + addresses. This is true of unix sbrk. It does not hurt too much to + set it true anyway, since malloc copes with non-contiguities. + Setting it false when definitely non-contiguous saves time + and possibly wasted space it would take to discover this though. + +MORECORE_CANNOT_TRIM default: NOT defined + True if MORECORE cannot release space back to the system when given + negative arguments. This is generally necessary only if you are + using a hand-crafted MORECORE function that cannot handle negative + arguments. + +NO_SEGMENT_TRAVERSAL default: 0 + If non-zero, suppresses traversals of memory segments + returned by either MORECORE or CALL_MMAP. This disables + merging of segments that are contiguous, and selectively + releasing them to the OS if unused, but bounds execution times. + +HAVE_MMAP default: 1 (true) + True if this system supports mmap or an emulation of it. If so, and + HAVE_MORECORE is not true, MMAP is used for all system + allocation. If set and HAVE_MORECORE is true as well, MMAP is + primarily used to directly allocate very large blocks. It is also + used as a backup strategy in cases where MORECORE fails to provide + space from system. Note: A single call to MUNMAP is assumed to be + able to unmap memory that may have be allocated using multiple calls + to MMAP, so long as they are adjacent. + +HAVE_MREMAP default: 1 on linux, else 0 + If true realloc() uses mremap() to re-allocate large blocks and + extend or shrink allocation spaces. + +MMAP_CLEARS default: 1 except on WINCE. + True if mmap clears memory so calloc doesn't need to. This is true + for standard unix mmap using /dev/zero and on WIN32 except for WINCE. + +USE_BUILTIN_FFS default: 0 (i.e., not used) + Causes malloc to use the builtin ffs() function to compute indices. + Some compilers may recognize and intrinsify ffs to be faster than the + supplied C version. Also, the case of x86 using gcc is special-cased + to an asm instruction, so is already as fast as it can be, and so + this setting has no effect. Similarly for Win32 under recent MS compilers. + (On most x86s, the asm version is only slightly faster than the C version.) + +malloc_getpagesize default: derive from system includes, or 4096. + The system page size. To the extent possible, this malloc manages + memory from the system in page-size units. This may be (and + usually is) a function rather than a constant. This is ignored + if WIN32, where page size is determined using getSystemInfo during + initialization. + +USE_DEV_RANDOM default: 0 (i.e., not used) + Causes malloc to use /dev/random to initialize secure magic seed for + stamping footers. Otherwise, the current time is used. + +NO_MALLINFO default: 0 + If defined, don't compile "mallinfo". This can be a simple way + of dealing with mismatches between system declarations and + those in this file. + +MALLINFO_FIELD_TYPE default: size_t + The type of the fields in the mallinfo struct. This was originally + defined as "int" in SVID etc, but is more usefully defined as + size_t. The value is used only if HAVE_USR_INCLUDE_MALLOC_H is not set + +NO_MALLOC_STATS default: 0 + If defined, don't compile "malloc_stats". This avoids calls to + fprintf and bringing in stdio dependencies you might not want. + +REALLOC_ZERO_BYTES_FREES default: not defined + This should be set if a call to realloc with zero bytes should + be the same as a call to free. Some people think it should. Otherwise, + since this malloc returns a unique pointer for malloc(0), so does + realloc(p, 0). + +LACKS_UNISTD_H, LACKS_FCNTL_H, LACKS_SYS_PARAM_H, LACKS_SYS_MMAN_H +LACKS_STRINGS_H, LACKS_STRING_H, LACKS_SYS_TYPES_H, LACKS_ERRNO_H +LACKS_STDLIB_H LACKS_SCHED_H LACKS_TIME_H default: NOT defined unless on WIN32 + Define these if your system does not have these header files. + You might need to manually insert some of the declarations they provide. + +DEFAULT_GRANULARITY default: page size if MORECORE_CONTIGUOUS, + system_info.dwAllocationGranularity in WIN32, + otherwise 64K. + Also settable using mallopt(M_GRANULARITY, x) + The unit for allocating and deallocating memory from the system. On + most systems with contiguous MORECORE, there is no reason to + make this more than a page. However, systems with MMAP tend to + either require or encourage larger granularities. You can increase + this value to prevent system allocation functions to be called so + often, especially if they are slow. The value must be at least one + page and must be a power of two. Setting to 0 causes initialization + to either page size or win32 region size. (Note: In previous + versions of malloc, the equivalent of this option was called + "TOP_PAD") + +DEFAULT_TRIM_THRESHOLD default: 2MB + Also settable using mallopt(M_TRIM_THRESHOLD, x) + The maximum amount of unused top-most memory to keep before + releasing via malloc_trim in free(). Automatic trimming is mainly + useful in long-lived programs using contiguous MORECORE. Because + trimming via sbrk can be slow on some systems, and can sometimes be + wasteful (in cases where programs immediately afterward allocate + more large chunks) the value should be high enough so that your + overall system performance would improve by releasing this much + memory. As a rough guide, you might set to a value close to the + average size of a process (program) running on your system. + Releasing this much memory would allow such a process to run in + memory. Generally, it is worth tuning trim thresholds when a + program undergoes phases where several large chunks are allocated + and released in ways that can reuse each other's storage, perhaps + mixed with phases where there are no such chunks at all. The trim + value must be greater than page size to have any useful effect. To + disable trimming completely, you can set to MAX_SIZE_T. Note that the trick + some people use of mallocing a huge space and then freeing it at + program startup, in an attempt to reserve system memory, doesn't + have the intended effect under automatic trimming, since that memory + will immediately be returned to the system. + +DEFAULT_MMAP_THRESHOLD default: 256K + Also settable using mallopt(M_MMAP_THRESHOLD, x) + The request size threshold for using MMAP to directly service a + request. Requests of at least this size that cannot be allocated + using already-existing space will be serviced via mmap. (If enough + normal freed space already exists it is used instead.) Using mmap + segregates relatively large chunks of memory so that they can be + individually obtained and released from the host system. A request + serviced through mmap is never reused by any other request (at least + not directly; the system may just so happen to remap successive + requests to the same locations). Segregating space in this way has + the benefits that: Mmapped space can always be individually released + back to the system, which helps keep the system level memory demands + of a long-lived program low. Also, mapped memory doesn't become + `locked' between other chunks, as can happen with normally allocated + chunks, which means that even trimming via malloc_trim would not + release them. However, it has the disadvantage that the space + cannot be reclaimed, consolidated, and then used to service later + requests, as happens with normal chunks. The advantages of mmap + nearly always outweigh disadvantages for "large" chunks, but the + value of "large" may vary across systems. The default is an + empirically derived value that works well in most systems. You can + disable mmap by setting to MAX_SIZE_T. + +MAX_RELEASE_CHECK_RATE default: 4095 unless not HAVE_MMAP + The number of consolidated frees between checks to release + unused segments when freeing. When using non-contiguous segments, + especially with multiple mspaces, checking only for topmost space + doesn't always suffice to trigger trimming. To compensate for this, + free() will, with a period of MAX_RELEASE_CHECK_RATE (or the + current number of segments, if greater) try to release unused + segments to the OS when freeing chunks that result in + consolidation. The best value for this parameter is a compromise + between slowing down frees with relatively costly checks that + rarely trigger versus holding on to unused memory. To effectively + disable, set to MAX_SIZE_T. This may lead to a very slight speed + improvement at the expense of carrying around more memory. +*/ + +/* Version identifier to allow people to support multiple versions */ +#ifndef DLMALLOC_VERSION +#define DLMALLOC_VERSION 20806 +#endif /* DLMALLOC_VERSION */ + +#ifndef DLMALLOC_EXPORT +#define DLMALLOC_EXPORT extern +#endif + +#ifndef WIN32 +#ifdef _WIN32 +#define WIN32 1 +#endif /* _WIN32 */ +#ifdef _WIN32_WCE +#define LACKS_FCNTL_H +#define WIN32 1 +#endif /* _WIN32_WCE */ +#endif /* WIN32 */ +#ifdef WIN32 +#define WIN32_LEAN_AND_MEAN +#include +#include +#define HAVE_MMAP 1 +#define HAVE_MORECORE 0 +#define LACKS_UNISTD_H +#define LACKS_SYS_PARAM_H +#define LACKS_SYS_MMAN_H +#define LACKS_STRING_H +#define LACKS_STRINGS_H +#define LACKS_SYS_TYPES_H +#define LACKS_ERRNO_H +#define LACKS_SCHED_H +#ifndef MALLOC_FAILURE_ACTION +#define MALLOC_FAILURE_ACTION +#endif /* MALLOC_FAILURE_ACTION */ +#ifndef MMAP_CLEARS +#ifdef _WIN32_WCE /* WINCE reportedly does not clear */ +#define MMAP_CLEARS 0 +#else +#define MMAP_CLEARS 1 +#endif /* _WIN32_WCE */ +#endif /*MMAP_CLEARS */ +#endif /* WIN32 */ + +#if defined(DARWIN) || defined(_DARWIN) +/* Mac OSX docs advise not to use sbrk; it seems better to use mmap */ +#ifndef HAVE_MORECORE +#define HAVE_MORECORE 0 +#define HAVE_MMAP 1 +/* OSX allocators provide 16 byte alignment */ +#ifndef MALLOC_ALIGNMENT +#define MALLOC_ALIGNMENT ((size_t)16U) +#endif +#endif /* HAVE_MORECORE */ +#endif /* DARWIN */ + +#ifndef LACKS_SYS_TYPES_H +#include /* For size_t */ +#endif /* LACKS_SYS_TYPES_H */ + +/* The maximum possible size_t value has all bits set */ +#define MAX_SIZE_T (~(size_t)0) + +#ifndef USE_LOCKS /* ensure true if spin or recursive locks set */ +#define USE_LOCKS ((defined(USE_SPIN_LOCKS) && USE_SPIN_LOCKS != 0) || \ + (defined(USE_RECURSIVE_LOCKS) && USE_RECURSIVE_LOCKS != 0)) +#endif /* USE_LOCKS */ + +#if USE_LOCKS /* Spin locks for gcc >= 4.1, older gcc on x86, MSC >= 1310 */ +#if ((defined(__GNUC__) && \ + ((__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 1)) || \ + defined(__i386__) || defined(__x86_64__))) || \ + (defined(_MSC_VER) && _MSC_VER>=1310)) +#ifndef USE_SPIN_LOCKS +#define USE_SPIN_LOCKS 1 +#endif /* USE_SPIN_LOCKS */ +#elif USE_SPIN_LOCKS +#error "USE_SPIN_LOCKS defined without implementation" +#endif /* ... locks available... */ +#elif !defined(USE_SPIN_LOCKS) +#define USE_SPIN_LOCKS 0 +#endif /* USE_LOCKS */ + +#ifndef ONLY_MSPACES +#define ONLY_MSPACES 0 +#endif /* ONLY_MSPACES */ +#ifndef MSPACES +#if ONLY_MSPACES +#define MSPACES 1 +#else /* ONLY_MSPACES */ +#define MSPACES 0 +#endif /* ONLY_MSPACES */ +#endif /* MSPACES */ +#ifndef MALLOC_ALIGNMENT +#define MALLOC_ALIGNMENT ((size_t)(2 * sizeof(void *))) +#endif /* MALLOC_ALIGNMENT */ +#ifndef FOOTERS +#define FOOTERS 0 +#endif /* FOOTERS */ +#ifndef ABORT +#define ABORT abort() +#endif /* ABORT */ +#ifndef ABORT_ON_ASSERT_FAILURE +#define ABORT_ON_ASSERT_FAILURE 1 +#endif /* ABORT_ON_ASSERT_FAILURE */ +#ifndef PROCEED_ON_ERROR +#define PROCEED_ON_ERROR 0 +#endif /* PROCEED_ON_ERROR */ + +#ifndef INSECURE +#define INSECURE 0 +#endif /* INSECURE */ +#ifndef MALLOC_INSPECT_ALL +#define MALLOC_INSPECT_ALL 0 +#endif /* MALLOC_INSPECT_ALL */ +#ifndef HAVE_MMAP +#define HAVE_MMAP 1 +#endif /* HAVE_MMAP */ +#ifndef MMAP_CLEARS +#define MMAP_CLEARS 1 +#endif /* MMAP_CLEARS */ +#ifndef HAVE_MREMAP +#ifdef linux +#define HAVE_MREMAP 1 +#define _GNU_SOURCE /* Turns on mremap() definition */ +#else /* linux */ +#define HAVE_MREMAP 0 +#endif /* linux */ +#endif /* HAVE_MREMAP */ +#ifndef MALLOC_FAILURE_ACTION +#define MALLOC_FAILURE_ACTION errno = ENOMEM; +#endif /* MALLOC_FAILURE_ACTION */ +#ifndef HAVE_MORECORE +#if ONLY_MSPACES +#define HAVE_MORECORE 0 +#else /* ONLY_MSPACES */ +#define HAVE_MORECORE 1 +#endif /* ONLY_MSPACES */ +#endif /* HAVE_MORECORE */ +#if !HAVE_MORECORE +#define MORECORE_CONTIGUOUS 0 +#else /* !HAVE_MORECORE */ +#define MORECORE_DEFAULT sbrk +#ifndef MORECORE_CONTIGUOUS +#define MORECORE_CONTIGUOUS 1 +#endif /* MORECORE_CONTIGUOUS */ +#endif /* HAVE_MORECORE */ +#ifndef DEFAULT_GRANULARITY +#if (MORECORE_CONTIGUOUS || defined(WIN32)) +#define DEFAULT_GRANULARITY (0) /* 0 means to compute in init_mparams */ +#else /* MORECORE_CONTIGUOUS */ +#define DEFAULT_GRANULARITY ((size_t)64U * (size_t)1024U) +#endif /* MORECORE_CONTIGUOUS */ +#endif /* DEFAULT_GRANULARITY */ +#ifndef DEFAULT_TRIM_THRESHOLD +#ifndef MORECORE_CANNOT_TRIM +#define DEFAULT_TRIM_THRESHOLD ((size_t)2U * (size_t)1024U * (size_t)1024U) +#else /* MORECORE_CANNOT_TRIM */ +#define DEFAULT_TRIM_THRESHOLD MAX_SIZE_T +#endif /* MORECORE_CANNOT_TRIM */ +#endif /* DEFAULT_TRIM_THRESHOLD */ +#ifndef DEFAULT_MMAP_THRESHOLD +#if HAVE_MMAP +#define DEFAULT_MMAP_THRESHOLD ((size_t)256U * (size_t)1024U) +#else /* HAVE_MMAP */ +#define DEFAULT_MMAP_THRESHOLD MAX_SIZE_T +#endif /* HAVE_MMAP */ +#endif /* DEFAULT_MMAP_THRESHOLD */ +#ifndef MAX_RELEASE_CHECK_RATE +#if HAVE_MMAP +#define MAX_RELEASE_CHECK_RATE 4095 +#else +#define MAX_RELEASE_CHECK_RATE MAX_SIZE_T +#endif /* HAVE_MMAP */ +#endif /* MAX_RELEASE_CHECK_RATE */ +#ifndef USE_BUILTIN_FFS +#define USE_BUILTIN_FFS 0 +#endif /* USE_BUILTIN_FFS */ +#ifndef USE_DEV_RANDOM +#define USE_DEV_RANDOM 0 +#endif /* USE_DEV_RANDOM */ +#ifndef NO_MALLINFO +#define NO_MALLINFO 0 +#endif /* NO_MALLINFO */ +#ifndef MALLINFO_FIELD_TYPE +#define MALLINFO_FIELD_TYPE size_t +#endif /* MALLINFO_FIELD_TYPE */ +#ifndef NO_MALLOC_STATS +#define NO_MALLOC_STATS 0 +#endif /* NO_MALLOC_STATS */ +#ifndef NO_SEGMENT_TRAVERSAL +#define NO_SEGMENT_TRAVERSAL 0 +#endif /* NO_SEGMENT_TRAVERSAL */ + +/* + mallopt tuning options. SVID/XPG defines four standard parameter + numbers for mallopt, normally defined in malloc.h. None of these + are used in this malloc, so setting them has no effect. But this + malloc does support the following options. +*/ + +#define M_TRIM_THRESHOLD (-1) +#define M_GRANULARITY (-2) +#define M_MMAP_THRESHOLD (-3) + +/* ------------------------ Mallinfo declarations ------------------------ */ + +#if !NO_MALLINFO +/* + This version of malloc supports the standard SVID/XPG mallinfo + routine that returns a struct containing usage properties and + statistics. It should work on any system that has a + /usr/include/malloc.h defining struct mallinfo. The main + declaration needed is the mallinfo struct that is returned (by-copy) + by mallinfo(). The malloinfo struct contains a bunch of fields that + are not even meaningful in this version of malloc. These fields are + are instead filled by mallinfo() with other numbers that might be of + interest. + + HAVE_USR_INCLUDE_MALLOC_H should be set if you have a + /usr/include/malloc.h file that includes a declaration of struct + mallinfo. If so, it is included; else a compliant version is + declared below. These must be precisely the same for mallinfo() to + work. The original SVID version of this struct, defined on most + systems with mallinfo, declares all fields as ints. But some others + define as unsigned long. If your system defines the fields using a + type of different width than listed here, you MUST #include your + system version and #define HAVE_USR_INCLUDE_MALLOC_H. +*/ + +/* #define HAVE_USR_INCLUDE_MALLOC_H */ + +#ifdef HAVE_USR_INCLUDE_MALLOC_H +#include "/usr/include/malloc.h" +#else /* HAVE_USR_INCLUDE_MALLOC_H */ +#ifndef STRUCT_MALLINFO_DECLARED +/* HP-UX (and others?) redefines mallinfo unless _STRUCT_MALLINFO is defined */ +#define _STRUCT_MALLINFO +#define STRUCT_MALLINFO_DECLARED 1 +struct mallinfo { + MALLINFO_FIELD_TYPE arena; /* non-mmapped space allocated from system */ + MALLINFO_FIELD_TYPE ordblks; /* number of free chunks */ + MALLINFO_FIELD_TYPE smblks; /* always 0 */ + MALLINFO_FIELD_TYPE hblks; /* always 0 */ + MALLINFO_FIELD_TYPE hblkhd; /* space in mmapped regions */ + MALLINFO_FIELD_TYPE usmblks; /* maximum total allocated space */ + MALLINFO_FIELD_TYPE fsmblks; /* always 0 */ + MALLINFO_FIELD_TYPE uordblks; /* total allocated space */ + MALLINFO_FIELD_TYPE fordblks; /* total free space */ + MALLINFO_FIELD_TYPE keepcost; /* releasable (via malloc_trim) space */ +}; +#endif /* STRUCT_MALLINFO_DECLARED */ +#endif /* HAVE_USR_INCLUDE_MALLOC_H */ +#endif /* NO_MALLINFO */ + +/* + Try to persuade compilers to inline. The most critical functions for + inlining are defined as macros, so these aren't used for them. +*/ + +#ifndef FORCEINLINE + #if defined(__GNUC__) +#define FORCEINLINE __inline __attribute__ ((always_inline)) + #elif defined(_MSC_VER) + #define FORCEINLINE __forceinline + #endif +#endif +#ifndef NOINLINE + #if defined(__GNUC__) + #define NOINLINE __attribute__ ((noinline)) + #elif defined(_MSC_VER) + #define NOINLINE __declspec(noinline) + #else + #define NOINLINE + #endif +#endif + +#ifdef __cplusplus +extern "C" { +#ifndef FORCEINLINE + #define FORCEINLINE inline +#endif +#endif /* __cplusplus */ +#ifndef FORCEINLINE + #define FORCEINLINE +#endif + +#if !ONLY_MSPACES + +/* ------------------- Declarations of public routines ------------------- */ + +#ifndef USE_DL_PREFIX +#define dlcalloc calloc +#define dlfree free +#define dlmalloc malloc +#define dlmemalign memalign +#define dlposix_memalign posix_memalign +#define dlrealloc realloc +#define dlrealloc_in_place realloc_in_place +#define dlvalloc valloc +#define dlpvalloc pvalloc +#define dlmallinfo mallinfo +#define dlmallopt mallopt +#define dlmalloc_trim malloc_trim +#define dlmalloc_stats malloc_stats +#define dlmalloc_usable_size malloc_usable_size +#define dlmalloc_memory_usage malloc_memory_usage +#define dlmalloc_footprint malloc_footprint +#define dlmalloc_max_footprint malloc_max_footprint +#define dlmalloc_footprint_limit malloc_footprint_limit +#define dlmalloc_set_footprint_limit malloc_set_footprint_limit +#define dlmalloc_inspect_all malloc_inspect_all +#define dlindependent_calloc independent_calloc +#define dlindependent_comalloc independent_comalloc +#define dlbulk_free bulk_free +#endif /* USE_DL_PREFIX */ + +/* + malloc(size_t n) + Returns a pointer to a newly allocated chunk of at least n bytes, or + null if no space is available, in which case errno is set to ENOMEM + on ANSI C systems. + + If n is zero, malloc returns a minimum-sized chunk. (The minimum + size is 16 bytes on most 32bit systems, and 32 bytes on 64bit + systems.) Note that size_t is an unsigned type, so calls with + arguments that would be negative if signed are interpreted as + requests for huge amounts of space, which will often fail. The + maximum supported value of n differs across systems, but is in all + cases less than the maximum representable value of a size_t. +*/ +DLMALLOC_EXPORT void* dlmalloc(size_t); + +/* + free(void* p) + Releases the chunk of memory pointed to by p, that had been previously + allocated using malloc or a related routine such as realloc. + It has no effect if p is null. If p was not malloced or already + freed, free(p) will by default cause the current program to abort. +*/ +DLMALLOC_EXPORT void dlfree(void*); + +/* + calloc(size_t n_elements, size_t element_size); + Returns a pointer to n_elements * element_size bytes, with all locations + set to zero. +*/ +DLMALLOC_EXPORT void* dlcalloc(size_t, size_t); + +/* + realloc(void* p, size_t n) + Returns a pointer to a chunk of size n that contains the same data + as does chunk p up to the minimum of (n, p's size) bytes, or null + if no space is available. + + The returned pointer may or may not be the same as p. The algorithm + prefers extending p in most cases when possible, otherwise it + employs the equivalent of a malloc-copy-free sequence. + + If p is null, realloc is equivalent to malloc. + + If space is not available, realloc returns null, errno is set (if on + ANSI) and p is NOT freed. + + if n is for fewer bytes than already held by p, the newly unused + space is lopped off and freed if possible. realloc with a size + argument of zero (re)allocates a minimum-sized chunk. + + The old unix realloc convention of allowing the last-free'd chunk + to be used as an argument to realloc is not supported. +*/ +DLMALLOC_EXPORT void* dlrealloc(void*, size_t); + +/* + realloc_in_place(void* p, size_t n) + Resizes the space allocated for p to size n, only if this can be + done without moving p (i.e., only if there is adjacent space + available if n is greater than p's current allocated size, or n is + less than or equal to p's size). This may be used instead of plain + realloc if an alternative allocation strategy is needed upon failure + to expand space; for example, reallocation of a buffer that must be + memory-aligned or cleared. You can use realloc_in_place to trigger + these alternatives only when needed. + + Returns p if successful; otherwise null. +*/ +DLMALLOC_EXPORT void* dlrealloc_in_place(void*, size_t); + +/* + memalign(size_t alignment, size_t n); + Returns a pointer to a newly allocated chunk of n bytes, aligned + in accord with the alignment argument. + + The alignment argument should be a power of two. If the argument is + not a power of two, the nearest greater power is used. + 8-byte alignment is guaranteed by normal malloc calls, so don't + bother calling memalign with an argument of 8 or less. + + Overreliance on memalign is a sure way to fragment space. +*/ +DLMALLOC_EXPORT void* dlmemalign(size_t, size_t); + +/* + int posix_memalign(void** pp, size_t alignment, size_t n); + Allocates a chunk of n bytes, aligned in accord with the alignment + argument. Differs from memalign only in that it (1) assigns the + allocated memory to *pp rather than returning it, (2) fails and + returns -1, setting errno to EINVAL if the alignment is not a + power of two (3) fails and returns -1, setting errno to ENOMEM if + memory cannot be allocated. +*/ +DLMALLOC_EXPORT int dlposix_memalign(void**, size_t, size_t); + +/* + valloc(size_t n); + Equivalent to memalign(pagesize, n), where pagesize is the page + size of the system. If the pagesize is unknown, 4096 is used. +*/ +DLMALLOC_EXPORT void* dlvalloc(size_t); + +/* + mallopt(int parameter_number, int parameter_value) + Sets tunable parameters The format is to provide a + (parameter-number, parameter-value) pair. mallopt then sets the + corresponding parameter to the argument value if it can (i.e., so + long as the value is meaningful), and returns 1 if successful else + 0. To workaround the fact that mallopt is specified to use int, + not size_t parameters, the value -1 is specially treated as the + maximum unsigned size_t value. + + SVID/XPG/ANSI defines four standard param numbers for mallopt, + normally defined in malloc.h. None of these are use in this malloc, + so setting them has no effect. But this malloc also supports other + options in mallopt. See below for details. Briefly, supported + parameters are as follows (listed defaults are for "typical" + configurations). + + Symbol param # default allowed param values + M_TRIM_THRESHOLD -1 2*1024*1024 any (-1 disables) + M_GRANULARITY -2 page size any power of 2 >= page size + M_MMAP_THRESHOLD -3 256*1024 any (or 0 if no MMAP support) +*/ +DLMALLOC_EXPORT int dlmallopt(int, int); + +/* + malloc_memory_usage(); + Returns total number of bytes allocated by malloc, realloc etc. This + value is the same as the uordblks field in the mallinfo structure but + the value is precomputed value that is updated on each call to malloc, + free, etc. + Unlike malloc_footprint it does not counts the bytes obtained from the + system but not currently allocated. +*/ +DLMALLOC_EXPORT size_t dlmalloc_memory_usage(void); + +/* + malloc_footprint(); + Returns the number of bytes obtained from the system. The total + number of bytes allocated by malloc, realloc etc., is less than this + value. Unlike mallinfo, this function returns only a precomputed + result, so can be called frequently to monitor memory consumption. + Even if locks are otherwise defined, this function does not use them, + so results might not be up to date. +*/ +DLMALLOC_EXPORT size_t dlmalloc_footprint(void); + +/* + malloc_max_footprint(); + Returns the maximum number of bytes obtained from the system. This + value will be greater than current footprint if deallocated space + has been reclaimed by the system. The peak number of bytes allocated + by malloc, realloc etc., is less than this value. Unlike mallinfo, + this function returns only a precomputed result, so can be called + frequently to monitor memory consumption. Even if locks are + otherwise defined, this function does not use them, so results might + not be up to date. +*/ +DLMALLOC_EXPORT size_t dlmalloc_max_footprint(void); + +/* + malloc_footprint_limit(); + Returns the number of bytes that the heap is allowed to obtain from + the system, returning the last value returned by + malloc_set_footprint_limit, or the maximum size_t value if + never set. The returned value reflects a permission. There is no + guarantee that this number of bytes can actually be obtained from + the system. +*/ +DLMALLOC_EXPORT size_t dlmalloc_footprint_limit(); + +/* + malloc_set_footprint_limit(); + Sets the maximum number of bytes to obtain from the system, causing + failure returns from malloc and related functions upon attempts to + exceed this value. The argument value may be subject to page + rounding to an enforceable limit; this actual value is returned. + Using an argument of the maximum possible size_t effectively + disables checks. If the argument is less than or equal to the + current malloc_footprint, then all future allocations that require + additional system memory will fail. However, invocation cannot + retroactively deallocate existing used memory. +*/ +DLMALLOC_EXPORT size_t dlmalloc_set_footprint_limit(size_t bytes); + +#if MALLOC_INSPECT_ALL +/* + malloc_inspect_all(void(*handler)(void *start, + void *end, + size_t used_bytes, + void* callback_arg), + void* arg); + Traverses the heap and calls the given handler for each managed + region, skipping all bytes that are (or may be) used for bookkeeping + purposes. Traversal does not include include chunks that have been + directly memory mapped. Each reported region begins at the start + address, and continues up to but not including the end address. The + first used_bytes of the region contain allocated data. If + used_bytes is zero, the region is unallocated. The handler is + invoked with the given callback argument. If locks are defined, they + are held during the entire traversal. It is a bad idea to invoke + other malloc functions from within the handler. + + For example, to count the number of in-use chunks with size greater + than 1000, you could write: + static int count = 0; + void count_chunks(void* start, void* end, size_t used, void* arg) { + if (used >= 1000) ++count; + } + then: + malloc_inspect_all(count_chunks, NULL); + + malloc_inspect_all is compiled only if MALLOC_INSPECT_ALL is defined. +*/ +DLMALLOC_EXPORT void dlmalloc_inspect_all(void(*handler)(void*, void *, size_t, void*), + void* arg); + +#endif /* MALLOC_INSPECT_ALL */ + +#if !NO_MALLINFO +/* + mallinfo() + Returns (by copy) a struct containing various summary statistics: + + arena: current total non-mmapped bytes allocated from system + ordblks: the number of free chunks + smblks: always zero. + hblks: current number of mmapped regions + hblkhd: total bytes held in mmapped regions + usmblks: the maximum total allocated space. This will be greater + than current total if trimming has occurred. + fsmblks: always zero + uordblks: current total allocated space (normal or mmapped) + fordblks: total free space + keepcost: the maximum number of bytes that could ideally be released + back to system via malloc_trim. ("ideally" means that + it ignores page restrictions etc.) + + Because these fields are ints, but internal bookkeeping may + be kept as longs, the reported values may wrap around zero and + thus be inaccurate. +*/ +DLMALLOC_EXPORT struct mallinfo dlmallinfo(void); +#endif /* NO_MALLINFO */ + +/* + independent_calloc(size_t n_elements, size_t element_size, void* chunks[]); + + independent_calloc is similar to calloc, but instead of returning a + single cleared space, it returns an array of pointers to n_elements + independent elements that can hold contents of size elem_size, each + of which starts out cleared, and can be independently freed, + realloc'ed etc. The elements are guaranteed to be adjacently + allocated (this is not guaranteed to occur with multiple callocs or + mallocs), which may also improve cache locality in some + applications. + + The "chunks" argument is optional (i.e., may be null, which is + probably the most typical usage). If it is null, the returned array + is itself dynamically allocated and should also be freed when it is + no longer needed. Otherwise, the chunks array must be of at least + n_elements in length. It is filled in with the pointers to the + chunks. + + In either case, independent_calloc returns this pointer array, or + null if the allocation failed. If n_elements is zero and "chunks" + is null, it returns a chunk representing an array with zero elements + (which should be freed if not wanted). + + Each element must be freed when it is no longer needed. This can be + done all at once using bulk_free. + + independent_calloc simplifies and speeds up implementations of many + kinds of pools. It may also be useful when constructing large data + structures that initially have a fixed number of fixed-sized nodes, + but the number is not known at compile time, and some of the nodes + may later need to be freed. For example: + + struct Node { int item; struct Node* next; }; + + struct Node* build_list() { + struct Node** pool; + int n = read_number_of_nodes_needed(); + if (n <= 0) return 0; + pool = (struct Node**)(independent_calloc(n, sizeof(struct Node), 0); + if (pool == 0) die(); + // organize into a linked list... + struct Node* first = pool[0]; + for (i = 0; i < n-1; ++i) + pool[i]->next = pool[i+1]; + free(pool); // Can now free the array (or not, if it is needed later) + return first; + } +*/ +DLMALLOC_EXPORT void** dlindependent_calloc(size_t, size_t, void**); + +/* + independent_comalloc(size_t n_elements, size_t sizes[], void* chunks[]); + + independent_comalloc allocates, all at once, a set of n_elements + chunks with sizes indicated in the "sizes" array. It returns + an array of pointers to these elements, each of which can be + independently freed, realloc'ed etc. The elements are guaranteed to + be adjacently allocated (this is not guaranteed to occur with + multiple callocs or mallocs), which may also improve cache locality + in some applications. + + The "chunks" argument is optional (i.e., may be null). If it is null + the returned array is itself dynamically allocated and should also + be freed when it is no longer needed. Otherwise, the chunks array + must be of at least n_elements in length. It is filled in with the + pointers to the chunks. + + In either case, independent_comalloc returns this pointer array, or + null if the allocation failed. If n_elements is zero and chunks is + null, it returns a chunk representing an array with zero elements + (which should be freed if not wanted). + + Each element must be freed when it is no longer needed. This can be + done all at once using bulk_free. + + independent_comallac differs from independent_calloc in that each + element may have a different size, and also that it does not + automatically clear elements. + + independent_comalloc can be used to speed up allocation in cases + where several structs or objects must always be allocated at the + same time. For example: + + struct Head { ... } + struct Foot { ... } + + void send_message(char* msg) { + int msglen = strlen(msg); + size_t sizes[3] = { sizeof(struct Head), msglen, sizeof(struct Foot) }; + void* chunks[3]; + if (independent_comalloc(3, sizes, chunks) == 0) + die(); + struct Head* head = (struct Head*)(chunks[0]); + char* body = (char*)(chunks[1]); + struct Foot* foot = (struct Foot*)(chunks[2]); + // ... + } + + In general though, independent_comalloc is worth using only for + larger values of n_elements. For small values, you probably won't + detect enough difference from series of malloc calls to bother. + + Overuse of independent_comalloc can increase overall memory usage, + since it cannot reuse existing noncontiguous small chunks that + might be available for some of the elements. +*/ +DLMALLOC_EXPORT void** dlindependent_comalloc(size_t, size_t*, void**); + +/* + bulk_free(void* array[], size_t n_elements) + Frees and clears (sets to null) each non-null pointer in the given + array. This is likely to be faster than freeing them one-by-one. + If footers are used, pointers that have been allocated in different + mspaces are not freed or cleared, and the count of all such pointers + is returned. For large arrays of pointers with poor locality, it + may be worthwhile to sort this array before calling bulk_free. +*/ +DLMALLOC_EXPORT size_t dlbulk_free(void**, size_t n_elements); + +/* + pvalloc(size_t n); + Equivalent to valloc(minimum-page-that-holds(n)), that is, + round up n to nearest pagesize. + */ +DLMALLOC_EXPORT void* dlpvalloc(size_t); + +/* + malloc_trim(size_t pad); + + If possible, gives memory back to the system (via negative arguments + to sbrk) if there is unused memory at the `high' end of the malloc + pool or in unused MMAP segments. You can call this after freeing + large blocks of memory to potentially reduce the system-level memory + requirements of a program. However, it cannot guarantee to reduce + memory. Under some allocation patterns, some large free blocks of + memory will be locked between two used chunks, so they cannot be + given back to the system. + + The `pad' argument to malloc_trim represents the amount of free + trailing space to leave untrimmed. If this argument is zero, only + the minimum amount of memory to maintain internal data structures + will be left. Non-zero arguments can be supplied to maintain enough + trailing space to service future expected allocations without having + to re-obtain memory from the system. + + Malloc_trim returns 1 if it actually released any memory, else 0. +*/ +DLMALLOC_EXPORT int dlmalloc_trim(size_t); + +/* + malloc_stats(); + Prints on stderr the amount of space obtained from the system (both + via sbrk and mmap), the maximum amount (which may be more than + current if malloc_trim and/or munmap got called), and the current + number of bytes allocated via malloc (or realloc, etc) but not yet + freed. Note that this is the number of bytes allocated, not the + number requested. It will be larger than the number requested + because of alignment and bookkeeping overhead. Because it includes + alignment wastage as being in use, this figure may be greater than + zero even when no user-level chunks are allocated. + + The reported current and maximum system memory can be inaccurate if + a program makes other calls to system memory allocation functions + (normally sbrk) outside of malloc. + + malloc_stats prints only the most commonly interesting statistics. + More information can be obtained by calling mallinfo. +*/ +DLMALLOC_EXPORT void dlmalloc_stats(void); + +/* + malloc_usable_size(void* p); + + Returns the number of bytes you can actually use in + an allocated chunk, which may be more than you requested (although + often not) due to alignment and minimum size constraints. + You can use this many bytes without worrying about + overwriting other allocated objects. This is not a particularly great + programming practice. malloc_usable_size can be more useful in + debugging and assertions, for example: + + p = malloc(n); + assert(malloc_usable_size(p) >= 256); +*/ +size_t dlmalloc_usable_size(void*); + +#endif /* ONLY_MSPACES */ + +#if MSPACES + +/* + mspace is an opaque type representing an independent + region of space that supports mspace_malloc, etc. +*/ +typedef void* mspace; + +/* + create_mspace creates and returns a new independent space with the + given initial capacity, or, if 0, the default granularity size. It + returns null if there is no system memory available to create the + space. If argument locked is non-zero, the space uses a separate + lock to control access. The capacity of the space will grow + dynamically as needed to service mspace_malloc requests. You can + control the sizes of incremental increases of this space by + compiling with a different DEFAULT_GRANULARITY or dynamically + setting with mallopt(M_GRANULARITY, value). +*/ +DLMALLOC_EXPORT mspace create_mspace(size_t capacity, int locked); + +/* + destroy_mspace destroys the given space, and attempts to return all + of its memory back to the system, returning the total number of + bytes freed. After destruction, the results of access to all memory + used by the space become undefined. +*/ +DLMALLOC_EXPORT size_t destroy_mspace(mspace msp); + +/* + create_mspace_with_base uses the memory supplied as the initial base + of a new mspace. Part (less than 128*sizeof(size_t) bytes) of this + space is used for bookkeeping, so the capacity must be at least this + large. (Otherwise 0 is returned.) When this initial space is + exhausted, additional memory will be obtained from the system. + Destroying this space will deallocate all additionally allocated + space (if possible) but not the initial base. +*/ +DLMALLOC_EXPORT mspace create_mspace_with_base(void* base, size_t capacity, int locked); + +/* + mspace_track_large_chunks controls whether requests for large chunks + are allocated in their own untracked mmapped regions, separate from + others in this mspace. By default large chunks are not tracked, + which reduces fragmentation. However, such chunks are not + necessarily released to the system upon destroy_mspace. Enabling + tracking by setting to true may increase fragmentation, but avoids + leakage when relying on destroy_mspace to release all memory + allocated using this space. The function returns the previous + setting. +*/ +DLMALLOC_EXPORT int mspace_track_large_chunks(mspace msp, int enable); + + +/* + mspace_malloc behaves as malloc, but operates within + the given space. +*/ +DLMALLOC_EXPORT void* mspace_malloc(mspace msp, size_t bytes); + +/* + mspace_free behaves as free, but operates within + the given space. + + If compiled with FOOTERS==1, mspace_free is not actually needed. + free may be called instead of mspace_free because freed chunks from + any space are handled by their originating spaces. +*/ +DLMALLOC_EXPORT void mspace_free(mspace msp, void* mem); + +/* + mspace_realloc behaves as realloc, but operates within + the given space. + + If compiled with FOOTERS==1, mspace_realloc is not actually + needed. realloc may be called instead of mspace_realloc because + realloced chunks from any space are handled by their originating + spaces. +*/ +DLMALLOC_EXPORT void* mspace_realloc(mspace msp, void* mem, size_t newsize); + +/* + mspace_calloc behaves as calloc, but operates within + the given space. +*/ +DLMALLOC_EXPORT void* mspace_calloc(mspace msp, size_t n_elements, size_t elem_size); + +/* + mspace_memalign behaves as memalign, but operates within + the given space. +*/ +DLMALLOC_EXPORT void* mspace_memalign(mspace msp, size_t alignment, size_t bytes); + +/* + mspace_independent_calloc behaves as independent_calloc, but + operates within the given space. +*/ +DLMALLOC_EXPORT void** mspace_independent_calloc(mspace msp, size_t n_elements, + size_t elem_size, void* chunks[]); + +/* + mspace_independent_comalloc behaves as independent_comalloc, but + operates within the given space. +*/ +DLMALLOC_EXPORT void** mspace_independent_comalloc(mspace msp, size_t n_elements, + size_t sizes[], void* chunks[]); + +/* + mspace_footprint() returns the number of bytes obtained from the + system for this space. +*/ +DLMALLOC_EXPORT size_t mspace_footprint(mspace msp); + +/* + mspace_max_footprint() returns the peak number of bytes obtained from the + system for this space. +*/ +DLMALLOC_EXPORT size_t mspace_max_footprint(mspace msp); + + +#if !NO_MALLINFO +/* + mspace_mallinfo behaves as mallinfo, but reports properties of + the given space. +*/ +DLMALLOC_EXPORT struct mallinfo mspace_mallinfo(mspace msp); +#endif /* NO_MALLINFO */ + +/* + malloc_usable_size(void* p) behaves the same as malloc_usable_size; +*/ +DLMALLOC_EXPORT size_t mspace_usable_size(const void* mem); + +/* + mspace_malloc_stats behaves as malloc_stats, but reports + properties of the given space. +*/ +DLMALLOC_EXPORT void mspace_malloc_stats(mspace msp); + +/* + mspace_trim behaves as malloc_trim, but + operates within the given space. +*/ +DLMALLOC_EXPORT int mspace_trim(mspace msp, size_t pad); + +/* + An alias for mallopt. +*/ +DLMALLOC_EXPORT int mspace_mallopt(int, int); + +#endif /* MSPACES */ + +#ifdef __cplusplus +} /* end of extern "C" */ +#endif /* __cplusplus */ + +/* + ======================================================================== + To make a fully customizable malloc.h header file, cut everything + above this line, put into file malloc.h, edit to suit, and #include it + on the next line, as well as in programs that use this malloc. + ======================================================================== +*/ + +/* #include "malloc.h" */ + +/*------------------------------ internal #includes ---------------------- */ + +#ifdef _MSC_VER +#pragma warning( disable : 4146 ) /* no "unsigned" warnings */ +#endif /* _MSC_VER */ +#if !NO_MALLOC_STATS +#include /* for printing in malloc_stats */ +#endif /* NO_MALLOC_STATS */ +#ifndef LACKS_ERRNO_H +#include /* for MALLOC_FAILURE_ACTION */ +#endif /* LACKS_ERRNO_H */ +#ifdef DEBUG +#if ABORT_ON_ASSERT_FAILURE +#undef assert +#define assert(x) if(!(x)) ABORT +#else /* ABORT_ON_ASSERT_FAILURE */ +#include +#endif /* ABORT_ON_ASSERT_FAILURE */ +#else /* DEBUG */ +#ifndef assert +#define assert(x) +#endif +#define DEBUG 0 +#endif /* DEBUG */ +#if !defined(WIN32) && !defined(LACKS_TIME_H) +#include /* for magic initialization */ +#endif /* WIN32 */ +#ifndef LACKS_STDLIB_H +#include /* for abort() */ +#endif /* LACKS_STDLIB_H */ +#ifndef LACKS_STRING_H +#include /* for memset etc */ +#endif /* LACKS_STRING_H */ +#if USE_BUILTIN_FFS +#ifndef LACKS_STRINGS_H +#include /* for ffs */ +#endif /* LACKS_STRINGS_H */ +#endif /* USE_BUILTIN_FFS */ +#if HAVE_MMAP +#ifndef LACKS_SYS_MMAN_H +/* On some versions of linux, mremap decl in mman.h needs __USE_GNU set */ +#if (defined(linux) && !defined(__USE_GNU)) +#define __USE_GNU 1 +#include /* for mmap */ +#undef __USE_GNU +#else +#include /* for mmap */ +#endif /* linux */ +#endif /* LACKS_SYS_MMAN_H */ +#ifndef LACKS_FCNTL_H +#include +#endif /* LACKS_FCNTL_H */ +#endif /* HAVE_MMAP */ +#ifndef LACKS_UNISTD_H +#include /* for sbrk, sysconf */ +#else /* LACKS_UNISTD_H */ +#if !defined(__FreeBSD__) && !defined(__OpenBSD__) && !defined(__NetBSD__) +extern void* sbrk(ptrdiff_t); +#endif /* FreeBSD etc */ +#endif /* LACKS_UNISTD_H */ + +/* Declarations for locking */ +#if USE_LOCKS +#ifndef WIN32 +#if defined (__SVR4) && defined (__sun) /* solaris */ +#include +#elif !defined(LACKS_SCHED_H) +#include +#endif /* solaris or LACKS_SCHED_H */ +#if (defined(USE_RECURSIVE_LOCKS) && USE_RECURSIVE_LOCKS != 0) || !USE_SPIN_LOCKS +#include +#endif /* USE_RECURSIVE_LOCKS ... */ +#elif defined(_MSC_VER) +#ifndef _M_AMD64 +/* These are already defined on AMD64 builds */ +#ifdef __cplusplus +extern "C" { +#endif /* __cplusplus */ +LONG __cdecl _InterlockedCompareExchange(LONG volatile *Dest, LONG Exchange, LONG Comp); +LONG __cdecl _InterlockedExchange(LONG volatile *Target, LONG Value); +#ifdef __cplusplus +} +#endif /* __cplusplus */ +#endif /* _M_AMD64 */ +#pragma intrinsic (_InterlockedCompareExchange) +#pragma intrinsic (_InterlockedExchange) +#define interlockedcompareexchange _InterlockedCompareExchange +#define interlockedexchange _InterlockedExchange +#elif defined(WIN32) && defined(__GNUC__) +#define interlockedcompareexchange(a, b, c) __sync_val_compare_and_swap(a, c, b) +#define interlockedexchange __sync_lock_test_and_set +#endif /* Win32 */ +#else /* USE_LOCKS */ +#endif /* USE_LOCKS */ + +#ifndef LOCK_AT_FORK +#define LOCK_AT_FORK 0 +#endif + +/* Declarations for bit scanning on win32 */ +#if defined(_MSC_VER) && _MSC_VER>=1300 +#ifndef BitScanForward /* Try to avoid pulling in WinNT.h */ +#ifdef __cplusplus +extern "C" { +#endif /* __cplusplus */ +unsigned char _BitScanForward(unsigned long *index, unsigned long mask); +unsigned char _BitScanReverse(unsigned long *index, unsigned long mask); +#ifdef __cplusplus +} +#endif /* __cplusplus */ + +#define BitScanForward _BitScanForward +#define BitScanReverse _BitScanReverse +#pragma intrinsic(_BitScanForward) +#pragma intrinsic(_BitScanReverse) +#endif /* BitScanForward */ +#endif /* defined(_MSC_VER) && _MSC_VER>=1300 */ + +#ifndef WIN32 +#ifndef malloc_getpagesize +# ifdef _SC_PAGESIZE /* some SVR4 systems omit an underscore */ +# ifndef _SC_PAGE_SIZE +# define _SC_PAGE_SIZE _SC_PAGESIZE +# endif +# endif +# ifdef _SC_PAGE_SIZE +# define malloc_getpagesize sysconf(_SC_PAGE_SIZE) +# else +# if defined(BSD) || defined(DGUX) || defined(HAVE_GETPAGESIZE) + extern size_t getpagesize(); +# define malloc_getpagesize getpagesize() +# else +# ifdef WIN32 /* use supplied emulation of getpagesize */ +# define malloc_getpagesize getpagesize() +# else +# ifndef LACKS_SYS_PARAM_H +# include +# endif +# ifdef EXEC_PAGESIZE +# define malloc_getpagesize EXEC_PAGESIZE +# else +# ifdef NBPG +# ifndef CLSIZE +# define malloc_getpagesize NBPG +# else +# define malloc_getpagesize (NBPG * CLSIZE) +# endif +# else +# ifdef NBPC +# define malloc_getpagesize NBPC +# else +# ifdef PAGESIZE +# define malloc_getpagesize PAGESIZE +# else /* just guess */ +# define malloc_getpagesize ((size_t)4096U) +# endif +# endif +# endif +# endif +# endif +# endif +# endif +#endif +#endif + +/* ------------------- size_t and alignment properties -------------------- */ + +/* The byte and bit size of a size_t */ +#define SIZE_T_SIZE (sizeof(size_t)) +#define SIZE_T_BITSIZE (sizeof(size_t) << 3) + +/* Some constants coerced to size_t */ +/* Annoying but necessary to avoid errors on some platforms */ +#define SIZE_T_ZERO ((size_t)0) +#define SIZE_T_ONE ((size_t)1) +#define SIZE_T_TWO ((size_t)2) +#define SIZE_T_FOUR ((size_t)4) +#define TWO_SIZE_T_SIZES (SIZE_T_SIZE<<1) +#define FOUR_SIZE_T_SIZES (SIZE_T_SIZE<<2) +#define SIX_SIZE_T_SIZES (FOUR_SIZE_T_SIZES+TWO_SIZE_T_SIZES) +#define HALF_MAX_SIZE_T (MAX_SIZE_T / 2U) + +/* The bit mask value corresponding to MALLOC_ALIGNMENT */ +#define CHUNK_ALIGN_MASK (MALLOC_ALIGNMENT - SIZE_T_ONE) + +/* True if address a has acceptable alignment */ +#define is_aligned(A) (((size_t)((A)) & (CHUNK_ALIGN_MASK)) == 0) + +/* the number of bytes to offset an address to align it */ +#define align_offset(A)\ + ((((size_t)(A) & CHUNK_ALIGN_MASK) == 0)? 0 :\ + ((MALLOC_ALIGNMENT - ((size_t)(A) & CHUNK_ALIGN_MASK)) & CHUNK_ALIGN_MASK)) + +/* -------------------------- MMAP preliminaries ------------------------- */ + +/* + If HAVE_MORECORE or HAVE_MMAP are false, we just define calls and + checks to fail so compiler optimizer can delete code rather than + using so many "#if"s. +*/ + + +/* MORECORE and MMAP must return MFAIL on failure */ +#define MFAIL ((void*)(MAX_SIZE_T)) +#define CMFAIL ((char*)(MFAIL)) /* defined for convenience */ + +#if HAVE_MMAP + +#ifndef WIN32 +#define MUNMAP_DEFAULT(a, s) munmap((a), (s)) +#define MMAP_PROT (PROT_READ|PROT_WRITE) +#if !defined(MAP_ANONYMOUS) && defined(MAP_ANON) +#define MAP_ANONYMOUS MAP_ANON +#endif /* MAP_ANON */ +#ifdef MAP_ANONYMOUS +#define MMAP_FLAGS (MAP_PRIVATE|MAP_ANONYMOUS) +#define MMAP_DEFAULT(s) mmap(0, (s), MMAP_PROT, MMAP_FLAGS, -1, 0) +#else /* MAP_ANONYMOUS */ +/* + Nearly all versions of mmap support MAP_ANONYMOUS, so the following + is unlikely to be needed, but is supplied just in case. +*/ +#define MMAP_FLAGS (MAP_PRIVATE) +static int dev_zero_fd = -1; /* Cached file descriptor for /dev/zero. */ +#define MMAP_DEFAULT(s) ((dev_zero_fd < 0) ? \ + (dev_zero_fd = open("/dev/zero", O_RDWR), \ + mmap(0, (s), MMAP_PROT, MMAP_FLAGS, dev_zero_fd, 0)) : \ + mmap(0, (s), MMAP_PROT, MMAP_FLAGS, dev_zero_fd, 0)) +#endif /* MAP_ANONYMOUS */ + +#define DIRECT_MMAP_DEFAULT(s) MMAP_DEFAULT(s) + +#else /* WIN32 */ + +/* Win32 MMAP via VirtualAlloc */ +static FORCEINLINE void* win32mmap(size_t size) { + void* ptr = VirtualAlloc(0, size, MEM_RESERVE|MEM_COMMIT, PAGE_READWRITE); + return (ptr != 0)? ptr: MFAIL; +} + +/* For direct MMAP, use MEM_TOP_DOWN to minimize interference */ +static FORCEINLINE void* win32direct_mmap(size_t size) { + void* ptr = VirtualAlloc(0, size, MEM_RESERVE|MEM_COMMIT|MEM_TOP_DOWN, + PAGE_READWRITE); + return (ptr != 0)? ptr: MFAIL; +} + +/* This function supports releasing coalesed segments */ +static FORCEINLINE int win32munmap(void* ptr, size_t size) { + MEMORY_BASIC_INFORMATION minfo; + char* cptr = (char*)ptr; + while (size) { + if (VirtualQuery(cptr, &minfo, sizeof(minfo)) == 0) + return -1; + if (minfo.BaseAddress != cptr || minfo.AllocationBase != cptr || + minfo.State != MEM_COMMIT || minfo.RegionSize > size) + return -1; + if (VirtualFree(cptr, 0, MEM_RELEASE) == 0) + return -1; + cptr += minfo.RegionSize; + size -= minfo.RegionSize; + } + return 0; +} + +#define MMAP_DEFAULT(s) win32mmap(s) +#define MUNMAP_DEFAULT(a, s) win32munmap((a), (s)) +#define DIRECT_MMAP_DEFAULT(s) win32direct_mmap(s) +#endif /* WIN32 */ +#endif /* HAVE_MMAP */ + +#if HAVE_MREMAP +#ifndef WIN32 +#define MREMAP_DEFAULT(addr, osz, nsz, mv) mremap((addr), (osz), (nsz), (mv)) +#endif /* WIN32 */ +#endif /* HAVE_MREMAP */ + +/** + * Define CALL_MORECORE + */ +#if HAVE_MORECORE + #ifdef MORECORE + #define CALL_MORECORE(S) MORECORE(S) + #else /* MORECORE */ + #define CALL_MORECORE(S) MORECORE_DEFAULT(S) + #endif /* MORECORE */ +#else /* HAVE_MORECORE */ + #define CALL_MORECORE(S) MFAIL +#endif /* HAVE_MORECORE */ + +/** + * Define CALL_MMAP/CALL_MUNMAP/CALL_DIRECT_MMAP + */ +#if HAVE_MMAP + #define USE_MMAP_BIT (SIZE_T_ONE) + + #ifdef MMAP + #define CALL_MMAP(s) MMAP(s) + #else /* MMAP */ + #define CALL_MMAP(s) MMAP_DEFAULT(s) + #endif /* MMAP */ + #ifdef MUNMAP + #define CALL_MUNMAP(a, s) MUNMAP((a), (s)) + #else /* MUNMAP */ + #define CALL_MUNMAP(a, s) MUNMAP_DEFAULT((a), (s)) + #endif /* MUNMAP */ + #ifdef DIRECT_MMAP + #define CALL_DIRECT_MMAP(s) DIRECT_MMAP(s) + #else /* DIRECT_MMAP */ + #define CALL_DIRECT_MMAP(s) DIRECT_MMAP_DEFAULT(s) + #endif /* DIRECT_MMAP */ +#else /* HAVE_MMAP */ + #define USE_MMAP_BIT (SIZE_T_ZERO) + + #define MMAP(s) MFAIL + #define MUNMAP(a, s) (-1) + #define DIRECT_MMAP(s) MFAIL + #define CALL_DIRECT_MMAP(s) DIRECT_MMAP(s) + #define CALL_MMAP(s) MMAP(s) + #define CALL_MUNMAP(a, s) MUNMAP((a), (s)) +#endif /* HAVE_MMAP */ + +/** + * Define CALL_MREMAP + */ +#if HAVE_MMAP && HAVE_MREMAP + #ifdef MREMAP + #define CALL_MREMAP(addr, osz, nsz, mv) MREMAP((addr), (osz), (nsz), (mv)) + #else /* MREMAP */ + #define CALL_MREMAP(addr, osz, nsz, mv) MREMAP_DEFAULT((addr), (osz), (nsz), (mv)) + #endif /* MREMAP */ +#else /* HAVE_MMAP && HAVE_MREMAP */ + #define CALL_MREMAP(addr, osz, nsz, mv) MFAIL +#endif /* HAVE_MMAP && HAVE_MREMAP */ + +/* mstate bit set if continguous morecore disabled or failed */ +#define USE_NONCONTIGUOUS_BIT (4U) + +/* segment bit set in create_mspace_with_base */ +#define EXTERN_BIT (8U) + + +/* --------------------------- Lock preliminaries ------------------------ */ + +/* + When locks are defined, there is one global lock, plus + one per-mspace lock. + + The global lock_ensures that mparams.magic and other unique + mparams values are initialized only once. It also protects + sequences of calls to MORECORE. In many cases sys_alloc requires + two calls, that should not be interleaved with calls by other + threads. This does not protect against direct calls to MORECORE + by other threads not using this lock, so there is still code to + cope the best we can on interference. + + Per-mspace locks surround calls to malloc, free, etc. + By default, locks are simple non-reentrant mutexes. + + Because lock-protected regions generally have bounded times, it is + OK to use the supplied simple spinlocks. Spinlocks are likely to + improve performance for lightly contended applications, but worsen + performance under heavy contention. + + If USE_LOCKS is > 1, the definitions of lock routines here are + bypassed, in which case you will need to define the type MLOCK_T, + and at least INITIAL_LOCK, DESTROY_LOCK, ACQUIRE_LOCK, RELEASE_LOCK + and TRY_LOCK. You must also declare a + static MLOCK_T malloc_global_mutex = { initialization values };. + +*/ + +#if !USE_LOCKS +#define USE_LOCK_BIT (0U) +#define INITIAL_LOCK(l) (0) +#define DESTROY_LOCK(l) (0) +#define ACQUIRE_MALLOC_GLOBAL_LOCK() +#define RELEASE_MALLOC_GLOBAL_LOCK() + +#else +#if USE_LOCKS > 1 +/* ----------------------- User-defined locks ------------------------ */ +/* Define your own lock implementation here */ +/* #define INITIAL_LOCK(lk) ... */ +/* #define DESTROY_LOCK(lk) ... */ +/* #define ACQUIRE_LOCK(lk) ... */ +/* #define RELEASE_LOCK(lk) ... */ +/* #define TRY_LOCK(lk) ... */ +/* static MLOCK_T malloc_global_mutex = ... */ + +#elif USE_SPIN_LOCKS + +/* First, define CAS_LOCK and CLEAR_LOCK on ints */ +/* Note CAS_LOCK defined to return 0 on success */ + +#if defined(__GNUC__)&& (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 1)) +#define CAS_LOCK(sl) __sync_lock_test_and_set(sl, 1) +#define CLEAR_LOCK(sl) __sync_lock_release(sl) + +#elif (defined(__GNUC__) && (defined(__i386__) || defined(__x86_64__))) +/* Custom spin locks for older gcc on x86 */ +static FORCEINLINE int x86_cas_lock(int *sl) { + int ret; + int val = 1; + int cmp = 0; + __asm__ __volatile__ ("lock; cmpxchgl %1, %2" + : "=a" (ret) + : "r" (val), "m" (*(sl)), "0"(cmp) + : "memory", "cc"); + return ret; +} + +static FORCEINLINE void x86_clear_lock(int* sl) { + assert(*sl != 0); + int prev = 0; + int ret; + __asm__ __volatile__ ("lock; xchgl %0, %1" + : "=r" (ret) + : "m" (*(sl)), "0"(prev) + : "memory"); +} + +#define CAS_LOCK(sl) x86_cas_lock(sl) +#define CLEAR_LOCK(sl) x86_clear_lock(sl) + +#else /* Win32 MSC */ +#define CAS_LOCK(sl) interlockedexchange(sl, (LONG)1) +#define CLEAR_LOCK(sl) interlockedexchange (sl, (LONG)0) + +#endif /* ... gcc spins locks ... */ + +/* How to yield for a spin lock */ +#define SPINS_PER_YIELD 63 +#if defined(_MSC_VER) +#define SLEEP_EX_DURATION 50 /* delay for yield/sleep */ +#define SPIN_LOCK_YIELD SleepEx(SLEEP_EX_DURATION, FALSE) +#elif defined (__SVR4) && defined (__sun) /* solaris */ +#define SPIN_LOCK_YIELD thr_yield(); +#elif !defined(LACKS_SCHED_H) +#define SPIN_LOCK_YIELD sched_yield(); +#else +#define SPIN_LOCK_YIELD +#endif /* ... yield ... */ + +#if !defined(USE_RECURSIVE_LOCKS) || USE_RECURSIVE_LOCKS == 0 +/* Plain spin locks use single word (embedded in malloc_states) */ +static int spin_acquire_lock(int *sl) { + int spins = 0; + while (*(volatile int *)sl != 0 || CAS_LOCK(sl)) { + if ((++spins & SPINS_PER_YIELD) == 0) { + SPIN_LOCK_YIELD; + } + } + return 0; +} + +#define MLOCK_T int +#define TRY_LOCK(sl) !CAS_LOCK(sl) +#define RELEASE_LOCK(sl) CLEAR_LOCK(sl) +#define ACQUIRE_LOCK(sl) (CAS_LOCK(sl)? spin_acquire_lock(sl) : 0) +#define INITIAL_LOCK(sl) (*sl = 0) +#define DESTROY_LOCK(sl) (0) +static MLOCK_T malloc_global_mutex = 0; + +#else /* USE_RECURSIVE_LOCKS */ +/* types for lock owners */ +#ifdef WIN32 +#define THREAD_ID_T DWORD +#define CURRENT_THREAD GetCurrentThreadId() +#define EQ_OWNER(X,Y) ((X) == (Y)) +#else +/* + Note: the following assume that pthread_t is a type that can be + initialized to (casted) zero. If this is not the case, you will need to + somehow redefine these or not use spin locks. +*/ +#define THREAD_ID_T pthread_t +#define CURRENT_THREAD pthread_self() +#define EQ_OWNER(X,Y) pthread_equal(X, Y) +#endif + +struct malloc_recursive_lock { + int sl; + unsigned int c; + THREAD_ID_T threadid; +}; + +#define MLOCK_T struct malloc_recursive_lock +static MLOCK_T malloc_global_mutex = { 0, 0, (THREAD_ID_T)0}; + +static FORCEINLINE void recursive_release_lock(MLOCK_T *lk) { + assert(lk->sl != 0); + if (--lk->c == 0) { + CLEAR_LOCK(&lk->sl); + } +} + +static FORCEINLINE int recursive_acquire_lock(MLOCK_T *lk) { + THREAD_ID_T mythreadid = CURRENT_THREAD; + int spins = 0; + for (;;) { + if (*((volatile int *)(&lk->sl)) == 0) { + if (!CAS_LOCK(&lk->sl)) { + lk->threadid = mythreadid; + lk->c = 1; + return 0; + } + } + else if (EQ_OWNER(lk->threadid, mythreadid)) { + ++lk->c; + return 0; + } + if ((++spins & SPINS_PER_YIELD) == 0) { + SPIN_LOCK_YIELD; + } + } +} + +static FORCEINLINE int recursive_try_lock(MLOCK_T *lk) { + THREAD_ID_T mythreadid = CURRENT_THREAD; + if (*((volatile int *)(&lk->sl)) == 0) { + if (!CAS_LOCK(&lk->sl)) { + lk->threadid = mythreadid; + lk->c = 1; + return 1; + } + } + else if (EQ_OWNER(lk->threadid, mythreadid)) { + ++lk->c; + return 1; + } + return 0; +} + +#define RELEASE_LOCK(lk) recursive_release_lock(lk) +#define TRY_LOCK(lk) recursive_try_lock(lk) +#define ACQUIRE_LOCK(lk) recursive_acquire_lock(lk) +#define INITIAL_LOCK(lk) ((lk)->threadid = (THREAD_ID_T)0, (lk)->sl = 0, (lk)->c = 0) +#define DESTROY_LOCK(lk) (0) +#endif /* USE_RECURSIVE_LOCKS */ + +#elif defined(WIN32) /* Win32 critical sections */ +#define MLOCK_T CRITICAL_SECTION +#define ACQUIRE_LOCK(lk) (EnterCriticalSection(lk), 0) +#define RELEASE_LOCK(lk) LeaveCriticalSection(lk) +#define TRY_LOCK(lk) TryEnterCriticalSection(lk) +#define INITIAL_LOCK(lk) (!InitializeCriticalSectionAndSpinCount((lk), 0x80000000|4000)) +#define DESTROY_LOCK(lk) (DeleteCriticalSection(lk), 0) +#define NEED_GLOBAL_LOCK_INIT + +static MLOCK_T malloc_global_mutex; +static volatile LONG malloc_global_mutex_status; + +/* Use spin loop to initialize global lock */ +static void init_malloc_global_mutex() { + for (;;) { + long stat = malloc_global_mutex_status; + if (stat > 0) + return; + /* transition to < 0 while initializing, then to > 0) */ + if (stat == 0 && + interlockedcompareexchange(&malloc_global_mutex_status, (LONG)-1, (LONG)0) == 0) { + InitializeCriticalSection(&malloc_global_mutex); + interlockedexchange(&malloc_global_mutex_status, (LONG)1); + return; + } + SleepEx(0, FALSE); + } +} + +#else /* pthreads-based locks */ +#define MLOCK_T pthread_mutex_t +#define ACQUIRE_LOCK(lk) pthread_mutex_lock(lk) +#define RELEASE_LOCK(lk) pthread_mutex_unlock(lk) +#define TRY_LOCK(lk) (!pthread_mutex_trylock(lk)) +#define INITIAL_LOCK(lk) pthread_init_lock(lk) +#define DESTROY_LOCK(lk) pthread_mutex_destroy(lk) + +#if defined(USE_RECURSIVE_LOCKS) && USE_RECURSIVE_LOCKS != 0 && defined(linux) && !defined(PTHREAD_MUTEX_RECURSIVE) +/* Cope with old-style linux recursive lock initialization by adding */ +/* skipped internal declaration from pthread.h */ +extern int pthread_mutexattr_setkind_np __P ((pthread_mutexattr_t *__attr, + int __kind)); +#define PTHREAD_MUTEX_RECURSIVE PTHREAD_MUTEX_RECURSIVE_NP +#define pthread_mutexattr_settype(x,y) pthread_mutexattr_setkind_np(x,y) +#endif /* USE_RECURSIVE_LOCKS ... */ + +static MLOCK_T malloc_global_mutex = PTHREAD_MUTEX_INITIALIZER; + +static int pthread_init_lock (MLOCK_T *lk) { + pthread_mutexattr_t attr; + if (pthread_mutexattr_init(&attr)) return 1; +#if defined(USE_RECURSIVE_LOCKS) && USE_RECURSIVE_LOCKS != 0 + if (pthread_mutexattr_settype(&attr, PTHREAD_MUTEX_RECURSIVE)) return 1; +#endif + if (pthread_mutex_init(lk, &attr)) return 1; + if (pthread_mutexattr_destroy(&attr)) return 1; + return 0; +} + +#endif /* ... lock types ... */ + +/* Common code for all lock types */ +#define USE_LOCK_BIT (2U) + +#ifndef ACQUIRE_MALLOC_GLOBAL_LOCK +#define ACQUIRE_MALLOC_GLOBAL_LOCK() ACQUIRE_LOCK(&malloc_global_mutex); +#endif + +#ifndef RELEASE_MALLOC_GLOBAL_LOCK +#define RELEASE_MALLOC_GLOBAL_LOCK() RELEASE_LOCK(&malloc_global_mutex); +#endif + +#endif /* USE_LOCKS */ + +/* ----------------------- Chunk representations ------------------------ */ + +/* + (The following includes lightly edited explanations by Colin Plumb.) + + The malloc_chunk declaration below is misleading (but accurate and + necessary). It declares a "view" into memory allowing access to + necessary fields at known offsets from a given base. + + Chunks of memory are maintained using a `boundary tag' method as + originally described by Knuth. (See the paper by Paul Wilson + ftp://ftp.cs.utexas.edu/pub/garbage/allocsrv.ps for a survey of such + techniques.) Sizes of free chunks are stored both in the front of + each chunk and at the end. This makes consolidating fragmented + chunks into bigger chunks fast. The head fields also hold bits + representing whether chunks are free or in use. + + Here are some pictures to make it clearer. They are "exploded" to + show that the state of a chunk can be thought of as extending from + the high 31 bits of the head field of its header through the + prev_foot and PINUSE_BIT bit of the following chunk header. + + A chunk that's in use looks like: + + chunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Size of previous chunk (if P = 0) | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |P| + | Size of this chunk 1| +-+ + mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | | + +- -+ + | | + +- -+ + | : + +- size - sizeof(size_t) available payload bytes -+ + : | + chunk-> +- -+ + | | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |1| + | Size of next chunk (may or may not be in use) | +-+ + mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + + And if it's free, it looks like this: + + chunk-> +- -+ + | User payload (must be in use, or we would have merged!) | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |P| + | Size of this chunk 0| +-+ + mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Next pointer | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Prev pointer | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | : + +- size - sizeof(struct chunk) unused bytes -+ + : | + chunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Size of this chunk | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |0| + | Size of next chunk (must be in use, or we would have merged)| +-+ + mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | : + +- User payload -+ + : | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + |0| + +-+ + Note that since we always merge adjacent free chunks, the chunks + adjacent to a free chunk must be in use. + + Given a pointer to a chunk (which can be derived trivially from the + payload pointer) we can, in O(1) time, find out whether the adjacent + chunks are free, and if so, unlink them from the lists that they + are on and merge them with the current chunk. + + Chunks always begin on even word boundaries, so the mem portion + (which is returned to the user) is also on an even word boundary, and + thus at least double-word aligned. + + The P (PINUSE_BIT) bit, stored in the unused low-order bit of the + chunk size (which is always a multiple of two words), is an in-use + bit for the *previous* chunk. If that bit is *clear*, then the + word before the current chunk size contains the previous chunk + size, and can be used to find the front of the previous chunk. + The very first chunk allocated always has this bit set, preventing + access to non-existent (or non-owned) memory. If pinuse is set for + any given chunk, then you CANNOT determine the size of the + previous chunk, and might even get a memory addressing fault when + trying to do so. + + The C (CINUSE_BIT) bit, stored in the unused second-lowest bit of + the chunk size redundantly records whether the current chunk is + inuse (unless the chunk is mmapped). This redundancy enables usage + checks within free and realloc, and reduces indirection when freeing + and consolidating chunks. + + Each freshly allocated chunk must have both cinuse and pinuse set. + That is, each allocated chunk borders either a previously allocated + and still in-use chunk, or the base of its memory arena. This is + ensured by making all allocations from the `lowest' part of any + found chunk. Further, no free chunk physically borders another one, + so each free chunk is known to be preceded and followed by either + inuse chunks or the ends of memory. + + Note that the `foot' of the current chunk is actually represented + as the prev_foot of the NEXT chunk. This makes it easier to + deal with alignments etc but can be very confusing when trying + to extend or adapt this code. + + The exceptions to all this are + + 1. The special chunk `top' is the top-most available chunk (i.e., + the one bordering the end of available memory). It is treated + specially. Top is never included in any bin, is used only if + no other chunk is available, and is released back to the + system if it is very large (see M_TRIM_THRESHOLD). In effect, + the top chunk is treated as larger (and thus less well + fitting) than any other available chunk. The top chunk + doesn't update its trailing size field since there is no next + contiguous chunk that would have to index off it. However, + space is still allocated for it (TOP_FOOT_SIZE) to enable + separation or merging when space is extended. + + 3. Chunks allocated via mmap, have both cinuse and pinuse bits + cleared in their head fields. Because they are allocated + one-by-one, each must carry its own prev_foot field, which is + also used to hold the offset this chunk has within its mmapped + region, which is needed to preserve alignment. Each mmapped + chunk is trailed by the first two fields of a fake next-chunk + for sake of usage checks. + +*/ + +struct malloc_chunk { + size_t prev_foot; /* Size of previous chunk (if free). */ + size_t head; /* Size and inuse bits. */ + struct malloc_chunk* fd; /* double links -- used only if free. */ + struct malloc_chunk* bk; +}; + +typedef struct malloc_chunk mchunk; +typedef struct malloc_chunk* mchunkptr; +typedef struct malloc_chunk* sbinptr; /* The type of bins of chunks */ +typedef unsigned int bindex_t; /* Described below */ +typedef unsigned int binmap_t; /* Described below */ +typedef unsigned int flag_t; /* The type of various bit flag sets */ + +/* ------------------- Chunks sizes and alignments ----------------------- */ + +#define MCHUNK_SIZE (sizeof(mchunk)) + +#if FOOTERS +#define CHUNK_OVERHEAD (TWO_SIZE_T_SIZES) +#else /* FOOTERS */ +#define CHUNK_OVERHEAD (SIZE_T_SIZE) +#endif /* FOOTERS */ + +/* MMapped chunks need a second word of overhead ... */ +#define MMAP_CHUNK_OVERHEAD (TWO_SIZE_T_SIZES) +/* ... and additional padding for fake next-chunk at foot */ +#define MMAP_FOOT_PAD (FOUR_SIZE_T_SIZES) + +/* The smallest size we can malloc is an aligned minimal chunk */ +#define MIN_CHUNK_SIZE\ + ((MCHUNK_SIZE + CHUNK_ALIGN_MASK) & ~CHUNK_ALIGN_MASK) + +/* conversion from malloc headers to user pointers, and back */ +#define chunk2mem(p) ((void*)((char*)(p) + TWO_SIZE_T_SIZES)) +#define mem2chunk(mem) ((mchunkptr)((char*)(mem) - TWO_SIZE_T_SIZES)) +/* chunk associated with aligned address A */ +#define align_as_chunk(A) (mchunkptr)((A) + align_offset(chunk2mem(A))) + +/* Bounds on request (not chunk) sizes. */ +#define MAX_REQUEST ((-MIN_CHUNK_SIZE) << 2) +#define MIN_REQUEST (MIN_CHUNK_SIZE - CHUNK_OVERHEAD - SIZE_T_ONE) + +/* pad request bytes into a usable size */ +#define pad_request(req) \ + (((req) + CHUNK_OVERHEAD + CHUNK_ALIGN_MASK) & ~CHUNK_ALIGN_MASK) + +/* pad request, checking for minimum (but not maximum) */ +#define request2size(req) \ + (((req) < MIN_REQUEST)? MIN_CHUNK_SIZE : pad_request(req)) + + +/* ------------------ Operations on head and foot fields ----------------- */ + +/* + The head field of a chunk is or'ed with PINUSE_BIT when previous + adjacent chunk in use, and or'ed with CINUSE_BIT if this chunk is in + use, unless mmapped, in which case both bits are cleared. + + FLAG4_BIT is not used by this malloc, but might be useful in extensions. +*/ + +#define PINUSE_BIT (SIZE_T_ONE) +#define CINUSE_BIT (SIZE_T_TWO) +#define FLAG4_BIT (SIZE_T_FOUR) +#define INUSE_BITS (PINUSE_BIT|CINUSE_BIT) +#define FLAG_BITS (PINUSE_BIT|CINUSE_BIT|FLAG4_BIT) + +/* Head value for fenceposts */ +#define FENCEPOST_HEAD (INUSE_BITS|SIZE_T_SIZE) + +/* extraction of fields from head words */ +#define cinuse(p) ((p)->head & CINUSE_BIT) +#define pinuse(p) ((p)->head & PINUSE_BIT) +#define flag4inuse(p) ((p)->head & FLAG4_BIT) +#define is_inuse(p) (((p)->head & INUSE_BITS) != PINUSE_BIT) +#define is_mmapped(p) (((p)->head & INUSE_BITS) == 0) + +#define chunksize(p) ((p)->head & ~(FLAG_BITS)) + +#define clear_pinuse(p) ((p)->head &= ~PINUSE_BIT) +#define set_flag4(p) ((p)->head |= FLAG4_BIT) +#define clear_flag4(p) ((p)->head &= ~FLAG4_BIT) + +/* Treat space at ptr +/- offset as a chunk */ +#define chunk_plus_offset(p, s) ((mchunkptr)(((char*)(p)) + (s))) +#define chunk_minus_offset(p, s) ((mchunkptr)(((char*)(p)) - (s))) + +/* Ptr to next or previous physical malloc_chunk. */ +#define next_chunk(p) ((mchunkptr)( ((char*)(p)) + ((p)->head & ~FLAG_BITS))) +#define prev_chunk(p) ((mchunkptr)( ((char*)(p)) - ((p)->prev_foot) )) + +/* extract next chunk's pinuse bit */ +#define next_pinuse(p) ((next_chunk(p)->head) & PINUSE_BIT) + +/* Get/set size at footer */ +#define get_foot(p, s) (((mchunkptr)((char*)(p) + (s)))->prev_foot) +#define set_foot(p, s) (((mchunkptr)((char*)(p) + (s)))->prev_foot = (s)) + +/* Set size, pinuse bit, and foot */ +#define set_size_and_pinuse_of_free_chunk(p, s)\ + ((p)->head = (s|PINUSE_BIT), set_foot(p, s)) + +/* Set size, pinuse bit, foot, and clear next pinuse */ +#define set_free_with_pinuse(p, s, n)\ + (clear_pinuse(n), set_size_and_pinuse_of_free_chunk(p, s)) + +/* Get the internal overhead associated with chunk p */ +#define overhead_for(p)\ + (is_mmapped(p)? MMAP_CHUNK_OVERHEAD : CHUNK_OVERHEAD) + +/* Return true if malloced space is not necessarily cleared */ +#if MMAP_CLEARS +#define calloc_must_clear(p) (!is_mmapped(p)) +#else /* MMAP_CLEARS */ +#define calloc_must_clear(p) (1) +#endif /* MMAP_CLEARS */ + +/* ---------------------- Overlaid data structures ----------------------- */ + +/* + When chunks are not in use, they are treated as nodes of either + lists or trees. + + "Small" chunks are stored in circular doubly-linked lists, and look + like this: + + chunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Size of previous chunk | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + `head:' | Size of chunk, in bytes |P| + mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Forward pointer to next chunk in list | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Back pointer to previous chunk in list | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Unused space (may be 0 bytes long) . + . . + . | +nextchunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + `foot:' | Size of chunk, in bytes | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + + Larger chunks are kept in a form of bitwise digital trees (aka + tries) keyed on chunksizes. Because malloc_tree_chunks are only for + free chunks greater than 256 bytes, their size doesn't impose any + constraints on user chunk sizes. Each node looks like: + + chunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Size of previous chunk | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + `head:' | Size of chunk, in bytes |P| + mem-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Forward pointer to next chunk of same size | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Back pointer to previous chunk of same size | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Pointer to left child (child[0]) | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Pointer to right child (child[1]) | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Pointer to parent | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | bin index of this chunk | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + | Unused space . + . | +nextchunk-> +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + `foot:' | Size of chunk, in bytes | + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + + Each tree holding treenodes is a tree of unique chunk sizes. Chunks + of the same size are arranged in a circularly-linked list, with only + the oldest chunk (the next to be used, in our FIFO ordering) + actually in the tree. (Tree members are distinguished by a non-null + parent pointer.) If a chunk with the same size an an existing node + is inserted, it is linked off the existing node using pointers that + work in the same way as fd/bk pointers of small chunks. + + Each tree contains a power of 2 sized range of chunk sizes (the + smallest is 0x100 <= x < 0x180), which is is divided in half at each + tree level, with the chunks in the smaller half of the range (0x100 + <= x < 0x140 for the top nose) in the left subtree and the larger + half (0x140 <= x < 0x180) in the right subtree. This is, of course, + done by inspecting individual bits. + + Using these rules, each node's left subtree contains all smaller + sizes than its right subtree. However, the node at the root of each + subtree has no particular ordering relationship to either. (The + dividing line between the subtree sizes is based on trie relation.) + If we remove the last chunk of a given size from the interior of the + tree, we need to replace it with a leaf node. The tree ordering + rules permit a node to be replaced by any leaf below it. + + The smallest chunk in a tree (a common operation in a best-fit + allocator) can be found by walking a path to the leftmost leaf in + the tree. Unlike a usual binary tree, where we follow left child + pointers until we reach a null, here we follow the right child + pointer any time the left one is null, until we reach a leaf with + both child pointers null. The smallest chunk in the tree will be + somewhere along that path. + + The worst case number of steps to add, find, or remove a node is + bounded by the number of bits differentiating chunks within + bins. Under current bin calculations, this ranges from 6 up to 21 + (for 32 bit sizes) or up to 53 (for 64 bit sizes). The typical case + is of course much better. +*/ + +struct malloc_tree_chunk { + /* The first four fields must be compatible with malloc_chunk */ + size_t prev_foot; + size_t head; + struct malloc_tree_chunk* fd; + struct malloc_tree_chunk* bk; + + struct malloc_tree_chunk* child[2]; + struct malloc_tree_chunk* parent; + bindex_t index; +}; + +typedef struct malloc_tree_chunk tchunk; +typedef struct malloc_tree_chunk* tchunkptr; +typedef struct malloc_tree_chunk* tbinptr; /* The type of bins of trees */ + +/* A little helper macro for trees */ +#define leftmost_child(t) ((t)->child[0] != 0? (t)->child[0] : (t)->child[1]) + +/* ----------------------------- Segments -------------------------------- */ + +/* + Each malloc space may include non-contiguous segments, held in a + list headed by an embedded malloc_segment record representing the + top-most space. Segments also include flags holding properties of + the space. Large chunks that are directly allocated by mmap are not + included in this list. They are instead independently created and + destroyed without otherwise keeping track of them. + + Segment management mainly comes into play for spaces allocated by + MMAP. Any call to MMAP might or might not return memory that is + adjacent to an existing segment. MORECORE normally contiguously + extends the current space, so this space is almost always adjacent, + which is simpler and faster to deal with. (This is why MORECORE is + used preferentially to MMAP when both are available -- see + sys_alloc.) When allocating using MMAP, we don't use any of the + hinting mechanisms (inconsistently) supported in various + implementations of unix mmap, or distinguish reserving from + committing memory. Instead, we just ask for space, and exploit + contiguity when we get it. It is probably possible to do + better than this on some systems, but no general scheme seems + to be significantly better. + + Management entails a simpler variant of the consolidation scheme + used for chunks to reduce fragmentation -- new adjacent memory is + normally prepended or appended to an existing segment. However, + there are limitations compared to chunk consolidation that mostly + reflect the fact that segment processing is relatively infrequent + (occurring only when getting memory from system) and that we + don't expect to have huge numbers of segments: + + * Segments are not indexed, so traversal requires linear scans. (It + would be possible to index these, but is not worth the extra + overhead and complexity for most programs on most platforms.) + * New segments are only appended to old ones when holding top-most + memory; if they cannot be prepended to others, they are held in + different segments. + + Except for the top-most segment of an mstate, each segment record + is kept at the tail of its segment. Segments are added by pushing + segment records onto the list headed by &mstate.seg for the + containing mstate. + + Segment flags control allocation/merge/deallocation policies: + * If EXTERN_BIT set, then we did not allocate this segment, + and so should not try to deallocate or merge with others. + (This currently holds only for the initial segment passed + into create_mspace_with_base.) + * If USE_MMAP_BIT set, the segment may be merged with + other surrounding mmapped segments and trimmed/de-allocated + using munmap. + * If neither bit is set, then the segment was obtained using + MORECORE so can be merged with surrounding MORECORE'd segments + and deallocated/trimmed using MORECORE with negative arguments. +*/ + +struct malloc_segment { + char* base; /* base address */ + size_t size; /* allocated size */ + struct malloc_segment* next; /* ptr to next segment */ + flag_t sflags; /* mmap and extern flag */ +}; + +#define is_mmapped_segment(S) ((S)->sflags & USE_MMAP_BIT) +#define is_extern_segment(S) ((S)->sflags & EXTERN_BIT) + +typedef struct malloc_segment msegment; +typedef struct malloc_segment* msegmentptr; + +/* ---------------------------- malloc_state ----------------------------- */ + +/* + A malloc_state holds all of the bookkeeping for a space. + The main fields are: + + Top + The topmost chunk of the currently active segment. Its size is + cached in topsize. The actual size of topmost space is + topsize+TOP_FOOT_SIZE, which includes space reserved for adding + fenceposts and segment records if necessary when getting more + space from the system. The size at which to autotrim top is + cached from mparams in trim_check, except that it is disabled if + an autotrim fails. + + Designated victim (dv) + This is the preferred chunk for servicing small requests that + don't have exact fits. It is normally the chunk split off most + recently to service another small request. Its size is cached in + dvsize. The link fields of this chunk are not maintained since it + is not kept in a bin. + + SmallBins + An array of bin headers for free chunks. These bins hold chunks + with sizes less than MIN_LARGE_SIZE bytes. Each bin contains + chunks of all the same size, spaced 8 bytes apart. To simplify + use in double-linked lists, each bin header acts as a malloc_chunk + pointing to the real first node, if it exists (else pointing to + itself). This avoids special-casing for headers. But to avoid + waste, we allocate only the fd/bk pointers of bins, and then use + repositioning tricks to treat these as the fields of a chunk. + + TreeBins + Treebins are pointers to the roots of trees holding a range of + sizes. There are 2 equally spaced treebins for each power of two + from TREE_SHIFT to TREE_SHIFT+16. The last bin holds anything + larger. + + Bin maps + There is one bit map for small bins ("smallmap") and one for + treebins ("treemap). Each bin sets its bit when non-empty, and + clears the bit when empty. Bit operations are then used to avoid + bin-by-bin searching -- nearly all "search" is done without ever + looking at bins that won't be selected. The bit maps + conservatively use 32 bits per map word, even if on 64bit system. + For a good description of some of the bit-based techniques used + here, see Henry S. Warren Jr's book "Hacker's Delight" (and + supplement at http://hackersdelight.org/). Many of these are + intended to reduce the branchiness of paths through malloc etc, as + well as to reduce the number of memory locations read or written. + + Segments + A list of segments headed by an embedded malloc_segment record + representing the initial space. + + Address check support + The least_addr field is the least address ever obtained from + MORECORE or MMAP. Attempted frees and reallocs of any address less + than this are trapped (unless INSECURE is defined). + + Magic tag + A cross-check field that should always hold same value as mparams.magic. + + Max allowed footprint + The maximum allowed bytes to allocate from system (zero means no limit) + + Flags + Bits recording whether to use MMAP, locks, or contiguous MORECORE + + Statistics + Each space keeps track of current and maximum system memory + obtained via MORECORE or MMAP. + + Trim support + Fields holding the amount of unused topmost memory that should trigger + trimming, and a counter to force periodic scanning to release unused + non-topmost segments. + + Locking + If USE_LOCKS is defined, the "mutex" lock is acquired and released + around every public call using this mspace. + + Extension support + A void* pointer and a size_t field that can be used to help implement + extensions to this malloc. +*/ + +/* Bin types, widths and sizes */ +#define NSMALLBINS (32U) +#define NTREEBINS (32U) +#define SMALLBIN_SHIFT (3U) +#define SMALLBIN_WIDTH (SIZE_T_ONE << SMALLBIN_SHIFT) +#define TREEBIN_SHIFT (8U) +#define MIN_LARGE_SIZE (SIZE_T_ONE << TREEBIN_SHIFT) +#define MAX_SMALL_SIZE (MIN_LARGE_SIZE - SIZE_T_ONE) +#define MAX_SMALL_REQUEST (MAX_SMALL_SIZE - CHUNK_ALIGN_MASK - CHUNK_OVERHEAD) + +struct malloc_state { + binmap_t smallmap; + binmap_t treemap; + size_t dvsize; + size_t topsize; + char* least_addr; + mchunkptr dv; + mchunkptr top; + size_t trim_check; + size_t release_checks; + size_t magic; + mchunkptr smallbins[(NSMALLBINS+1)*2]; + tbinptr treebins[NTREEBINS]; + size_t footprint; + size_t max_footprint; + size_t footprint_limit; /* zero means no limit */ + flag_t mflags; +#if USE_LOCKS + MLOCK_T mutex; /* locate lock among fields that rarely change */ +#endif /* USE_LOCKS */ + msegment seg; + void* extp; /* Unused but available for extensions */ + size_t exts; + size_t internal_memory_usage; /* count memory allocation and free */ +}; + +typedef struct malloc_state* mstate; + +/* ------------- Global malloc_state and malloc_params ------------------- */ + +/* + malloc_params holds global properties, including those that can be + dynamically set using mallopt. There is a single instance, mparams, + initialized in init_mparams. Note that the non-zeroness of "magic" + also serves as an initialization flag. +*/ + +struct malloc_params { + size_t magic; + size_t page_size; + size_t granularity; + size_t mmap_threshold; + size_t trim_threshold; + flag_t default_mflags; +}; + +static struct malloc_params mparams; + +/* Ensure mparams initialized */ +#define ensure_initialization() (void)(mparams.magic != 0 || init_mparams()) + +#if !ONLY_MSPACES + +/* The global malloc_state used for all non-"mspace" calls */ +static struct malloc_state _gm_; +#define gm (&_gm_) +#define is_global(M) ((M) == &_gm_) + +#endif /* !ONLY_MSPACES */ + +#define is_initialized(M) ((M)->top != 0) + +/* -------------------------- system alloc setup ------------------------- */ + +/* Operations on mflags */ + +#define use_lock(M) ((M)->mflags & USE_LOCK_BIT) +#define enable_lock(M) ((M)->mflags |= USE_LOCK_BIT) +#if USE_LOCKS +#define disable_lock(M) ((M)->mflags &= ~USE_LOCK_BIT) +#else +#define disable_lock(M) +#endif + +#define use_mmap(M) ((M)->mflags & USE_MMAP_BIT) +#define enable_mmap(M) ((M)->mflags |= USE_MMAP_BIT) +#if HAVE_MMAP +#define disable_mmap(M) ((M)->mflags &= ~USE_MMAP_BIT) +#else +#define disable_mmap(M) +#endif + +#define use_noncontiguous(M) ((M)->mflags & USE_NONCONTIGUOUS_BIT) +#define disable_contiguous(M) ((M)->mflags |= USE_NONCONTIGUOUS_BIT) + +#define set_lock(M,L)\ + ((M)->mflags = (L)?\ + ((M)->mflags | USE_LOCK_BIT) :\ + ((M)->mflags & ~USE_LOCK_BIT)) + +/* page-align a size */ +#define page_align(S)\ + (((S) + (mparams.page_size - SIZE_T_ONE)) & ~(mparams.page_size - SIZE_T_ONE)) + +/* granularity-align a size */ +#define granularity_align(S)\ + (((S) + (mparams.granularity - SIZE_T_ONE))\ + & ~(mparams.granularity - SIZE_T_ONE)) + + +/* For mmap, use granularity alignment on windows, else page-align */ +#ifdef WIN32 +#define mmap_align(S) granularity_align(S) +#else +#define mmap_align(S) page_align(S) +#endif + +/* For sys_alloc, enough padding to ensure can malloc request on success */ +#define SYS_ALLOC_PADDING (TOP_FOOT_SIZE + MALLOC_ALIGNMENT) + +#define is_page_aligned(S)\ + (((size_t)(S) & (mparams.page_size - SIZE_T_ONE)) == 0) +#define is_granularity_aligned(S)\ + (((size_t)(S) & (mparams.granularity - SIZE_T_ONE)) == 0) + +/* True if segment S holds address A */ +#define segment_holds(S, A)\ + ((char*)(A) >= S->base && (char*)(A) < S->base + S->size) + +/* Return segment holding given address */ +static msegmentptr segment_holding(mstate m, char* addr) { + msegmentptr sp = &m->seg; + for (;;) { + if (addr >= sp->base && addr < sp->base + sp->size) + return sp; + if ((sp = sp->next) == 0) + return 0; + } +} + +/* Return true if segment contains a segment link */ +static int has_segment_link(mstate m, msegmentptr ss) { + msegmentptr sp = &m->seg; + for (;;) { + if ((char*)sp >= ss->base && (char*)sp < ss->base + ss->size) + return 1; + if ((sp = sp->next) == 0) + return 0; + } +} + +#ifndef MORECORE_CANNOT_TRIM +#define should_trim(M,s) ((s) > (M)->trim_check) +#else /* MORECORE_CANNOT_TRIM */ +#define should_trim(M,s) (0) +#endif /* MORECORE_CANNOT_TRIM */ + +/* + TOP_FOOT_SIZE is padding at the end of a segment, including space + that may be needed to place segment records and fenceposts when new + noncontiguous segments are added. +*/ +#define TOP_FOOT_SIZE\ + (align_offset(chunk2mem(0))+pad_request(sizeof(struct malloc_segment))+MIN_CHUNK_SIZE) + + +/* ------------------------------- Hooks -------------------------------- */ + +/* + PREACTION should be defined to return 0 on success, and nonzero on + failure. If you are not using locking, you can redefine these to do + anything you like. +*/ + +#if USE_LOCKS +#define PREACTION(M) ((use_lock(M))? ACQUIRE_LOCK(&(M)->mutex) : 0) +#define POSTACTION(M) { if (use_lock(M)) RELEASE_LOCK(&(M)->mutex); } +#else /* USE_LOCKS */ + +#ifndef PREACTION +#define PREACTION(M) (0) +#endif /* PREACTION */ + +#ifndef POSTACTION +#define POSTACTION(M) +#endif /* POSTACTION */ + +#endif /* USE_LOCKS */ + +/* + CORRUPTION_ERROR_ACTION is triggered upon detected bad addresses. + USAGE_ERROR_ACTION is triggered on detected bad frees and + reallocs. The argument p is an address that might have triggered the + fault. It is ignored by the two predefined actions, but might be + useful in custom actions that try to help diagnose errors. +*/ + +#if PROCEED_ON_ERROR + +/* A count of the number of corruption errors causing resets */ +int malloc_corruption_error_count; + +/* default corruption action */ +static void reset_on_error(mstate m); + +#define CORRUPTION_ERROR_ACTION(m) reset_on_error(m) +#define USAGE_ERROR_ACTION(m, p) + +#else /* PROCEED_ON_ERROR */ + +#ifndef CORRUPTION_ERROR_ACTION +#define CORRUPTION_ERROR_ACTION(m) ABORT +#endif /* CORRUPTION_ERROR_ACTION */ + +#ifndef USAGE_ERROR_ACTION +#define USAGE_ERROR_ACTION(m,p) ABORT +#endif /* USAGE_ERROR_ACTION */ + +#endif /* PROCEED_ON_ERROR */ + + +/* -------------------------- Debugging setup ---------------------------- */ + +#if ! DEBUG + +#define check_free_chunk(M,P) +#define check_inuse_chunk(M,P) +#define check_malloced_chunk(M,P,N) +#define check_mmapped_chunk(M,P) +#define check_malloc_state(M) +#define check_top_chunk(M,P) + +#else /* DEBUG */ +#define check_free_chunk(M,P) do_check_free_chunk(M,P) +#define check_inuse_chunk(M,P) do_check_inuse_chunk(M,P) +#define check_top_chunk(M,P) do_check_top_chunk(M,P) +#define check_malloced_chunk(M,P,N) do_check_malloced_chunk(M,P,N) +#define check_mmapped_chunk(M,P) do_check_mmapped_chunk(M,P) +#define check_malloc_state(M) do_check_malloc_state(M) + +static void do_check_any_chunk(mstate m, mchunkptr p); +static void do_check_top_chunk(mstate m, mchunkptr p); +static void do_check_mmapped_chunk(mstate m, mchunkptr p); +static void do_check_inuse_chunk(mstate m, mchunkptr p); +static void do_check_free_chunk(mstate m, mchunkptr p); +static void do_check_malloced_chunk(mstate m, void* mem, size_t s); +static void do_check_tree(mstate m, tchunkptr t); +static void do_check_treebin(mstate m, bindex_t i); +static void do_check_smallbin(mstate m, bindex_t i); +static void do_check_malloc_state(mstate m); +static int bin_find(mstate m, mchunkptr x); +static size_t traverse_and_check(mstate m); +#endif /* DEBUG */ + +/* ---------------------------- Indexing Bins ---------------------------- */ + +#define is_small(s) (((s) >> SMALLBIN_SHIFT) < NSMALLBINS) +#define small_index(s) (bindex_t)((s) >> SMALLBIN_SHIFT) +#define small_index2size(i) ((i) << SMALLBIN_SHIFT) +#define MIN_SMALL_INDEX (small_index(MIN_CHUNK_SIZE)) + +/* addressing by index. See above about smallbin repositioning */ +#define smallbin_at(M, i) ((sbinptr)((char*)&((M)->smallbins[(i)<<1]))) +#define treebin_at(M,i) (&((M)->treebins[i])) + +/* assign tree index for size S to variable I. Use x86 asm if possible */ +#if defined(__GNUC__) && (defined(__i386__) || defined(__x86_64__)) +#define compute_tree_index(S, I)\ +{\ + unsigned int X = S >> TREEBIN_SHIFT;\ + if (X == 0)\ + I = 0;\ + else if (X > 0xFFFF)\ + I = NTREEBINS-1;\ + else {\ + unsigned int K = (unsigned) sizeof(X)*__CHAR_BIT__ - 1 - (unsigned) __builtin_clz(X); \ + I = (bindex_t)((K << 1) + ((S >> (K + (TREEBIN_SHIFT-1)) & 1)));\ + }\ +} + +#elif defined (__INTEL_COMPILER) +#define compute_tree_index(S, I)\ +{\ + size_t X = S >> TREEBIN_SHIFT;\ + if (X == 0)\ + I = 0;\ + else if (X > 0xFFFF)\ + I = NTREEBINS-1;\ + else {\ + unsigned int K = _bit_scan_reverse (X); \ + I = (bindex_t)((K << 1) + ((S >> (K + (TREEBIN_SHIFT-1)) & 1)));\ + }\ +} + +#elif defined(_MSC_VER) && _MSC_VER>=1300 +#define compute_tree_index(S, I)\ +{\ + size_t X = S >> TREEBIN_SHIFT;\ + if (X == 0)\ + I = 0;\ + else if (X > 0xFFFF)\ + I = NTREEBINS-1;\ + else {\ + unsigned int K;\ + _BitScanReverse((DWORD *) &K, (DWORD) X);\ + I = (bindex_t)((K << 1) + ((S >> (K + (TREEBIN_SHIFT-1)) & 1)));\ + }\ +} + +#else /* GNUC */ +#define compute_tree_index(S, I)\ +{\ + size_t X = S >> TREEBIN_SHIFT;\ + if (X == 0)\ + I = 0;\ + else if (X > 0xFFFF)\ + I = NTREEBINS-1;\ + else {\ + unsigned int Y = (unsigned int)X;\ + unsigned int N = ((Y - 0x100) >> 16) & 8;\ + unsigned int K = (((Y <<= N) - 0x1000) >> 16) & 4;\ + N += K;\ + N += K = (((Y <<= K) - 0x4000) >> 16) & 2;\ + K = 14 - N + ((Y <<= K) >> 15);\ + I = (K << 1) + ((S >> (K + (TREEBIN_SHIFT-1)) & 1));\ + }\ +} +#endif /* GNUC */ + +/* Bit representing maximum resolved size in a treebin at i */ +#define bit_for_tree_index(i) \ + (i == NTREEBINS-1)? (SIZE_T_BITSIZE-1) : (((i) >> 1) + TREEBIN_SHIFT - 2) + +/* Shift placing maximum resolved bit in a treebin at i as sign bit */ +#define leftshift_for_tree_index(i) \ + ((i == NTREEBINS-1)? 0 : \ + ((SIZE_T_BITSIZE-SIZE_T_ONE) - (((i) >> 1) + TREEBIN_SHIFT - 2))) + +/* The size of the smallest chunk held in bin with index i */ +#define minsize_for_tree_index(i) \ + ((SIZE_T_ONE << (((i) >> 1) + TREEBIN_SHIFT)) | \ + (((size_t)((i) & SIZE_T_ONE)) << (((i) >> 1) + TREEBIN_SHIFT - 1))) + + +/* ------------------------ Operations on bin maps ----------------------- */ + +/* bit corresponding to given index */ +#define idx2bit(i) ((binmap_t)(1) << (i)) + +/* Mark/Clear bits with given index */ +#define mark_smallmap(M,i) ((M)->smallmap |= idx2bit(i)) +#define clear_smallmap(M,i) ((M)->smallmap &= ~idx2bit(i)) +#define smallmap_is_marked(M,i) ((M)->smallmap & idx2bit(i)) + +#define mark_treemap(M,i) ((M)->treemap |= idx2bit(i)) +#define clear_treemap(M,i) ((M)->treemap &= ~idx2bit(i)) +#define treemap_is_marked(M,i) ((M)->treemap & idx2bit(i)) + +/* isolate the least set bit of a bitmap */ +#define least_bit(x) ((x) & -(x)) + +/* mask with all bits to left of least bit of x on */ +#define left_bits(x) ((x<<1) | -(x<<1)) + +/* mask with all bits to left of or equal to least bit of x on */ +#define same_or_left_bits(x) ((x) | -(x)) + +/* index corresponding to given bit. Use x86 asm if possible */ + +#if defined(__GNUC__) && (defined(__i386__) || defined(__x86_64__)) +#define compute_bit2idx(X, I)\ +{\ + unsigned int J;\ + J = __builtin_ctz(X); \ + I = (bindex_t)J;\ +} + +#elif defined (__INTEL_COMPILER) +#define compute_bit2idx(X, I)\ +{\ + unsigned int J;\ + J = _bit_scan_forward (X); \ + I = (bindex_t)J;\ +} + +#elif defined(_MSC_VER) && _MSC_VER>=1300 +#define compute_bit2idx(X, I)\ +{\ + unsigned int J;\ + _BitScanForward((DWORD *) &J, X);\ + I = (bindex_t)J;\ +} + +#elif USE_BUILTIN_FFS +#define compute_bit2idx(X, I) I = ffs(X)-1 + +#else +#define compute_bit2idx(X, I)\ +{\ + unsigned int Y = X - 1;\ + unsigned int K = Y >> (16-4) & 16;\ + unsigned int N = K; Y >>= K;\ + N += K = Y >> (8-3) & 8; Y >>= K;\ + N += K = Y >> (4-2) & 4; Y >>= K;\ + N += K = Y >> (2-1) & 2; Y >>= K;\ + N += K = Y >> (1-0) & 1; Y >>= K;\ + I = (bindex_t)(N + Y);\ +} +#endif /* GNUC */ + + +/* ----------------------- Runtime Check Support ------------------------- */ + +/* + For security, the main invariant is that malloc/free/etc never + writes to a static address other than malloc_state, unless static + malloc_state itself has been corrupted, which cannot occur via + malloc (because of these checks). In essence this means that we + believe all pointers, sizes, maps etc held in malloc_state, but + check all of those linked or offsetted from other embedded data + structures. These checks are interspersed with main code in a way + that tends to minimize their run-time cost. + + When FOOTERS is defined, in addition to range checking, we also + verify footer fields of inuse chunks, which can be used guarantee + that the mstate controlling malloc/free is intact. This is a + streamlined version of the approach described by William Robertson + et al in "Run-time Detection of Heap-based Overflows" LISA'03 + http://www.usenix.org/events/lisa03/tech/robertson.html The footer + of an inuse chunk holds the xor of its mstate and a random seed, + that is checked upon calls to free() and realloc(). This is + (probabalistically) unguessable from outside the program, but can be + computed by any code successfully malloc'ing any chunk, so does not + itself provide protection against code that has already broken + security through some other means. Unlike Robertson et al, we + always dynamically check addresses of all offset chunks (previous, + next, etc). This turns out to be cheaper than relying on hashes. +*/ + +#if !INSECURE +/* Check if address a is at least as high as any from MORECORE or MMAP */ +#define ok_address(M, a) ((char*)(a) >= (M)->least_addr) +/* Check if address of next chunk n is higher than base chunk p */ +#define ok_next(p, n) ((char*)(p) < (char*)(n)) +/* Check if p has inuse status */ +#define ok_inuse(p) is_inuse(p) +/* Check if p has its pinuse bit on */ +#define ok_pinuse(p) pinuse(p) + +#else /* !INSECURE */ +#define ok_address(M, a) (1) +#define ok_next(b, n) (1) +#define ok_inuse(p) (1) +#define ok_pinuse(p) (1) +#endif /* !INSECURE */ + +#if (FOOTERS && !INSECURE) +/* Check if (alleged) mstate m has expected magic field */ +#define ok_magic(M) ((M)->magic == mparams.magic) +#else /* (FOOTERS && !INSECURE) */ +#define ok_magic(M) (1) +#endif /* (FOOTERS && !INSECURE) */ + +/* In gcc, use __builtin_expect to minimize impact of checks */ +#if !INSECURE +#if defined(__GNUC__) && __GNUC__ >= 3 +#define RTCHECK(e) __builtin_expect(e, 1) +#else /* GNUC */ +#define RTCHECK(e) (e) +#endif /* GNUC */ +#else /* !INSECURE */ +#define RTCHECK(e) (1) +#endif /* !INSECURE */ + +/* macros to set up inuse chunks with or without footers */ + +#if !FOOTERS + +#define mark_inuse_foot(M,p,s) + +/* Macros for setting head/foot of non-mmapped chunks */ + +/* Set cinuse bit and pinuse bit of next chunk */ +#define set_inuse(M,p,s)\ + ((p)->head = (((p)->head & PINUSE_BIT)|s|CINUSE_BIT),\ + ((mchunkptr)(((char*)(p)) + (s)))->head |= PINUSE_BIT) + +/* Set cinuse and pinuse of this chunk and pinuse of next chunk */ +#define set_inuse_and_pinuse(M,p,s)\ + ((p)->head = (s|PINUSE_BIT|CINUSE_BIT),\ + ((mchunkptr)(((char*)(p)) + (s)))->head |= PINUSE_BIT) + +/* Set size, cinuse and pinuse bit of this chunk */ +#define set_size_and_pinuse_of_inuse_chunk(M, p, s)\ + ((p)->head = (s|PINUSE_BIT|CINUSE_BIT)) + +#else /* FOOTERS */ + +/* Set foot of inuse chunk to be xor of mstate and seed */ +#define mark_inuse_foot(M,p,s)\ + (((mchunkptr)((char*)(p) + (s)))->prev_foot = ((size_t)(M) ^ mparams.magic)) + +#define get_mstate_for(p)\ + ((mstate)(((mchunkptr)((char*)(p) +\ + (chunksize(p))))->prev_foot ^ mparams.magic)) + +#define set_inuse(M,p,s)\ + ((p)->head = (((p)->head & PINUSE_BIT)|s|CINUSE_BIT),\ + (((mchunkptr)(((char*)(p)) + (s)))->head |= PINUSE_BIT), \ + mark_inuse_foot(M,p,s)) + +#define set_inuse_and_pinuse(M,p,s)\ + ((p)->head = (s|PINUSE_BIT|CINUSE_BIT),\ + (((mchunkptr)(((char*)(p)) + (s)))->head |= PINUSE_BIT),\ + mark_inuse_foot(M,p,s)) + +#define set_size_and_pinuse_of_inuse_chunk(M, p, s)\ + ((p)->head = (s|PINUSE_BIT|CINUSE_BIT),\ + mark_inuse_foot(M, p, s)) + +#endif /* !FOOTERS */ + +/* ---------------------------- setting mparams -------------------------- */ + +#if LOCK_AT_FORK +static void pre_fork(void) { ACQUIRE_LOCK(&(gm)->mutex); } +static void post_fork_parent(void) { RELEASE_LOCK(&(gm)->mutex); } +static void post_fork_child(void) { INITIAL_LOCK(&(gm)->mutex); } +#endif /* LOCK_AT_FORK */ + +/* Initialize mparams */ +static int init_mparams(void) { +#ifdef NEED_GLOBAL_LOCK_INIT + if (malloc_global_mutex_status <= 0) + init_malloc_global_mutex(); +#endif + + ACQUIRE_MALLOC_GLOBAL_LOCK(); + if (mparams.magic == 0) { + size_t magic; + size_t psize; + size_t gsize; + +#ifndef WIN32 + psize = malloc_getpagesize; + gsize = ((DEFAULT_GRANULARITY != 0)? DEFAULT_GRANULARITY : psize); +#else /* WIN32 */ + { + SYSTEM_INFO system_info; + GetSystemInfo(&system_info); + psize = system_info.dwPageSize; + gsize = ((DEFAULT_GRANULARITY != 0)? + DEFAULT_GRANULARITY : system_info.dwAllocationGranularity); + } +#endif /* WIN32 */ + + /* Sanity-check configuration: + size_t must be unsigned and as wide as pointer type. + ints must be at least 4 bytes. + alignment must be at least 8. + Alignment, min chunk size, and page size must all be powers of 2. + */ + if ((sizeof(size_t) != sizeof(char*)) || + (MAX_SIZE_T < MIN_CHUNK_SIZE) || + (sizeof(int) < 4) || + (MALLOC_ALIGNMENT < (size_t)8U) || + ((MALLOC_ALIGNMENT & (MALLOC_ALIGNMENT-SIZE_T_ONE)) != 0) || + ((MCHUNK_SIZE & (MCHUNK_SIZE-SIZE_T_ONE)) != 0) || + ((gsize & (gsize-SIZE_T_ONE)) != 0) || + ((psize & (psize-SIZE_T_ONE)) != 0)) + ABORT; + mparams.granularity = gsize; + mparams.page_size = psize; + mparams.mmap_threshold = DEFAULT_MMAP_THRESHOLD; + mparams.trim_threshold = DEFAULT_TRIM_THRESHOLD; +#if MORECORE_CONTIGUOUS + mparams.default_mflags = USE_LOCK_BIT|USE_MMAP_BIT; +#else /* MORECORE_CONTIGUOUS */ + mparams.default_mflags = USE_LOCK_BIT|USE_MMAP_BIT|USE_NONCONTIGUOUS_BIT; +#endif /* MORECORE_CONTIGUOUS */ + +#if !ONLY_MSPACES + /* Set up lock for main malloc area */ + gm->mflags = mparams.default_mflags; + (void)INITIAL_LOCK(&gm->mutex); +#endif +#if LOCK_AT_FORK + pthread_atfork(&pre_fork, &post_fork_parent, &post_fork_child); +#endif + + { +#if USE_DEV_RANDOM + int fd; + unsigned char buf[sizeof(size_t)]; + /* Try to use /dev/urandom, else fall back on using time */ + if ((fd = open("/dev/urandom", O_RDONLY)) >= 0 && + read(fd, buf, sizeof(buf)) == sizeof(buf)) { + magic = *((size_t *) buf); + close(fd); + } + else +#endif /* USE_DEV_RANDOM */ +#ifdef __ocaml_solo5__ + magic = (size_t)(solo5_clock_monotonic() ^ 0x55555555UL); +#else /* __ocaml_solo5__ */ +#ifdef WIN32 + magic = (size_t)(GetTickCount() ^ (size_t)0x55555555U); +#elif defined(LACKS_TIME_H) + magic = (size_t)&magic ^ (size_t)0x55555555U; +#else + magic = (size_t)(time(0) ^ (size_t)0x55555555U); +#endif +#endif + magic |= (size_t)8U; /* ensure nonzero */ + magic &= ~(size_t)7U; /* improve chances of fault for bad values */ + /* Until memory modes commonly available, use volatile-write */ + (*(volatile size_t *)(&(mparams.magic))) = magic; + } + } + + RELEASE_MALLOC_GLOBAL_LOCK(); + return 1; +} + +/* support for mallopt */ +static int change_mparam(int param_number, int value) { + size_t val; + ensure_initialization(); + val = (value == -1)? MAX_SIZE_T : (size_t)value; + switch(param_number) { + case M_TRIM_THRESHOLD: + mparams.trim_threshold = val; + return 1; + case M_GRANULARITY: + if (val >= mparams.page_size && ((val & (val-1)) == 0)) { + mparams.granularity = val; + return 1; + } + else + return 0; + case M_MMAP_THRESHOLD: + mparams.mmap_threshold = val; + return 1; + default: + return 0; + } +} + +#if DEBUG +/* ------------------------- Debugging Support --------------------------- */ + +/* Check properties of any chunk, whether free, inuse, mmapped etc */ +static void do_check_any_chunk(mstate m, mchunkptr p) { + assert((is_aligned(chunk2mem(p))) || (p->head == FENCEPOST_HEAD)); + assert(ok_address(m, p)); +} + +/* Check properties of top chunk */ +static void do_check_top_chunk(mstate m, mchunkptr p) { + msegmentptr sp = segment_holding(m, (char*)p); + size_t sz = p->head & ~INUSE_BITS; /* third-lowest bit can be set! */ + assert(sp != 0); + assert((is_aligned(chunk2mem(p))) || (p->head == FENCEPOST_HEAD)); + assert(ok_address(m, p)); + assert(sz == m->topsize); + assert(sz > 0); + assert(sz == ((sp->base + sp->size) - (char*)p) - TOP_FOOT_SIZE); + assert(pinuse(p)); + assert(!pinuse(chunk_plus_offset(p, sz))); +} + +/* Check properties of (inuse) mmapped chunks */ +static void do_check_mmapped_chunk(mstate m, mchunkptr p) { + size_t sz = chunksize(p); + size_t len = (sz + (p->prev_foot) + MMAP_FOOT_PAD); + assert(is_mmapped(p)); + assert(use_mmap(m)); + assert((is_aligned(chunk2mem(p))) || (p->head == FENCEPOST_HEAD)); + assert(ok_address(m, p)); + assert(!is_small(sz)); + assert((len & (mparams.page_size-SIZE_T_ONE)) == 0); + assert(chunk_plus_offset(p, sz)->head == FENCEPOST_HEAD); + assert(chunk_plus_offset(p, sz+SIZE_T_SIZE)->head == 0); +} + +/* Check properties of inuse chunks */ +static void do_check_inuse_chunk(mstate m, mchunkptr p) { + do_check_any_chunk(m, p); + assert(is_inuse(p)); + assert(next_pinuse(p)); + /* If not pinuse and not mmapped, previous chunk has OK offset */ + assert(is_mmapped(p) || pinuse(p) || next_chunk(prev_chunk(p)) == p); + if (is_mmapped(p)) + do_check_mmapped_chunk(m, p); +} + +/* Check properties of free chunks */ +static void do_check_free_chunk(mstate m, mchunkptr p) { + size_t sz = chunksize(p); + mchunkptr next = chunk_plus_offset(p, sz); + do_check_any_chunk(m, p); + assert(!is_inuse(p)); + assert(!next_pinuse(p)); + assert (!is_mmapped(p)); + if (p != m->dv && p != m->top) { + if (sz >= MIN_CHUNK_SIZE) { + assert((sz & CHUNK_ALIGN_MASK) == 0); + assert(is_aligned(chunk2mem(p))); + assert(next->prev_foot == sz); + assert(pinuse(p)); + assert (next == m->top || is_inuse(next)); + assert(p->fd->bk == p); + assert(p->bk->fd == p); + } + else /* markers are always of size SIZE_T_SIZE */ + assert(sz == SIZE_T_SIZE); + } +} + +/* Check properties of malloced chunks at the point they are malloced */ +static void do_check_malloced_chunk(mstate m, void* mem, size_t s) { + if (mem != 0) { + mchunkptr p = mem2chunk(mem); + size_t sz = p->head & ~INUSE_BITS; + do_check_inuse_chunk(m, p); + assert((sz & CHUNK_ALIGN_MASK) == 0); + assert(sz >= MIN_CHUNK_SIZE); + assert(sz >= s); + /* unless mmapped, size is less than MIN_CHUNK_SIZE more than request */ + assert(is_mmapped(p) || sz < (s + MIN_CHUNK_SIZE)); + } +} + +/* Check a tree and its subtrees. */ +static void do_check_tree(mstate m, tchunkptr t) { + tchunkptr head = 0; + tchunkptr u = t; + bindex_t tindex = t->index; + size_t tsize = chunksize(t); + bindex_t idx; + compute_tree_index(tsize, idx); + assert(tindex == idx); + assert(tsize >= MIN_LARGE_SIZE); + assert(tsize >= minsize_for_tree_index(idx)); + assert((idx == NTREEBINS-1) || (tsize < minsize_for_tree_index((idx+1)))); + + do { /* traverse through chain of same-sized nodes */ + do_check_any_chunk(m, ((mchunkptr)u)); + assert(u->index == tindex); + assert(chunksize(u) == tsize); + assert(!is_inuse(u)); + assert(!next_pinuse(u)); + assert(u->fd->bk == u); + assert(u->bk->fd == u); + if (u->parent == 0) { + assert(u->child[0] == 0); + assert(u->child[1] == 0); + } + else { + assert(head == 0); /* only one node on chain has parent */ + head = u; + assert(u->parent != u); + assert (u->parent->child[0] == u || + u->parent->child[1] == u || + *((tbinptr*)(u->parent)) == u); + if (u->child[0] != 0) { + assert(u->child[0]->parent == u); + assert(u->child[0] != u); + do_check_tree(m, u->child[0]); + } + if (u->child[1] != 0) { + assert(u->child[1]->parent == u); + assert(u->child[1] != u); + do_check_tree(m, u->child[1]); + } + if (u->child[0] != 0 && u->child[1] != 0) { + assert(chunksize(u->child[0]) < chunksize(u->child[1])); + } + } + u = u->fd; + } while (u != t); + assert(head != 0); +} + +/* Check all the chunks in a treebin. */ +static void do_check_treebin(mstate m, bindex_t i) { + tbinptr* tb = treebin_at(m, i); + tchunkptr t = *tb; + int empty = (m->treemap & (1U << i)) == 0; + if (t == 0) + assert(empty); + if (!empty) + do_check_tree(m, t); +} + +/* Check all the chunks in a smallbin. */ +static void do_check_smallbin(mstate m, bindex_t i) { + sbinptr b = smallbin_at(m, i); + mchunkptr p = b->bk; + unsigned int empty = (m->smallmap & (1U << i)) == 0; + if (p == b) + assert(empty); + if (!empty) { + for (; p != b; p = p->bk) { + size_t size = chunksize(p); + mchunkptr q; + /* each chunk claims to be free */ + do_check_free_chunk(m, p); + /* chunk belongs in bin */ + assert(small_index(size) == i); + assert(p->bk == b || chunksize(p->bk) == chunksize(p)); + /* chunk is followed by an inuse chunk */ + q = next_chunk(p); + if (q->head != FENCEPOST_HEAD) + do_check_inuse_chunk(m, q); + } + } +} + +/* Find x in a bin. Used in other check functions. */ +static int bin_find(mstate m, mchunkptr x) { + size_t size = chunksize(x); + if (is_small(size)) { + bindex_t sidx = small_index(size); + sbinptr b = smallbin_at(m, sidx); + if (smallmap_is_marked(m, sidx)) { + mchunkptr p = b; + do { + if (p == x) + return 1; + } while ((p = p->fd) != b); + } + } + else { + bindex_t tidx; + compute_tree_index(size, tidx); + if (treemap_is_marked(m, tidx)) { + tchunkptr t = *treebin_at(m, tidx); + size_t sizebits = size << leftshift_for_tree_index(tidx); + while (t != 0 && chunksize(t) != size) { + t = t->child[(sizebits >> (SIZE_T_BITSIZE-SIZE_T_ONE)) & 1]; + sizebits <<= 1; + } + if (t != 0) { + tchunkptr u = t; + do { + if (u == (tchunkptr)x) + return 1; + } while ((u = u->fd) != t); + } + } + } + return 0; +} + +/* Traverse each chunk and check it; return total */ +static size_t traverse_and_check(mstate m) { + size_t sum = 0; + if (is_initialized(m)) { + msegmentptr s = &m->seg; + sum += m->topsize + TOP_FOOT_SIZE; + while (s != 0) { + mchunkptr q = align_as_chunk(s->base); + mchunkptr lastq = 0; + assert(pinuse(q)); + while (segment_holds(s, q) && + q != m->top && q->head != FENCEPOST_HEAD) { + sum += chunksize(q); + if (is_inuse(q)) { + assert(!bin_find(m, q)); + do_check_inuse_chunk(m, q); + } + else { + assert(q == m->dv || bin_find(m, q)); + assert(lastq == 0 || is_inuse(lastq)); /* Not 2 consecutive free */ + do_check_free_chunk(m, q); + } + lastq = q; + q = next_chunk(q); + } + s = s->next; + } + } + return sum; +} + + +/* Check all properties of malloc_state. */ +static void do_check_malloc_state(mstate m) { + bindex_t i; + size_t total; + /* check bins */ + for (i = 0; i < NSMALLBINS; ++i) + do_check_smallbin(m, i); + for (i = 0; i < NTREEBINS; ++i) + do_check_treebin(m, i); + + if (m->dvsize != 0) { /* check dv chunk */ + do_check_any_chunk(m, m->dv); + assert(m->dvsize == chunksize(m->dv)); + assert(m->dvsize >= MIN_CHUNK_SIZE); + assert(bin_find(m, m->dv) == 0); + } + + if (m->top != 0) { /* check top chunk */ + do_check_top_chunk(m, m->top); + /*assert(m->topsize == chunksize(m->top)); redundant */ + assert(m->topsize > 0); + assert(bin_find(m, m->top) == 0); + } + + total = traverse_and_check(m); + assert(total <= m->footprint); + assert(m->footprint <= m->max_footprint); +} +#endif /* DEBUG */ + +/* ----------------------------- statistics ------------------------------ */ + +#if !NO_MALLINFO +static struct mallinfo internal_mallinfo(mstate m) { + struct mallinfo nm = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; + ensure_initialization(); + if (!PREACTION(m)) { + check_malloc_state(m); + if (is_initialized(m)) { + size_t nfree = SIZE_T_ONE; /* top always free */ + size_t mfree = m->topsize + TOP_FOOT_SIZE; + size_t sum = mfree; + msegmentptr s = &m->seg; + while (s != 0) { + mchunkptr q = align_as_chunk(s->base); + while (segment_holds(s, q) && + q != m->top && q->head != FENCEPOST_HEAD) { + size_t sz = chunksize(q); + sum += sz; + if (!is_inuse(q)) { + mfree += sz; + ++nfree; + } + q = next_chunk(q); + } + s = s->next; + } + + nm.arena = sum; + nm.ordblks = nfree; + nm.hblkhd = m->footprint - sum; + nm.usmblks = m->max_footprint; + nm.uordblks = m->footprint - mfree; + nm.fordblks = mfree; + nm.keepcost = m->topsize; + } + + POSTACTION(m); + } + return nm; +} +#endif /* !NO_MALLINFO */ + +#if !NO_MALLOC_STATS +static void internal_malloc_stats(mstate m) { + ensure_initialization(); + if (!PREACTION(m)) { + size_t maxfp = 0; + size_t fp = 0; + size_t used = 0; + check_malloc_state(m); + if (is_initialized(m)) { + msegmentptr s = &m->seg; + maxfp = m->max_footprint; + fp = m->footprint; + used = fp - (m->topsize + TOP_FOOT_SIZE); + + while (s != 0) { + mchunkptr q = align_as_chunk(s->base); + while (segment_holds(s, q) && + q != m->top && q->head != FENCEPOST_HEAD) { + if (!is_inuse(q)) + used -= chunksize(q); + q = next_chunk(q); + } + s = s->next; + } + } + POSTACTION(m); /* drop lock */ + fprintf(stderr, "max system bytes = %10lu\n", (unsigned long)(maxfp)); + fprintf(stderr, "system bytes = %10lu\n", (unsigned long)(fp)); + fprintf(stderr, "in use bytes = %10lu\n", (unsigned long)(used)); + } +} +#endif /* NO_MALLOC_STATS */ + +/* ----------------------- Operations on smallbins ----------------------- */ + +/* + Various forms of linking and unlinking are defined as macros. Even + the ones for trees, which are very long but have very short typical + paths. This is ugly but reduces reliance on inlining support of + compilers. +*/ + +/* Link a free chunk into a smallbin */ +#define insert_small_chunk(M, P, S) {\ + bindex_t I = small_index(S);\ + mchunkptr B = smallbin_at(M, I);\ + mchunkptr F = B;\ + assert(S >= MIN_CHUNK_SIZE);\ + if (!smallmap_is_marked(M, I))\ + mark_smallmap(M, I);\ + else if (RTCHECK(ok_address(M, B->fd)))\ + F = B->fd;\ + else {\ + CORRUPTION_ERROR_ACTION(M);\ + }\ + B->fd = P;\ + F->bk = P;\ + P->fd = F;\ + P->bk = B;\ +} + +/* Unlink a chunk from a smallbin */ +#define unlink_small_chunk(M, P, S) {\ + mchunkptr F = P->fd;\ + mchunkptr B = P->bk;\ + bindex_t I = small_index(S);\ + assert(P != B);\ + assert(P != F);\ + assert(chunksize(P) == small_index2size(I));\ + if (RTCHECK(F == smallbin_at(M,I) || (ok_address(M, F) && F->bk == P))) { \ + if (B == F) {\ + clear_smallmap(M, I);\ + }\ + else if (RTCHECK(B == smallbin_at(M,I) ||\ + (ok_address(M, B) && B->fd == P))) {\ + F->bk = B;\ + B->fd = F;\ + }\ + else {\ + CORRUPTION_ERROR_ACTION(M);\ + }\ + }\ + else {\ + CORRUPTION_ERROR_ACTION(M);\ + }\ +} + +/* Unlink the first chunk from a smallbin */ +#define unlink_first_small_chunk(M, B, P, I) {\ + mchunkptr F = P->fd;\ + assert(P != B);\ + assert(P != F);\ + assert(chunksize(P) == small_index2size(I));\ + if (B == F) {\ + clear_smallmap(M, I);\ + }\ + else if (RTCHECK(ok_address(M, F) && F->bk == P)) {\ + F->bk = B;\ + B->fd = F;\ + }\ + else {\ + CORRUPTION_ERROR_ACTION(M);\ + }\ +} + +/* Replace dv node, binning the old one */ +/* Used only when dvsize known to be small */ +#define replace_dv(M, P, S) {\ + size_t DVS = M->dvsize;\ + assert(is_small(DVS));\ + if (DVS != 0) {\ + mchunkptr DV = M->dv;\ + insert_small_chunk(M, DV, DVS);\ + }\ + M->dvsize = S;\ + M->dv = P;\ +} + +/* ------------------------- Operations on trees ------------------------- */ + +/* Insert chunk into tree */ +#define insert_large_chunk(M, X, S) {\ + tbinptr* H;\ + bindex_t I;\ + compute_tree_index(S, I);\ + H = treebin_at(M, I);\ + X->index = I;\ + X->child[0] = X->child[1] = 0;\ + if (!treemap_is_marked(M, I)) {\ + mark_treemap(M, I);\ + *H = X;\ + X->parent = (tchunkptr)H;\ + X->fd = X->bk = X;\ + }\ + else {\ + tchunkptr T = *H;\ + size_t K = S << leftshift_for_tree_index(I);\ + for (;;) {\ + if (chunksize(T) != S) {\ + tchunkptr* C = &(T->child[(K >> (SIZE_T_BITSIZE-SIZE_T_ONE)) & 1]);\ + K <<= 1;\ + if (*C != 0)\ + T = *C;\ + else if (RTCHECK(ok_address(M, C))) {\ + *C = X;\ + X->parent = T;\ + X->fd = X->bk = X;\ + break;\ + }\ + else {\ + CORRUPTION_ERROR_ACTION(M);\ + break;\ + }\ + }\ + else {\ + tchunkptr F = T->fd;\ + if (RTCHECK(ok_address(M, T) && ok_address(M, F))) {\ + T->fd = F->bk = X;\ + X->fd = F;\ + X->bk = T;\ + X->parent = 0;\ + break;\ + }\ + else {\ + CORRUPTION_ERROR_ACTION(M);\ + break;\ + }\ + }\ + }\ + }\ +} + +/* + Unlink steps: + + 1. If x is a chained node, unlink it from its same-sized fd/bk links + and choose its bk node as its replacement. + 2. If x was the last node of its size, but not a leaf node, it must + be replaced with a leaf node (not merely one with an open left or + right), to make sure that lefts and rights of descendents + correspond properly to bit masks. We use the rightmost descendent + of x. We could use any other leaf, but this is easy to locate and + tends to counteract removal of leftmosts elsewhere, and so keeps + paths shorter than minimally guaranteed. This doesn't loop much + because on average a node in a tree is near the bottom. + 3. If x is the base of a chain (i.e., has parent links) relink + x's parent and children to x's replacement (or null if none). +*/ + +#define unlink_large_chunk(M, X) {\ + tchunkptr XP = X->parent;\ + tchunkptr R;\ + if (X->bk != X) {\ + tchunkptr F = X->fd;\ + R = X->bk;\ + if (RTCHECK(ok_address(M, F) && F->bk == X && R->fd == X)) {\ + F->bk = R;\ + R->fd = F;\ + }\ + else {\ + CORRUPTION_ERROR_ACTION(M);\ + }\ + }\ + else {\ + tchunkptr* RP;\ + if (((R = *(RP = &(X->child[1]))) != 0) ||\ + ((R = *(RP = &(X->child[0]))) != 0)) {\ + tchunkptr* CP;\ + while ((*(CP = &(R->child[1])) != 0) ||\ + (*(CP = &(R->child[0])) != 0)) {\ + R = *(RP = CP);\ + }\ + if (RTCHECK(ok_address(M, RP)))\ + *RP = 0;\ + else {\ + CORRUPTION_ERROR_ACTION(M);\ + }\ + }\ + }\ + if (XP != 0) {\ + tbinptr* H = treebin_at(M, X->index);\ + if (X == *H) {\ + if ((*H = R) == 0) \ + clear_treemap(M, X->index);\ + }\ + else if (RTCHECK(ok_address(M, XP))) {\ + if (XP->child[0] == X) \ + XP->child[0] = R;\ + else \ + XP->child[1] = R;\ + }\ + else\ + CORRUPTION_ERROR_ACTION(M);\ + if (R != 0) {\ + if (RTCHECK(ok_address(M, R))) {\ + tchunkptr C0, C1;\ + R->parent = XP;\ + if ((C0 = X->child[0]) != 0) {\ + if (RTCHECK(ok_address(M, C0))) {\ + R->child[0] = C0;\ + C0->parent = R;\ + }\ + else\ + CORRUPTION_ERROR_ACTION(M);\ + }\ + if ((C1 = X->child[1]) != 0) {\ + if (RTCHECK(ok_address(M, C1))) {\ + R->child[1] = C1;\ + C1->parent = R;\ + }\ + else\ + CORRUPTION_ERROR_ACTION(M);\ + }\ + }\ + else\ + CORRUPTION_ERROR_ACTION(M);\ + }\ + }\ +} + +/* Relays to large vs small bin operations */ + +#define insert_chunk(M, P, S)\ + if (is_small(S)) insert_small_chunk(M, P, S)\ + else { tchunkptr TP = (tchunkptr)(P); insert_large_chunk(M, TP, S); } + +#define unlink_chunk(M, P, S)\ + if (is_small(S)) unlink_small_chunk(M, P, S)\ + else { tchunkptr TP = (tchunkptr)(P); unlink_large_chunk(M, TP); } + + +/* Relays to internal calls to malloc/free from realloc, memalign etc */ + +#if ONLY_MSPACES +#define internal_malloc(m, b) mspace_malloc(m, b) +#define internal_free(m, mem) mspace_free(m,mem); +#else /* ONLY_MSPACES */ +#if MSPACES +#define internal_malloc(m, b)\ + ((m == gm)? dlmalloc(b) : mspace_malloc(m, b)) +#define internal_free(m, mem)\ + if (m == gm) dlfree(mem); else mspace_free(m,mem); +#else /* MSPACES */ +#define internal_malloc(m, b) dlmalloc(b) +#define internal_free(m, mem) dlfree(mem) +#endif /* MSPACES */ +#endif /* ONLY_MSPACES */ + +/* ----------------------- Direct-mmapping chunks ----------------------- */ + +/* + Directly mmapped chunks are set up with an offset to the start of + the mmapped region stored in the prev_foot field of the chunk. This + allows reconstruction of the required argument to MUNMAP when freed, + and also allows adjustment of the returned chunk to meet alignment + requirements (especially in memalign). +*/ + +/* Malloc using mmap */ +static void* mmap_alloc(mstate m, size_t nb) { + size_t mmsize = mmap_align(nb + SIX_SIZE_T_SIZES + CHUNK_ALIGN_MASK); + if (m->footprint_limit != 0) { + size_t fp = m->footprint + mmsize; + if (fp <= m->footprint || fp > m->footprint_limit) + return 0; + } + if (mmsize > nb) { /* Check for wrap around 0 */ + char* mm = (char*)(CALL_DIRECT_MMAP(mmsize)); + if (mm != CMFAIL) { + size_t offset = align_offset(chunk2mem(mm)); + size_t psize = mmsize - offset - MMAP_FOOT_PAD; + mchunkptr p = (mchunkptr)(mm + offset); + p->prev_foot = offset; + p->head = psize; + mark_inuse_foot(m, p, psize); + chunk_plus_offset(p, psize)->head = FENCEPOST_HEAD; + chunk_plus_offset(p, psize+SIZE_T_SIZE)->head = 0; + + if (m->least_addr == 0 || mm < m->least_addr) + m->least_addr = mm; + if ((m->footprint += mmsize) > m->max_footprint) + m->max_footprint = m->footprint; + assert(is_aligned(chunk2mem(p))); + check_mmapped_chunk(m, p); + return chunk2mem(p); + } + } + return 0; +} + +/* Realloc using mmap */ +static mchunkptr mmap_resize(mstate m, mchunkptr oldp, size_t nb, int flags) { + size_t oldsize = chunksize(oldp); + (void)flags; /* placate people compiling -Wunused */ + if (is_small(nb)) /* Can't shrink mmap regions below small size */ + return 0; + /* Keep old chunk if big enough but not too big */ + if (oldsize >= nb + SIZE_T_SIZE && + (oldsize - nb) <= (mparams.granularity << 1)) + return oldp; + else { + size_t offset = oldp->prev_foot; + size_t oldmmsize = oldsize + offset + MMAP_FOOT_PAD; + size_t newmmsize = mmap_align(nb + SIX_SIZE_T_SIZES + CHUNK_ALIGN_MASK); + char* cp = (char*)CALL_MREMAP((char*)oldp - offset, + oldmmsize, newmmsize, flags); + if (cp != CMFAIL) { + mchunkptr newp = (mchunkptr)(cp + offset); + size_t psize = newmmsize - offset - MMAP_FOOT_PAD; + newp->head = psize; + mark_inuse_foot(m, newp, psize); + chunk_plus_offset(newp, psize)->head = FENCEPOST_HEAD; + chunk_plus_offset(newp, psize+SIZE_T_SIZE)->head = 0; + + if (cp < m->least_addr) + m->least_addr = cp; + if ((m->footprint += newmmsize - oldmmsize) > m->max_footprint) + m->max_footprint = m->footprint; + check_mmapped_chunk(m, newp); + return newp; + } + } + return 0; +} + + +/* -------------------------- mspace management -------------------------- */ + +/* Initialize top chunk and its size */ +static void init_top(mstate m, mchunkptr p, size_t psize) { + /* Ensure alignment */ + size_t offset = align_offset(chunk2mem(p)); + p = (mchunkptr)((char*)p + offset); + psize -= offset; + + m->top = p; + m->topsize = psize; + p->head = psize | PINUSE_BIT; + /* set size of fake trailing chunk holding overhead space only once */ + chunk_plus_offset(p, psize)->head = TOP_FOOT_SIZE; + m->trim_check = mparams.trim_threshold; /* reset on each update */ +} + +/* Initialize bins for a new mstate that is otherwise zeroed out */ +static void init_bins(mstate m) { + /* Establish circular links for smallbins */ + bindex_t i; + for (i = 0; i < NSMALLBINS; ++i) { + sbinptr bin = smallbin_at(m,i); + bin->fd = bin->bk = bin; + } +} + +#if PROCEED_ON_ERROR + +/* default corruption action */ +static void reset_on_error(mstate m) { + int i; + ++malloc_corruption_error_count; + /* Reinitialize fields to forget about all memory */ + m->smallmap = m->treemap = 0; + m->dvsize = m->topsize = 0; + m->seg.base = 0; + m->seg.size = 0; + m->seg.next = 0; + m->top = m->dv = 0; + for (i = 0; i < NTREEBINS; ++i) + *treebin_at(m, i) = 0; + init_bins(m); +} +#endif /* PROCEED_ON_ERROR */ + +/* Allocate chunk and prepend remainder with chunk in successor base. */ +static void* prepend_alloc(mstate m, char* newbase, char* oldbase, + size_t nb) { + mchunkptr p = align_as_chunk(newbase); + mchunkptr oldfirst = align_as_chunk(oldbase); + size_t psize = (char*)oldfirst - (char*)p; + mchunkptr q = chunk_plus_offset(p, nb); + size_t qsize = psize - nb; + set_size_and_pinuse_of_inuse_chunk(m, p, nb); + + assert((char*)oldfirst > (char*)q); + assert(pinuse(oldfirst)); + assert(qsize >= MIN_CHUNK_SIZE); + + /* consolidate remainder with first chunk of old base */ + if (oldfirst == m->top) { + size_t tsize = m->topsize += qsize; + m->top = q; + q->head = tsize | PINUSE_BIT; + check_top_chunk(m, q); + } + else if (oldfirst == m->dv) { + size_t dsize = m->dvsize += qsize; + m->dv = q; + set_size_and_pinuse_of_free_chunk(q, dsize); + } + else { + if (!is_inuse(oldfirst)) { + size_t nsize = chunksize(oldfirst); + unlink_chunk(m, oldfirst, nsize); + oldfirst = chunk_plus_offset(oldfirst, nsize); + qsize += nsize; + } + set_free_with_pinuse(q, qsize, oldfirst); + insert_chunk(m, q, qsize); + check_free_chunk(m, q); + } + + check_malloced_chunk(m, chunk2mem(p), nb); + return chunk2mem(p); +} + +/* Add a segment to hold a new noncontiguous region */ +static void add_segment(mstate m, char* tbase, size_t tsize, flag_t mmapped) { + /* Determine locations and sizes of segment, fenceposts, old top */ + char* old_top = (char*)m->top; + msegmentptr oldsp = segment_holding(m, old_top); + char* old_end = oldsp->base + oldsp->size; + size_t ssize = pad_request(sizeof(struct malloc_segment)); + char* rawsp = old_end - (ssize + FOUR_SIZE_T_SIZES + CHUNK_ALIGN_MASK); + size_t offset = align_offset(chunk2mem(rawsp)); + char* asp = rawsp + offset; + char* csp = (asp < (old_top + MIN_CHUNK_SIZE))? old_top : asp; + mchunkptr sp = (mchunkptr)csp; + msegmentptr ss = (msegmentptr)(chunk2mem(sp)); + mchunkptr tnext = chunk_plus_offset(sp, ssize); + mchunkptr p = tnext; + int nfences = 0; + + /* reset top to new space */ + init_top(m, (mchunkptr)tbase, tsize - TOP_FOOT_SIZE); + + /* Set up segment record */ + assert(is_aligned(ss)); + set_size_and_pinuse_of_inuse_chunk(m, sp, ssize); + *ss = m->seg; /* Push current record */ + m->seg.base = tbase; + m->seg.size = tsize; + m->seg.sflags = mmapped; + m->seg.next = ss; + + /* Insert trailing fenceposts */ + for (;;) { + mchunkptr nextp = chunk_plus_offset(p, SIZE_T_SIZE); + p->head = FENCEPOST_HEAD; + ++nfences; + if ((char*)(&(nextp->head)) < old_end) + p = nextp; + else + break; + } + assert(nfences >= 2); + + /* Insert the rest of old top into a bin as an ordinary free chunk */ + if (csp != old_top) { + mchunkptr q = (mchunkptr)old_top; + size_t psize = csp - old_top; + mchunkptr tn = chunk_plus_offset(q, psize); + set_free_with_pinuse(q, psize, tn); + insert_chunk(m, q, psize); + } + + check_top_chunk(m, m->top); +} + +/* -------------------------- System allocation -------------------------- */ + +/* Get memory from system using MORECORE or MMAP */ +static void* sys_alloc(mstate m, size_t nb) { + char* tbase = CMFAIL; + size_t tsize = 0; + flag_t mmap_flag = 0; + size_t asize; /* allocation size */ + + ensure_initialization(); + + /* Directly map large chunks, but only if already initialized */ + if (use_mmap(m) && nb >= mparams.mmap_threshold && m->topsize != 0) { + void* mem = mmap_alloc(m, nb); + if (mem != 0) + return mem; + } + + asize = granularity_align(nb + SYS_ALLOC_PADDING); + if (asize <= nb) + return 0; /* wraparound */ + if (m->footprint_limit != 0) { + size_t fp = m->footprint + asize; + if (fp <= m->footprint || fp > m->footprint_limit) + return 0; + } + + /* + Try getting memory in any of three ways (in most-preferred to + least-preferred order): + 1. A call to MORECORE that can normally contiguously extend memory. + (disabled if not MORECORE_CONTIGUOUS or not HAVE_MORECORE or + or main space is mmapped or a previous contiguous call failed) + 2. A call to MMAP new space (disabled if not HAVE_MMAP). + Note that under the default settings, if MORECORE is unable to + fulfill a request, and HAVE_MMAP is true, then mmap is + used as a noncontiguous system allocator. This is a useful backup + strategy for systems with holes in address spaces -- in this case + sbrk cannot contiguously expand the heap, but mmap may be able to + find space. + 3. A call to MORECORE that cannot usually contiguously extend memory. + (disabled if not HAVE_MORECORE) + + In all cases, we need to request enough bytes from system to ensure + we can malloc nb bytes upon success, so pad with enough space for + top_foot, plus alignment-pad to make sure we don't lose bytes if + not on boundary, and round this up to a granularity unit. + */ + + if (MORECORE_CONTIGUOUS && !use_noncontiguous(m)) { + char* br = CMFAIL; + size_t ssize = asize; /* sbrk call size */ + msegmentptr ss = (m->top == 0)? 0 : segment_holding(m, (char*)m->top); + ACQUIRE_MALLOC_GLOBAL_LOCK(); + + if (ss == 0) { /* First time through or recovery */ + char* base = (char*)CALL_MORECORE(0); + if (base != CMFAIL) { + size_t fp; + /* Adjust to end on a page boundary */ + if (!is_page_aligned(base)) + ssize += (page_align((size_t)base) - (size_t)base); + fp = m->footprint + ssize; /* recheck limits */ + if (ssize > nb && ssize < HALF_MAX_SIZE_T && + (m->footprint_limit == 0 || + (fp > m->footprint && fp <= m->footprint_limit)) && + (br = (char*)(CALL_MORECORE(ssize))) == base) { + tbase = base; + tsize = ssize; + } + } + } + else { + /* Subtract out existing available top space from MORECORE request. */ + ssize = granularity_align(nb - m->topsize + SYS_ALLOC_PADDING); + /* Use mem here only if it did continuously extend old space */ + if (ssize < HALF_MAX_SIZE_T && + (br = (char*)(CALL_MORECORE(ssize))) == ss->base+ss->size) { + tbase = br; + tsize = ssize; + } + } + + if (tbase == CMFAIL) { /* Cope with partial failure */ + if (br != CMFAIL) { /* Try to use/extend the space we did get */ + if (ssize < HALF_MAX_SIZE_T && + ssize < nb + SYS_ALLOC_PADDING) { + size_t esize = granularity_align(nb + SYS_ALLOC_PADDING - ssize); + if (esize < HALF_MAX_SIZE_T) { + char* end = (char*)CALL_MORECORE(esize); + if (end != CMFAIL) + ssize += esize; + else { /* Can't use; try to release */ + (void) CALL_MORECORE(-ssize); + br = CMFAIL; + } + } + } + } + if (br != CMFAIL) { /* Use the space we did get */ + tbase = br; + tsize = ssize; + } + else + disable_contiguous(m); /* Don't try contiguous path in the future */ + } + + RELEASE_MALLOC_GLOBAL_LOCK(); + } + + if (HAVE_MMAP && tbase == CMFAIL) { /* Try MMAP */ + char* mp = (char*)(CALL_MMAP(asize)); + if (mp != CMFAIL) { + tbase = mp; + tsize = asize; + mmap_flag = USE_MMAP_BIT; + } + } + + if (HAVE_MORECORE && tbase == CMFAIL) { /* Try noncontiguous MORECORE */ + if (asize < HALF_MAX_SIZE_T) { + char* br = CMFAIL; + char* end = CMFAIL; + ACQUIRE_MALLOC_GLOBAL_LOCK(); + br = (char*)(CALL_MORECORE(asize)); + end = (char*)(CALL_MORECORE(0)); + RELEASE_MALLOC_GLOBAL_LOCK(); + if (br != CMFAIL && end != CMFAIL && br < end) { + size_t ssize = end - br; + if (ssize > nb + TOP_FOOT_SIZE) { + tbase = br; + tsize = ssize; + } + } + } + } + + if (tbase != CMFAIL) { + + if ((m->footprint += tsize) > m->max_footprint) + m->max_footprint = m->footprint; + + if (!is_initialized(m)) { /* first-time initialization */ + if (m->least_addr == 0 || tbase < m->least_addr) + m->least_addr = tbase; + m->seg.base = tbase; + m->seg.size = tsize; + m->seg.sflags = mmap_flag; + m->magic = mparams.magic; + m->release_checks = MAX_RELEASE_CHECK_RATE; + init_bins(m); +#if !ONLY_MSPACES + if (is_global(m)) + init_top(m, (mchunkptr)tbase, tsize - TOP_FOOT_SIZE); + else +#endif + { + /* Offset top by embedded malloc_state */ + mchunkptr mn = next_chunk(mem2chunk(m)); + init_top(m, mn, (size_t)((tbase + tsize) - (char*)mn) -TOP_FOOT_SIZE); + } + } + + else { + /* Try to merge with an existing segment */ + msegmentptr sp = &m->seg; + /* Only consider most recent segment if traversal suppressed */ + while (sp != 0 && tbase != sp->base + sp->size) + sp = (NO_SEGMENT_TRAVERSAL) ? 0 : sp->next; + if (sp != 0 && + !is_extern_segment(sp) && + (sp->sflags & USE_MMAP_BIT) == mmap_flag && + segment_holds(sp, m->top)) { /* append */ + sp->size += tsize; + init_top(m, m->top, m->topsize + tsize); + } + else { + if (tbase < m->least_addr) + m->least_addr = tbase; + sp = &m->seg; + while (sp != 0 && sp->base != tbase + tsize) + sp = (NO_SEGMENT_TRAVERSAL) ? 0 : sp->next; + if (sp != 0 && + !is_extern_segment(sp) && + (sp->sflags & USE_MMAP_BIT) == mmap_flag) { + char* oldbase = sp->base; + sp->base = tbase; + sp->size += tsize; + return prepend_alloc(m, tbase, oldbase, nb); + } + else + add_segment(m, tbase, tsize, mmap_flag); + } + } + + if (nb < m->topsize) { /* Allocate from new or extended top space */ + size_t rsize = m->topsize -= nb; + mchunkptr p = m->top; + mchunkptr r = m->top = chunk_plus_offset(p, nb); + r->head = rsize | PINUSE_BIT; + set_size_and_pinuse_of_inuse_chunk(m, p, nb); + check_top_chunk(m, m->top); + check_malloced_chunk(m, chunk2mem(p), nb); + return chunk2mem(p); + } + } + + MALLOC_FAILURE_ACTION; + return 0; +} + +/* ----------------------- system deallocation -------------------------- */ + +/* Unmap and unlink any mmapped segments that don't contain used chunks */ +static size_t release_unused_segments(mstate m) { + size_t released = 0; + int nsegs = 0; + msegmentptr pred = &m->seg; + msegmentptr sp = pred->next; + while (sp != 0) { + char* base = sp->base; + size_t size = sp->size; + msegmentptr next = sp->next; + ++nsegs; + if (is_mmapped_segment(sp) && !is_extern_segment(sp)) { + mchunkptr p = align_as_chunk(base); + size_t psize = chunksize(p); + /* Can unmap if first chunk holds entire segment and not pinned */ + if (!is_inuse(p) && (char*)p + psize >= base + size - TOP_FOOT_SIZE) { + tchunkptr tp = (tchunkptr)p; + assert(segment_holds(sp, (char*)sp)); + if (p == m->dv) { + m->dv = 0; + m->dvsize = 0; + } + else { + unlink_large_chunk(m, tp); + } + if (CALL_MUNMAP(base, size) == 0) { + released += size; + m->footprint -= size; + /* unlink obsoleted record */ + sp = pred; + sp->next = next; + } + else { /* back out if cannot unmap */ + insert_large_chunk(m, tp, psize); + } + } + } + if (NO_SEGMENT_TRAVERSAL) /* scan only first segment */ + break; + pred = sp; + sp = next; + } + /* Reset check counter */ + m->release_checks = (((size_t) nsegs > (size_t) MAX_RELEASE_CHECK_RATE)? + (size_t) nsegs : (size_t) MAX_RELEASE_CHECK_RATE); + return released; +} + +static int sys_trim(mstate m, size_t pad) { + size_t released = 0; + ensure_initialization(); + if (pad < MAX_REQUEST && is_initialized(m)) { + pad += TOP_FOOT_SIZE; /* ensure enough room for segment overhead */ + + if (m->topsize > pad) { + /* Shrink top space in granularity-size units, keeping at least one */ + size_t unit = mparams.granularity; + size_t extra = ((m->topsize - pad + (unit - SIZE_T_ONE)) / unit - + SIZE_T_ONE) * unit; + msegmentptr sp = segment_holding(m, (char*)m->top); + + if (!is_extern_segment(sp)) { + if (is_mmapped_segment(sp)) { + if (HAVE_MMAP && + sp->size >= extra && + !has_segment_link(m, sp)) { /* can't shrink if pinned */ + size_t newsize = sp->size - extra; + (void)newsize; /* placate people compiling -Wunused-variable */ + /* Prefer mremap, fall back to munmap */ + if ((CALL_MREMAP(sp->base, sp->size, newsize, 0) != MFAIL) || + (CALL_MUNMAP(sp->base + newsize, extra) == 0)) { + released = extra; + } + } + } + else if (HAVE_MORECORE) { + if (extra >= HALF_MAX_SIZE_T) /* Avoid wrapping negative */ + extra = (HALF_MAX_SIZE_T) + SIZE_T_ONE - unit; + ACQUIRE_MALLOC_GLOBAL_LOCK(); + { + /* Make sure end of memory is where we last set it. */ + char* old_br = (char*)(CALL_MORECORE(0)); + if (old_br == sp->base + sp->size) { + char* rel_br = (char*)(CALL_MORECORE(-extra)); + char* new_br = (char*)(CALL_MORECORE(0)); + if (rel_br != CMFAIL && new_br < old_br) + released = old_br - new_br; + } + } + RELEASE_MALLOC_GLOBAL_LOCK(); + } + } + + if (released != 0) { + sp->size -= released; + m->footprint -= released; + init_top(m, m->top, m->topsize - released); + check_top_chunk(m, m->top); + } + } + + /* Unmap any unused mmapped segments */ + if (HAVE_MMAP) + released += release_unused_segments(m); + + /* On failure, disable autotrim to avoid repeated failed future calls */ + if (released == 0 && m->topsize > m->trim_check) + m->trim_check = MAX_SIZE_T; + } + + return (released != 0)? 1 : 0; +} + +/* Consolidate and bin a chunk. Differs from exported versions + of free mainly in that the chunk need not be marked as inuse. +*/ +static void dispose_chunk(mstate m, mchunkptr p, size_t psize) { + mchunkptr next = chunk_plus_offset(p, psize); + if (!pinuse(p)) { + mchunkptr prev; + size_t prevsize = p->prev_foot; + if (is_mmapped(p)) { + psize += prevsize + MMAP_FOOT_PAD; + if (CALL_MUNMAP((char*)p - prevsize, psize) == 0) + m->footprint -= psize; + return; + } + prev = chunk_minus_offset(p, prevsize); + psize += prevsize; + p = prev; + if (RTCHECK(ok_address(m, prev))) { /* consolidate backward */ + if (p != m->dv) { + unlink_chunk(m, p, prevsize); + } + else if ((next->head & INUSE_BITS) == INUSE_BITS) { + m->dvsize = psize; + set_free_with_pinuse(p, psize, next); + return; + } + } + else { + CORRUPTION_ERROR_ACTION(m); + return; + } + } + if (RTCHECK(ok_address(m, next))) { + if (!cinuse(next)) { /* consolidate forward */ + if (next == m->top) { + size_t tsize = m->topsize += psize; + m->top = p; + p->head = tsize | PINUSE_BIT; + if (p == m->dv) { + m->dv = 0; + m->dvsize = 0; + } + return; + } + else if (next == m->dv) { + size_t dsize = m->dvsize += psize; + m->dv = p; + set_size_and_pinuse_of_free_chunk(p, dsize); + return; + } + else { + size_t nsize = chunksize(next); + psize += nsize; + unlink_chunk(m, next, nsize); + set_size_and_pinuse_of_free_chunk(p, psize); + if (p == m->dv) { + m->dvsize = psize; + return; + } + } + } + else { + set_free_with_pinuse(p, psize, next); + } + insert_chunk(m, p, psize); + } + else { + CORRUPTION_ERROR_ACTION(m); + } +} + +/* ---------------------------- malloc --------------------------- */ + +/* allocate a large request from the best fitting chunk in a treebin */ +static void* tmalloc_large(mstate m, size_t nb) { + tchunkptr v = 0; + size_t rsize = -nb; /* Unsigned negation */ + tchunkptr t; + bindex_t idx; + compute_tree_index(nb, idx); + if ((t = *treebin_at(m, idx)) != 0) { + /* Traverse tree for this bin looking for node with size == nb */ + size_t sizebits = nb << leftshift_for_tree_index(idx); + tchunkptr rst = 0; /* The deepest untaken right subtree */ + for (;;) { + tchunkptr rt; + size_t trem = chunksize(t) - nb; + if (trem < rsize) { + v = t; + if ((rsize = trem) == 0) + break; + } + rt = t->child[1]; + t = t->child[(sizebits >> (SIZE_T_BITSIZE-SIZE_T_ONE)) & 1]; + if (rt != 0 && rt != t) + rst = rt; + if (t == 0) { + t = rst; /* set t to least subtree holding sizes > nb */ + break; + } + sizebits <<= 1; + } + } + if (t == 0 && v == 0) { /* set t to root of next non-empty treebin */ + binmap_t leftbits = left_bits(idx2bit(idx)) & m->treemap; + if (leftbits != 0) { + bindex_t i; + binmap_t leastbit = least_bit(leftbits); + compute_bit2idx(leastbit, i); + t = *treebin_at(m, i); + } + } + + while (t != 0) { /* find smallest of tree or subtree */ + size_t trem = chunksize(t) - nb; + if (trem < rsize) { + rsize = trem; + v = t; + } + t = leftmost_child(t); + } + + /* If dv is a better fit, return 0 so malloc will use it */ + if (v != 0 && rsize < (size_t)(m->dvsize - nb)) { + if (RTCHECK(ok_address(m, v))) { /* split */ + mchunkptr r = chunk_plus_offset(v, nb); + assert(chunksize(v) == rsize + nb); + if (RTCHECK(ok_next(v, r))) { + unlink_large_chunk(m, v); + if (rsize < MIN_CHUNK_SIZE) + set_inuse_and_pinuse(m, v, (rsize + nb)); + else { + set_size_and_pinuse_of_inuse_chunk(m, v, nb); + set_size_and_pinuse_of_free_chunk(r, rsize); + insert_chunk(m, r, rsize); + } + return chunk2mem(v); + } + } + CORRUPTION_ERROR_ACTION(m); + } + return 0; +} + +/* allocate a small request from the best fitting chunk in a treebin */ +static void* tmalloc_small(mstate m, size_t nb) { + tchunkptr t, v; + size_t rsize; + bindex_t i; + binmap_t leastbit = least_bit(m->treemap); + compute_bit2idx(leastbit, i); + v = t = *treebin_at(m, i); + rsize = chunksize(t) - nb; + + while ((t = leftmost_child(t)) != 0) { + size_t trem = chunksize(t) - nb; + if (trem < rsize) { + rsize = trem; + v = t; + } + } + + if (RTCHECK(ok_address(m, v))) { + mchunkptr r = chunk_plus_offset(v, nb); + assert(chunksize(v) == rsize + nb); + if (RTCHECK(ok_next(v, r))) { + unlink_large_chunk(m, v); + if (rsize < MIN_CHUNK_SIZE) + set_inuse_and_pinuse(m, v, (rsize + nb)); + else { + set_size_and_pinuse_of_inuse_chunk(m, v, nb); + set_size_and_pinuse_of_free_chunk(r, rsize); + replace_dv(m, r, rsize); + } + return chunk2mem(v); + } + } + + CORRUPTION_ERROR_ACTION(m); + return 0; +} + +#if !ONLY_MSPACES + +void* dlmalloc(size_t bytes) { + /* + Basic algorithm: + If a small request (< 256 bytes minus per-chunk overhead): + 1. If one exists, use a remainderless chunk in associated smallbin. + (Remainderless means that there are too few excess bytes to + represent as a chunk.) + 2. If it is big enough, use the dv chunk, which is normally the + chunk adjacent to the one used for the most recent small request. + 3. If one exists, split the smallest available chunk in a bin, + saving remainder in dv. + 4. If it is big enough, use the top chunk. + 5. If available, get memory from system and use it + Otherwise, for a large request: + 1. Find the smallest available binned chunk that fits, and use it + if it is better fitting than dv chunk, splitting if necessary. + 2. If better fitting than any binned chunk, use the dv chunk. + 3. If it is big enough, use the top chunk. + 4. If request size >= mmap threshold, try to directly mmap this chunk. + 5. If available, get memory from system and use it + + The ugly goto's here ensure that postaction occurs along all paths. + */ + +#if USE_LOCKS + ensure_initialization(); /* initialize in sys_alloc if not using locks */ +#endif + + if (!PREACTION(gm)) { + void* mem; + size_t nb; + if (bytes <= MAX_SMALL_REQUEST) { + bindex_t idx; + binmap_t smallbits; + nb = (bytes < MIN_REQUEST)? MIN_CHUNK_SIZE : pad_request(bytes); + assert(1); + idx = small_index(nb); + smallbits = gm->smallmap >> idx; + + if ((smallbits & 0x3U) != 0) { /* Remainderless fit to a smallbin. */ + mchunkptr b, p; + idx += ~smallbits & 1; /* Uses next bin if idx empty */ + b = smallbin_at(gm, idx); + p = b->fd; + assert(chunksize(p) == small_index2size(idx)); + unlink_first_small_chunk(gm, b, p, idx); + set_inuse_and_pinuse(gm, p, small_index2size(idx)); + mem = chunk2mem(p); + check_malloced_chunk(gm, mem, nb); + goto postaction; + } + + else if (nb > gm->dvsize) { + if (smallbits != 0) { /* Use chunk in next nonempty smallbin */ + mchunkptr b, p, r; + size_t rsize; + bindex_t i; + binmap_t leftbits = (smallbits << idx) & left_bits(idx2bit(idx)); + binmap_t leastbit = least_bit(leftbits); + compute_bit2idx(leastbit, i); + b = smallbin_at(gm, i); + p = b->fd; + assert(chunksize(p) == small_index2size(i)); + unlink_first_small_chunk(gm, b, p, i); + rsize = small_index2size(i) - nb; + /* Fit here cannot be remainderless if 4byte sizes */ + if (SIZE_T_SIZE != 4 && rsize < MIN_CHUNK_SIZE) + set_inuse_and_pinuse(gm, p, small_index2size(i)); + else { + set_size_and_pinuse_of_inuse_chunk(gm, p, nb); + r = chunk_plus_offset(p, nb); + set_size_and_pinuse_of_free_chunk(r, rsize); + replace_dv(gm, r, rsize); + } + mem = chunk2mem(p); + check_malloced_chunk(gm, mem, nb); + goto postaction; + } + + else if (gm->treemap != 0 && (mem = tmalloc_small(gm, nb)) != 0) { + check_malloced_chunk(gm, mem, nb); + goto postaction; + } + } + } + else if (bytes >= MAX_REQUEST) + nb = MAX_SIZE_T; /* Too big to allocate. Force failure (in sys alloc) */ + else { + nb = pad_request(bytes); + if (gm->treemap != 0 && (mem = tmalloc_large(gm, nb)) != 0) { + check_malloced_chunk(gm, mem, nb); + goto postaction; + } + } + + if (nb <= gm->dvsize) { + size_t rsize = gm->dvsize - nb; + mchunkptr p = gm->dv; + if (rsize >= MIN_CHUNK_SIZE) { /* split dv */ + mchunkptr r = gm->dv = chunk_plus_offset(p, nb); + gm->dvsize = rsize; + set_size_and_pinuse_of_free_chunk(r, rsize); + set_size_and_pinuse_of_inuse_chunk(gm, p, nb); + } + else { /* exhaust dv */ + size_t dvs = gm->dvsize; + gm->dvsize = 0; + gm->dv = 0; + set_inuse_and_pinuse(gm, p, dvs); + } + mem = chunk2mem(p); + check_malloced_chunk(gm, mem, nb); + goto postaction; + } + + else if (nb < gm->topsize) { /* Split top */ + size_t rsize = gm->topsize -= nb; + mchunkptr p = gm->top; + mchunkptr r = gm->top = chunk_plus_offset(p, nb); + r->head = rsize | PINUSE_BIT; + set_size_and_pinuse_of_inuse_chunk(gm, p, nb); + mem = chunk2mem(p); + check_top_chunk(gm, gm->top); + check_malloced_chunk(gm, mem, nb); + goto postaction; + } + + mem = sys_alloc(gm, nb); + + postaction: + /* + If we failed to get more memory from the system with the + prefious sys_alloc() call mem will be NULL and we cannot get + chunk information there. + */ + if (mem != NULL) gm->internal_memory_usage += chunksize(mem2chunk(mem)); + + POSTACTION(gm); + return mem; + } + + return 0; +} + +/* ---------------------------- free --------------------------- */ + +void dlfree(void* mem) { + /* + Consolidate freed chunks with preceeding or succeeding bordering + free chunks, if they exist, and then place in a bin. Intermixed + with special cases for top, dv, mmapped chunks, and usage errors. + */ + + if (mem != 0) { + mchunkptr p = mem2chunk(mem); + if (is_inuse(p)) { + gm->internal_memory_usage -= chunksize(p); + } +#if FOOTERS + mstate fm = get_mstate_for(p); + if (!ok_magic(fm)) { + USAGE_ERROR_ACTION(fm, p); + return; + } +#else /* FOOTERS */ +#define fm gm +#endif /* FOOTERS */ + if (!PREACTION(fm)) { + check_inuse_chunk(fm, p); + if (RTCHECK(ok_address(fm, p) && ok_inuse(p))) { + size_t psize = chunksize(p); + mchunkptr next = chunk_plus_offset(p, psize); + if (!pinuse(p)) { + size_t prevsize = p->prev_foot; + if (is_mmapped(p)) { + psize += prevsize + MMAP_FOOT_PAD; + if (CALL_MUNMAP((char*)p - prevsize, psize) == 0) + fm->footprint -= psize; + goto postaction; + } + else { + mchunkptr prev = chunk_minus_offset(p, prevsize); + psize += prevsize; + p = prev; + if (RTCHECK(ok_address(fm, prev))) { /* consolidate backward */ + if (p != fm->dv) { + unlink_chunk(fm, p, prevsize); + } + else if ((next->head & INUSE_BITS) == INUSE_BITS) { + fm->dvsize = psize; + set_free_with_pinuse(p, psize, next); + goto postaction; + } + } + else + goto erroraction; + } + } + + if (RTCHECK(ok_next(p, next) && ok_pinuse(next))) { + if (!cinuse(next)) { /* consolidate forward */ + if (next == fm->top) { + size_t tsize = fm->topsize += psize; + fm->top = p; + p->head = tsize | PINUSE_BIT; + if (p == fm->dv) { + fm->dv = 0; + fm->dvsize = 0; + } + if (should_trim(fm, tsize)) + sys_trim(fm, 0); + goto postaction; + } + else if (next == fm->dv) { + size_t dsize = fm->dvsize += psize; + fm->dv = p; + set_size_and_pinuse_of_free_chunk(p, dsize); + goto postaction; + } + else { + size_t nsize = chunksize(next); + psize += nsize; + unlink_chunk(fm, next, nsize); + set_size_and_pinuse_of_free_chunk(p, psize); + if (p == fm->dv) { + fm->dvsize = psize; + goto postaction; + } + } + } + else + set_free_with_pinuse(p, psize, next); + + if (is_small(psize)) { + insert_small_chunk(fm, p, psize); + check_free_chunk(fm, p); + } + else { + tchunkptr tp = (tchunkptr)p; + insert_large_chunk(fm, tp, psize); + check_free_chunk(fm, p); + if (--fm->release_checks == 0) + release_unused_segments(fm); + } + goto postaction; + } + } + erroraction: + USAGE_ERROR_ACTION(fm, p); + postaction: + POSTACTION(fm); + } + } +#if !FOOTERS +#undef fm +#endif /* FOOTERS */ +} + +void* dlcalloc(size_t n_elements, size_t elem_size) { + void* mem; + size_t req = 0; + if (n_elements != 0) { + req = n_elements * elem_size; + if (((n_elements | elem_size) & ~(size_t)0xffff) && + (req / n_elements != elem_size)) + req = MAX_SIZE_T; /* force downstream failure on overflow */ + } + mem = dlmalloc(req); + if (mem != 0 && calloc_must_clear(mem2chunk(mem))) + memset(mem, 0, req); + return mem; +} + +#endif /* !ONLY_MSPACES */ + +/* ------------ Internal support for realloc, memalign, etc -------------- */ + +/* Try to realloc; only in-place unless can_move true */ +static mchunkptr try_realloc_chunk(mstate m, mchunkptr p, size_t nb, + int can_move) { + mchunkptr newp = 0; + size_t oldsize = chunksize(p); + mchunkptr next = chunk_plus_offset(p, oldsize); + if (RTCHECK(ok_address(m, p) && ok_inuse(p) && + ok_next(p, next) && ok_pinuse(next))) { + if (is_mmapped(p)) { + newp = mmap_resize(m, p, nb, can_move); + } + else if (oldsize >= nb) { /* already big enough */ + size_t rsize = oldsize - nb; + if (rsize >= MIN_CHUNK_SIZE) { /* split off remainder */ + mchunkptr r = chunk_plus_offset(p, nb); + set_inuse(m, p, nb); + set_inuse(m, r, rsize); + dispose_chunk(m, r, rsize); + } + newp = p; + } + else if (next == m->top) { /* extend into top */ + if (oldsize + m->topsize > nb) { + size_t newsize = oldsize + m->topsize; + size_t newtopsize = newsize - nb; + mchunkptr newtop = chunk_plus_offset(p, nb); + set_inuse(m, p, nb); + newtop->head = newtopsize |PINUSE_BIT; + m->top = newtop; + m->topsize = newtopsize; + newp = p; + } + } + else if (next == m->dv) { /* extend into dv */ + size_t dvs = m->dvsize; + if (oldsize + dvs >= nb) { + size_t dsize = oldsize + dvs - nb; + if (dsize >= MIN_CHUNK_SIZE) { + mchunkptr r = chunk_plus_offset(p, nb); + mchunkptr n = chunk_plus_offset(r, dsize); + set_inuse(m, p, nb); + set_size_and_pinuse_of_free_chunk(r, dsize); + clear_pinuse(n); + m->dvsize = dsize; + m->dv = r; + } + else { /* exhaust dv */ + size_t newsize = oldsize + dvs; + set_inuse(m, p, newsize); + m->dvsize = 0; + m->dv = 0; + } + newp = p; + } + } + else if (!cinuse(next)) { /* extend into next free chunk */ + size_t nextsize = chunksize(next); + if (oldsize + nextsize >= nb) { + size_t rsize = oldsize + nextsize - nb; + unlink_chunk(m, next, nextsize); + if (rsize < MIN_CHUNK_SIZE) { + size_t newsize = oldsize + nextsize; + set_inuse(m, p, newsize); + } + else { + mchunkptr r = chunk_plus_offset(p, nb); + set_inuse(m, p, nb); + set_inuse(m, r, rsize); + dispose_chunk(m, r, rsize); + } + newp = p; + } + } + } + else { + USAGE_ERROR_ACTION(m, chunk2mem(p)); + } + + return newp; +} + +static void* internal_memalign(mstate m, size_t alignment, size_t bytes) { + void* mem = 0; + if (alignment < MIN_CHUNK_SIZE) /* must be at least a minimum chunk size */ + alignment = MIN_CHUNK_SIZE; + if ((alignment & (alignment-SIZE_T_ONE)) != 0) {/* Ensure a power of 2 */ + size_t a = MALLOC_ALIGNMENT << 1; + while (a < alignment) a <<= 1; + alignment = a; + } + if (bytes >= MAX_REQUEST - alignment) { + if (m != 0) { /* Test isn't needed but avoids compiler warning */ + MALLOC_FAILURE_ACTION; + } + } + else { + size_t nb = request2size(bytes); + size_t req = nb + alignment + MIN_CHUNK_SIZE - CHUNK_OVERHEAD; + mem = internal_malloc(m, req); + if (mem != 0) { + mchunkptr p = mem2chunk(mem); + size_t prevsize = chunksize(p); + if (PREACTION(m)) + return 0; + if ((((size_t)(mem)) & (alignment - 1)) != 0) { /* misaligned */ + /* + Find an aligned spot inside chunk. Since we need to give + back leading space in a chunk of at least MIN_CHUNK_SIZE, if + the first calculation places us at a spot with less than + MIN_CHUNK_SIZE leader, we can move to the next aligned spot. + We've allocated enough total room so that this is always + possible. + */ + char* br = (char*)mem2chunk((size_t)(((size_t)((char*)mem + alignment - + SIZE_T_ONE)) & + -alignment)); + char* pos = ((size_t)(br - (char*)(p)) >= MIN_CHUNK_SIZE)? + br : br+alignment; + mchunkptr newp = (mchunkptr)pos; + size_t leadsize = pos - (char*)(p); + size_t newsize = chunksize(p) - leadsize; + + if (is_mmapped(p)) { /* For mmapped chunks, just adjust offset */ + newp->prev_foot = p->prev_foot + leadsize; + newp->head = newsize; + } + else { /* Otherwise, give back leader, use the rest */ + set_inuse(m, newp, newsize); + set_inuse(m, p, leadsize); + dispose_chunk(m, p, leadsize); + } + p = newp; + } + + /* Give back spare room at the end */ + if (!is_mmapped(p)) { + size_t size = chunksize(p); + if (size > nb + MIN_CHUNK_SIZE) { + size_t remainder_size = size - nb; + mchunkptr remainder = chunk_plus_offset(p, nb); + set_inuse(m, p, nb); + set_inuse(m, remainder, remainder_size); + dispose_chunk(m, remainder, remainder_size); + } + } + + mem = chunk2mem(p); + assert (chunksize(p) >= nb); + assert(((size_t)mem & (alignment - 1)) == 0); + check_inuse_chunk(m, p); + /* internal_malloc has been called, but the allocated block might be reduced, so manually update internal_memory_usage */ + gm->internal_memory_usage += chunksize(p) - prevsize; + POSTACTION(m); + } + } + return mem; +} + +/* + Common support for independent_X routines, handling + all of the combinations that can result. + The opts arg has: + bit 0 set if all elements are same size (using sizes[0]) + bit 1 set if elements should be zeroed +*/ +static void** ialloc(mstate m, + size_t n_elements, + size_t* sizes, + int opts, + void* chunks[]) { + + size_t element_size; /* chunksize of each element, if all same */ + size_t contents_size; /* total size of elements */ + size_t array_size; /* request size of pointer array */ + void* mem; /* malloced aggregate space */ + mchunkptr p; /* corresponding chunk */ + size_t remainder_size; /* remaining bytes while splitting */ + void** marray; /* either "chunks" or malloced ptr array */ + mchunkptr array_chunk; /* chunk for malloced ptr array */ + flag_t was_enabled; /* to disable mmap */ + size_t size; + size_t i; + + ensure_initialization(); + /* compute array length, if needed */ + if (chunks != 0) { + if (n_elements == 0) + return chunks; /* nothing to do */ + marray = chunks; + array_size = 0; + } + else { + /* if empty req, must still return chunk representing empty array */ + if (n_elements == 0) + return (void**)internal_malloc(m, 0); + marray = 0; + array_size = request2size(n_elements * (sizeof(void*))); + } + + /* compute total element size */ + if (opts & 0x1) { /* all-same-size */ + element_size = request2size(*sizes); + contents_size = n_elements * element_size; + } + else { /* add up all the sizes */ + element_size = 0; + contents_size = 0; + for (i = 0; i != n_elements; ++i) + contents_size += request2size(sizes[i]); + } + + size = contents_size + array_size; + + /* + Allocate the aggregate chunk. First disable direct-mmapping so + malloc won't use it, since we would not be able to later + free/realloc space internal to a segregated mmap region. + */ + was_enabled = use_mmap(m); + disable_mmap(m); + mem = internal_malloc(m, size - CHUNK_OVERHEAD); + if (was_enabled) + enable_mmap(m); + if (mem == 0) + return 0; + + if (PREACTION(m)) return 0; + p = mem2chunk(mem); + remainder_size = chunksize(p); + + assert(!is_mmapped(p)); + + if (opts & 0x2) { /* optionally clear the elements */ + memset((size_t*)mem, 0, remainder_size - SIZE_T_SIZE - array_size); + } + + /* If not provided, allocate the pointer array as final part of chunk */ + if (marray == 0) { + size_t array_chunk_size; + array_chunk = chunk_plus_offset(p, contents_size); + array_chunk_size = remainder_size - contents_size; + marray = (void**) (chunk2mem(array_chunk)); + set_size_and_pinuse_of_inuse_chunk(m, array_chunk, array_chunk_size); + remainder_size = contents_size; + } + + /* split out elements */ + for (i = 0; ; ++i) { + marray[i] = chunk2mem(p); + if (i != n_elements-1) { + if (element_size != 0) + size = element_size; + else + size = request2size(sizes[i]); + remainder_size -= size; + set_size_and_pinuse_of_inuse_chunk(m, p, size); + p = chunk_plus_offset(p, size); + } + else { /* the final element absorbs any overallocation slop */ + set_size_and_pinuse_of_inuse_chunk(m, p, remainder_size); + break; + } + } + +#if DEBUG + if (marray != chunks) { + /* final element must have exactly exhausted chunk */ + if (element_size != 0) { + assert(remainder_size == element_size); + } + else { + assert(remainder_size == request2size(sizes[i])); + } + check_inuse_chunk(m, mem2chunk(marray)); + } + for (i = 0; i != n_elements; ++i) + check_inuse_chunk(m, mem2chunk(marray[i])); + +#endif /* DEBUG */ + + POSTACTION(m); + return marray; +} + +/* Try to free all pointers in the given array. + Note: this could be made faster, by delaying consolidation, + at the price of disabling some user integrity checks, We + still optimize some consolidations by combining adjacent + chunks before freeing, which will occur often if allocated + with ialloc or the array is sorted. +*/ +static size_t internal_bulk_free(mstate m, void* array[], size_t nelem) { + size_t unfreed = 0; + if (!PREACTION(m)) { + void** a; + void** fence = &(array[nelem]); + for (a = array; a != fence; ++a) { + void* mem = *a; + if (mem != 0) { + mchunkptr p = mem2chunk(mem); + size_t psize = chunksize(p); +#if FOOTERS + if (get_mstate_for(p) != m) { + ++unfreed; + continue; + } +#endif + check_inuse_chunk(m, p); + *a = 0; + if (RTCHECK(ok_address(m, p) && ok_inuse(p))) { + void ** b = a + 1; /* try to merge with next chunk */ + mchunkptr next = next_chunk(p); + if (b != fence && *b == chunk2mem(next)) { + size_t newsize = chunksize(next) + psize; + set_inuse(m, p, newsize); + *b = chunk2mem(p); + } + else + dispose_chunk(m, p, psize); + } + else { + CORRUPTION_ERROR_ACTION(m); + break; + } + } + } + if (should_trim(m, m->topsize)) + sys_trim(m, 0); + POSTACTION(m); + } + return unfreed; +} + +/* Traversal */ +#if MALLOC_INSPECT_ALL +static void internal_inspect_all(mstate m, + void(*handler)(void *start, + void *end, + size_t used_bytes, + void* callback_arg), + void* arg) { + if (is_initialized(m)) { + mchunkptr top = m->top; + msegmentptr s; + for (s = &m->seg; s != 0; s = s->next) { + mchunkptr q = align_as_chunk(s->base); + while (segment_holds(s, q) && q->head != FENCEPOST_HEAD) { + mchunkptr next = next_chunk(q); + size_t sz = chunksize(q); + size_t used; + void* start; + if (is_inuse(q)) { + used = sz - CHUNK_OVERHEAD; /* must not be mmapped */ + start = chunk2mem(q); + } + else { + used = 0; + if (is_small(sz)) { /* offset by possible bookkeeping */ + start = (void*)((char*)q + sizeof(struct malloc_chunk)); + } + else { + start = (void*)((char*)q + sizeof(struct malloc_tree_chunk)); + } + } + if (start < (void*)next) /* skip if all space is bookkeeping */ + handler(start, next, used, arg); + if (q == top) + break; + q = next; + } + } + } +} +#endif /* MALLOC_INSPECT_ALL */ + +/* ------------------ Exported realloc, memalign, etc -------------------- */ + +#if !ONLY_MSPACES + +void* dlrealloc(void* oldmem, size_t bytes) { + void* mem = 0; + if (oldmem == 0) { + mem = dlmalloc(bytes); + } + else if (bytes >= MAX_REQUEST) { + MALLOC_FAILURE_ACTION; + } +#ifdef REALLOC_ZERO_BYTES_FREES + else if (bytes == 0) { + dlfree(oldmem); + } +#endif /* REALLOC_ZERO_BYTES_FREES */ + else { + size_t nb = request2size(bytes); + mchunkptr oldp = mem2chunk(oldmem); + size_t oldp_size = chunksize(oldp); +#if ! FOOTERS + mstate m = gm; +#else /* FOOTERS */ + mstate m = get_mstate_for(oldp); + if (!ok_magic(m)) { + USAGE_ERROR_ACTION(m, oldmem); + return 0; + } +#endif /* FOOTERS */ + if (!PREACTION(m)) { + mchunkptr newp = try_realloc_chunk(m, oldp, nb, 1); + POSTACTION(m); + if (newp != 0) { + check_inuse_chunk(m, newp); + mem = chunk2mem(newp); + /* In the case of an in_place reallocation, neither malloc or free are called, so manually update internal_memory_usage */ + gm->internal_memory_usage += chunksize(newp)-oldp_size; + } + else { + mem = internal_malloc(m, bytes); + if (mem != 0) { + size_t oc = chunksize(oldp) - overhead_for(oldp); + memcpy(mem, oldmem, (oc < bytes)? oc : bytes); + internal_free(m, oldmem); + } + } + } + } + + return mem; +} + +void* dlrealloc_in_place(void* oldmem, size_t bytes) { + void* mem = 0; + if (oldmem != 0) { + if (bytes >= MAX_REQUEST) { + MALLOC_FAILURE_ACTION; + } + else { + size_t nb = request2size(bytes); + mchunkptr oldp = mem2chunk(oldmem); + size_t oldp_size = chunksize(oldp); +#if ! FOOTERS + mstate m = gm; +#else /* FOOTERS */ + mstate m = get_mstate_for(oldp); + if (!ok_magic(m)) { + USAGE_ERROR_ACTION(m, oldmem); + return 0; + } +#endif /* FOOTERS */ + if (!PREACTION(m)) { + mchunkptr newp = try_realloc_chunk(m, oldp, nb, 0); + POSTACTION(m); + if (newp == oldp) { + /* In the case of an in_place reallocation, neither malloc or free are called, so manually update internal_memory_usage */ + gm->internal_memory_usage += chunksize(newp)-oldp_size; + check_inuse_chunk(m, newp); + mem = oldmem; + } + } + } + } + return mem; +} + +void* dlmemalign(size_t alignment, size_t bytes) { + if (alignment <= MALLOC_ALIGNMENT) { + return dlmalloc(bytes); + } + return internal_memalign(gm, alignment, bytes); +} + +int dlposix_memalign(void** pp, size_t alignment, size_t bytes) { + void* mem = 0; + if (alignment == MALLOC_ALIGNMENT) + mem = dlmalloc(bytes); + else { + size_t d = alignment / sizeof(void*); + size_t r = alignment % sizeof(void*); + if (r != 0 || d == 0 || (d & (d-SIZE_T_ONE)) != 0) { + errno = EINVAL; + return -1; + } + else if (bytes <= MAX_REQUEST - alignment) { + if (alignment < MIN_CHUNK_SIZE) + alignment = MIN_CHUNK_SIZE; + mem = internal_memalign(gm, alignment, bytes); + } + } + if (mem == 0) { + errno = ENOMEM; + return -1; + } + else { + *pp = mem; + return 0; + } +} + +void* dlvalloc(size_t bytes) { + size_t pagesz; + ensure_initialization(); + pagesz = mparams.page_size; + return dlmemalign(pagesz, bytes); +} + +void* dlpvalloc(size_t bytes) { + size_t pagesz; + ensure_initialization(); + pagesz = mparams.page_size; + return dlmemalign(pagesz, (bytes + pagesz - SIZE_T_ONE) & ~(pagesz - SIZE_T_ONE)); +} + +void** dlindependent_calloc(size_t n_elements, size_t elem_size, + void* chunks[]) { + size_t sz = elem_size; /* serves as 1-element array */ + return ialloc(gm, n_elements, &sz, 3, chunks); +} + +void** dlindependent_comalloc(size_t n_elements, size_t sizes[], + void* chunks[]) { + return ialloc(gm, n_elements, sizes, 0, chunks); +} + +size_t dlbulk_free(void* array[], size_t nelem) { + return internal_bulk_free(gm, array, nelem); +} + +#if MALLOC_INSPECT_ALL +void dlmalloc_inspect_all(void(*handler)(void *start, + void *end, + size_t used_bytes, + void* callback_arg), + void* arg) { + ensure_initialization(); + if (!PREACTION(gm)) { + internal_inspect_all(gm, handler, arg); + POSTACTION(gm); + } +} +#endif /* MALLOC_INSPECT_ALL */ + +int dlmalloc_trim(size_t pad) { + int result = 0; + ensure_initialization(); + if (!PREACTION(gm)) { + result = sys_trim(gm, pad); + POSTACTION(gm); + } + return result; +} + +size_t dlmalloc_footprint(void) { + return gm->footprint; +} + +size_t dlmalloc_memory_usage(void) { + return gm->internal_memory_usage; +} + +size_t dlmalloc_max_footprint(void) { + return gm->max_footprint; +} + +size_t dlmalloc_footprint_limit(void) { + size_t maf = gm->footprint_limit; + return maf == 0 ? MAX_SIZE_T : maf; +} + +size_t dlmalloc_set_footprint_limit(size_t bytes) { + size_t result; /* invert sense of 0 */ + if (bytes == 0) + result = granularity_align(1); /* Use minimal size */ + if (bytes == MAX_SIZE_T) + result = 0; /* disable */ + else + result = granularity_align(bytes); + return gm->footprint_limit = result; +} + +#if !NO_MALLINFO +struct mallinfo dlmallinfo(void) { + return internal_mallinfo(gm); +} +#endif /* NO_MALLINFO */ + +#if !NO_MALLOC_STATS +void dlmalloc_stats() { + internal_malloc_stats(gm); +} +#endif /* NO_MALLOC_STATS */ + +int dlmallopt(int param_number, int value) { + return change_mparam(param_number, value); +} + +size_t dlmalloc_usable_size(void* mem) { + if (mem != 0) { + mchunkptr p = mem2chunk(mem); + if (is_inuse(p)) + return chunksize(p) - overhead_for(p); + } + return 0; +} + +#endif /* !ONLY_MSPACES */ + +/* ----------------------------- user mspaces ---------------------------- */ + +#if MSPACES + +static mstate init_user_mstate(char* tbase, size_t tsize) { + size_t msize = pad_request(sizeof(struct malloc_state)); + mchunkptr mn; + mchunkptr msp = align_as_chunk(tbase); + mstate m = (mstate)(chunk2mem(msp)); + memset(m, 0, msize); + (void)INITIAL_LOCK(&m->mutex); + msp->head = (msize|INUSE_BITS); + m->seg.base = m->least_addr = tbase; + m->seg.size = m->footprint = m->max_footprint = tsize; + m->magic = mparams.magic; + m->release_checks = MAX_RELEASE_CHECK_RATE; + m->mflags = mparams.default_mflags; + m->extp = 0; + m->exts = 0; + disable_contiguous(m); + init_bins(m); + mn = next_chunk(mem2chunk(m)); + init_top(m, mn, (size_t)((tbase + tsize) - (char*)mn) - TOP_FOOT_SIZE); + check_top_chunk(m, m->top); + return m; +} + +mspace create_mspace(size_t capacity, int locked) { + mstate m = 0; + size_t msize; + ensure_initialization(); + msize = pad_request(sizeof(struct malloc_state)); + if (capacity < (size_t) -(msize + TOP_FOOT_SIZE + mparams.page_size)) { + size_t rs = ((capacity == 0)? mparams.granularity : + (capacity + TOP_FOOT_SIZE + msize)); + size_t tsize = granularity_align(rs); + char* tbase = (char*)(CALL_MMAP(tsize)); + if (tbase != CMFAIL) { + m = init_user_mstate(tbase, tsize); + m->seg.sflags = USE_MMAP_BIT; + set_lock(m, locked); + } + } + return (mspace)m; +} + +mspace create_mspace_with_base(void* base, size_t capacity, int locked) { + mstate m = 0; + size_t msize; + ensure_initialization(); + msize = pad_request(sizeof(struct malloc_state)); + if (capacity > msize + TOP_FOOT_SIZE && + capacity < (size_t) -(msize + TOP_FOOT_SIZE + mparams.page_size)) { + m = init_user_mstate((char*)base, capacity); + m->seg.sflags = EXTERN_BIT; + set_lock(m, locked); + } + return (mspace)m; +} + +int mspace_track_large_chunks(mspace msp, int enable) { + int ret = 0; + mstate ms = (mstate)msp; + if (!PREACTION(ms)) { + if (!use_mmap(ms)) { + ret = 1; + } + if (!enable) { + enable_mmap(ms); + } else { + disable_mmap(ms); + } + POSTACTION(ms); + } + return ret; +} + +size_t destroy_mspace(mspace msp) { + size_t freed = 0; + mstate ms = (mstate)msp; + if (ok_magic(ms)) { + msegmentptr sp = &ms->seg; + (void)DESTROY_LOCK(&ms->mutex); /* destroy before unmapped */ + while (sp != 0) { + char* base = sp->base; + size_t size = sp->size; + flag_t flag = sp->sflags; + (void)base; /* placate people compiling -Wunused-variable */ + sp = sp->next; + if ((flag & USE_MMAP_BIT) && !(flag & EXTERN_BIT) && + CALL_MUNMAP(base, size) == 0) + freed += size; + } + } + else { + USAGE_ERROR_ACTION(ms,ms); + } + return freed; +} + +/* + mspace versions of routines are near-clones of the global + versions. This is not so nice but better than the alternatives. +*/ + +void* mspace_malloc(mspace msp, size_t bytes) { + mstate ms = (mstate)msp; + if (!ok_magic(ms)) { + USAGE_ERROR_ACTION(ms,ms); + return 0; + } + if (!PREACTION(ms)) { + void* mem; + size_t nb; + if (bytes <= MAX_SMALL_REQUEST) { + bindex_t idx; + binmap_t smallbits; + nb = (bytes < MIN_REQUEST)? MIN_CHUNK_SIZE : pad_request(bytes); + idx = small_index(nb); + smallbits = ms->smallmap >> idx; + + if ((smallbits & 0x3U) != 0) { /* Remainderless fit to a smallbin. */ + mchunkptr b, p; + idx += ~smallbits & 1; /* Uses next bin if idx empty */ + b = smallbin_at(ms, idx); + p = b->fd; + assert(chunksize(p) == small_index2size(idx)); + unlink_first_small_chunk(ms, b, p, idx); + set_inuse_and_pinuse(ms, p, small_index2size(idx)); + mem = chunk2mem(p); + check_malloced_chunk(ms, mem, nb); + goto postaction; + } + + else if (nb > ms->dvsize) { + if (smallbits != 0) { /* Use chunk in next nonempty smallbin */ + mchunkptr b, p, r; + size_t rsize; + bindex_t i; + binmap_t leftbits = (smallbits << idx) & left_bits(idx2bit(idx)); + binmap_t leastbit = least_bit(leftbits); + compute_bit2idx(leastbit, i); + b = smallbin_at(ms, i); + p = b->fd; + assert(chunksize(p) == small_index2size(i)); + unlink_first_small_chunk(ms, b, p, i); + rsize = small_index2size(i) - nb; + /* Fit here cannot be remainderless if 4byte sizes */ + if (SIZE_T_SIZE != 4 && rsize < MIN_CHUNK_SIZE) + set_inuse_and_pinuse(ms, p, small_index2size(i)); + else { + set_size_and_pinuse_of_inuse_chunk(ms, p, nb); + r = chunk_plus_offset(p, nb); + set_size_and_pinuse_of_free_chunk(r, rsize); + replace_dv(ms, r, rsize); + } + mem = chunk2mem(p); + check_malloced_chunk(ms, mem, nb); + goto postaction; + } + + else if (ms->treemap != 0 && (mem = tmalloc_small(ms, nb)) != 0) { + check_malloced_chunk(ms, mem, nb); + goto postaction; + } + } + } + else if (bytes >= MAX_REQUEST) + nb = MAX_SIZE_T; /* Too big to allocate. Force failure (in sys alloc) */ + else { + nb = pad_request(bytes); + if (ms->treemap != 0 && (mem = tmalloc_large(ms, nb)) != 0) { + check_malloced_chunk(ms, mem, nb); + goto postaction; + } + } + + if (nb <= ms->dvsize) { + size_t rsize = ms->dvsize - nb; + mchunkptr p = ms->dv; + if (rsize >= MIN_CHUNK_SIZE) { /* split dv */ + mchunkptr r = ms->dv = chunk_plus_offset(p, nb); + ms->dvsize = rsize; + set_size_and_pinuse_of_free_chunk(r, rsize); + set_size_and_pinuse_of_inuse_chunk(ms, p, nb); + } + else { /* exhaust dv */ + size_t dvs = ms->dvsize; + ms->dvsize = 0; + ms->dv = 0; + set_inuse_and_pinuse(ms, p, dvs); + } + mem = chunk2mem(p); + check_malloced_chunk(ms, mem, nb); + goto postaction; + } + + else if (nb < ms->topsize) { /* Split top */ + size_t rsize = ms->topsize -= nb; + mchunkptr p = ms->top; + mchunkptr r = ms->top = chunk_plus_offset(p, nb); + r->head = rsize | PINUSE_BIT; + set_size_and_pinuse_of_inuse_chunk(ms, p, nb); + mem = chunk2mem(p); + check_top_chunk(ms, ms->top); + check_malloced_chunk(ms, mem, nb); + goto postaction; + } + + mem = sys_alloc(ms, nb); + + postaction: + POSTACTION(ms); + return mem; + } + + return 0; +} + +void mspace_free(mspace msp, void* mem) { + if (mem != 0) { + mchunkptr p = mem2chunk(mem); +#if FOOTERS + mstate fm = get_mstate_for(p); + (void)msp; /* placate people compiling -Wunused */ +#else /* FOOTERS */ + mstate fm = (mstate)msp; +#endif /* FOOTERS */ + if (!ok_magic(fm)) { + USAGE_ERROR_ACTION(fm, p); + return; + } + if (!PREACTION(fm)) { + check_inuse_chunk(fm, p); + if (RTCHECK(ok_address(fm, p) && ok_inuse(p))) { + size_t psize = chunksize(p); + mchunkptr next = chunk_plus_offset(p, psize); + if (!pinuse(p)) { + size_t prevsize = p->prev_foot; + if (is_mmapped(p)) { + psize += prevsize + MMAP_FOOT_PAD; + if (CALL_MUNMAP((char*)p - prevsize, psize) == 0) + fm->footprint -= psize; + goto postaction; + } + else { + mchunkptr prev = chunk_minus_offset(p, prevsize); + psize += prevsize; + p = prev; + if (RTCHECK(ok_address(fm, prev))) { /* consolidate backward */ + if (p != fm->dv) { + unlink_chunk(fm, p, prevsize); + } + else if ((next->head & INUSE_BITS) == INUSE_BITS) { + fm->dvsize = psize; + set_free_with_pinuse(p, psize, next); + goto postaction; + } + } + else + goto erroraction; + } + } + + if (RTCHECK(ok_next(p, next) && ok_pinuse(next))) { + if (!cinuse(next)) { /* consolidate forward */ + if (next == fm->top) { + size_t tsize = fm->topsize += psize; + fm->top = p; + p->head = tsize | PINUSE_BIT; + if (p == fm->dv) { + fm->dv = 0; + fm->dvsize = 0; + } + if (should_trim(fm, tsize)) + sys_trim(fm, 0); + goto postaction; + } + else if (next == fm->dv) { + size_t dsize = fm->dvsize += psize; + fm->dv = p; + set_size_and_pinuse_of_free_chunk(p, dsize); + goto postaction; + } + else { + size_t nsize = chunksize(next); + psize += nsize; + unlink_chunk(fm, next, nsize); + set_size_and_pinuse_of_free_chunk(p, psize); + if (p == fm->dv) { + fm->dvsize = psize; + goto postaction; + } + } + } + else + set_free_with_pinuse(p, psize, next); + + if (is_small(psize)) { + insert_small_chunk(fm, p, psize); + check_free_chunk(fm, p); + } + else { + tchunkptr tp = (tchunkptr)p; + insert_large_chunk(fm, tp, psize); + check_free_chunk(fm, p); + if (--fm->release_checks == 0) + release_unused_segments(fm); + } + goto postaction; + } + } + erroraction: + USAGE_ERROR_ACTION(fm, p); + postaction: + POSTACTION(fm); + } + } +} + +void* mspace_calloc(mspace msp, size_t n_elements, size_t elem_size) { + void* mem; + size_t req = 0; + mstate ms = (mstate)msp; + if (!ok_magic(ms)) { + USAGE_ERROR_ACTION(ms,ms); + return 0; + } + if (n_elements != 0) { + req = n_elements * elem_size; + if (((n_elements | elem_size) & ~(size_t)0xffff) && + (req / n_elements != elem_size)) + req = MAX_SIZE_T; /* force downstream failure on overflow */ + } + mem = internal_malloc(ms, req); + if (mem != 0 && calloc_must_clear(mem2chunk(mem))) + memset(mem, 0, req); + return mem; +} + +void* mspace_realloc(mspace msp, void* oldmem, size_t bytes) { + void* mem = 0; + if (oldmem == 0) { + mem = mspace_malloc(msp, bytes); + } + else if (bytes >= MAX_REQUEST) { + MALLOC_FAILURE_ACTION; + } +#ifdef REALLOC_ZERO_BYTES_FREES + else if (bytes == 0) { + mspace_free(msp, oldmem); + } +#endif /* REALLOC_ZERO_BYTES_FREES */ + else { + size_t nb = request2size(bytes); + mchunkptr oldp = mem2chunk(oldmem); +#if ! FOOTERS + mstate m = (mstate)msp; +#else /* FOOTERS */ + mstate m = get_mstate_for(oldp); + if (!ok_magic(m)) { + USAGE_ERROR_ACTION(m, oldmem); + return 0; + } +#endif /* FOOTERS */ + if (!PREACTION(m)) { + mchunkptr newp = try_realloc_chunk(m, oldp, nb, 1); + POSTACTION(m); + if (newp != 0) { + check_inuse_chunk(m, newp); + mem = chunk2mem(newp); + } + else { + mem = mspace_malloc(m, bytes); + if (mem != 0) { + size_t oc = chunksize(oldp) - overhead_for(oldp); + memcpy(mem, oldmem, (oc < bytes)? oc : bytes); + mspace_free(m, oldmem); + } + } + } + } + return mem; +} + +void* mspace_realloc_in_place(mspace msp, void* oldmem, size_t bytes) { + void* mem = 0; + if (oldmem != 0) { + if (bytes >= MAX_REQUEST) { + MALLOC_FAILURE_ACTION; + } + else { + size_t nb = request2size(bytes); + mchunkptr oldp = mem2chunk(oldmem); +#if ! FOOTERS + mstate m = (mstate)msp; +#else /* FOOTERS */ + mstate m = get_mstate_for(oldp); + (void)msp; /* placate people compiling -Wunused */ + if (!ok_magic(m)) { + USAGE_ERROR_ACTION(m, oldmem); + return 0; + } +#endif /* FOOTERS */ + if (!PREACTION(m)) { + mchunkptr newp = try_realloc_chunk(m, oldp, nb, 0); + POSTACTION(m); + if (newp == oldp) { + check_inuse_chunk(m, newp); + mem = oldmem; + } + } + } + } + return mem; +} + +void* mspace_memalign(mspace msp, size_t alignment, size_t bytes) { + mstate ms = (mstate)msp; + if (!ok_magic(ms)) { + USAGE_ERROR_ACTION(ms,ms); + return 0; + } + if (alignment <= MALLOC_ALIGNMENT) + return mspace_malloc(msp, bytes); + return internal_memalign(ms, alignment, bytes); +} + +void** mspace_independent_calloc(mspace msp, size_t n_elements, + size_t elem_size, void* chunks[]) { + size_t sz = elem_size; /* serves as 1-element array */ + mstate ms = (mstate)msp; + if (!ok_magic(ms)) { + USAGE_ERROR_ACTION(ms,ms); + return 0; + } + return ialloc(ms, n_elements, &sz, 3, chunks); +} + +void** mspace_independent_comalloc(mspace msp, size_t n_elements, + size_t sizes[], void* chunks[]) { + mstate ms = (mstate)msp; + if (!ok_magic(ms)) { + USAGE_ERROR_ACTION(ms,ms); + return 0; + } + return ialloc(ms, n_elements, sizes, 0, chunks); +} + +size_t mspace_bulk_free(mspace msp, void* array[], size_t nelem) { + return internal_bulk_free((mstate)msp, array, nelem); +} + +#if MALLOC_INSPECT_ALL +void mspace_inspect_all(mspace msp, + void(*handler)(void *start, + void *end, + size_t used_bytes, + void* callback_arg), + void* arg) { + mstate ms = (mstate)msp; + if (ok_magic(ms)) { + if (!PREACTION(ms)) { + internal_inspect_all(ms, handler, arg); + POSTACTION(ms); + } + } + else { + USAGE_ERROR_ACTION(ms,ms); + } +} +#endif /* MALLOC_INSPECT_ALL */ + +int mspace_trim(mspace msp, size_t pad) { + int result = 0; + mstate ms = (mstate)msp; + if (ok_magic(ms)) { + if (!PREACTION(ms)) { + result = sys_trim(ms, pad); + POSTACTION(ms); + } + } + else { + USAGE_ERROR_ACTION(ms,ms); + } + return result; +} + +#if !NO_MALLOC_STATS +void mspace_malloc_stats(mspace msp) { + mstate ms = (mstate)msp; + if (ok_magic(ms)) { + internal_malloc_stats(ms); + } + else { + USAGE_ERROR_ACTION(ms,ms); + } +} +#endif /* NO_MALLOC_STATS */ + +size_t mspace_footprint(mspace msp) { + size_t result = 0; + mstate ms = (mstate)msp; + if (ok_magic(ms)) { + result = ms->footprint; + } + else { + USAGE_ERROR_ACTION(ms,ms); + } + return result; +} + +size_t mspace_max_footprint(mspace msp) { + size_t result = 0; + mstate ms = (mstate)msp; + if (ok_magic(ms)) { + result = ms->max_footprint; + } + else { + USAGE_ERROR_ACTION(ms,ms); + } + return result; +} + +size_t mspace_footprint_limit(mspace msp) { + size_t result = 0; + mstate ms = (mstate)msp; + if (ok_magic(ms)) { + size_t maf = ms->footprint_limit; + result = (maf == 0) ? MAX_SIZE_T : maf; + } + else { + USAGE_ERROR_ACTION(ms,ms); + } + return result; +} + +size_t mspace_set_footprint_limit(mspace msp, size_t bytes) { + size_t result = 0; + mstate ms = (mstate)msp; + if (ok_magic(ms)) { + if (bytes == 0) + result = granularity_align(1); /* Use minimal size */ + if (bytes == MAX_SIZE_T) + result = 0; /* disable */ + else + result = granularity_align(bytes); + ms->footprint_limit = result; + } + else { + USAGE_ERROR_ACTION(ms,ms); + } + return result; +} + +#if !NO_MALLINFO +struct mallinfo mspace_mallinfo(mspace msp) { + mstate ms = (mstate)msp; + if (!ok_magic(ms)) { + USAGE_ERROR_ACTION(ms,ms); + } + return internal_mallinfo(ms); +} +#endif /* NO_MALLINFO */ + +size_t mspace_usable_size(const void* mem) { + if (mem != 0) { + mchunkptr p = mem2chunk(mem); + if (is_inuse(p)) + return chunksize(p) - overhead_for(p); + } + return 0; +} + +int mspace_mallopt(int param_number, int value) { + return change_mparam(param_number, value); +} + +#endif /* MSPACES */ + + +/* -------------------- Alternative MORECORE functions ------------------- */ + +/* + Guidelines for creating a custom version of MORECORE: + + * For best performance, MORECORE should allocate in multiples of pagesize. + * MORECORE may allocate more memory than requested. (Or even less, + but this will usually result in a malloc failure.) + * MORECORE must not allocate memory when given argument zero, but + instead return one past the end address of memory from previous + nonzero call. + * For best performance, consecutive calls to MORECORE with positive + arguments should return increasing addresses, indicating that + space has been contiguously extended. + * Even though consecutive calls to MORECORE need not return contiguous + addresses, it must be OK for malloc'ed chunks to span multiple + regions in those cases where they do happen to be contiguous. + * MORECORE need not handle negative arguments -- it may instead + just return MFAIL when given negative arguments. + Negative arguments are always multiples of pagesize. MORECORE + must not misinterpret negative args as large positive unsigned + args. You can suppress all such calls from even occurring by defining + MORECORE_CANNOT_TRIM, + + As an example alternative MORECORE, here is a custom allocator + kindly contributed for pre-OSX macOS. It uses virtually but not + necessarily physically contiguous non-paged memory (locked in, + present and won't get swapped out). You can use it by uncommenting + this section, adding some #includes, and setting up the appropriate + defines above: + + #define MORECORE osMoreCore + + There is also a shutdown routine that should somehow be called for + cleanup upon program exit. + + #define MAX_POOL_ENTRIES 100 + #define MINIMUM_MORECORE_SIZE (64 * 1024U) + static int next_os_pool; + void *our_os_pools[MAX_POOL_ENTRIES]; + + void *osMoreCore(int size) + { + void *ptr = 0; + static void *sbrk_top = 0; + + if (size > 0) + { + if (size < MINIMUM_MORECORE_SIZE) + size = MINIMUM_MORECORE_SIZE; + if (CurrentExecutionLevel() == kTaskLevel) + ptr = PoolAllocateResident(size + RM_PAGE_SIZE, 0); + if (ptr == 0) + { + return (void *) MFAIL; + } + // save ptrs so they can be freed during cleanup + our_os_pools[next_os_pool] = ptr; + next_os_pool++; + ptr = (void *) ((((size_t) ptr) + RM_PAGE_MASK) & ~RM_PAGE_MASK); + sbrk_top = (char *) ptr + size; + return ptr; + } + else if (size < 0) + { + // we don't currently support shrink behavior + return (void *) MFAIL; + } + else + { + return sbrk_top; + } + } + + // cleanup any allocated memory pools + // called as last thing before shutting down driver + + void osCleanupMem(void) + { + void **ptr; + + for (ptr = our_os_pools; ptr < &our_os_pools[MAX_POOL_ENTRIES]; ptr++) + if (*ptr) + { + PoolDeallocate(*ptr); + *ptr = 0; + } + } + +*/ + + +/* ----------------------------------------------------------------------- +History: + v2.8.6 Wed Aug 29 06:57:58 2012 Doug Lea + * fix bad comparison in dlposix_memalign + * don't reuse adjusted asize in sys_alloc + * add LOCK_AT_FORK -- thanks to Kirill Artamonov for the suggestion + * reduce compiler warnings -- thanks to all who reported/suggested these + + v2.8.5 Sun May 22 10:26:02 2011 Doug Lea (dl at gee) + * Always perform unlink checks unless INSECURE + * Add posix_memalign. + * Improve realloc to expand in more cases; expose realloc_in_place. + Thanks to Peter Buhr for the suggestion. + * Add footprint_limit, inspect_all, bulk_free. Thanks + to Barry Hayes and others for the suggestions. + * Internal refactorings to avoid calls while holding locks + * Use non-reentrant locks by default. Thanks to Roland McGrath + for the suggestion. + * Small fixes to mspace_destroy, reset_on_error. + * Various configuration extensions/changes. Thanks + to all who contributed these. + + V2.8.4a Thu Apr 28 14:39:43 2011 (dl at gee.cs.oswego.edu) + * Update Creative Commons URL + + V2.8.4 Wed May 27 09:56:23 2009 Doug Lea (dl at gee) + * Use zeros instead of prev foot for is_mmapped + * Add mspace_track_large_chunks; thanks to Jean Brouwers + * Fix set_inuse in internal_realloc; thanks to Jean Brouwers + * Fix insufficient sys_alloc padding when using 16byte alignment + * Fix bad error check in mspace_footprint + * Adaptations for ptmalloc; thanks to Wolfram Gloger. + * Reentrant spin locks; thanks to Earl Chew and others + * Win32 improvements; thanks to Niall Douglas and Earl Chew + * Add NO_SEGMENT_TRAVERSAL and MAX_RELEASE_CHECK_RATE options + * Extension hook in malloc_state + * Various small adjustments to reduce warnings on some compilers + * Various configuration extensions/changes for more platforms. Thanks + to all who contributed these. + + V2.8.3 Thu Sep 22 11:16:32 2005 Doug Lea (dl at gee) + * Add max_footprint functions + * Ensure all appropriate literals are size_t + * Fix conditional compilation problem for some #define settings + * Avoid concatenating segments with the one provided + in create_mspace_with_base + * Rename some variables to avoid compiler shadowing warnings + * Use explicit lock initialization. + * Better handling of sbrk interference. + * Simplify and fix segment insertion, trimming and mspace_destroy + * Reinstate REALLOC_ZERO_BYTES_FREES option from 2.7.x + * Thanks especially to Dennis Flanagan for help on these. + + V2.8.2 Sun Jun 12 16:01:10 2005 Doug Lea (dl at gee) + * Fix memalign brace error. + + V2.8.1 Wed Jun 8 16:11:46 2005 Doug Lea (dl at gee) + * Fix improper #endif nesting in C++ + * Add explicit casts needed for C++ + + V2.8.0 Mon May 30 14:09:02 2005 Doug Lea (dl at gee) + * Use trees for large bins + * Support mspaces + * Use segments to unify sbrk-based and mmap-based system allocation, + removing need for emulation on most platforms without sbrk. + * Default safety checks + * Optional footer checks. Thanks to William Robertson for the idea. + * Internal code refactoring + * Incorporate suggestions and platform-specific changes. + Thanks to Dennis Flanagan, Colin Plumb, Niall Douglas, + Aaron Bachmann, Emery Berger, and others. + * Speed up non-fastbin processing enough to remove fastbins. + * Remove useless cfree() to avoid conflicts with other apps. + * Remove internal memcpy, memset. Compilers handle builtins better. + * Remove some options that no one ever used and rename others. + + V2.7.2 Sat Aug 17 09:07:30 2002 Doug Lea (dl at gee) + * Fix malloc_state bitmap array misdeclaration + + V2.7.1 Thu Jul 25 10:58:03 2002 Doug Lea (dl at gee) + * Allow tuning of FIRST_SORTED_BIN_SIZE + * Use PTR_UINT as type for all ptr->int casts. Thanks to John Belmonte. + * Better detection and support for non-contiguousness of MORECORE. + Thanks to Andreas Mueller, Conal Walsh, and Wolfram Gloger + * Bypass most of malloc if no frees. Thanks To Emery Berger. + * Fix freeing of old top non-contiguous chunk im sysmalloc. + * Raised default trim and map thresholds to 256K. + * Fix mmap-related #defines. Thanks to Lubos Lunak. + * Fix copy macros; added LACKS_FCNTL_H. Thanks to Neal Walfield. + * Branch-free bin calculation + * Default trim and mmap thresholds now 256K. + + V2.7.0 Sun Mar 11 14:14:06 2001 Doug Lea (dl at gee) + * Introduce independent_comalloc and independent_calloc. + Thanks to Michael Pachos for motivation and help. + * Make optional .h file available + * Allow > 2GB requests on 32bit systems. + * new WIN32 sbrk, mmap, munmap, lock code from . + Thanks also to Andreas Mueller , + and Anonymous. + * Allow override of MALLOC_ALIGNMENT (Thanks to Ruud Waij for + helping test this.) + * memalign: check alignment arg + * realloc: don't try to shift chunks backwards, since this + leads to more fragmentation in some programs and doesn't + seem to help in any others. + * Collect all cases in malloc requiring system memory into sysmalloc + * Use mmap as backup to sbrk + * Place all internal state in malloc_state + * Introduce fastbins (although similar to 2.5.1) + * Many minor tunings and cosmetic improvements + * Introduce USE_PUBLIC_MALLOC_WRAPPERS, USE_MALLOC_LOCK + * Introduce MALLOC_FAILURE_ACTION, MORECORE_CONTIGUOUS + Thanks to Tony E. Bennett and others. + * Include errno.h to support default failure action. + + V2.6.6 Sun Dec 5 07:42:19 1999 Doug Lea (dl at gee) + * return null for negative arguments + * Added Several WIN32 cleanups from Martin C. Fong + * Add 'LACKS_SYS_PARAM_H' for those systems without 'sys/param.h' + (e.g. WIN32 platforms) + * Cleanup header file inclusion for WIN32 platforms + * Cleanup code to avoid Microsoft Visual C++ compiler complaints + * Add 'USE_DL_PREFIX' to quickly allow co-existence with existing + memory allocation routines + * Set 'malloc_getpagesize' for WIN32 platforms (needs more work) + * Use 'assert' rather than 'ASSERT' in WIN32 code to conform to + usage of 'assert' in non-WIN32 code + * Improve WIN32 'sbrk()' emulation's 'findRegion()' routine to + avoid infinite loop + * Always call 'fREe()' rather than 'free()' + + V2.6.5 Wed Jun 17 15:57:31 1998 Doug Lea (dl at gee) + * Fixed ordering problem with boundary-stamping + + V2.6.3 Sun May 19 08:17:58 1996 Doug Lea (dl at gee) + * Added pvalloc, as recommended by H.J. Liu + * Added 64bit pointer support mainly from Wolfram Gloger + * Added anonymously donated WIN32 sbrk emulation + * Malloc, calloc, getpagesize: add optimizations from Raymond Nijssen + * malloc_extend_top: fix mask error that caused wastage after + foreign sbrks + * Add linux mremap support code from HJ Liu + + V2.6.2 Tue Dec 5 06:52:55 1995 Doug Lea (dl at gee) + * Integrated most documentation with the code. + * Add support for mmap, with help from + Wolfram Gloger (Gloger@lrz.uni-muenchen.de). + * Use last_remainder in more cases. + * Pack bins using idea from colin@nyx10.cs.du.edu + * Use ordered bins instead of best-fit threshhold + * Eliminate block-local decls to simplify tracing and debugging. + * Support another case of realloc via move into top + * Fix error occuring when initial sbrk_base not word-aligned. + * Rely on page size for units instead of SBRK_UNIT to + avoid surprises about sbrk alignment conventions. + * Add mallinfo, mallopt. Thanks to Raymond Nijssen + (raymond@es.ele.tue.nl) for the suggestion. + * Add `pad' argument to malloc_trim and top_pad mallopt parameter. + * More precautions for cases where other routines call sbrk, + courtesy of Wolfram Gloger (Gloger@lrz.uni-muenchen.de). + * Added macros etc., allowing use in linux libc from + H.J. Lu (hjl@gnu.ai.mit.edu) + * Inverted this history list + + V2.6.1 Sat Dec 2 14:10:57 1995 Doug Lea (dl at gee) + * Re-tuned and fixed to behave more nicely with V2.6.0 changes. + * Removed all preallocation code since under current scheme + the work required to undo bad preallocations exceeds + the work saved in good cases for most test programs. + * No longer use return list or unconsolidated bins since + no scheme using them consistently outperforms those that don't + given above changes. + * Use best fit for very large chunks to prevent some worst-cases. + * Added some support for debugging + + V2.6.0 Sat Nov 4 07:05:23 1995 Doug Lea (dl at gee) + * Removed footers when chunks are in use. Thanks to + Paul Wilson (wilson@cs.texas.edu) for the suggestion. + + V2.5.4 Wed Nov 1 07:54:51 1995 Doug Lea (dl at gee) + * Added malloc_trim, with help from Wolfram Gloger + (wmglo@Dent.MED.Uni-Muenchen.DE). + + V2.5.3 Tue Apr 26 10:16:01 1994 Doug Lea (dl at g) + + V2.5.2 Tue Apr 5 16:20:40 1994 Doug Lea (dl at g) + * realloc: try to expand in both directions + * malloc: swap order of clean-bin strategy; + * realloc: only conditionally expand backwards + * Try not to scavenge used bins + * Use bin counts as a guide to preallocation + * Occasionally bin return list chunks in first scan + * Add a few optimizations from colin@nyx10.cs.du.edu + + V2.5.1 Sat Aug 14 15:40:43 1993 Doug Lea (dl at g) + * faster bin computation & slightly different binning + * merged all consolidations to one part of malloc proper + (eliminating old malloc_find_space & malloc_clean_bin) + * Scan 2 returns chunks (not just 1) + * Propagate failure in realloc if malloc returns 0 + * Add stuff to allow compilation on non-ANSI compilers + from kpv@research.att.com + + V2.5 Sat Aug 7 07:41:59 1993 Doug Lea (dl at g.oswego.edu) + * removed potential for odd address access in prev_chunk + * removed dependency on getpagesize.h + * misc cosmetics and a bit more internal documentation + * anticosmetics: mangled names in macros to evade debugger strangeness + * tested on sparc, hp-700, dec-mips, rs6000 + with gcc & native cc (hp, dec only) allowing + Detlefs & Zorn comparison study (in SIGPLAN Notices.) + + Trial version Fri Aug 28 13:14:29 1992 Doug Lea (dl at g.oswego.edu) + * Based loosely on libg++-1.2X malloc. (It retains some of the overall + structure of old version, but most details differ.) + +*/ diff --git a/nolibc/dtoa.c b/nolibc/dtoa.c new file mode 100644 index 0000000..bc9efeb --- /dev/null +++ b/nolibc/dtoa.c @@ -0,0 +1,6234 @@ +/**************************************************************** + * + * The author of this software is David M. Gay. + * + * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. + * + * Permission to use, copy, modify, and distribute this software for any + * purpose without fee is hereby granted, provided that this entire notice + * is included in all copies of any software which is or includes a copy + * or modification of this software and in all copies of the supporting + * documentation for such software. + * + * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED + * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY + * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY + * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. + * + ***************************************************************/ + +/* Configuration and modifications specific to compliation for + * ocaml-freestanding. + */ + +#if defined(__x86_64__) || defined(__aarch64__) +#define IEEE_8087 +#define Long int +#else +#error Unsupported architecture +#endif + +/* Force Flt_Rounds to 1, avoiding pulling in __flt_rounds via FLT_ROUNDS on + * FreeBSD. A fixed value of 1 is used by GCC on Linux and previous versions of + * this code, so we should be fine here. + */ +#define Flt_Rounds 1 + +/* Compile only strtod() and its dependencies + */ +#define STRTOD_ONLY + +#if !defined(__clang__) +#pragma GCC diagnostic ignored "-Wmaybe-uninitialized" +#endif + +/* Please send bug reports to David M. Gay (dmg at acm dot org, + * with " at " changed at "@" and " dot " changed to "."). */ + +/* On a machine with IEEE extended-precision registers, it is + * necessary to specify double-precision (53-bit) rounding precision + * before invoking strtod or dtoa. If the machine uses (the equivalent + * of) Intel 80x87 arithmetic, the call + * _control87(PC_53, MCW_PC); + * does this with many compilers. Whether this or another call is + * appropriate depends on the compiler; for this to work, it may be + * necessary to #include "float.h" or another system-dependent header + * file. + */ + +/* strtod for IEEE-, VAX-, and IBM-arithmetic machines. + * (Note that IEEE arithmetic is disabled by gcc's -ffast-math flag.) + * + * This strtod returns a nearest machine number to the input decimal + * string (or sets errno to ERANGE). With IEEE arithmetic, ties are + * broken by the IEEE round-even rule. Otherwise ties are broken by + * biased rounding (add half and chop). + * + * Inspired loosely by William D. Clinger's paper "How to Read Floating + * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. + * + * Modifications: + * + * 1. We only require IEEE, IBM, or VAX double-precision + * arithmetic (not IEEE double-extended). + * 2. We get by with floating-point arithmetic in a case that + * Clinger missed -- when we're computing d * 10^n + * for a small integer d and the integer n is not too + * much larger than 22 (the maximum integer k for which + * we can represent 10^k exactly), we may be able to + * compute (d*10^k) * 10^(e-k) with just one roundoff. + * 3. Rather than a bit-at-a-time adjustment of the binary + * result in the hard case, we use floating-point + * arithmetic to determine the adjustment to within + * one bit; only in really hard cases do we need to + * compute a second residual. + * 4. Because of 3., we don't need a large table of powers of 10 + * for ten-to-e (just some small tables, e.g. of 10^k + * for 0 <= k <= 22). + */ + +/* + * #define IEEE_8087 for IEEE-arithmetic machines where the least + * significant byte has the lowest address. + * #define IEEE_MC68k for IEEE-arithmetic machines where the most + * significant byte has the lowest address. + * #define Long int on machines with 32-bit ints and 64-bit longs. + * #define IBM for IBM mainframe-style floating-point arithmetic. + * #define VAX for VAX-style floating-point arithmetic (D_floating). + * #define No_leftright to omit left-right logic in fast floating-point + * computation of dtoa. This will cause dtoa modes 4 and 5 to be + * treated the same as modes 2 and 3 for some inputs. + * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 + * and strtod and dtoa should round accordingly. Unless Trust_FLT_ROUNDS + * is also #defined, fegetround() will be queried for the rounding mode. + * Note that both FLT_ROUNDS and fegetround() are specified by the C99 + * standard (and are specified to be consistent, with fesetround() + * affecting the value of FLT_ROUNDS), but that some (Linux) systems + * do not work correctly in this regard, so using fegetround() is more + * portable than using FLT_ROUNDS directly. + * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3 + * and Honor_FLT_ROUNDS is not #defined. + * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines + * that use extended-precision instructions to compute rounded + * products and quotients) with IBM. + * #define ROUND_BIASED for IEEE-format with biased rounding and arithmetic + * that rounds toward +Infinity. + * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased + * rounding when the underlying floating-point arithmetic uses + * unbiased rounding. This prevent using ordinary floating-point + * arithmetic when the result could be computed with one rounding error. + * #define Inaccurate_Divide for IEEE-format with correctly rounded + * products but inaccurate quotients, e.g., for Intel i860. + * #define NO_LONG_LONG on machines that do not have a "long long" + * integer type (of >= 64 bits). On such machines, you can + * #define Just_16 to store 16 bits per 32-bit Long when doing + * high-precision integer arithmetic. Whether this speeds things + * up or slows things down depends on the machine and the number + * being converted. If long long is available and the name is + * something other than "long long", #define Llong to be the name, + * and if "unsigned Llong" does not work as an unsigned version of + * Llong, #define #ULLong to be the corresponding unsigned type. + * #define Bad_float_h if your system lacks a float.h or if it does not + * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP, + * FLT_RADIX, FLT_ROUNDS, and DBL_MAX. + * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n) + * if memory is available and otherwise does something you deem + * appropriate. If MALLOC is undefined, malloc will be invoked + * directly -- and assumed always to succeed. Similarly, if you + * want something other than the system's free() to be called to + * recycle memory acquired from MALLOC, #define FREE to be the + * name of the alternate routine. (FREE or free is only called in + * pathological cases, e.g., in a dtoa call after a dtoa return in + * mode 3 with thousands of digits requested.) + * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making + * memory allocations from a private pool of memory when possible. + * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes, + * unless #defined to be a different length. This default length + * suffices to get rid of MALLOC calls except for unusual cases, + * such as decimal-to-binary conversion of a very long string of + * digits. The longest string dtoa can return is about 751 bytes + * long. For conversions by strtod of strings of 800 digits and + * all dtoa conversions in single-threaded executions with 8-byte + * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte + * pointers, PRIVATE_MEM >= 7112 appears adequate. + * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK + * #defined automatically on IEEE systems. On such systems, + * when INFNAN_CHECK is #defined, strtod checks + * for Infinity and NaN (case insensitively). On some systems + * (e.g., some HP systems), it may be necessary to #define NAN_WORD0 + * appropriately -- to the most significant word of a quiet NaN. + * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.) + * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined, + * strtod also accepts (case insensitively) strings of the form + * NaN(x), where x is a string of hexadecimal digits and spaces; + * if there is only one string of hexadecimal digits, it is taken + * for the 52 fraction bits of the resulting NaN; if there are two + * or more strings of hex digits, the first is for the high 20 bits, + * the second and subsequent for the low 32 bits, with intervening + * white space ignored; but if this results in none of the 52 + * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0 + * and NAN_WORD1 are used instead. + * #define MULTIPLE_THREADS if the system offers preemptively scheduled + * multiple threads. In this case, you must provide (or suitably + * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed + * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed + * in pow5mult, ensures lazy evaluation of only one copy of high + * powers of 5; omitting this lock would introduce a small + * probability of wasting memory, but would otherwise be harmless.) + * You must also invoke freedtoa(s) to free the value s returned by + * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined. + + * When MULTIPLE_THREADS is #defined, this source file provides + * void set_max_dtoa_threads(unsigned int n); + * and expects + * unsigned int dtoa_get_threadno(void); + * to be available (possibly provided by + * #define dtoa_get_threadno omp_get_thread_num + * if OpenMP is in use or by + * #define dtoa_get_threadno pthread_self + * if Pthreads is in use), to return the current thread number. + * If set_max_dtoa_threads(n) was called and the current thread + * number is k with k < n, then calls on ACQUIRE_DTOA_LOCK(...) and + * FREE_DTOA_LOCK(...) are avoided; instead each thread with thread + * number < n has a separate copy of relevant data structures. + * After set_max_dtoa_threads(n), a call set_max_dtoa_threads(m) + * with m <= n has has no effect, but a call with m > n is honored. + * Such a call invokes REALLOC (assumed to be "realloc" if REALLOC + * is not #defined) to extend the size of the relevant array. + + * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that + * avoids underflows on inputs whose result does not underflow. + * If you #define NO_IEEE_Scale on a machine that uses IEEE-format + * floating-point numbers and flushes underflows to zero rather + * than implementing gradual underflow, then you must also #define + * Sudden_Underflow. + * #define USE_LOCALE to use the current locale's decimal_point value. + * #define SET_INEXACT if IEEE arithmetic is being used and extra + * computation should be done to set the inexact flag when the + * result is inexact and avoid setting inexact when the result + * is exact. In this case, dtoa.c must be compiled in + * an environment, perhaps provided by #include "dtoa.c" in a + * suitable wrapper, that defines two functions, + * int get_inexact(void); + * void clear_inexact(void); + * such that get_inexact() returns a nonzero value if the + * inexact bit is already set, and clear_inexact() sets the + * inexact bit to 0. When SET_INEXACT is #defined, strtod + * also does extra computations to set the underflow and overflow + * flags when appropriate (i.e., when the result is tiny and + * inexact or when it is a numeric value rounded to +-infinity). + * #define NO_ERRNO if strtod should not assign errno = ERANGE when + * the result overflows to +-Infinity or underflows to 0. + * When errno should be assigned, under seemingly rare conditions + * it may be necessary to define Set_errno(x) suitably, e.g., in + * a local errno.h, such as + * #include + * #define Set_errno(x) _set_errno(x) + * #define NO_HEX_FP to omit recognition of hexadecimal floating-point + * values by strtod. + * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now) + * to disable logic for "fast" testing of very long input strings + * to strtod. This testing proceeds by initially truncating the + * input string, then if necessary comparing the whole string with + * a decimal expansion to decide close cases. This logic is only + * used for input more than STRTOD_DIGLIM digits long (default 40). + */ + +#ifndef Long +#define Long int +#endif +#ifndef ULong +typedef unsigned Long ULong; +#endif + +#ifdef DEBUG +#include +#include "stdio.h" +#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} +#define Debug(x) x +int dtoa_stats[7]; /* strtod_{64,96,bigcomp},dtoa_{exact,64,96,bigcomp} */ +#else +#define assert(x) /*nothing*/ +#define Debug(x) /*nothing*/ +#endif + +#include "stdlib.h" +#include "string.h" + +#ifdef USE_LOCALE +#include "locale.h" +#endif + +#ifdef Honor_FLT_ROUNDS +#ifndef Trust_FLT_ROUNDS +#include +#endif +#endif + +#ifdef __cplusplus +extern "C" { +#endif +#ifdef MALLOC +extern void *MALLOC(size_t); +#else +#define MALLOC malloc +#endif + +#ifdef REALLOC +extern void *REALLOC(void*,size_t); +#else +#define REALLOC realloc +#endif + +#ifndef FREE +#define FREE free +#endif + +#ifdef __cplusplus + } +#endif + +#ifndef Omit_Private_Memory +#ifndef PRIVATE_MEM +#define PRIVATE_MEM 2304 +#endif +#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) +static double private_mem[PRIVATE_mem], *pmem_next = private_mem; +#endif + +#undef IEEE_Arith +#undef Avoid_Underflow +#ifdef IEEE_MC68k +#define IEEE_Arith +#endif +#ifdef IEEE_8087 +#define IEEE_Arith +#endif + +#ifdef IEEE_Arith +#ifndef NO_INFNAN_CHECK +#undef INFNAN_CHECK +#define INFNAN_CHECK +#endif +#else +#undef INFNAN_CHECK +#define NO_STRTOD_BIGCOMP +#endif + +#include "errno.h" + +#ifdef NO_ERRNO /*{*/ +#undef Set_errno +#define Set_errno(x) +#else +#ifndef Set_errno +#define Set_errno(x) errno = x +#endif +#endif /*}*/ + +#ifdef Bad_float_h + +#ifdef IEEE_Arith +#define DBL_DIG 15 +#define DBL_MAX_10_EXP 308 +#define DBL_MAX_EXP 1024 +#define FLT_RADIX 2 +#endif /*IEEE_Arith*/ + +#ifdef IBM +#define DBL_DIG 16 +#define DBL_MAX_10_EXP 75 +#define DBL_MAX_EXP 63 +#define FLT_RADIX 16 +#define DBL_MAX 7.2370055773322621e+75 +#endif + +#ifdef VAX +#define DBL_DIG 16 +#define DBL_MAX_10_EXP 38 +#define DBL_MAX_EXP 127 +#define FLT_RADIX 2 +#define DBL_MAX 1.7014118346046923e+38 +#endif + +#ifndef LONG_MAX +#define LONG_MAX 2147483647 +#endif + +#else /* ifndef Bad_float_h */ +#include "float.h" +#endif /* Bad_float_h */ + +#ifndef __MATH_H__ +#include "math.h" +#endif + +#ifdef __cplusplus +extern "C" { +#endif + +#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1 +Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined. +#endif + +#undef USE_BF96 + +#ifdef NO_LONG_LONG /*{{*/ +#undef ULLong +#ifdef Just_16 +#undef Pack_32 +/* When Pack_32 is not defined, we store 16 bits per 32-bit Long. + * This makes some inner loops simpler and sometimes saves work + * during multiplications, but it often seems to make things slightly + * slower. Hence the default is now to store 32 bits per Long. + */ +#endif +#else /*}{ long long available */ +#ifndef Llong +#define Llong long long +#endif +#ifndef ULLong +#define ULLong unsigned Llong +#endif +#ifndef NO_BF96 /*{*/ +#define USE_BF96 + +#ifdef SET_INEXACT +#define dtoa_divmax 27 +#else +int dtoa_divmax = 2; /* Permit experimenting: on some systems, 64-bit integer */ + /* division is slow enough that we may sometimes want to */ + /* avoid using it. We assume (but do not check) that */ + /* dtoa_divmax <= 27.*/ +#endif + +typedef struct BF96 { /* Normalized 96-bit software floating point numbers */ + unsigned int b0,b1,b2; /* b0 = most significant, binary point just to its left */ + int e; /* number represented = b * 2^e, with .5 <= b < 1 */ + } BF96; + + static BF96 pten[667] = { + { 0xeef453d6, 0x923bd65a, 0x113faa29, -1136 }, + { 0x9558b466, 0x1b6565f8, 0x4ac7ca59, -1132 }, + { 0xbaaee17f, 0xa23ebf76, 0x5d79bcf0, -1129 }, + { 0xe95a99df, 0x8ace6f53, 0xf4d82c2c, -1126 }, + { 0x91d8a02b, 0xb6c10594, 0x79071b9b, -1122 }, + { 0xb64ec836, 0xa47146f9, 0x9748e282, -1119 }, + { 0xe3e27a44, 0x4d8d98b7, 0xfd1b1b23, -1116 }, + { 0x8e6d8c6a, 0xb0787f72, 0xfe30f0f5, -1112 }, + { 0xb208ef85, 0x5c969f4f, 0xbdbd2d33, -1109 }, + { 0xde8b2b66, 0xb3bc4723, 0xad2c7880, -1106 }, + { 0x8b16fb20, 0x3055ac76, 0x4c3bcb50, -1102 }, + { 0xaddcb9e8, 0x3c6b1793, 0xdf4abe24, -1099 }, + { 0xd953e862, 0x4b85dd78, 0xd71d6dad, -1096 }, + { 0x87d4713d, 0x6f33aa6b, 0x8672648c, -1092 }, + { 0xa9c98d8c, 0xcb009506, 0x680efdaf, -1089 }, + { 0xd43bf0ef, 0xfdc0ba48, 0x0212bd1b, -1086 }, + { 0x84a57695, 0xfe98746d, 0x014bb630, -1082 }, + { 0xa5ced43b, 0x7e3e9188, 0x419ea3bd, -1079 }, + { 0xcf42894a, 0x5dce35ea, 0x52064cac, -1076 }, + { 0x818995ce, 0x7aa0e1b2, 0x7343efeb, -1072 }, + { 0xa1ebfb42, 0x19491a1f, 0x1014ebe6, -1069 }, + { 0xca66fa12, 0x9f9b60a6, 0xd41a26e0, -1066 }, + { 0xfd00b897, 0x478238d0, 0x8920b098, -1063 }, + { 0x9e20735e, 0x8cb16382, 0x55b46e5f, -1059 }, + { 0xc5a89036, 0x2fddbc62, 0xeb2189f7, -1056 }, + { 0xf712b443, 0xbbd52b7b, 0xa5e9ec75, -1053 }, + { 0x9a6bb0aa, 0x55653b2d, 0x47b233c9, -1049 }, + { 0xc1069cd4, 0xeabe89f8, 0x999ec0bb, -1046 }, + { 0xf148440a, 0x256e2c76, 0xc00670ea, -1043 }, + { 0x96cd2a86, 0x5764dbca, 0x38040692, -1039 }, + { 0xbc807527, 0xed3e12bc, 0xc6050837, -1036 }, + { 0xeba09271, 0xe88d976b, 0xf7864a44, -1033 }, + { 0x93445b87, 0x31587ea3, 0x7ab3ee6a, -1029 }, + { 0xb8157268, 0xfdae9e4c, 0x5960ea05, -1026 }, + { 0xe61acf03, 0x3d1a45df, 0x6fb92487, -1023 }, + { 0x8fd0c162, 0x06306bab, 0xa5d3b6d4, -1019 }, + { 0xb3c4f1ba, 0x87bc8696, 0x8f48a489, -1016 }, + { 0xe0b62e29, 0x29aba83c, 0x331acdab, -1013 }, + { 0x8c71dcd9, 0xba0b4925, 0x9ff0c08b, -1009 }, + { 0xaf8e5410, 0x288e1b6f, 0x07ecf0ae, -1006 }, + { 0xdb71e914, 0x32b1a24a, 0xc9e82cd9, -1003 }, + { 0x892731ac, 0x9faf056e, 0xbe311c08, -999 }, + { 0xab70fe17, 0xc79ac6ca, 0x6dbd630a, -996 }, + { 0xd64d3d9d, 0xb981787d, 0x092cbbcc, -993 }, + { 0x85f04682, 0x93f0eb4e, 0x25bbf560, -989 }, + { 0xa76c5823, 0x38ed2621, 0xaf2af2b8, -986 }, + { 0xd1476e2c, 0x07286faa, 0x1af5af66, -983 }, + { 0x82cca4db, 0x847945ca, 0x50d98d9f, -979 }, + { 0xa37fce12, 0x6597973c, 0xe50ff107, -976 }, + { 0xcc5fc196, 0xfefd7d0c, 0x1e53ed49, -973 }, + { 0xff77b1fc, 0xbebcdc4f, 0x25e8e89c, -970 }, + { 0x9faacf3d, 0xf73609b1, 0x77b19161, -966 }, + { 0xc795830d, 0x75038c1d, 0xd59df5b9, -963 }, + { 0xf97ae3d0, 0xd2446f25, 0x4b057328, -960 }, + { 0x9becce62, 0x836ac577, 0x4ee367f9, -956 }, + { 0xc2e801fb, 0x244576d5, 0x229c41f7, -953 }, + { 0xf3a20279, 0xed56d48a, 0x6b435275, -950 }, + { 0x9845418c, 0x345644d6, 0x830a1389, -946 }, + { 0xbe5691ef, 0x416bd60c, 0x23cc986b, -943 }, + { 0xedec366b, 0x11c6cb8f, 0x2cbfbe86, -940 }, + { 0x94b3a202, 0xeb1c3f39, 0x7bf7d714, -936 }, + { 0xb9e08a83, 0xa5e34f07, 0xdaf5ccd9, -933 }, + { 0xe858ad24, 0x8f5c22c9, 0xd1b3400f, -930 }, + { 0x91376c36, 0xd99995be, 0x23100809, -926 }, + { 0xb5854744, 0x8ffffb2d, 0xabd40a0c, -923 }, + { 0xe2e69915, 0xb3fff9f9, 0x16c90c8f, -920 }, + { 0x8dd01fad, 0x907ffc3b, 0xae3da7d9, -916 }, + { 0xb1442798, 0xf49ffb4a, 0x99cd11cf, -913 }, + { 0xdd95317f, 0x31c7fa1d, 0x40405643, -910 }, + { 0x8a7d3eef, 0x7f1cfc52, 0x482835ea, -906 }, + { 0xad1c8eab, 0x5ee43b66, 0xda324365, -903 }, + { 0xd863b256, 0x369d4a40, 0x90bed43e, -900 }, + { 0x873e4f75, 0xe2224e68, 0x5a7744a6, -896 }, + { 0xa90de353, 0x5aaae202, 0x711515d0, -893 }, + { 0xd3515c28, 0x31559a83, 0x0d5a5b44, -890 }, + { 0x8412d999, 0x1ed58091, 0xe858790a, -886 }, + { 0xa5178fff, 0x668ae0b6, 0x626e974d, -883 }, + { 0xce5d73ff, 0x402d98e3, 0xfb0a3d21, -880 }, + { 0x80fa687f, 0x881c7f8e, 0x7ce66634, -876 }, + { 0xa139029f, 0x6a239f72, 0x1c1fffc1, -873 }, + { 0xc9874347, 0x44ac874e, 0xa327ffb2, -870 }, + { 0xfbe91419, 0x15d7a922, 0x4bf1ff9f, -867 }, + { 0x9d71ac8f, 0xada6c9b5, 0x6f773fc3, -863 }, + { 0xc4ce17b3, 0x99107c22, 0xcb550fb4, -860 }, + { 0xf6019da0, 0x7f549b2b, 0x7e2a53a1, -857 }, + { 0x99c10284, 0x4f94e0fb, 0x2eda7444, -853 }, + { 0xc0314325, 0x637a1939, 0xfa911155, -850 }, + { 0xf03d93ee, 0xbc589f88, 0x793555ab, -847 }, + { 0x96267c75, 0x35b763b5, 0x4bc1558b, -843 }, + { 0xbbb01b92, 0x83253ca2, 0x9eb1aaed, -840 }, + { 0xea9c2277, 0x23ee8bcb, 0x465e15a9, -837 }, + { 0x92a1958a, 0x7675175f, 0x0bfacd89, -833 }, + { 0xb749faed, 0x14125d36, 0xcef980ec, -830 }, + { 0xe51c79a8, 0x5916f484, 0x82b7e127, -827 }, + { 0x8f31cc09, 0x37ae58d2, 0xd1b2ecb8, -823 }, + { 0xb2fe3f0b, 0x8599ef07, 0x861fa7e6, -820 }, + { 0xdfbdcece, 0x67006ac9, 0x67a791e0, -817 }, + { 0x8bd6a141, 0x006042bd, 0xe0c8bb2c, -813 }, + { 0xaecc4991, 0x4078536d, 0x58fae9f7, -810 }, + { 0xda7f5bf5, 0x90966848, 0xaf39a475, -807 }, + { 0x888f9979, 0x7a5e012d, 0x6d8406c9, -803 }, + { 0xaab37fd7, 0xd8f58178, 0xc8e5087b, -800 }, + { 0xd5605fcd, 0xcf32e1d6, 0xfb1e4a9a, -797 }, + { 0x855c3be0, 0xa17fcd26, 0x5cf2eea0, -793 }, + { 0xa6b34ad8, 0xc9dfc06f, 0xf42faa48, -790 }, + { 0xd0601d8e, 0xfc57b08b, 0xf13b94da, -787 }, + { 0x823c1279, 0x5db6ce57, 0x76c53d08, -783 }, + { 0xa2cb1717, 0xb52481ed, 0x54768c4b, -780 }, + { 0xcb7ddcdd, 0xa26da268, 0xa9942f5d, -777 }, + { 0xfe5d5415, 0x0b090b02, 0xd3f93b35, -774 }, + { 0x9efa548d, 0x26e5a6e1, 0xc47bc501, -770 }, + { 0xc6b8e9b0, 0x709f109a, 0x359ab641, -767 }, + { 0xf867241c, 0x8cc6d4c0, 0xc30163d2, -764 }, + { 0x9b407691, 0xd7fc44f8, 0x79e0de63, -760 }, + { 0xc2109436, 0x4dfb5636, 0x985915fc, -757 }, + { 0xf294b943, 0xe17a2bc4, 0x3e6f5b7b, -754 }, + { 0x979cf3ca, 0x6cec5b5a, 0xa705992c, -750 }, + { 0xbd8430bd, 0x08277231, 0x50c6ff78, -747 }, + { 0xece53cec, 0x4a314ebd, 0xa4f8bf56, -744 }, + { 0x940f4613, 0xae5ed136, 0x871b7795, -740 }, + { 0xb9131798, 0x99f68584, 0x28e2557b, -737 }, + { 0xe757dd7e, 0xc07426e5, 0x331aeada, -734 }, + { 0x9096ea6f, 0x3848984f, 0x3ff0d2c8, -730 }, + { 0xb4bca50b, 0x065abe63, 0x0fed077a, -727 }, + { 0xe1ebce4d, 0xc7f16dfb, 0xd3e84959, -724 }, + { 0x8d3360f0, 0x9cf6e4bd, 0x64712dd7, -720 }, + { 0xb080392c, 0xc4349dec, 0xbd8d794d, -717 }, + { 0xdca04777, 0xf541c567, 0xecf0d7a0, -714 }, + { 0x89e42caa, 0xf9491b60, 0xf41686c4, -710 }, + { 0xac5d37d5, 0xb79b6239, 0x311c2875, -707 }, + { 0xd77485cb, 0x25823ac7, 0x7d633293, -704 }, + { 0x86a8d39e, 0xf77164bc, 0xae5dff9c, -700 }, + { 0xa8530886, 0xb54dbdeb, 0xd9f57f83, -697 }, + { 0xd267caa8, 0x62a12d66, 0xd072df63, -694 }, + { 0x8380dea9, 0x3da4bc60, 0x4247cb9e, -690 }, + { 0xa4611653, 0x8d0deb78, 0x52d9be85, -687 }, + { 0xcd795be8, 0x70516656, 0x67902e27, -684 }, + { 0x806bd971, 0x4632dff6, 0x00ba1cd8, -680 }, + { 0xa086cfcd, 0x97bf97f3, 0x80e8a40e, -677 }, + { 0xc8a883c0, 0xfdaf7df0, 0x6122cd12, -674 }, + { 0xfad2a4b1, 0x3d1b5d6c, 0x796b8057, -671 }, + { 0x9cc3a6ee, 0xc6311a63, 0xcbe33036, -667 }, + { 0xc3f490aa, 0x77bd60fc, 0xbedbfc44, -664 }, + { 0xf4f1b4d5, 0x15acb93b, 0xee92fb55, -661 }, + { 0x99171105, 0x2d8bf3c5, 0x751bdd15, -657 }, + { 0xbf5cd546, 0x78eef0b6, 0xd262d45a, -654 }, + { 0xef340a98, 0x172aace4, 0x86fb8971, -651 }, + { 0x9580869f, 0x0e7aac0e, 0xd45d35e6, -647 }, + { 0xbae0a846, 0xd2195712, 0x89748360, -644 }, + { 0xe998d258, 0x869facd7, 0x2bd1a438, -641 }, + { 0x91ff8377, 0x5423cc06, 0x7b6306a3, -637 }, + { 0xb67f6455, 0x292cbf08, 0x1a3bc84c, -634 }, + { 0xe41f3d6a, 0x7377eeca, 0x20caba5f, -631 }, + { 0x8e938662, 0x882af53e, 0x547eb47b, -627 }, + { 0xb23867fb, 0x2a35b28d, 0xe99e619a, -624 }, + { 0xdec681f9, 0xf4c31f31, 0x6405fa00, -621 }, + { 0x8b3c113c, 0x38f9f37e, 0xde83bc40, -617 }, + { 0xae0b158b, 0x4738705e, 0x9624ab50, -614 }, + { 0xd98ddaee, 0x19068c76, 0x3badd624, -611 }, + { 0x87f8a8d4, 0xcfa417c9, 0xe54ca5d7, -607 }, + { 0xa9f6d30a, 0x038d1dbc, 0x5e9fcf4c, -604 }, + { 0xd47487cc, 0x8470652b, 0x7647c320, -601 }, + { 0x84c8d4df, 0xd2c63f3b, 0x29ecd9f4, -597 }, + { 0xa5fb0a17, 0xc777cf09, 0xf4681071, -594 }, + { 0xcf79cc9d, 0xb955c2cc, 0x7182148d, -591 }, + { 0x81ac1fe2, 0x93d599bf, 0xc6f14cd8, -587 }, + { 0xa21727db, 0x38cb002f, 0xb8ada00e, -584 }, + { 0xca9cf1d2, 0x06fdc03b, 0xa6d90811, -581 }, + { 0xfd442e46, 0x88bd304a, 0x908f4a16, -578 }, + { 0x9e4a9cec, 0x15763e2e, 0x9a598e4e, -574 }, + { 0xc5dd4427, 0x1ad3cdba, 0x40eff1e1, -571 }, + { 0xf7549530, 0xe188c128, 0xd12bee59, -568 }, + { 0x9a94dd3e, 0x8cf578b9, 0x82bb74f8, -564 }, + { 0xc13a148e, 0x3032d6e7, 0xe36a5236, -561 }, + { 0xf18899b1, 0xbc3f8ca1, 0xdc44e6c3, -558 }, + { 0x96f5600f, 0x15a7b7e5, 0x29ab103a, -554 }, + { 0xbcb2b812, 0xdb11a5de, 0x7415d448, -551 }, + { 0xebdf6617, 0x91d60f56, 0x111b495b, -548 }, + { 0x936b9fce, 0xbb25c995, 0xcab10dd9, -544 }, + { 0xb84687c2, 0x69ef3bfb, 0x3d5d514f, -541 }, + { 0xe65829b3, 0x046b0afa, 0x0cb4a5a3, -538 }, + { 0x8ff71a0f, 0xe2c2e6dc, 0x47f0e785, -534 }, + { 0xb3f4e093, 0xdb73a093, 0x59ed2167, -531 }, + { 0xe0f218b8, 0xd25088b8, 0x306869c1, -528 }, + { 0x8c974f73, 0x83725573, 0x1e414218, -524 }, + { 0xafbd2350, 0x644eeacf, 0xe5d1929e, -521 }, + { 0xdbac6c24, 0x7d62a583, 0xdf45f746, -518 }, + { 0x894bc396, 0xce5da772, 0x6b8bba8c, -514 }, + { 0xab9eb47c, 0x81f5114f, 0x066ea92f, -511 }, + { 0xd686619b, 0xa27255a2, 0xc80a537b, -508 }, + { 0x8613fd01, 0x45877585, 0xbd06742c, -504 }, + { 0xa798fc41, 0x96e952e7, 0x2c481138, -501 }, + { 0xd17f3b51, 0xfca3a7a0, 0xf75a1586, -498 }, + { 0x82ef8513, 0x3de648c4, 0x9a984d73, -494 }, + { 0xa3ab6658, 0x0d5fdaf5, 0xc13e60d0, -491 }, + { 0xcc963fee, 0x10b7d1b3, 0x318df905, -488 }, + { 0xffbbcfe9, 0x94e5c61f, 0xfdf17746, -485 }, + { 0x9fd561f1, 0xfd0f9bd3, 0xfeb6ea8b, -481 }, + { 0xc7caba6e, 0x7c5382c8, 0xfe64a52e, -478 }, + { 0xf9bd690a, 0x1b68637b, 0x3dfdce7a, -475 }, + { 0x9c1661a6, 0x51213e2d, 0x06bea10c, -471 }, + { 0xc31bfa0f, 0xe5698db8, 0x486e494f, -468 }, + { 0xf3e2f893, 0xdec3f126, 0x5a89dba3, -465 }, + { 0x986ddb5c, 0x6b3a76b7, 0xf8962946, -461 }, + { 0xbe895233, 0x86091465, 0xf6bbb397, -458 }, + { 0xee2ba6c0, 0x678b597f, 0x746aa07d, -455 }, + { 0x94db4838, 0x40b717ef, 0xa8c2a44e, -451 }, + { 0xba121a46, 0x50e4ddeb, 0x92f34d62, -448 }, + { 0xe896a0d7, 0xe51e1566, 0x77b020ba, -445 }, + { 0x915e2486, 0xef32cd60, 0x0ace1474, -441 }, + { 0xb5b5ada8, 0xaaff80b8, 0x0d819992, -438 }, + { 0xe3231912, 0xd5bf60e6, 0x10e1fff6, -435 }, + { 0x8df5efab, 0xc5979c8f, 0xca8d3ffa, -431 }, + { 0xb1736b96, 0xb6fd83b3, 0xbd308ff8, -428 }, + { 0xddd0467c, 0x64bce4a0, 0xac7cb3f6, -425 }, + { 0x8aa22c0d, 0xbef60ee4, 0x6bcdf07a, -421 }, + { 0xad4ab711, 0x2eb3929d, 0x86c16c98, -418 }, + { 0xd89d64d5, 0x7a607744, 0xe871c7bf, -415 }, + { 0x87625f05, 0x6c7c4a8b, 0x11471cd7, -411 }, + { 0xa93af6c6, 0xc79b5d2d, 0xd598e40d, -408 }, + { 0xd389b478, 0x79823479, 0x4aff1d10, -405 }, + { 0x843610cb, 0x4bf160cb, 0xcedf722a, -401 }, + { 0xa54394fe, 0x1eedb8fe, 0xc2974eb4, -398 }, + { 0xce947a3d, 0xa6a9273e, 0x733d2262, -395 }, + { 0x811ccc66, 0x8829b887, 0x0806357d, -391 }, + { 0xa163ff80, 0x2a3426a8, 0xca07c2dc, -388 }, + { 0xc9bcff60, 0x34c13052, 0xfc89b393, -385 }, + { 0xfc2c3f38, 0x41f17c67, 0xbbac2078, -382 }, + { 0x9d9ba783, 0x2936edc0, 0xd54b944b, -378 }, + { 0xc5029163, 0xf384a931, 0x0a9e795e, -375 }, + { 0xf64335bc, 0xf065d37d, 0x4d4617b5, -372 }, + { 0x99ea0196, 0x163fa42e, 0x504bced1, -368 }, + { 0xc06481fb, 0x9bcf8d39, 0xe45ec286, -365 }, + { 0xf07da27a, 0x82c37088, 0x5d767327, -362 }, + { 0x964e858c, 0x91ba2655, 0x3a6a07f8, -358 }, + { 0xbbe226ef, 0xb628afea, 0x890489f7, -355 }, + { 0xeadab0ab, 0xa3b2dbe5, 0x2b45ac74, -352 }, + { 0x92c8ae6b, 0x464fc96f, 0x3b0b8bc9, -348 }, + { 0xb77ada06, 0x17e3bbcb, 0x09ce6ebb, -345 }, + { 0xe5599087, 0x9ddcaabd, 0xcc420a6a, -342 }, + { 0x8f57fa54, 0xc2a9eab6, 0x9fa94682, -338 }, + { 0xb32df8e9, 0xf3546564, 0x47939822, -335 }, + { 0xdff97724, 0x70297ebd, 0x59787e2b, -332 }, + { 0x8bfbea76, 0xc619ef36, 0x57eb4edb, -328 }, + { 0xaefae514, 0x77a06b03, 0xede62292, -325 }, + { 0xdab99e59, 0x958885c4, 0xe95fab36, -322 }, + { 0x88b402f7, 0xfd75539b, 0x11dbcb02, -318 }, + { 0xaae103b5, 0xfcd2a881, 0xd652bdc2, -315 }, + { 0xd59944a3, 0x7c0752a2, 0x4be76d33, -312 }, + { 0x857fcae6, 0x2d8493a5, 0x6f70a440, -308 }, + { 0xa6dfbd9f, 0xb8e5b88e, 0xcb4ccd50, -305 }, + { 0xd097ad07, 0xa71f26b2, 0x7e2000a4, -302 }, + { 0x825ecc24, 0xc873782f, 0x8ed40066, -298 }, + { 0xa2f67f2d, 0xfa90563b, 0x72890080, -295 }, + { 0xcbb41ef9, 0x79346bca, 0x4f2b40a0, -292 }, + { 0xfea126b7, 0xd78186bc, 0xe2f610c8, -289 }, + { 0x9f24b832, 0xe6b0f436, 0x0dd9ca7d, -285 }, + { 0xc6ede63f, 0xa05d3143, 0x91503d1c, -282 }, + { 0xf8a95fcf, 0x88747d94, 0x75a44c63, -279 }, + { 0x9b69dbe1, 0xb548ce7c, 0xc986afbe, -275 }, + { 0xc24452da, 0x229b021b, 0xfbe85bad, -272 }, + { 0xf2d56790, 0xab41c2a2, 0xfae27299, -269 }, + { 0x97c560ba, 0x6b0919a5, 0xdccd879f, -265 }, + { 0xbdb6b8e9, 0x05cb600f, 0x5400e987, -262 }, + { 0xed246723, 0x473e3813, 0x290123e9, -259 }, + { 0x9436c076, 0x0c86e30b, 0xf9a0b672, -255 }, + { 0xb9447093, 0x8fa89bce, 0xf808e40e, -252 }, + { 0xe7958cb8, 0x7392c2c2, 0xb60b1d12, -249 }, + { 0x90bd77f3, 0x483bb9b9, 0xb1c6f22b, -245 }, + { 0xb4ecd5f0, 0x1a4aa828, 0x1e38aeb6, -242 }, + { 0xe2280b6c, 0x20dd5232, 0x25c6da63, -239 }, + { 0x8d590723, 0x948a535f, 0x579c487e, -235 }, + { 0xb0af48ec, 0x79ace837, 0x2d835a9d, -232 }, + { 0xdcdb1b27, 0x98182244, 0xf8e43145, -229 }, + { 0x8a08f0f8, 0xbf0f156b, 0x1b8e9ecb, -225 }, + { 0xac8b2d36, 0xeed2dac5, 0xe272467e, -222 }, + { 0xd7adf884, 0xaa879177, 0x5b0ed81d, -219 }, + { 0x86ccbb52, 0xea94baea, 0x98e94712, -215 }, + { 0xa87fea27, 0xa539e9a5, 0x3f2398d7, -212 }, + { 0xd29fe4b1, 0x8e88640e, 0x8eec7f0d, -209 }, + { 0x83a3eeee, 0xf9153e89, 0x1953cf68, -205 }, + { 0xa48ceaaa, 0xb75a8e2b, 0x5fa8c342, -202 }, + { 0xcdb02555, 0x653131b6, 0x3792f412, -199 }, + { 0x808e1755, 0x5f3ebf11, 0xe2bbd88b, -195 }, + { 0xa0b19d2a, 0xb70e6ed6, 0x5b6aceae, -192 }, + { 0xc8de0475, 0x64d20a8b, 0xf245825a, -189 }, + { 0xfb158592, 0xbe068d2e, 0xeed6e2f0, -186 }, + { 0x9ced737b, 0xb6c4183d, 0x55464dd6, -182 }, + { 0xc428d05a, 0xa4751e4c, 0xaa97e14c, -179 }, + { 0xf5330471, 0x4d9265df, 0xd53dd99f, -176 }, + { 0x993fe2c6, 0xd07b7fab, 0xe546a803, -172 }, + { 0xbf8fdb78, 0x849a5f96, 0xde985204, -169 }, + { 0xef73d256, 0xa5c0f77c, 0x963e6685, -166 }, + { 0x95a86376, 0x27989aad, 0xdde70013, -162 }, + { 0xbb127c53, 0xb17ec159, 0x5560c018, -159 }, + { 0xe9d71b68, 0x9dde71af, 0xaab8f01e, -156 }, + { 0x92267121, 0x62ab070d, 0xcab39613, -152 }, + { 0xb6b00d69, 0xbb55c8d1, 0x3d607b97, -149 }, + { 0xe45c10c4, 0x2a2b3b05, 0x8cb89a7d, -146 }, + { 0x8eb98a7a, 0x9a5b04e3, 0x77f3608e, -142 }, + { 0xb267ed19, 0x40f1c61c, 0x55f038b2, -139 }, + { 0xdf01e85f, 0x912e37a3, 0x6b6c46de, -136 }, + { 0x8b61313b, 0xbabce2c6, 0x2323ac4b, -132 }, + { 0xae397d8a, 0xa96c1b77, 0xabec975e, -129 }, + { 0xd9c7dced, 0x53c72255, 0x96e7bd35, -126 }, + { 0x881cea14, 0x545c7575, 0x7e50d641, -122 }, + { 0xaa242499, 0x697392d2, 0xdde50bd1, -119 }, + { 0xd4ad2dbf, 0xc3d07787, 0x955e4ec6, -116 }, + { 0x84ec3c97, 0xda624ab4, 0xbd5af13b, -112 }, + { 0xa6274bbd, 0xd0fadd61, 0xecb1ad8a, -109 }, + { 0xcfb11ead, 0x453994ba, 0x67de18ed, -106 }, + { 0x81ceb32c, 0x4b43fcf4, 0x80eacf94, -102 }, + { 0xa2425ff7, 0x5e14fc31, 0xa1258379, -99 }, + { 0xcad2f7f5, 0x359a3b3e, 0x096ee458, -96 }, + { 0xfd87b5f2, 0x8300ca0d, 0x8bca9d6e, -93 }, + { 0x9e74d1b7, 0x91e07e48, 0x775ea264, -89 }, + { 0xc6120625, 0x76589dda, 0x95364afe, -86 }, + { 0xf79687ae, 0xd3eec551, 0x3a83ddbd, -83 }, + { 0x9abe14cd, 0x44753b52, 0xc4926a96, -79 }, + { 0xc16d9a00, 0x95928a27, 0x75b7053c, -76 }, + { 0xf1c90080, 0xbaf72cb1, 0x5324c68b, -73 }, + { 0x971da050, 0x74da7bee, 0xd3f6fc16, -69 }, + { 0xbce50864, 0x92111aea, 0x88f4bb1c, -66 }, + { 0xec1e4a7d, 0xb69561a5, 0x2b31e9e3, -63 }, + { 0x9392ee8e, 0x921d5d07, 0x3aff322e, -59 }, + { 0xb877aa32, 0x36a4b449, 0x09befeb9, -56 }, + { 0xe69594be, 0xc44de15b, 0x4c2ebe68, -53 }, + { 0x901d7cf7, 0x3ab0acd9, 0x0f9d3701, -49 }, + { 0xb424dc35, 0x095cd80f, 0x538484c1, -46 }, + { 0xe12e1342, 0x4bb40e13, 0x2865a5f2, -43 }, + { 0x8cbccc09, 0x6f5088cb, 0xf93f87b7, -39 }, + { 0xafebff0b, 0xcb24aafe, 0xf78f69a5, -36 }, + { 0xdbe6fece, 0xbdedd5be, 0xb573440e, -33 }, + { 0x89705f41, 0x36b4a597, 0x31680a88, -29 }, + { 0xabcc7711, 0x8461cefc, 0xfdc20d2b, -26 }, + { 0xd6bf94d5, 0xe57a42bc, 0x3d329076, -23 }, + { 0x8637bd05, 0xaf6c69b5, 0xa63f9a49, -19 }, + { 0xa7c5ac47, 0x1b478423, 0x0fcf80dc, -16 }, + { 0xd1b71758, 0xe219652b, 0xd3c36113, -13 }, + { 0x83126e97, 0x8d4fdf3b, 0x645a1cac, -9 }, + { 0xa3d70a3d, 0x70a3d70a, 0x3d70a3d7, -6 }, + { 0xcccccccc, 0xcccccccc, 0xcccccccc, -3 }, + { 0x80000000, 0x00000000, 0x00000000, 1 }, + { 0xa0000000, 0x00000000, 0x00000000, 4 }, + { 0xc8000000, 0x00000000, 0x00000000, 7 }, + { 0xfa000000, 0x00000000, 0x00000000, 10 }, + { 0x9c400000, 0x00000000, 0x00000000, 14 }, + { 0xc3500000, 0x00000000, 0x00000000, 17 }, + { 0xf4240000, 0x00000000, 0x00000000, 20 }, + { 0x98968000, 0x00000000, 0x00000000, 24 }, + { 0xbebc2000, 0x00000000, 0x00000000, 27 }, + { 0xee6b2800, 0x00000000, 0x00000000, 30 }, + { 0x9502f900, 0x00000000, 0x00000000, 34 }, + { 0xba43b740, 0x00000000, 0x00000000, 37 }, + { 0xe8d4a510, 0x00000000, 0x00000000, 40 }, + { 0x9184e72a, 0x00000000, 0x00000000, 44 }, + { 0xb5e620f4, 0x80000000, 0x00000000, 47 }, + { 0xe35fa931, 0xa0000000, 0x00000000, 50 }, + { 0x8e1bc9bf, 0x04000000, 0x00000000, 54 }, + { 0xb1a2bc2e, 0xc5000000, 0x00000000, 57 }, + { 0xde0b6b3a, 0x76400000, 0x00000000, 60 }, + { 0x8ac72304, 0x89e80000, 0x00000000, 64 }, + { 0xad78ebc5, 0xac620000, 0x00000000, 67 }, + { 0xd8d726b7, 0x177a8000, 0x00000000, 70 }, + { 0x87867832, 0x6eac9000, 0x00000000, 74 }, + { 0xa968163f, 0x0a57b400, 0x00000000, 77 }, + { 0xd3c21bce, 0xcceda100, 0x00000000, 80 }, + { 0x84595161, 0x401484a0, 0x00000000, 84 }, + { 0xa56fa5b9, 0x9019a5c8, 0x00000000, 87 }, + { 0xcecb8f27, 0xf4200f3a, 0x00000000, 90 }, + { 0x813f3978, 0xf8940984, 0x40000000, 94 }, + { 0xa18f07d7, 0x36b90be5, 0x50000000, 97 }, + { 0xc9f2c9cd, 0x04674ede, 0xa4000000, 100 }, + { 0xfc6f7c40, 0x45812296, 0x4d000000, 103 }, + { 0x9dc5ada8, 0x2b70b59d, 0xf0200000, 107 }, + { 0xc5371912, 0x364ce305, 0x6c280000, 110 }, + { 0xf684df56, 0xc3e01bc6, 0xc7320000, 113 }, + { 0x9a130b96, 0x3a6c115c, 0x3c7f4000, 117 }, + { 0xc097ce7b, 0xc90715b3, 0x4b9f1000, 120 }, + { 0xf0bdc21a, 0xbb48db20, 0x1e86d400, 123 }, + { 0x96769950, 0xb50d88f4, 0x13144480, 127 }, + { 0xbc143fa4, 0xe250eb31, 0x17d955a0, 130 }, + { 0xeb194f8e, 0x1ae525fd, 0x5dcfab08, 133 }, + { 0x92efd1b8, 0xd0cf37be, 0x5aa1cae5, 137 }, + { 0xb7abc627, 0x050305ad, 0xf14a3d9e, 140 }, + { 0xe596b7b0, 0xc643c719, 0x6d9ccd05, 143 }, + { 0x8f7e32ce, 0x7bea5c6f, 0xe4820023, 147 }, + { 0xb35dbf82, 0x1ae4f38b, 0xdda2802c, 150 }, + { 0xe0352f62, 0xa19e306e, 0xd50b2037, 153 }, + { 0x8c213d9d, 0xa502de45, 0x4526f422, 157 }, + { 0xaf298d05, 0x0e4395d6, 0x9670b12b, 160 }, + { 0xdaf3f046, 0x51d47b4c, 0x3c0cdd76, 163 }, + { 0x88d8762b, 0xf324cd0f, 0xa5880a69, 167 }, + { 0xab0e93b6, 0xefee0053, 0x8eea0d04, 170 }, + { 0xd5d238a4, 0xabe98068, 0x72a49045, 173 }, + { 0x85a36366, 0xeb71f041, 0x47a6da2b, 177 }, + { 0xa70c3c40, 0xa64e6c51, 0x999090b6, 180 }, + { 0xd0cf4b50, 0xcfe20765, 0xfff4b4e3, 183 }, + { 0x82818f12, 0x81ed449f, 0xbff8f10e, 187 }, + { 0xa321f2d7, 0x226895c7, 0xaff72d52, 190 }, + { 0xcbea6f8c, 0xeb02bb39, 0x9bf4f8a6, 193 }, + { 0xfee50b70, 0x25c36a08, 0x02f236d0, 196 }, + { 0x9f4f2726, 0x179a2245, 0x01d76242, 200 }, + { 0xc722f0ef, 0x9d80aad6, 0x424d3ad2, 203 }, + { 0xf8ebad2b, 0x84e0d58b, 0xd2e08987, 206 }, + { 0x9b934c3b, 0x330c8577, 0x63cc55f4, 210 }, + { 0xc2781f49, 0xffcfa6d5, 0x3cbf6b71, 213 }, + { 0xf316271c, 0x7fc3908a, 0x8bef464e, 216 }, + { 0x97edd871, 0xcfda3a56, 0x97758bf0, 220 }, + { 0xbde94e8e, 0x43d0c8ec, 0x3d52eeed, 223 }, + { 0xed63a231, 0xd4c4fb27, 0x4ca7aaa8, 226 }, + { 0x945e455f, 0x24fb1cf8, 0x8fe8caa9, 230 }, + { 0xb975d6b6, 0xee39e436, 0xb3e2fd53, 233 }, + { 0xe7d34c64, 0xa9c85d44, 0x60dbbca8, 236 }, + { 0x90e40fbe, 0xea1d3a4a, 0xbc8955e9, 240 }, + { 0xb51d13ae, 0xa4a488dd, 0x6babab63, 243 }, + { 0xe264589a, 0x4dcdab14, 0xc696963c, 246 }, + { 0x8d7eb760, 0x70a08aec, 0xfc1e1de5, 250 }, + { 0xb0de6538, 0x8cc8ada8, 0x3b25a55f, 253 }, + { 0xdd15fe86, 0xaffad912, 0x49ef0eb7, 256 }, + { 0x8a2dbf14, 0x2dfcc7ab, 0x6e356932, 260 }, + { 0xacb92ed9, 0x397bf996, 0x49c2c37f, 263 }, + { 0xd7e77a8f, 0x87daf7fb, 0xdc33745e, 266 }, + { 0x86f0ac99, 0xb4e8dafd, 0x69a028bb, 270 }, + { 0xa8acd7c0, 0x222311bc, 0xc40832ea, 273 }, + { 0xd2d80db0, 0x2aabd62b, 0xf50a3fa4, 276 }, + { 0x83c7088e, 0x1aab65db, 0x792667c6, 280 }, + { 0xa4b8cab1, 0xa1563f52, 0x577001b8, 283 }, + { 0xcde6fd5e, 0x09abcf26, 0xed4c0226, 286 }, + { 0x80b05e5a, 0xc60b6178, 0x544f8158, 290 }, + { 0xa0dc75f1, 0x778e39d6, 0x696361ae, 293 }, + { 0xc913936d, 0xd571c84c, 0x03bc3a19, 296 }, + { 0xfb587849, 0x4ace3a5f, 0x04ab48a0, 299 }, + { 0x9d174b2d, 0xcec0e47b, 0x62eb0d64, 303 }, + { 0xc45d1df9, 0x42711d9a, 0x3ba5d0bd, 306 }, + { 0xf5746577, 0x930d6500, 0xca8f44ec, 309 }, + { 0x9968bf6a, 0xbbe85f20, 0x7e998b13, 313 }, + { 0xbfc2ef45, 0x6ae276e8, 0x9e3fedd8, 316 }, + { 0xefb3ab16, 0xc59b14a2, 0xc5cfe94e, 319 }, + { 0x95d04aee, 0x3b80ece5, 0xbba1f1d1, 323 }, + { 0xbb445da9, 0xca61281f, 0x2a8a6e45, 326 }, + { 0xea157514, 0x3cf97226, 0xf52d09d7, 329 }, + { 0x924d692c, 0xa61be758, 0x593c2626, 333 }, + { 0xb6e0c377, 0xcfa2e12e, 0x6f8b2fb0, 336 }, + { 0xe498f455, 0xc38b997a, 0x0b6dfb9c, 339 }, + { 0x8edf98b5, 0x9a373fec, 0x4724bd41, 343 }, + { 0xb2977ee3, 0x00c50fe7, 0x58edec91, 346 }, + { 0xdf3d5e9b, 0xc0f653e1, 0x2f2967b6, 349 }, + { 0x8b865b21, 0x5899f46c, 0xbd79e0d2, 353 }, + { 0xae67f1e9, 0xaec07187, 0xecd85906, 356 }, + { 0xda01ee64, 0x1a708de9, 0xe80e6f48, 359 }, + { 0x884134fe, 0x908658b2, 0x3109058d, 363 }, + { 0xaa51823e, 0x34a7eede, 0xbd4b46f0, 366 }, + { 0xd4e5e2cd, 0xc1d1ea96, 0x6c9e18ac, 369 }, + { 0x850fadc0, 0x9923329e, 0x03e2cf6b, 373 }, + { 0xa6539930, 0xbf6bff45, 0x84db8346, 376 }, + { 0xcfe87f7c, 0xef46ff16, 0xe6126418, 379 }, + { 0x81f14fae, 0x158c5f6e, 0x4fcb7e8f, 383 }, + { 0xa26da399, 0x9aef7749, 0xe3be5e33, 386 }, + { 0xcb090c80, 0x01ab551c, 0x5cadf5bf, 389 }, + { 0xfdcb4fa0, 0x02162a63, 0x73d9732f, 392 }, + { 0x9e9f11c4, 0x014dda7e, 0x2867e7fd, 396 }, + { 0xc646d635, 0x01a1511d, 0xb281e1fd, 399 }, + { 0xf7d88bc2, 0x4209a565, 0x1f225a7c, 402 }, + { 0x9ae75759, 0x6946075f, 0x3375788d, 406 }, + { 0xc1a12d2f, 0xc3978937, 0x0052d6b1, 409 }, + { 0xf209787b, 0xb47d6b84, 0xc0678c5d, 412 }, + { 0x9745eb4d, 0x50ce6332, 0xf840b7ba, 416 }, + { 0xbd176620, 0xa501fbff, 0xb650e5a9, 419 }, + { 0xec5d3fa8, 0xce427aff, 0xa3e51f13, 422 }, + { 0x93ba47c9, 0x80e98cdf, 0xc66f336c, 426 }, + { 0xb8a8d9bb, 0xe123f017, 0xb80b0047, 429 }, + { 0xe6d3102a, 0xd96cec1d, 0xa60dc059, 432 }, + { 0x9043ea1a, 0xc7e41392, 0x87c89837, 436 }, + { 0xb454e4a1, 0x79dd1877, 0x29babe45, 439 }, + { 0xe16a1dc9, 0xd8545e94, 0xf4296dd6, 442 }, + { 0x8ce2529e, 0x2734bb1d, 0x1899e4a6, 446 }, + { 0xb01ae745, 0xb101e9e4, 0x5ec05dcf, 449 }, + { 0xdc21a117, 0x1d42645d, 0x76707543, 452 }, + { 0x899504ae, 0x72497eba, 0x6a06494a, 456 }, + { 0xabfa45da, 0x0edbde69, 0x0487db9d, 459 }, + { 0xd6f8d750, 0x9292d603, 0x45a9d284, 462 }, + { 0x865b8692, 0x5b9bc5c2, 0x0b8a2392, 466 }, + { 0xa7f26836, 0xf282b732, 0x8e6cac77, 469 }, + { 0xd1ef0244, 0xaf2364ff, 0x3207d795, 472 }, + { 0x8335616a, 0xed761f1f, 0x7f44e6bd, 476 }, + { 0xa402b9c5, 0xa8d3a6e7, 0x5f16206c, 479 }, + { 0xcd036837, 0x130890a1, 0x36dba887, 482 }, + { 0x80222122, 0x6be55a64, 0xc2494954, 486 }, + { 0xa02aa96b, 0x06deb0fd, 0xf2db9baa, 489 }, + { 0xc83553c5, 0xc8965d3d, 0x6f928294, 492 }, + { 0xfa42a8b7, 0x3abbf48c, 0xcb772339, 495 }, + { 0x9c69a972, 0x84b578d7, 0xff2a7604, 499 }, + { 0xc38413cf, 0x25e2d70d, 0xfef51385, 502 }, + { 0xf46518c2, 0xef5b8cd1, 0x7eb25866, 505 }, + { 0x98bf2f79, 0xd5993802, 0xef2f773f, 509 }, + { 0xbeeefb58, 0x4aff8603, 0xaafb550f, 512 }, + { 0xeeaaba2e, 0x5dbf6784, 0x95ba2a53, 515 }, + { 0x952ab45c, 0xfa97a0b2, 0xdd945a74, 519 }, + { 0xba756174, 0x393d88df, 0x94f97111, 522 }, + { 0xe912b9d1, 0x478ceb17, 0x7a37cd56, 525 }, + { 0x91abb422, 0xccb812ee, 0xac62e055, 529 }, + { 0xb616a12b, 0x7fe617aa, 0x577b986b, 532 }, + { 0xe39c4976, 0x5fdf9d94, 0xed5a7e85, 535 }, + { 0x8e41ade9, 0xfbebc27d, 0x14588f13, 539 }, + { 0xb1d21964, 0x7ae6b31c, 0x596eb2d8, 542 }, + { 0xde469fbd, 0x99a05fe3, 0x6fca5f8e, 545 }, + { 0x8aec23d6, 0x80043bee, 0x25de7bb9, 549 }, + { 0xada72ccc, 0x20054ae9, 0xaf561aa7, 552 }, + { 0xd910f7ff, 0x28069da4, 0x1b2ba151, 555 }, + { 0x87aa9aff, 0x79042286, 0x90fb44d2, 559 }, + { 0xa99541bf, 0x57452b28, 0x353a1607, 562 }, + { 0xd3fa922f, 0x2d1675f2, 0x42889b89, 565 }, + { 0x847c9b5d, 0x7c2e09b7, 0x69956135, 569 }, + { 0xa59bc234, 0xdb398c25, 0x43fab983, 572 }, + { 0xcf02b2c2, 0x1207ef2e, 0x94f967e4, 575 }, + { 0x8161afb9, 0x4b44f57d, 0x1d1be0ee, 579 }, + { 0xa1ba1ba7, 0x9e1632dc, 0x6462d92a, 582 }, + { 0xca28a291, 0x859bbf93, 0x7d7b8f75, 585 }, + { 0xfcb2cb35, 0xe702af78, 0x5cda7352, 588 }, + { 0x9defbf01, 0xb061adab, 0x3a088813, 592 }, + { 0xc56baec2, 0x1c7a1916, 0x088aaa18, 595 }, + { 0xf6c69a72, 0xa3989f5b, 0x8aad549e, 598 }, + { 0x9a3c2087, 0xa63f6399, 0x36ac54e2, 602 }, + { 0xc0cb28a9, 0x8fcf3c7f, 0x84576a1b, 605 }, + { 0xf0fdf2d3, 0xf3c30b9f, 0x656d44a2, 608 }, + { 0x969eb7c4, 0x7859e743, 0x9f644ae5, 612 }, + { 0xbc4665b5, 0x96706114, 0x873d5d9f, 615 }, + { 0xeb57ff22, 0xfc0c7959, 0xa90cb506, 618 }, + { 0x9316ff75, 0xdd87cbd8, 0x09a7f124, 622 }, + { 0xb7dcbf53, 0x54e9bece, 0x0c11ed6d, 625 }, + { 0xe5d3ef28, 0x2a242e81, 0x8f1668c8, 628 }, + { 0x8fa47579, 0x1a569d10, 0xf96e017d, 632 }, + { 0xb38d92d7, 0x60ec4455, 0x37c981dc, 635 }, + { 0xe070f78d, 0x3927556a, 0x85bbe253, 638 }, + { 0x8c469ab8, 0x43b89562, 0x93956d74, 642 }, + { 0xaf584166, 0x54a6babb, 0x387ac8d1, 645 }, + { 0xdb2e51bf, 0xe9d0696a, 0x06997b05, 648 }, + { 0x88fcf317, 0xf22241e2, 0x441fece3, 652 }, + { 0xab3c2fdd, 0xeeaad25a, 0xd527e81c, 655 }, + { 0xd60b3bd5, 0x6a5586f1, 0x8a71e223, 658 }, + { 0x85c70565, 0x62757456, 0xf6872d56, 662 }, + { 0xa738c6be, 0xbb12d16c, 0xb428f8ac, 665 }, + { 0xd106f86e, 0x69d785c7, 0xe13336d7, 668 }, + { 0x82a45b45, 0x0226b39c, 0xecc00246, 672 }, + { 0xa34d7216, 0x42b06084, 0x27f002d7, 675 }, + { 0xcc20ce9b, 0xd35c78a5, 0x31ec038d, 678 }, + { 0xff290242, 0xc83396ce, 0x7e670471, 681 }, + { 0x9f79a169, 0xbd203e41, 0x0f0062c6, 685 }, + { 0xc75809c4, 0x2c684dd1, 0x52c07b78, 688 }, + { 0xf92e0c35, 0x37826145, 0xa7709a56, 691 }, + { 0x9bbcc7a1, 0x42b17ccb, 0x88a66076, 695 }, + { 0xc2abf989, 0x935ddbfe, 0x6acff893, 698 }, + { 0xf356f7eb, 0xf83552fe, 0x0583f6b8, 701 }, + { 0x98165af3, 0x7b2153de, 0xc3727a33, 705 }, + { 0xbe1bf1b0, 0x59e9a8d6, 0x744f18c0, 708 }, + { 0xeda2ee1c, 0x7064130c, 0x1162def0, 711 }, + { 0x9485d4d1, 0xc63e8be7, 0x8addcb56, 715 }, + { 0xb9a74a06, 0x37ce2ee1, 0x6d953e2b, 718 }, + { 0xe8111c87, 0xc5c1ba99, 0xc8fa8db6, 721 }, + { 0x910ab1d4, 0xdb9914a0, 0x1d9c9892, 725 }, + { 0xb54d5e4a, 0x127f59c8, 0x2503beb6, 728 }, + { 0xe2a0b5dc, 0x971f303a, 0x2e44ae64, 731 }, + { 0x8da471a9, 0xde737e24, 0x5ceaecfe, 735 }, + { 0xb10d8e14, 0x56105dad, 0x7425a83e, 738 }, + { 0xdd50f199, 0x6b947518, 0xd12f124e, 741 }, + { 0x8a5296ff, 0xe33cc92f, 0x82bd6b70, 745 }, + { 0xace73cbf, 0xdc0bfb7b, 0x636cc64d, 748 }, + { 0xd8210bef, 0xd30efa5a, 0x3c47f7e0, 751 }, + { 0x8714a775, 0xe3e95c78, 0x65acfaec, 755 }, + { 0xa8d9d153, 0x5ce3b396, 0x7f1839a7, 758 }, + { 0xd31045a8, 0x341ca07c, 0x1ede4811, 761 }, + { 0x83ea2b89, 0x2091e44d, 0x934aed0a, 765 }, + { 0xa4e4b66b, 0x68b65d60, 0xf81da84d, 768 }, + { 0xce1de406, 0x42e3f4b9, 0x36251260, 771 }, + { 0x80d2ae83, 0xe9ce78f3, 0xc1d72b7c, 775 }, + { 0xa1075a24, 0xe4421730, 0xb24cf65b, 778 }, + { 0xc94930ae, 0x1d529cfc, 0xdee033f2, 781 }, + { 0xfb9b7cd9, 0xa4a7443c, 0x169840ef, 784 }, + { 0x9d412e08, 0x06e88aa5, 0x8e1f2895, 788 }, + { 0xc491798a, 0x08a2ad4e, 0xf1a6f2ba, 791 }, + { 0xf5b5d7ec, 0x8acb58a2, 0xae10af69, 794 }, + { 0x9991a6f3, 0xd6bf1765, 0xacca6da1, 798 }, + { 0xbff610b0, 0xcc6edd3f, 0x17fd090a, 801 }, + { 0xeff394dc, 0xff8a948e, 0xddfc4b4c, 804 }, + { 0x95f83d0a, 0x1fb69cd9, 0x4abdaf10, 808 }, + { 0xbb764c4c, 0xa7a4440f, 0x9d6d1ad4, 811 }, + { 0xea53df5f, 0xd18d5513, 0x84c86189, 814 }, + { 0x92746b9b, 0xe2f8552c, 0x32fd3cf5, 818 }, + { 0xb7118682, 0xdbb66a77, 0x3fbc8c33, 821 }, + { 0xe4d5e823, 0x92a40515, 0x0fabaf3f, 824 }, + { 0x8f05b116, 0x3ba6832d, 0x29cb4d87, 828 }, + { 0xb2c71d5b, 0xca9023f8, 0x743e20e9, 831 }, + { 0xdf78e4b2, 0xbd342cf6, 0x914da924, 834 }, + { 0x8bab8eef, 0xb6409c1a, 0x1ad089b6, 838 }, + { 0xae9672ab, 0xa3d0c320, 0xa184ac24, 841 }, + { 0xda3c0f56, 0x8cc4f3e8, 0xc9e5d72d, 844 }, + { 0x88658996, 0x17fb1871, 0x7e2fa67c, 848 }, + { 0xaa7eebfb, 0x9df9de8d, 0xddbb901b, 851 }, + { 0xd51ea6fa, 0x85785631, 0x552a7422, 854 }, + { 0x8533285c, 0x936b35de, 0xd53a8895, 858 }, + { 0xa67ff273, 0xb8460356, 0x8a892aba, 861 }, + { 0xd01fef10, 0xa657842c, 0x2d2b7569, 864 }, + { 0x8213f56a, 0x67f6b29b, 0x9c3b2962, 868 }, + { 0xa298f2c5, 0x01f45f42, 0x8349f3ba, 871 }, + { 0xcb3f2f76, 0x42717713, 0x241c70a9, 874 }, + { 0xfe0efb53, 0xd30dd4d7, 0xed238cd3, 877 }, + { 0x9ec95d14, 0x63e8a506, 0xf4363804, 881 }, + { 0xc67bb459, 0x7ce2ce48, 0xb143c605, 884 }, + { 0xf81aa16f, 0xdc1b81da, 0xdd94b786, 887 }, + { 0x9b10a4e5, 0xe9913128, 0xca7cf2b4, 891 }, + { 0xc1d4ce1f, 0x63f57d72, 0xfd1c2f61, 894 }, + { 0xf24a01a7, 0x3cf2dccf, 0xbc633b39, 897 }, + { 0x976e4108, 0x8617ca01, 0xd5be0503, 901 }, + { 0xbd49d14a, 0xa79dbc82, 0x4b2d8644, 904 }, + { 0xec9c459d, 0x51852ba2, 0xddf8e7d6, 907 }, + { 0x93e1ab82, 0x52f33b45, 0xcabb90e5, 911 }, + { 0xb8da1662, 0xe7b00a17, 0x3d6a751f, 914 }, + { 0xe7109bfb, 0xa19c0c9d, 0x0cc51267, 917 }, + { 0x906a617d, 0x450187e2, 0x27fb2b80, 921 }, + { 0xb484f9dc, 0x9641e9da, 0xb1f9f660, 924 }, + { 0xe1a63853, 0xbbd26451, 0x5e7873f8, 927 }, + { 0x8d07e334, 0x55637eb2, 0xdb0b487b, 931 }, + { 0xb049dc01, 0x6abc5e5f, 0x91ce1a9a, 934 }, + { 0xdc5c5301, 0xc56b75f7, 0x7641a140, 937 }, + { 0x89b9b3e1, 0x1b6329ba, 0xa9e904c8, 941 }, + { 0xac2820d9, 0x623bf429, 0x546345fa, 944 }, + { 0xd732290f, 0xbacaf133, 0xa97c1779, 947 }, + { 0x867f59a9, 0xd4bed6c0, 0x49ed8eab, 951 }, + { 0xa81f3014, 0x49ee8c70, 0x5c68f256, 954 }, + { 0xd226fc19, 0x5c6a2f8c, 0x73832eec, 957 }, + { 0x83585d8f, 0xd9c25db7, 0xc831fd53, 961 }, + { 0xa42e74f3, 0xd032f525, 0xba3e7ca8, 964 }, + { 0xcd3a1230, 0xc43fb26f, 0x28ce1bd2, 967 }, + { 0x80444b5e, 0x7aa7cf85, 0x7980d163, 971 }, + { 0xa0555e36, 0x1951c366, 0xd7e105bc, 974 }, + { 0xc86ab5c3, 0x9fa63440, 0x8dd9472b, 977 }, + { 0xfa856334, 0x878fc150, 0xb14f98f6, 980 }, + { 0x9c935e00, 0xd4b9d8d2, 0x6ed1bf9a, 984 }, + { 0xc3b83581, 0x09e84f07, 0x0a862f80, 987 }, + { 0xf4a642e1, 0x4c6262c8, 0xcd27bb61, 990 }, + { 0x98e7e9cc, 0xcfbd7dbd, 0x8038d51c, 994 }, + { 0xbf21e440, 0x03acdd2c, 0xe0470a63, 997 }, + { 0xeeea5d50, 0x04981478, 0x1858ccfc, 1000 }, + { 0x95527a52, 0x02df0ccb, 0x0f37801e, 1004 }, + { 0xbaa718e6, 0x8396cffd, 0xd3056025, 1007 }, + { 0xe950df20, 0x247c83fd, 0x47c6b82e, 1010 }, + { 0x91d28b74, 0x16cdd27e, 0x4cdc331d, 1014 }, + { 0xb6472e51, 0x1c81471d, 0xe0133fe4, 1017 }, + { 0xe3d8f9e5, 0x63a198e5, 0x58180fdd, 1020 }, + { 0x8e679c2f, 0x5e44ff8f, 0x570f09ea, 1024 }, + { 0xb201833b, 0x35d63f73, 0x2cd2cc65, 1027 }, + { 0xde81e40a, 0x034bcf4f, 0xf8077f7e, 1030 }, + { 0x8b112e86, 0x420f6191, 0xfb04afaf, 1034 }, + { 0xadd57a27, 0xd29339f6, 0x79c5db9a, 1037 }, + { 0xd94ad8b1, 0xc7380874, 0x18375281, 1040 }, + { 0x87cec76f, 0x1c830548, 0x8f229391, 1044 }, + { 0xa9c2794a, 0xe3a3c69a, 0xb2eb3875, 1047 }, + { 0xd433179d, 0x9c8cb841, 0x5fa60692, 1050 }, + { 0x849feec2, 0x81d7f328, 0xdbc7c41b, 1054 }, + { 0xa5c7ea73, 0x224deff3, 0x12b9b522, 1057 }, + { 0xcf39e50f, 0xeae16bef, 0xd768226b, 1060 }, + { 0x81842f29, 0xf2cce375, 0xe6a11583, 1064 }, + { 0xa1e53af4, 0x6f801c53, 0x60495ae3, 1067 }, + { 0xca5e89b1, 0x8b602368, 0x385bb19c, 1070 }, + { 0xfcf62c1d, 0xee382c42, 0x46729e03, 1073 }, + { 0x9e19db92, 0xb4e31ba9, 0x6c07a2c2, 1077 } + }; +#ifndef STRTOD_ONLY + static short int Lhint[2098] = { + /*18,*/19, 19, 19, 19, 20, 20, 20, 21, 21, + 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, + 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, + 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, + 30, 31, 31, 31, 32, 32, 32, 32, 33, 33, + 33, 34, 34, 34, 35, 35, 35, 35, 36, 36, + 36, 37, 37, 37, 38, 38, 38, 38, 39, 39, + 39, 40, 40, 40, 41, 41, 41, 41, 42, 42, + 42, 43, 43, 43, 44, 44, 44, 44, 45, 45, + 45, 46, 46, 46, 47, 47, 47, 47, 48, 48, + 48, 49, 49, 49, 50, 50, 50, 51, 51, 51, + 51, 52, 52, 52, 53, 53, 53, 54, 54, 54, + 54, 55, 55, 55, 56, 56, 56, 57, 57, 57, + 57, 58, 58, 58, 59, 59, 59, 60, 60, 60, + 60, 61, 61, 61, 62, 62, 62, 63, 63, 63, + 63, 64, 64, 64, 65, 65, 65, 66, 66, 66, + 66, 67, 67, 67, 68, 68, 68, 69, 69, 69, + 69, 70, 70, 70, 71, 71, 71, 72, 72, 72, + 72, 73, 73, 73, 74, 74, 74, 75, 75, 75, + 75, 76, 76, 76, 77, 77, 77, 78, 78, 78, + 78, 79, 79, 79, 80, 80, 80, 81, 81, 81, + 82, 82, 82, 82, 83, 83, 83, 84, 84, 84, + 85, 85, 85, 85, 86, 86, 86, 87, 87, 87, + 88, 88, 88, 88, 89, 89, 89, 90, 90, 90, + 91, 91, 91, 91, 92, 92, 92, 93, 93, 93, + 94, 94, 94, 94, 95, 95, 95, 96, 96, 96, + 97, 97, 97, 97, 98, 98, 98, 99, 99, 99, + 100, 100, 100, 100, 101, 101, 101, 102, 102, 102, + 103, 103, 103, 103, 104, 104, 104, 105, 105, 105, + 106, 106, 106, 106, 107, 107, 107, 108, 108, 108, + 109, 109, 109, 110, 110, 110, 110, 111, 111, 111, + 112, 112, 112, 113, 113, 113, 113, 114, 114, 114, + 115, 115, 115, 116, 116, 116, 116, 117, 117, 117, + 118, 118, 118, 119, 119, 119, 119, 120, 120, 120, + 121, 121, 121, 122, 122, 122, 122, 123, 123, 123, + 124, 124, 124, 125, 125, 125, 125, 126, 126, 126, + 127, 127, 127, 128, 128, 128, 128, 129, 129, 129, + 130, 130, 130, 131, 131, 131, 131, 132, 132, 132, + 133, 133, 133, 134, 134, 134, 134, 135, 135, 135, + 136, 136, 136, 137, 137, 137, 137, 138, 138, 138, + 139, 139, 139, 140, 140, 140, 141, 141, 141, 141, + 142, 142, 142, 143, 143, 143, 144, 144, 144, 144, + 145, 145, 145, 146, 146, 146, 147, 147, 147, 147, + 148, 148, 148, 149, 149, 149, 150, 150, 150, 150, + 151, 151, 151, 152, 152, 152, 153, 153, 153, 153, + 154, 154, 154, 155, 155, 155, 156, 156, 156, 156, + 157, 157, 157, 158, 158, 158, 159, 159, 159, 159, + 160, 160, 160, 161, 161, 161, 162, 162, 162, 162, + 163, 163, 163, 164, 164, 164, 165, 165, 165, 165, + 166, 166, 166, 167, 167, 167, 168, 168, 168, 169, + 169, 169, 169, 170, 170, 170, 171, 171, 171, 172, + 172, 172, 172, 173, 173, 173, 174, 174, 174, 175, + 175, 175, 175, 176, 176, 176, 177, 177, 177, 178, + 178, 178, 178, 179, 179, 179, 180, 180, 180, 181, + 181, 181, 181, 182, 182, 182, 183, 183, 183, 184, + 184, 184, 184, 185, 185, 185, 186, 186, 186, 187, + 187, 187, 187, 188, 188, 188, 189, 189, 189, 190, + 190, 190, 190, 191, 191, 191, 192, 192, 192, 193, + 193, 193, 193, 194, 194, 194, 195, 195, 195, 196, + 196, 196, 197, 197, 197, 197, 198, 198, 198, 199, + 199, 199, 200, 200, 200, 200, 201, 201, 201, 202, + 202, 202, 203, 203, 203, 203, 204, 204, 204, 205, + 205, 205, 206, 206, 206, 206, 207, 207, 207, 208, + 208, 208, 209, 209, 209, 209, 210, 210, 210, 211, + 211, 211, 212, 212, 212, 212, 213, 213, 213, 214, + 214, 214, 215, 215, 215, 215, 216, 216, 216, 217, + 217, 217, 218, 218, 218, 218, 219, 219, 219, 220, + 220, 220, 221, 221, 221, 221, 222, 222, 222, 223, + 223, 223, 224, 224, 224, 224, 225, 225, 225, 226, + 226, 226, 227, 227, 227, 228, 228, 228, 228, 229, + 229, 229, 230, 230, 230, 231, 231, 231, 231, 232, + 232, 232, 233, 233, 233, 234, 234, 234, 234, 235, + 235, 235, 236, 236, 236, 237, 237, 237, 237, 238, + 238, 238, 239, 239, 239, 240, 240, 240, 240, 241, + 241, 241, 242, 242, 242, 243, 243, 243, 243, 244, + 244, 244, 245, 245, 245, 246, 246, 246, 246, 247, + 247, 247, 248, 248, 248, 249, 249, 249, 249, 250, + 250, 250, 251, 251, 251, 252, 252, 252, 252, 253, + 253, 253, 254, 254, 254, 255, 255, 255, 256, 256, + 256, 256, 257, 257, 257, 258, 258, 258, 259, 259, + 259, 259, 260, 260, 260, 261, 261, 261, 262, 262, + 262, 262, 263, 263, 263, 264, 264, 264, 265, 265, + 265, 265, 266, 266, 266, 267, 267, 267, 268, 268, + 268, 268, 269, 269, 269, 270, 270, 270, 271, 271, + 271, 271, 272, 272, 272, 273, 273, 273, 274, 274, + 274, 274, 275, 275, 275, 276, 276, 276, 277, 277, + 277, 277, 278, 278, 278, 279, 279, 279, 280, 280, + 280, 280, 281, 281, 281, 282, 282, 282, 283, 283, + 283, 283, 284, 284, 284, 285, 285, 285, 286, 286, + 286, 287, 287, 287, 287, 288, 288, 288, 289, 289, + 289, 290, 290, 290, 290, 291, 291, 291, 292, 292, + 292, 293, 293, 293, 293, 294, 294, 294, 295, 295, + 295, 296, 296, 296, 296, 297, 297, 297, 298, 298, + 298, 299, 299, 299, 299, 300, 300, 300, 301, 301, + 301, 302, 302, 302, 302, 303, 303, 303, 304, 304, + 304, 305, 305, 305, 305, 306, 306, 306, 307, 307, + 307, 308, 308, 308, 308, 309, 309, 309, 310, 310, + 310, 311, 311, 311, 311, 312, 312, 312, 313, 313, + 313, 314, 314, 314, 315, 315, 315, 315, 316, 316, + 316, 317, 317, 317, 318, 318, 318, 318, 319, 319, + 319, 320, 320, 320, 321, 321, 321, 321, 322, 322, + 322, 323, 323, 323, 324, 324, 324, 324, 325, 325, + 325, 326, 326, 326, 327, 327, 327, 327, 328, 328, + 328, 329, 329, 329, 330, 330, 330, 330, 331, 331, + 331, 332, 332, 332, 333, 333, 333, 333, 334, 334, + 334, 335, 335, 335, 336, 336, 336, 336, 337, 337, + 337, 338, 338, 338, 339, 339, 339, 339, 340, 340, + 340, 341, 341, 341, 342, 342, 342, 342, 343, 343, + 343, 344, 344, 344, 345, 345, 345, 346, 346, 346, + 346, 347, 347, 347, 348, 348, 348, 349, 349, 349, + 349, 350, 350, 350, 351, 351, 351, 352, 352, 352, + 352, 353, 353, 353, 354, 354, 354, 355, 355, 355, + 355, 356, 356, 356, 357, 357, 357, 358, 358, 358, + 358, 359, 359, 359, 360, 360, 360, 361, 361, 361, + 361, 362, 362, 362, 363, 363, 363, 364, 364, 364, + 364, 365, 365, 365, 366, 366, 366, 367, 367, 367, + 367, 368, 368, 368, 369, 369, 369, 370, 370, 370, + 370, 371, 371, 371, 372, 372, 372, 373, 373, 373, + 374, 374, 374, 374, 375, 375, 375, 376, 376, 376, + 377, 377, 377, 377, 378, 378, 378, 379, 379, 379, + 380, 380, 380, 380, 381, 381, 381, 382, 382, 382, + 383, 383, 383, 383, 384, 384, 384, 385, 385, 385, + 386, 386, 386, 386, 387, 387, 387, 388, 388, 388, + 389, 389, 389, 389, 390, 390, 390, 391, 391, 391, + 392, 392, 392, 392, 393, 393, 393, 394, 394, 394, + 395, 395, 395, 395, 396, 396, 396, 397, 397, 397, + 398, 398, 398, 398, 399, 399, 399, 400, 400, 400, + 401, 401, 401, 402, 402, 402, 402, 403, 403, 403, + 404, 404, 404, 405, 405, 405, 405, 406, 406, 406, + 407, 407, 407, 408, 408, 408, 408, 409, 409, 409, + 410, 410, 410, 411, 411, 411, 411, 412, 412, 412, + 413, 413, 413, 414, 414, 414, 414, 415, 415, 415, + 416, 416, 416, 417, 417, 417, 417, 418, 418, 418, + 419, 419, 419, 420, 420, 420, 420, 421, 421, 421, + 422, 422, 422, 423, 423, 423, 423, 424, 424, 424, + 425, 425, 425, 426, 426, 426, 426, 427, 427, 427, + 428, 428, 428, 429, 429, 429, 429, 430, 430, 430, + 431, 431, 431, 432, 432, 432, 433, 433, 433, 433, + 434, 434, 434, 435, 435, 435, 436, 436, 436, 436, + 437, 437, 437, 438, 438, 438, 439, 439, 439, 439, + 440, 440, 440, 441, 441, 441, 442, 442, 442, 442, + 443, 443, 443, 444, 444, 444, 445, 445, 445, 445, + 446, 446, 446, 447, 447, 447, 448, 448, 448, 448, + 449, 449, 449, 450, 450, 450, 451, 451, 451, 451, + 452, 452, 452, 453, 453, 453, 454, 454, 454, 454, + 455, 455, 455, 456, 456, 456, 457, 457, 457, 457, + 458, 458, 458, 459, 459, 459, 460, 460, 460, 461, + 461, 461, 461, 462, 462, 462, 463, 463, 463, 464, + 464, 464, 464, 465, 465, 465, 466, 466, 466, 467, + 467, 467, 467, 468, 468, 468, 469, 469, 469, 470, + 470, 470, 470, 471, 471, 471, 472, 472, 472, 473, + 473, 473, 473, 474, 474, 474, 475, 475, 475, 476, + 476, 476, 476, 477, 477, 477, 478, 478, 478, 479, + 479, 479, 479, 480, 480, 480, 481, 481, 481, 482, + 482, 482, 482, 483, 483, 483, 484, 484, 484, 485, + 485, 485, 485, 486, 486, 486, 487, 487, 487, 488, + 488, 488, 488, 489, 489, 489, 490, 490, 490, 491, + 491, 491, 492, 492, 492, 492, 493, 493, 493, 494, + 494, 494, 495, 495, 495, 495, 496, 496, 496, 497, + 497, 497, 498, 498, 498, 498, 499, 499, 499, 500, + 500, 500, 501, 501, 501, 501, 502, 502, 502, 503, + 503, 503, 504, 504, 504, 504, 505, 505, 505, 506, + 506, 506, 507, 507, 507, 507, 508, 508, 508, 509, + 509, 509, 510, 510, 510, 510, 511, 511, 511, 512, + 512, 512, 513, 513, 513, 513, 514, 514, 514, 515, + 515, 515, 516, 516, 516, 516, 517, 517, 517, 518, + 518, 518, 519, 519, 519, 520, 520, 520, 520, 521, + 521, 521, 522, 522, 522, 523, 523, 523, 523, 524, + 524, 524, 525, 525, 525, 526, 526, 526, 526, 527, + 527, 527, 528, 528, 528, 529, 529, 529, 529, 530, + 530, 530, 531, 531, 531, 532, 532, 532, 532, 533, + 533, 533, 534, 534, 534, 535, 535, 535, 535, 536, + 536, 536, 537, 537, 537, 538, 538, 538, 538, 539, + 539, 539, 540, 540, 540, 541, 541, 541, 541, 542, + 542, 542, 543, 543, 543, 544, 544, 544, 544, 545, + 545, 545, 546, 546, 546, 547, 547, 547, 548, 548, + 548, 548, 549, 549, 549, 550, 550, 550, 551, 551, + 551, 551, 552, 552, 552, 553, 553, 553, 554, 554, + 554, 554, 555, 555, 555, 556, 556, 556, 557, 557, + 557, 557, 558, 558, 558, 559, 559, 559, 560, 560, + 560, 560, 561, 561, 561, 562, 562, 562, 563, 563, + 563, 563, 564, 564, 564, 565, 565, 565, 566, 566, + 566, 566, 567, 567, 567, 568, 568, 568, 569, 569, + 569, 569, 570, 570, 570, 571, 571, 571, 572, 572, + 572, 572, 573, 573, 573, 574, 574, 574, 575, 575, + 575, 575, 576, 576, 576, 577, 577, 577, 578, 578, + 578, 579, 579, 579, 579, 580, 580, 580, 581, 581, + 581, 582, 582, 582, 582, 583, 583, 583, 584, 584, + 584, 585, 585, 585, 585, 586, 586, 586, 587, 587, + 587, 588, 588, 588, 588, 589, 589, 589, 590, 590, + 590, 591, 591, 591, 591, 592, 592, 592, 593, 593, + 593, 594, 594, 594, 594, 595, 595, 595, 596, 596, + 596, 597, 597, 597, 597, 598, 598, 598, 599, 599, + 599, 600, 600, 600, 600, 601, 601, 601, 602, 602, + 602, 603, 603, 603, 603, 604, 604, 604, 605, 605, + 605, 606, 606, 606, 607, 607, 607, 607, 608, 608, + 608, 609, 609, 609, 610, 610, 610, 610, 611, 611, + 611, 612, 612, 612, 613, 613, 613, 613, 614, 614, + 614, 615, 615, 615, 616, 616, 616, 616, 617, 617, + 617, 618, 618, 618, 619, 619, 619, 619, 620, 620, + 620, 621, 621, 621, 622, 622, 622, 622, 623, 623, + 623, 624, 624, 624, 625, 625, 625, 625, 626, 626, + 626, 627, 627, 627, 628, 628, 628, 628, 629, 629, + 629, 630, 630, 630, 631, 631, 631, 631, 632, 632, + 632, 633, 633, 633, 634, 634, 634, 634, 635, 635, + 635, 636, 636, 636, 637, 637, 637, 638, 638, 638, + 638, 639, 639, 639, 640, 640, 640, 641, 641, 641, + 641, 642, 642, 642, 643, 643, 643, 644, 644, 644, + 644, 645, 645, 645, 646, 646, 646, 647, 647, 647, + 647, 648, 648, 648, 649, 649, 649, 650, 650 }; +#endif /* STRTOD_ONLY */ + static ULLong pfive[27] = { + 5ll, + 25ll, + 125ll, + 625ll, + 3125ll, + 15625ll, + 78125ll, + 390625ll, + 1953125ll, + 9765625ll, + 48828125ll, + 244140625ll, + 1220703125ll, + 6103515625ll, + 30517578125ll, + 152587890625ll, + 762939453125ll, + 3814697265625ll, + 19073486328125ll, + 95367431640625ll, + 476837158203125ll, + 2384185791015625ll, + 11920928955078125ll, + 59604644775390625ll, + 298023223876953125ll, + 1490116119384765625ll, + 7450580596923828125ll + }; + +#ifndef STRTOD_ONLY + static int pfivebits[25] = {3, 5, 7, 10, 12, 14, 17, 19, 21, 24, 26, 28, 31, + 33, 35, 38, 40, 42, 45, 47, 49, 52, 54, 56, 59}; +#endif /* STRTOD_ONLY */ +#endif /*}*/ +#endif /*}} NO_LONG_LONG */ + +typedef union { double d; ULong L[2]; +#ifdef USE_BF96 + ULLong LL; +#endif + } U; + +#ifdef IEEE_8087 +#define word0(x) (x)->L[1] +#define word1(x) (x)->L[0] +#else +#define word0(x) (x)->L[0] +#define word1(x) (x)->L[1] +#endif +#define dval(x) (x)->d +#define LLval(x) (x)->LL + +#ifndef STRTOD_DIGLIM +#define STRTOD_DIGLIM 40 +#endif + +#ifdef DIGLIM_DEBUG +extern int strtod_diglim; +#else +#define strtod_diglim STRTOD_DIGLIM +#endif + +/* The following definition of Storeinc is appropriate for MIPS processors. + * An alternative that might be better on some machines is + * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) + */ +#if defined(IEEE_8087) + defined(VAX) +#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ +((unsigned short *)a)[0] = (unsigned short)c, a++) +#else +#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ +((unsigned short *)a)[1] = (unsigned short)c, a++) +#endif + +/* #define P DBL_MANT_DIG */ +/* Ten_pmax = floor(P*log(2)/log(5)) */ +/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ +/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ +/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ + +#ifdef IEEE_Arith +#define Exp_shift 20 +#define Exp_shift1 20 +#define Exp_msk1 0x100000 +#define Exp_msk11 0x100000 +#define Exp_mask 0x7ff00000 +#define P 53 +#define Nbits 53 +#define Bias 1023 +#define Emax 1023 +#define Emin (-1022) +#define Exp_1 0x3ff00000 +#define Exp_11 0x3ff00000 +#define Ebits 11 +#define Frac_mask 0xfffff +#define Frac_mask1 0xfffff +#define Ten_pmax 22 +#define Bletch 0x10 +#define Bndry_mask 0xfffff +#define Bndry_mask1 0xfffff +#define LSB 1 +#define Sign_bit 0x80000000 +#define Log2P 1 +#define Tiny0 0 +#define Tiny1 1 +#define Quick_max 14 +#define Int_max 14 +#ifndef NO_IEEE_Scale +#define Avoid_Underflow +#ifdef Flush_Denorm /* debugging option */ +#undef Sudden_Underflow +#endif +#endif + +#ifndef Flt_Rounds +#ifdef FLT_ROUNDS +#define Flt_Rounds FLT_ROUNDS +#else +#define Flt_Rounds 1 +#endif +#endif /*Flt_Rounds*/ + +#ifdef Honor_FLT_ROUNDS +#undef Check_FLT_ROUNDS +#define Check_FLT_ROUNDS +#else +#define Rounding Flt_Rounds +#endif + +#else /* ifndef IEEE_Arith */ +#undef Check_FLT_ROUNDS +#undef Honor_FLT_ROUNDS +#undef SET_INEXACT +#undef Sudden_Underflow +#define Sudden_Underflow +#ifdef IBM +#undef Flt_Rounds +#define Flt_Rounds 0 +#define Exp_shift 24 +#define Exp_shift1 24 +#define Exp_msk1 0x1000000 +#define Exp_msk11 0x1000000 +#define Exp_mask 0x7f000000 +#define P 14 +#define Nbits 56 +#define Bias 65 +#define Emax 248 +#define Emin (-260) +#define Exp_1 0x41000000 +#define Exp_11 0x41000000 +#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */ +#define Frac_mask 0xffffff +#define Frac_mask1 0xffffff +#define Bletch 4 +#define Ten_pmax 22 +#define Bndry_mask 0xefffff +#define Bndry_mask1 0xffffff +#define LSB 1 +#define Sign_bit 0x80000000 +#define Log2P 4 +#define Tiny0 0x100000 +#define Tiny1 0 +#define Quick_max 14 +#define Int_max 15 +#else /* VAX */ +#undef Flt_Rounds +#define Flt_Rounds 1 +#define Exp_shift 23 +#define Exp_shift1 7 +#define Exp_msk1 0x80 +#define Exp_msk11 0x800000 +#define Exp_mask 0x7f80 +#define P 56 +#define Nbits 56 +#define Bias 129 +#define Emax 126 +#define Emin (-129) +#define Exp_1 0x40800000 +#define Exp_11 0x4080 +#define Ebits 8 +#define Frac_mask 0x7fffff +#define Frac_mask1 0xffff007f +#define Ten_pmax 24 +#define Bletch 2 +#define Bndry_mask 0xffff007f +#define Bndry_mask1 0xffff007f +#define LSB 0x10000 +#define Sign_bit 0x8000 +#define Log2P 1 +#define Tiny0 0x80 +#define Tiny1 0 +#define Quick_max 15 +#define Int_max 15 +#endif /* IBM, VAX */ +#endif /* IEEE_Arith */ + +#ifndef IEEE_Arith +#define ROUND_BIASED +#else +#ifdef ROUND_BIASED_without_Round_Up +#undef ROUND_BIASED +#define ROUND_BIASED +#endif +#endif + +#ifdef RND_PRODQUOT +#define rounded_product(a,b) a = rnd_prod(a, b) +#define rounded_quotient(a,b) a = rnd_quot(a, b) +extern double rnd_prod(double, double), rnd_quot(double, double); +#else +#define rounded_product(a,b) a *= b +#define rounded_quotient(a,b) a /= b +#endif + +#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) +#define Big1 0xffffffff + +#ifndef Pack_32 +#define Pack_32 +#endif + +typedef struct BCinfo BCinfo; + struct +BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; }; + +#define FFFFFFFF 0xffffffffUL + +#ifdef MULTIPLE_THREADS +#define MTa , PTI +#define MTb , &TI +#define MTd , ThInfo **PTI +static unsigned int maxthreads = 0; +#else +#define MTa /*nothing*/ +#define MTb /*nothing*/ +#define MTd /*nothing*/ +#endif + +#define Kmax 7 + +#ifdef __cplusplus +extern "C" double strtod(const char *s00, char **se); +extern "C" char *dtoa(double d, int mode, int ndigits, + int *decpt, int *sign, char **rve); +#endif + + struct +Bigint { + struct Bigint *next; + int k, maxwds, sign, wds; + ULong x[1]; + }; + + typedef struct Bigint Bigint; + typedef struct +ThInfo { + Bigint *Freelist[Kmax+1]; + Bigint *P5s; + } ThInfo; + + static ThInfo TI0; + +#ifdef MULTIPLE_THREADS + static ThInfo *TI1; + static int TI0_used; + + void +set_max_dtoa_threads(unsigned int n) +{ + size_t L; + + if (n > maxthreads) { + L = n*sizeof(ThInfo); + if (TI1) { + TI1 = (ThInfo*)REALLOC(TI1, L); + memset(TI1 + maxthreads, 0, (n-maxthreads)*sizeof(ThInfo)); + } + else { + TI1 = (ThInfo*)MALLOC(L); + if (TI0_used) { + memcpy(TI1, &TI0, sizeof(ThInfo)); + if (n > 1) + memset(TI1 + 1, 0, L - sizeof(ThInfo)); + memset(&TI0, 0, sizeof(ThInfo)); + } + else + memset(TI1, 0, L); + } + maxthreads = n; + } + } + + static ThInfo* +get_TI(void) +{ + unsigned int thno = dtoa_get_threadno(); + if (thno < maxthreads) + return TI1 + thno; + if (thno == 0) + TI0_used = 1; + return &TI0; + } +#define freelist TI->Freelist +#define p5s TI->P5s +#else +#define freelist TI0.Freelist +#define p5s TI0.P5s +#endif + + static Bigint * +Balloc(int k MTd) +{ + int x; + Bigint *rv; +#ifndef Omit_Private_Memory + unsigned int len; +#endif +#ifdef MULTIPLE_THREADS + ThInfo *TI; + + if (!(TI = *PTI)) + *PTI = TI = get_TI(); + if (TI == &TI0) + ACQUIRE_DTOA_LOCK(0); +#endif + /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */ + /* but this case seems very unlikely. */ + if (k <= Kmax && (rv = freelist[k])) + freelist[k] = rv->next; + else { + x = 1 << k; +#ifdef Omit_Private_Memory + rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong)); +#else + len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) + /sizeof(double); + if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem +#ifdef MULTIPLE_THREADS + && TI == TI1 +#endif + ) { + rv = (Bigint*)pmem_next; + pmem_next += len; + } + else + rv = (Bigint*)MALLOC(len*sizeof(double)); +#endif + rv->k = k; + rv->maxwds = x; + } +#ifdef MULTIPLE_THREADS + if (TI == &TI0) + FREE_DTOA_LOCK(0); +#endif + rv->sign = rv->wds = 0; + return rv; + } + + static void +Bfree(Bigint *v MTd) +{ +#ifdef MULTIPLE_THREADS + ThInfo *TI; +#endif + if (v) { + if (v->k > Kmax) + FREE((void*)v); + else { +#ifdef MULTIPLE_THREADS + if (!(TI = *PTI)) + *PTI = TI = get_TI(); + if (TI == &TI0) + ACQUIRE_DTOA_LOCK(0); +#endif + v->next = freelist[v->k]; + freelist[v->k] = v; +#ifdef MULTIPLE_THREADS + if (TI == &TI0) + FREE_DTOA_LOCK(0); +#endif + } + } + } + +#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ +y->wds*sizeof(Long) + 2*sizeof(int)) + + static Bigint * +multadd(Bigint *b, int m, int a MTd) /* multiply by m and add a */ +{ + int i, wds; +#ifdef ULLong + ULong *x; + ULLong carry, y; +#else + ULong carry, *x, y; +#ifdef Pack_32 + ULong xi, z; +#endif +#endif + Bigint *b1; + + wds = b->wds; + x = b->x; + i = 0; + carry = a; + do { +#ifdef ULLong + y = *x * (ULLong)m + carry; + carry = y >> 32; + *x++ = y & FFFFFFFF; +#else +#ifdef Pack_32 + xi = *x; + y = (xi & 0xffff) * m + carry; + z = (xi >> 16) * m + (y >> 16); + carry = z >> 16; + *x++ = (z << 16) + (y & 0xffff); +#else + y = *x * m + carry; + carry = y >> 16; + *x++ = y & 0xffff; +#endif +#endif + } + while(++i < wds); + if (carry) { + if (wds >= b->maxwds) { + b1 = Balloc(b->k+1 MTa); + Bcopy(b1, b); + Bfree(b MTa); + b = b1; + } + b->x[wds++] = carry; + b->wds = wds; + } + return b; + } + + static Bigint * +s2b(const char *s, int nd0, int nd, ULong y9, int dplen MTd) +{ + Bigint *b; + int i, k; + Long x, y; + + x = (nd + 8) / 9; + for(k = 0, y = 1; x > y; y <<= 1, k++) ; +#ifdef Pack_32 + b = Balloc(k MTa); + b->x[0] = y9; + b->wds = 1; +#else + b = Balloc(k+1 MTa); + b->x[0] = y9 & 0xffff; + b->wds = (b->x[1] = y9 >> 16) ? 2 : 1; +#endif + + i = 9; + if (9 < nd0) { + s += 9; + do b = multadd(b, 10, *s++ - '0' MTa); + while(++i < nd0); + s += dplen; + } + else + s += dplen + 9; + for(; i < nd; i++) + b = multadd(b, 10, *s++ - '0' MTa); + return b; + } + + static int +hi0bits(ULong x) +{ + int k = 0; + + if (!(x & 0xffff0000)) { + k = 16; + x <<= 16; + } + if (!(x & 0xff000000)) { + k += 8; + x <<= 8; + } + if (!(x & 0xf0000000)) { + k += 4; + x <<= 4; + } + if (!(x & 0xc0000000)) { + k += 2; + x <<= 2; + } + if (!(x & 0x80000000)) { + k++; + if (!(x & 0x40000000)) + return 32; + } + return k; + } + + static int +lo0bits(ULong *y) +{ + int k; + ULong x = *y; + + if (x & 7) { + if (x & 1) + return 0; + if (x & 2) { + *y = x >> 1; + return 1; + } + *y = x >> 2; + return 2; + } + k = 0; + if (!(x & 0xffff)) { + k = 16; + x >>= 16; + } + if (!(x & 0xff)) { + k += 8; + x >>= 8; + } + if (!(x & 0xf)) { + k += 4; + x >>= 4; + } + if (!(x & 0x3)) { + k += 2; + x >>= 2; + } + if (!(x & 1)) { + k++; + x >>= 1; + if (!x) + return 32; + } + *y = x; + return k; + } + + static Bigint * +i2b(int i MTd) +{ + Bigint *b; + + b = Balloc(1 MTa); + b->x[0] = i; + b->wds = 1; + return b; + } + + static Bigint * +mult(Bigint *a, Bigint *b MTd) +{ + Bigint *c; + int k, wa, wb, wc; + ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; + ULong y; +#ifdef ULLong + ULLong carry, z; +#else + ULong carry, z; +#ifdef Pack_32 + ULong z2; +#endif +#endif + + if (a->wds < b->wds) { + c = a; + a = b; + b = c; + } + k = a->k; + wa = a->wds; + wb = b->wds; + wc = wa + wb; + if (wc > a->maxwds) + k++; + c = Balloc(k MTa); + for(x = c->x, xa = x + wc; x < xa; x++) + *x = 0; + xa = a->x; + xae = xa + wa; + xb = b->x; + xbe = xb + wb; + xc0 = c->x; +#ifdef ULLong + for(; xb < xbe; xc0++) { + if ((y = *xb++)) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * (ULLong)y + *xc + carry; + carry = z >> 32; + *xc++ = z & FFFFFFFF; + } + while(x < xae); + *xc = carry; + } + } +#else +#ifdef Pack_32 + for(; xb < xbe; xb++, xc0++) { + if (y = *xb & 0xffff) { + x = xa; + xc = xc0; + carry = 0; + do { + z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; + carry = z >> 16; + z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; + carry = z2 >> 16; + Storeinc(xc, z2, z); + } + while(x < xae); + *xc = carry; + } + if (y = *xb >> 16) { + x = xa; + xc = xc0; + carry = 0; + z2 = *xc; + do { + z = (*x & 0xffff) * y + (*xc >> 16) + carry; + carry = z >> 16; + Storeinc(xc, z, z2); + z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; + carry = z2 >> 16; + } + while(x < xae); + *xc = z2; + } + } +#else + for(; xb < xbe; xc0++) { + if (y = *xb++) { + x = xa; + xc = xc0; + carry = 0; + do { + z = *x++ * y + *xc + carry; + carry = z >> 16; + *xc++ = z & 0xffff; + } + while(x < xae); + *xc = carry; + } + } +#endif +#endif + for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; + c->wds = wc; + return c; + } + + static Bigint * +pow5mult(Bigint *b, int k MTd) +{ + Bigint *b1, *p5, *p51; +#ifdef MULTIPLE_THREADS + ThInfo *TI; +#endif + int i; + static int p05[3] = { 5, 25, 125 }; + + if ((i = k & 3)) + b = multadd(b, p05[i-1], 0 MTa); + + if (!(k >>= 2)) + return b; +#ifdef MULTIPLE_THREADS + if (!(TI = *PTI)) + *PTI = TI = get_TI(); +#endif + if (!(p5 = p5s)) { + /* first time */ +#ifdef MULTIPLE_THREADS + if (!(TI = *PTI)) + *PTI = TI = get_TI(); + if (TI == &TI0) + ACQUIRE_DTOA_LOCK(1); + if (!(p5 = p5s)) { + p5 = p5s = i2b(625 MTa); + p5->next = 0; + } + if (TI == &TI0) + FREE_DTOA_LOCK(1); +#else + p5 = p5s = i2b(625 MTa); + p5->next = 0; +#endif + } + for(;;) { + if (k & 1) { + b1 = mult(b, p5 MTa); + Bfree(b MTa); + b = b1; + } + if (!(k >>= 1)) + break; + if (!(p51 = p5->next)) { +#ifdef MULTIPLE_THREADS + if (!TI && !(TI = *PTI)) + *PTI = TI = get_TI(); + if (TI == &TI0) + ACQUIRE_DTOA_LOCK(1); + if (!(p51 = p5->next)) { + p51 = p5->next = mult(p5,p5 MTa); + p51->next = 0; + } + if (TI == &TI0) + FREE_DTOA_LOCK(1); +#else + p51 = p5->next = mult(p5,p5); + p51->next = 0; +#endif + } + p5 = p51; + } + return b; + } + + static Bigint * +lshift(Bigint *b, int k MTd) +{ + int i, k1, n, n1; + Bigint *b1; + ULong *x, *x1, *xe, z; + +#ifdef Pack_32 + n = k >> 5; +#else + n = k >> 4; +#endif + k1 = b->k; + n1 = n + b->wds + 1; + for(i = b->maxwds; n1 > i; i <<= 1) + k1++; + b1 = Balloc(k1 MTa); + x1 = b1->x; + for(i = 0; i < n; i++) + *x1++ = 0; + x = b->x; + xe = x + b->wds; +#ifdef Pack_32 + if (k &= 0x1f) { + k1 = 32 - k; + z = 0; + do { + *x1++ = *x << k | z; + z = *x++ >> k1; + } + while(x < xe); + if ((*x1 = z)) + ++n1; + } +#else + if (k &= 0xf) { + k1 = 16 - k; + z = 0; + do { + *x1++ = *x << k & 0xffff | z; + z = *x++ >> k1; + } + while(x < xe); + if (*x1 = z) + ++n1; + } +#endif + else do + *x1++ = *x++; + while(x < xe); + b1->wds = n1 - 1; + Bfree(b MTa); + return b1; + } + + static int +cmp(Bigint *a, Bigint *b) +{ + ULong *xa, *xa0, *xb, *xb0; + int i, j; + + i = a->wds; + j = b->wds; +#ifdef DEBUG + if (i > 1 && !a->x[i-1]) + Bug("cmp called with a->x[a->wds-1] == 0"); + if (j > 1 && !b->x[j-1]) + Bug("cmp called with b->x[b->wds-1] == 0"); +#endif + if (i -= j) + return i; + xa0 = a->x; + xa = xa0 + j; + xb0 = b->x; + xb = xb0 + j; + for(;;) { + if (*--xa != *--xb) + return *xa < *xb ? -1 : 1; + if (xa <= xa0) + break; + } + return 0; + } + + static Bigint * +diff(Bigint *a, Bigint *b MTd) +{ + Bigint *c; + int i, wa, wb; + ULong *xa, *xae, *xb, *xbe, *xc; +#ifdef ULLong + ULLong borrow, y; +#else + ULong borrow, y; +#ifdef Pack_32 + ULong z; +#endif +#endif + + i = cmp(a,b); + if (!i) { + c = Balloc(0 MTa); + c->wds = 1; + c->x[0] = 0; + return c; + } + if (i < 0) { + c = a; + a = b; + b = c; + i = 1; + } + else + i = 0; + c = Balloc(a->k MTa); + c->sign = i; + wa = a->wds; + xa = a->x; + xae = xa + wa; + wb = b->wds; + xb = b->x; + xbe = xb + wb; + xc = c->x; + borrow = 0; +#ifdef ULLong + do { + y = (ULLong)*xa++ - *xb++ - borrow; + borrow = y >> 32 & (ULong)1; + *xc++ = y & FFFFFFFF; + } + while(xb < xbe); + while(xa < xae) { + y = *xa++ - borrow; + borrow = y >> 32 & (ULong)1; + *xc++ = y & FFFFFFFF; + } +#else +#ifdef Pack_32 + do { + y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(xc, z, y); + } + while(xb < xbe); + while(xa < xae) { + y = (*xa & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*xa++ >> 16) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(xc, z, y); + } +#else + do { + y = *xa++ - *xb++ - borrow; + borrow = (y & 0x10000) >> 16; + *xc++ = y & 0xffff; + } + while(xb < xbe); + while(xa < xae) { + y = *xa++ - borrow; + borrow = (y & 0x10000) >> 16; + *xc++ = y & 0xffff; + } +#endif +#endif + while(!*--xc) + wa--; + c->wds = wa; + return c; + } + + static double +ulp(U *x) +{ + Long L; + U u; + + L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; +#ifndef Avoid_Underflow +#ifndef Sudden_Underflow + if (L > 0) { +#endif +#endif +#ifdef IBM + L |= Exp_msk1 >> 4; +#endif + word0(&u) = L; + word1(&u) = 0; +#ifndef Avoid_Underflow +#ifndef Sudden_Underflow + } + else { + L = -L >> Exp_shift; + if (L < Exp_shift) { + word0(&u) = 0x80000 >> L; + word1(&u) = 0; + } + else { + word0(&u) = 0; + L -= Exp_shift; + word1(&u) = L >= 31 ? 1 : 1 << 31 - L; + } + } +#endif +#endif + return dval(&u); + } + + static double +b2d(Bigint *a, int *e) +{ + ULong *xa, *xa0, w, y, z; + int k; + U d; +#ifdef VAX + ULong d0, d1; +#else +#define d0 word0(&d) +#define d1 word1(&d) +#endif + + xa0 = a->x; + xa = xa0 + a->wds; + y = *--xa; +#ifdef DEBUG + if (!y) Bug("zero y in b2d"); +#endif + k = hi0bits(y); + *e = 32 - k; +#ifdef Pack_32 + if (k < Ebits) { + d0 = Exp_1 | y >> (Ebits - k); + w = xa > xa0 ? *--xa : 0; + d1 = y << ((32-Ebits) + k) | w >> (Ebits - k); + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + if (k -= Ebits) { + d0 = Exp_1 | y << k | z >> (32 - k); + y = xa > xa0 ? *--xa : 0; + d1 = z << k | y >> (32 - k); + } + else { + d0 = Exp_1 | y; + d1 = z; + } +#else + if (k < Ebits + 16) { + z = xa > xa0 ? *--xa : 0; + d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k; + w = xa > xa0 ? *--xa : 0; + y = xa > xa0 ? *--xa : 0; + d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k; + goto ret_d; + } + z = xa > xa0 ? *--xa : 0; + w = xa > xa0 ? *--xa : 0; + k -= Ebits + 16; + d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k; + y = xa > xa0 ? *--xa : 0; + d1 = w << k + 16 | y << k; +#endif + ret_d: +#ifdef VAX + word0(&d) = d0 >> 16 | d0 << 16; + word1(&d) = d1 >> 16 | d1 << 16; +#else +#undef d0 +#undef d1 +#endif + return dval(&d); + } + + static Bigint * +d2b(U *d, int *e, int *bits MTd) +{ + Bigint *b; + int de, k; + ULong *x, y, z; +#ifndef Sudden_Underflow + int i; +#endif +#ifdef VAX + ULong d0, d1; + d0 = word0(d) >> 16 | word0(d) << 16; + d1 = word1(d) >> 16 | word1(d) << 16; +#else +#define d0 word0(d) +#define d1 word1(d) +#endif + +#ifdef Pack_32 + b = Balloc(1 MTa); +#else + b = Balloc(2 MTa); +#endif + x = b->x; + + z = d0 & Frac_mask; + d0 &= 0x7fffffff; /* clear sign bit, which we ignore */ +#ifdef Sudden_Underflow + de = (int)(d0 >> Exp_shift); +#ifndef IBM + z |= Exp_msk11; +#endif +#else + if ((de = (int)(d0 >> Exp_shift))) + z |= Exp_msk1; +#endif +#ifdef Pack_32 + if ((y = d1)) { + if ((k = lo0bits(&y))) { + x[0] = y | z << (32 - k); + z >>= k; + } + else + x[0] = y; +#ifndef Sudden_Underflow + i = +#endif + b->wds = (x[1] = z) ? 2 : 1; + } + else { + k = lo0bits(&z); + x[0] = z; +#ifndef Sudden_Underflow + i = +#endif + b->wds = 1; + k += 32; + } +#else + if (y = d1) { + if (k = lo0bits(&y)) + if (k >= 16) { + x[0] = y | z << 32 - k & 0xffff; + x[1] = z >> k - 16 & 0xffff; + x[2] = z >> k; + i = 2; + } + else { + x[0] = y & 0xffff; + x[1] = y >> 16 | z << 16 - k & 0xffff; + x[2] = z >> k & 0xffff; + x[3] = z >> k+16; + i = 3; + } + else { + x[0] = y & 0xffff; + x[1] = y >> 16; + x[2] = z & 0xffff; + x[3] = z >> 16; + i = 3; + } + } + else { +#ifdef DEBUG + if (!z) + Bug("Zero passed to d2b"); +#endif + k = lo0bits(&z); + if (k >= 16) { + x[0] = z; + i = 0; + } + else { + x[0] = z & 0xffff; + x[1] = z >> 16; + i = 1; + } + k += 32; + } + while(!x[i]) + --i; + b->wds = i + 1; +#endif +#ifndef Sudden_Underflow + if (de) { +#endif +#ifdef IBM + *e = (de - Bias - (P-1) << 2) + k; + *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask); +#else + *e = de - Bias - (P-1) + k; + *bits = P - k; +#endif +#ifndef Sudden_Underflow + } + else { + *e = de - Bias - (P-1) + 1 + k; +#ifdef Pack_32 + *bits = 32*i - hi0bits(x[i-1]); +#else + *bits = (i+2)*16 - hi0bits(x[i]); +#endif + } +#endif + return b; + } +#undef d0 +#undef d1 + + static double +ratio(Bigint *a, Bigint *b) +{ + U da, db; + int k, ka, kb; + + dval(&da) = b2d(a, &ka); + dval(&db) = b2d(b, &kb); +#ifdef Pack_32 + k = ka - kb + 32*(a->wds - b->wds); +#else + k = ka - kb + 16*(a->wds - b->wds); +#endif +#ifdef IBM + if (k > 0) { + word0(&da) += (k >> 2)*Exp_msk1; + if (k &= 3) + dval(&da) *= 1 << k; + } + else { + k = -k; + word0(&db) += (k >> 2)*Exp_msk1; + if (k &= 3) + dval(&db) *= 1 << k; + } +#else + if (k > 0) + word0(&da) += k*Exp_msk1; + else { + k = -k; + word0(&db) += k*Exp_msk1; + } +#endif + return dval(&da) / dval(&db); + } + + static const double +tens[] = { + 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, + 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, + 1e20, 1e21, 1e22 +#ifdef VAX + , 1e23, 1e24 +#endif + }; + + static const double +#ifdef IEEE_Arith +bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; +static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, +#ifdef Avoid_Underflow + 9007199254740992.*9007199254740992.e-256 + /* = 2^106 * 1e-256 */ +#else + 1e-256 +#endif + }; +/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ +/* flag unnecessarily. It leads to a song and dance at the end of strtod. */ +#define Scale_Bit 0x10 +#define n_bigtens 5 +#else +#ifdef IBM +bigtens[] = { 1e16, 1e32, 1e64 }; +static const double tinytens[] = { 1e-16, 1e-32, 1e-64 }; +#define n_bigtens 3 +#else +bigtens[] = { 1e16, 1e32 }; +static const double tinytens[] = { 1e-16, 1e-32 }; +#define n_bigtens 2 +#endif +#endif + +#undef Need_Hexdig +#ifdef INFNAN_CHECK +#ifndef No_Hex_NaN +#define Need_Hexdig +#endif +#endif + +#ifndef Need_Hexdig +#ifndef NO_HEX_FP +#define Need_Hexdig +#endif +#endif + +#ifdef Need_Hexdig /*{*/ +#if 0 +static unsigned char hexdig[256]; + + static void +htinit(unsigned char *h, unsigned char *s, int inc) +{ + int i, j; + for(i = 0; (j = s[i]) !=0; i++) + h[j] = i + inc; + } + + static void +hexdig_init(void) /* Use of hexdig_init omitted 20121220 to avoid a */ + /* race condition when multiple threads are used. */ +{ +#define USC (unsigned char *) + htinit(hexdig, USC "0123456789", 0x10); + htinit(hexdig, USC "abcdef", 0x10 + 10); + htinit(hexdig, USC "ABCDEF", 0x10 + 10); + } +#else +static unsigned char hexdig[256] = { + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 16,17,18,19,20,21,22,23,24,25,0,0,0,0,0,0, + 0,26,27,28,29,30,31,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,26,27,28,29,30,31,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 + }; +#endif +#endif /* } Need_Hexdig */ + +#ifdef INFNAN_CHECK + +#ifndef NAN_WORD0 +#define NAN_WORD0 0x7ff80000 +#endif + +#ifndef NAN_WORD1 +#define NAN_WORD1 0 +#endif + + static int +match(const char **sp, const char *t) +{ + int c, d; + const char *s = *sp; + + while((d = *t++)) { + if ((c = *++s) >= 'A' && c <= 'Z') + c += 'a' - 'A'; + if (c != d) + return 0; + } + *sp = s + 1; + return 1; + } + +#ifndef No_Hex_NaN + static void +hexnan(U *rvp, const char **sp) +{ + ULong c, x[2]; + const char *s; + int c1, havedig, udx0, xshift; + + /**** if (!hexdig['0']) hexdig_init(); ****/ + x[0] = x[1] = 0; + havedig = xshift = 0; + udx0 = 1; + s = *sp; + /* allow optional initial 0x or 0X */ + while((c = *(const unsigned char*)(s+1)) && c <= ' ') + ++s; + if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X')) + s += 2; + while((c = *(const unsigned char*)++s)) { + if ((c1 = hexdig[c])) + c = c1 & 0xf; + else if (c <= ' ') { + if (udx0 && havedig) { + udx0 = 0; + xshift = 1; + } + continue; + } +#ifdef GDTOA_NON_PEDANTIC_NANCHECK + else if (/*(*/ c == ')' && havedig) { + *sp = s + 1; + break; + } + else + return; /* invalid form: don't change *sp */ +#else + else { + do { + if (/*(*/ c == ')') { + *sp = s + 1; + break; + } + } while((c = *++s)); + break; + } +#endif + havedig = 1; + if (xshift) { + xshift = 0; + x[0] = x[1]; + x[1] = 0; + } + if (udx0) + x[0] = (x[0] << 4) | (x[1] >> 28); + x[1] = (x[1] << 4) | c; + } + if ((x[0] &= 0xfffff) || x[1]) { + word0(rvp) = Exp_mask | x[0]; + word1(rvp) = x[1]; + } + } +#endif /*No_Hex_NaN*/ +#endif /* INFNAN_CHECK */ + +#ifdef Pack_32 +#define ULbits 32 +#define kshift 5 +#define kmask 31 +#else +#define ULbits 16 +#define kshift 4 +#define kmask 15 +#endif + +#if !defined(NO_HEX_FP) || defined(Honor_FLT_ROUNDS) /*{*/ + static Bigint * +increment(Bigint *b MTd) +{ + ULong *x, *xe; + Bigint *b1; + + x = b->x; + xe = x + b->wds; + do { + if (*x < (ULong)0xffffffffL) { + ++*x; + return b; + } + *x++ = 0; + } while(x < xe); + { + if (b->wds >= b->maxwds) { + b1 = Balloc(b->k+1 MTa); + Bcopy(b1,b); + Bfree(b MTa); + b = b1; + } + b->x[b->wds++] = 1; + } + return b; + } + +#endif /*}*/ + +#ifndef NO_HEX_FP /*{*/ + + static void +rshift(Bigint *b, int k) +{ + ULong *x, *x1, *xe, y; + int n; + + x = x1 = b->x; + n = k >> kshift; + if (n < b->wds) { + xe = x + b->wds; + x += n; + if (k &= kmask) { + n = 32 - k; + y = *x++ >> k; + while(x < xe) { + *x1++ = (y | (*x << n)) & 0xffffffff; + y = *x++ >> k; + } + if ((*x1 = y) !=0) + x1++; + } + else + while(x < xe) + *x1++ = *x++; + } + if ((b->wds = x1 - b->x) == 0) + b->x[0] = 0; + } + + static ULong +any_on(Bigint *b, int k) +{ + int n, nwds; + ULong *x, *x0, x1, x2; + + x = b->x; + nwds = b->wds; + n = k >> kshift; + if (n > nwds) + n = nwds; + else if (n < nwds && (k &= kmask)) { + x1 = x2 = x[n]; + x1 >>= k; + x1 <<= k; + if (x1 != x2) + return 1; + } + x0 = x; + x += n; + while(x > x0) + if (*--x) + return 1; + return 0; + } + +enum { /* rounding values: same as FLT_ROUNDS */ + Round_zero = 0, + Round_near = 1, + Round_up = 2, + Round_down = 3 + }; + + static void +gethex( const char **sp, U *rvp, int rounding, int sign MTd) +{ + Bigint *b; + const unsigned char *decpt, *s0, *s, *s1; + Long e, e1; + ULong L, lostbits, *x; + int big, denorm, esign, havedig, k, n, nbits, up, zret; +#ifdef IBM + int j; +#endif + enum { +#ifdef IEEE_Arith /*{{*/ + emax = 0x7fe - Bias - P + 1, + emin = Emin - P + 1 +#else /*}{*/ + emin = Emin - P, +#ifdef VAX + emax = 0x7ff - Bias - P + 1 +#endif +#ifdef IBM + emax = 0x7f - Bias - P +#endif +#endif /*}}*/ + }; +#ifdef USE_LOCALE + int i; +#ifdef NO_LOCALE_CACHE + const unsigned char *decimalpoint = (unsigned char*) + localeconv()->decimal_point; +#else + const unsigned char *decimalpoint; + static unsigned char *decimalpoint_cache; + if (!(s0 = decimalpoint_cache)) { + s0 = (unsigned char*)localeconv()->decimal_point; + if ((decimalpoint_cache = (unsigned char*) + MALLOC(strlen((const char*)s0) + 1))) { + strcpy((char*)decimalpoint_cache, (const char*)s0); + s0 = decimalpoint_cache; + } + } + decimalpoint = s0; +#endif +#endif + + /**** if (!hexdig['0']) hexdig_init(); ****/ + havedig = 0; + s0 = *(const unsigned char **)sp + 2; + while(s0[havedig] == '0') + havedig++; + s0 += havedig; + s = s0; + decpt = 0; + zret = 0; + e = 0; + if (hexdig[*s]) + havedig++; + else { + zret = 1; +#ifdef USE_LOCALE + for(i = 0; decimalpoint[i]; ++i) { + if (s[i] != decimalpoint[i]) + goto pcheck; + } + decpt = s += i; +#else + if (*s != '.') + goto pcheck; + decpt = ++s; +#endif + if (!hexdig[*s]) + goto pcheck; + while(*s == '0') + s++; + if (hexdig[*s]) + zret = 0; + havedig = 1; + s0 = s; + } + while(hexdig[*s]) + s++; +#ifdef USE_LOCALE + if (*s == *decimalpoint && !decpt) { + for(i = 1; decimalpoint[i]; ++i) { + if (s[i] != decimalpoint[i]) + goto pcheck; + } + decpt = s += i; +#else + if (*s == '.' && !decpt) { + decpt = ++s; +#endif + while(hexdig[*s]) + s++; + }/*}*/ + if (decpt) + e = -(((Long)(s-decpt)) << 2); + pcheck: + s1 = s; + big = esign = 0; + switch(*s) { + case 'p': + case 'P': + switch(*++s) { + case '-': + esign = 1; + /* no break */ + case '+': + s++; + } + if ((n = hexdig[*s]) == 0 || n > 0x19) { + s = s1; + break; + } + e1 = n - 0x10; + while((n = hexdig[*++s]) !=0 && n <= 0x19) { + if (e1 & 0xf8000000) + big = 1; + e1 = 10*e1 + n - 0x10; + } + if (esign) + e1 = -e1; + e += e1; + } + *sp = (char*)s; + if (!havedig) + *sp = (char*)s0 - 1; + if (zret) + goto retz1; + if (big) { + if (esign) { +#ifdef IEEE_Arith + switch(rounding) { + case Round_up: + if (sign) + break; + goto ret_tiny; + case Round_down: + if (!sign) + break; + goto ret_tiny; + } +#endif + goto retz; +#ifdef IEEE_Arith + ret_tinyf: + Bfree(b MTa); + ret_tiny: + Set_errno(ERANGE); + word0(rvp) = 0; + word1(rvp) = 1; + return; +#endif /* IEEE_Arith */ + } + switch(rounding) { + case Round_near: + goto ovfl1; + case Round_up: + if (!sign) + goto ovfl1; + goto ret_big; + case Round_down: + if (sign) + goto ovfl1; + goto ret_big; + } + ret_big: + word0(rvp) = Big0; + word1(rvp) = Big1; + return; + } + n = s1 - s0 - 1; + for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1) + k++; + b = Balloc(k MTa); + x = b->x; + n = 0; + L = 0; +#ifdef USE_LOCALE + for(i = 0; decimalpoint[i+1]; ++i); +#endif + while(s1 > s0) { +#ifdef USE_LOCALE + if (*--s1 == decimalpoint[i]) { + s1 -= i; + continue; + } +#else + if (*--s1 == '.') + continue; +#endif + if (n == ULbits) { + *x++ = L; + L = 0; + n = 0; + } + L |= (hexdig[*s1] & 0x0f) << n; + n += 4; + } + *x++ = L; + b->wds = n = x - b->x; + n = ULbits*n - hi0bits(L); + nbits = Nbits; + lostbits = 0; + x = b->x; + if (n > nbits) { + n -= nbits; + if (any_on(b,n)) { + lostbits = 1; + k = n - 1; + if (x[k>>kshift] & 1 << (k & kmask)) { + lostbits = 2; + if (k > 0 && any_on(b,k)) + lostbits = 3; + } + } + rshift(b, n); + e += n; + } + else if (n < nbits) { + n = nbits - n; + b = lshift(b, n MTa); + e -= n; + x = b->x; + } + if (e > emax) { + ovfl: + Bfree(b MTa); + ovfl1: + Set_errno(ERANGE); +#ifdef Honor_FLT_ROUNDS + switch (rounding) { + case Round_zero: + goto ret_big; + case Round_down: + if (!sign) + goto ret_big; + break; + case Round_up: + if (sign) + goto ret_big; + } +#endif + word0(rvp) = Exp_mask; + word1(rvp) = 0; + return; + } + denorm = 0; + if (e < emin) { + denorm = 1; + n = emin - e; + if (n >= nbits) { +#ifdef IEEE_Arith /*{*/ + switch (rounding) { + case Round_near: + if (n == nbits && (n < 2 || lostbits || any_on(b,n-1))) + goto ret_tinyf; + break; + case Round_up: + if (!sign) + goto ret_tinyf; + break; + case Round_down: + if (sign) + goto ret_tinyf; + } +#endif /* } IEEE_Arith */ + Bfree(b MTa); + retz: + Set_errno(ERANGE); + retz1: + rvp->d = 0.; + return; + } + k = n - 1; + if (lostbits) + lostbits = 1; + else if (k > 0) + lostbits = any_on(b,k); + if (x[k>>kshift] & 1 << (k & kmask)) + lostbits |= 2; + nbits -= n; + rshift(b,n); + e = emin; + } + if (lostbits) { + up = 0; + switch(rounding) { + case Round_zero: + break; + case Round_near: + if (lostbits & 2 + && (lostbits & 1) | (x[0] & 1)) + up = 1; + break; + case Round_up: + up = 1 - sign; + break; + case Round_down: + up = sign; + } + if (up) { + k = b->wds; + b = increment(b MTa); + x = b->x; + if (denorm) { +#if 0 + if (nbits == Nbits - 1 + && x[nbits >> kshift] & 1 << (nbits & kmask)) + denorm = 0; /* not currently used */ +#endif + } + else if (b->wds > k + || ((n = nbits & kmask) !=0 + && hi0bits(x[k-1]) < 32-n)) { + rshift(b,1); + if (++e > Emax) + goto ovfl; + } + } + } +#ifdef IEEE_Arith + if (denorm) + word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0; + else + word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20); + word1(rvp) = b->x[0]; +#endif +#ifdef IBM + if ((j = e & 3)) { + k = b->x[0] & ((1 << j) - 1); + rshift(b,j); + if (k) { + switch(rounding) { + case Round_up: + if (!sign) + increment(b); + break; + case Round_down: + if (sign) + increment(b); + break; + case Round_near: + j = 1 << (j-1); + if (k & j && ((k & (j-1)) | lostbits)) + increment(b); + } + } + } + e >>= 2; + word0(rvp) = b->x[1] | ((e + 65 + 13) << 24); + word1(rvp) = b->x[0]; +#endif +#ifdef VAX + /* The next two lines ignore swap of low- and high-order 2 bytes. */ + /* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */ + /* word1(rvp) = b->x[0]; */ + word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16); + word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16); +#endif + Bfree(b MTa); + } +#endif /*!NO_HEX_FP}*/ + + static int +dshift(Bigint *b, int p2) +{ + int rv = hi0bits(b->x[b->wds-1]) - 4; + if (p2 > 0) + rv -= p2; + return rv & kmask; + } + + static int +quorem(Bigint *b, Bigint *S) +{ + int n; + ULong *bx, *bxe, q, *sx, *sxe; +#ifdef ULLong + ULLong borrow, carry, y, ys; +#else + ULong borrow, carry, y, ys; +#ifdef Pack_32 + ULong si, z, zs; +#endif +#endif + + n = S->wds; +#ifdef DEBUG + /*debug*/ if (b->wds > n) + /*debug*/ Bug("oversize b in quorem"); +#endif + if (b->wds < n) + return 0; + sx = S->x; + sxe = sx + --n; + bx = b->x; + bxe = bx + n; + q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ +#ifdef DEBUG +#ifdef NO_STRTOD_BIGCOMP + /*debug*/ if (q > 9) +#else + /* An oversized q is possible when quorem is called from bigcomp and */ + /* the input is near, e.g., twice the smallest denormalized number. */ + /*debug*/ if (q > 15) +#endif + /*debug*/ Bug("oversized quotient in quorem"); +#endif + if (q) { + borrow = 0; + carry = 0; + do { +#ifdef ULLong + ys = *sx++ * (ULLong)q + carry; + carry = ys >> 32; + y = *bx - (ys & FFFFFFFF) - borrow; + borrow = y >> 32 & (ULong)1; + *bx++ = y & FFFFFFFF; +#else +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) * q + carry; + zs = (si >> 16) * q + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*bx >> 16) - (zs & 0xffff) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(bx, z, y); +#else + ys = *sx++ * q + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + *bx++ = y & 0xffff; +#endif +#endif + } + while(sx <= sxe); + if (!*bxe) { + bx = b->x; + while(--bxe > bx && !*bxe) + --n; + b->wds = n; + } + } + if (cmp(b, S) >= 0) { + q++; + borrow = 0; + carry = 0; + bx = b->x; + sx = S->x; + do { +#ifdef ULLong + ys = *sx++ + carry; + carry = ys >> 32; + y = *bx - (ys & FFFFFFFF) - borrow; + borrow = y >> 32 & (ULong)1; + *bx++ = y & FFFFFFFF; +#else +#ifdef Pack_32 + si = *sx++; + ys = (si & 0xffff) + carry; + zs = (si >> 16) + (ys >> 16); + carry = zs >> 16; + y = (*bx & 0xffff) - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + z = (*bx >> 16) - (zs & 0xffff) - borrow; + borrow = (z & 0x10000) >> 16; + Storeinc(bx, z, y); +#else + ys = *sx++ + carry; + carry = ys >> 16; + y = *bx - (ys & 0xffff) - borrow; + borrow = (y & 0x10000) >> 16; + *bx++ = y & 0xffff; +#endif +#endif + } + while(sx <= sxe); + bx = b->x; + bxe = bx + n; + if (!*bxe) { + while(--bxe > bx && !*bxe) + --n; + b->wds = n; + } + } + return q; + } + +#if defined(Avoid_Underflow) || !defined(NO_STRTOD_BIGCOMP) /*{*/ + static double +sulp(U *x, BCinfo *bc) +{ + U u; + double rv; + int i; + + rv = ulp(x); + if (!bc->scale || (i = 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift)) <= 0) + return rv; /* Is there an example where i <= 0 ? */ + word0(&u) = Exp_1 + (i << Exp_shift); + word1(&u) = 0; + return rv * u.d; + } +#endif /*}*/ + +#ifndef NO_STRTOD_BIGCOMP + static void +bigcomp(U *rv, const char *s0, BCinfo *bc MTd) +{ + Bigint *b, *d; + int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase; + + dsign = bc->dsign; + nd = bc->nd; + nd0 = bc->nd0; + p5 = nd + bc->e0 - 1; + speccase = 0; +#ifndef Sudden_Underflow + if (rv->d == 0.) { /* special case: value near underflow-to-zero */ + /* threshold was rounded to zero */ + b = i2b(1 MTa); + p2 = Emin - P + 1; + bbits = 1; +#ifdef Avoid_Underflow + word0(rv) = (P+2) << Exp_shift; +#else + word1(rv) = 1; +#endif + i = 0; +#ifdef Honor_FLT_ROUNDS + if (bc->rounding == 1) +#endif + { + speccase = 1; + --p2; + dsign = 0; + goto have_i; + } + } + else +#endif + b = d2b(rv, &p2, &bbits MTa); +#ifdef Avoid_Underflow + p2 -= bc->scale; +#endif + /* floor(log2(rv)) == bbits - 1 + p2 */ + /* Check for denormal case. */ + i = P - bbits; + if (i > (j = P - Emin - 1 + p2)) { +#ifdef Sudden_Underflow + Bfree(b MTa); + b = i2b(1); + p2 = Emin; + i = P - 1; +#ifdef Avoid_Underflow + word0(rv) = (1 + bc->scale) << Exp_shift; +#else + word0(rv) = Exp_msk1; +#endif + word1(rv) = 0; +#else + i = j; +#endif + } +#ifdef Honor_FLT_ROUNDS + if (bc->rounding != 1) { + if (i > 0) + b = lshift(b, i MTa); + if (dsign) + b = increment(b MTa); + } + else +#endif + { + b = lshift(b, ++i MTa); + b->x[0] |= 1; + } +#ifndef Sudden_Underflow + have_i: +#endif + p2 -= p5 + i; + d = i2b(1 MTa); + /* Arrange for convenient computation of quotients: + * shift left if necessary so divisor has 4 leading 0 bits. + */ + if (p5 > 0) + d = pow5mult(d, p5 MTa); + else if (p5 < 0) + b = pow5mult(b, -p5 MTa); + if (p2 > 0) { + b2 = p2; + d2 = 0; + } + else { + b2 = 0; + d2 = -p2; + } + i = dshift(d, d2); + if ((b2 += i) > 0) + b = lshift(b, b2 MTa); + if ((d2 += i) > 0) + d = lshift(d, d2 MTa); + + /* Now b/d = exactly half-way between the two floating-point values */ + /* on either side of the input string. Compute first digit of b/d. */ + + if (!(dig = quorem(b,d))) { + b = multadd(b, 10, 0 MTa); /* very unlikely */ + dig = quorem(b,d); + } + + /* Compare b/d with s0 */ + + for(i = 0; i < nd0; ) { + if ((dd = s0[i++] - '0' - dig)) + goto ret; + if (!b->x[0] && b->wds == 1) { + if (i < nd) + dd = 1; + goto ret; + } + b = multadd(b, 10, 0 MTa); + dig = quorem(b,d); + } + for(j = bc->dp1; i++ < nd;) { + if ((dd = s0[j++] - '0' - dig)) + goto ret; + if (!b->x[0] && b->wds == 1) { + if (i < nd) + dd = 1; + goto ret; + } + b = multadd(b, 10, 0 MTa); + dig = quorem(b,d); + } + if (dig > 0 || b->x[0] || b->wds > 1) + dd = -1; + ret: + Bfree(b MTa); + Bfree(d MTa); +#ifdef Honor_FLT_ROUNDS + if (bc->rounding != 1) { + if (dd < 0) { + if (bc->rounding == 0) { + if (!dsign) + goto retlow1; + } + else if (dsign) + goto rethi1; + } + else if (dd > 0) { + if (bc->rounding == 0) { + if (dsign) + goto rethi1; + goto ret1; + } + if (!dsign) + goto rethi1; + dval(rv) += 2.*sulp(rv,bc); + } + else { + bc->inexact = 0; + if (dsign) + goto rethi1; + } + } + else +#endif + if (speccase) { + if (dd <= 0) + rv->d = 0.; + } + else if (dd < 0) { + if (!dsign) /* does not happen for round-near */ +retlow1: + dval(rv) -= sulp(rv,bc); + } + else if (dd > 0) { + if (dsign) { + rethi1: + dval(rv) += sulp(rv,bc); + } + } + else { + /* Exact half-way case: apply round-even rule. */ + if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) { + i = 1 - j; + if (i <= 31) { + if (word1(rv) & (0x1 << i)) + goto odd; + } + else if (word0(rv) & (0x1 << (i-32))) + goto odd; + } + else if (word1(rv) & 1) { + odd: + if (dsign) + goto rethi1; + goto retlow1; + } + } + +#ifdef Honor_FLT_ROUNDS + ret1: +#endif + return; + } +#endif /* NO_STRTOD_BIGCOMP */ + + double +strtod(const char *s00, char **se) +{ + int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1; + int esign, i, j, k, nd, nd0, nf, nz, nz0, nz1, sign; + const char *s, *s0, *s1; + double aadj, aadj1; + Long L; + U aadj2, adj, rv, rv0; + ULong y, z; + BCinfo bc; + Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; +#ifdef USE_BF96 + ULLong bhi, blo, brv, t00, t01, t02, t10, t11, terv, tg, tlo, yz; + const BF96 *p10; + int bexact, erv; +#endif +#ifdef Avoid_Underflow + ULong Lsb, Lsb1; +#endif +#ifdef SET_INEXACT + int oldinexact; +#endif +#ifndef NO_STRTOD_BIGCOMP + int req_bigcomp = 0; +#endif +#ifdef MULTIPLE_THREADS + ThInfo *TI = 0; +#endif +#ifdef Honor_FLT_ROUNDS /*{*/ +#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */ + bc.rounding = Flt_Rounds; +#else /*}{*/ + bc.rounding = 1; + switch(fegetround()) { + case FE_TOWARDZERO: bc.rounding = 0; break; + case FE_UPWARD: bc.rounding = 2; break; + case FE_DOWNWARD: bc.rounding = 3; + } +#endif /*}}*/ +#endif /*}*/ +#ifdef USE_LOCALE + const char *s2; +#endif + + sign = nz0 = nz1 = nz = bc.dplen = bc.uflchk = 0; + dval(&rv) = 0.; + for(s = s00;;s++) switch(*s) { + case '-': + sign = 1; + /* no break */ + case '+': + if (*++s) + goto break2; + /* no break */ + case 0: + goto ret0; + case '\t': + case '\n': + case '\v': + case '\f': + case '\r': + case ' ': + continue; + default: + goto break2; + } + break2: + if (*s == '0') { +#ifndef NO_HEX_FP /*{*/ + switch(s[1]) { + case 'x': + case 'X': +#ifdef Honor_FLT_ROUNDS + gethex(&s, &rv, bc.rounding, sign MTb); +#else + gethex(&s, &rv, 1, sign MTb); +#endif + goto ret; + } +#endif /*}*/ + nz0 = 1; + while(*++s == '0') ; + if (!*s) + goto ret; + } + s0 = s; + nd = nf = 0; +#ifdef USE_BF96 + yz = 0; + for(; (c = *s) >= '0' && c <= '9'; nd++, s++) + if (nd < 19) + yz = 10*yz + c - '0'; +#else + y = z = 0; + for(; (c = *s) >= '0' && c <= '9'; nd++, s++) + if (nd < 9) + y = 10*y + c - '0'; + else if (nd < DBL_DIG + 2) + z = 10*z + c - '0'; +#endif + nd0 = nd; + bc.dp0 = bc.dp1 = s - s0; + for(s1 = s; s1 > s0 && *--s1 == '0'; ) + ++nz1; +#ifdef USE_LOCALE + s1 = localeconv()->decimal_point; + if (c == *s1) { + c = '.'; + if (*++s1) { + s2 = s; + for(;;) { + if (*++s2 != *s1) { + c = 0; + break; + } + if (!*++s1) { + s = s2; + break; + } + } + } + } +#endif + if (c == '.') { + c = *++s; + bc.dp1 = s - s0; + bc.dplen = bc.dp1 - bc.dp0; + if (!nd) { + for(; c == '0'; c = *++s) + nz++; + if (c > '0' && c <= '9') { + bc.dp0 = s0 - s; + bc.dp1 = bc.dp0 + bc.dplen; + s0 = s; + nf += nz; + nz = 0; + goto have_dig; + } + goto dig_done; + } + for(; c >= '0' && c <= '9'; c = *++s) { + have_dig: + nz++; + if (c -= '0') { + nf += nz; + i = 1; +#ifdef USE_BF96 + for(; i < nz; ++i) { + if (++nd <= 19) + yz *= 10; + } + if (++nd <= 19) + yz = 10*yz + c; +#else + for(; i < nz; ++i) { + if (nd++ < 9) + y *= 10; + else if (nd <= DBL_DIG + 2) + z *= 10; + } + if (nd++ < 9) + y = 10*y + c; + else if (nd <= DBL_DIG + 2) + z = 10*z + c; +#endif + nz = nz1 = 0; + } + } + } + dig_done: + e = 0; + if (c == 'e' || c == 'E') { + if (!nd && !nz && !nz0) { + goto ret0; + } + s00 = s; + esign = 0; + switch(c = *++s) { + case '-': + esign = 1; + case '+': + c = *++s; + } + if (c >= '0' && c <= '9') { + while(c == '0') + c = *++s; + if (c > '0' && c <= '9') { + L = c - '0'; + s1 = s; + while((c = *++s) >= '0' && c <= '9') + L = 10*L + c - '0'; + if (s - s1 > 8 || L > 19999) + /* Avoid confusion from exponents + * so large that e might overflow. + */ + e = 19999; /* safe for 16 bit ints */ + else + e = (int)L; + if (esign) + e = -e; + } + else + e = 0; + } + else + s = s00; + } + if (!nd) { + if (!nz && !nz0) { +#ifdef INFNAN_CHECK /*{*/ + /* Check for Nan and Infinity */ + if (!bc.dplen) + switch(c) { + case 'i': + case 'I': + if (match(&s,"nf")) { + --s; + if (!match(&s,"inity")) + ++s; + word0(&rv) = 0x7ff00000; + word1(&rv) = 0; + goto ret; + } + break; + case 'n': + case 'N': + if (match(&s, "an")) { + word0(&rv) = NAN_WORD0; + word1(&rv) = NAN_WORD1; +#ifndef No_Hex_NaN + if (*s == '(') /*)*/ + hexnan(&rv, &s); +#endif + goto ret; + } + } +#endif /*} INFNAN_CHECK */ + ret0: + s = s00; + sign = 0; + } + goto ret; + } + bc.e0 = e1 = e -= nf; + + /* Now we have nd0 digits, starting at s0, followed by a + * decimal point, followed by nd-nd0 digits. The number we're + * after is the integer represented by those digits times + * 10**e */ + + if (!nd0) + nd0 = nd; +#ifndef USE_BF96 + k = nd < DBL_DIG + 2 ? nd : DBL_DIG + 2; + dval(&rv) = y; + if (k > 9) { +#ifdef SET_INEXACT + if (k > DBL_DIG) + oldinexact = get_inexact(); +#endif + dval(&rv) = tens[k - 9] * dval(&rv) + z; + } +#endif + bd0 = 0; + if (nd <= DBL_DIG +#ifndef RND_PRODQUOT +#ifndef Honor_FLT_ROUNDS + && Flt_Rounds == 1 +#endif +#endif + ) { +#ifdef USE_BF96 + dval(&rv) = yz; +#endif + if (!e) + goto ret; +#ifndef ROUND_BIASED_without_Round_Up + if (e > 0) { + if (e <= Ten_pmax) { +#ifdef SET_INEXACT + bc.inexact = 0; + oldinexact = 1; +#endif +#ifdef VAX + goto vax_ovfl_check; +#else +#ifdef Honor_FLT_ROUNDS + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv.d = -rv.d; + sign = 0; + } +#endif + /* rv = */ rounded_product(dval(&rv), tens[e]); + goto ret; +#endif + } + i = DBL_DIG - nd; + if (e <= Ten_pmax + i) { + /* A fancier test would sometimes let us do + * this for larger i values. + */ +#ifdef SET_INEXACT + bc.inexact = 0; + oldinexact = 1; +#endif +#ifdef Honor_FLT_ROUNDS + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv.d = -rv.d; + sign = 0; + } +#endif + e -= i; + dval(&rv) *= tens[i]; +#ifdef VAX + /* VAX exponent range is so narrow we must + * worry about overflow here... + */ + vax_ovfl_check: + word0(&rv) -= P*Exp_msk1; + /* rv = */ rounded_product(dval(&rv), tens[e]); + if ((word0(&rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) + goto ovfl; + word0(&rv) += P*Exp_msk1; +#else + /* rv = */ rounded_product(dval(&rv), tens[e]); +#endif + goto ret; + } + } +#ifndef Inaccurate_Divide + else if (e >= -Ten_pmax) { +#ifdef SET_INEXACT + bc.inexact = 0; + oldinexact = 1; +#endif +#ifdef Honor_FLT_ROUNDS + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv.d = -rv.d; + sign = 0; + } +#endif + /* rv = */ rounded_quotient(dval(&rv), tens[-e]); + goto ret; + } +#endif +#endif /* ROUND_BIASED_without_Round_Up */ + } +#ifdef USE_BF96 + k = nd < 19 ? nd : 19; +#endif + e1 += nd - k; /* scale factor = 10^e1 */ + +#ifdef IEEE_Arith +#ifdef SET_INEXACT + bc.inexact = 1; +#ifndef USE_BF96 + if (k <= DBL_DIG) +#endif + oldinexact = get_inexact(); +#endif +#ifdef Honor_FLT_ROUNDS + if (bc.rounding >= 2) { + if (sign) + bc.rounding = bc.rounding == 2 ? 0 : 2; + else + if (bc.rounding != 2) + bc.rounding = 0; + } +#endif +#endif /*IEEE_Arith*/ + +#ifdef USE_BF96 /*{*/ + Debug(++dtoa_stats[0]); + i = e1 + 342; + if (i < 0) + goto undfl; + if (i > 650) + goto ovfl; + p10 = &pten[i]; + brv = yz; + /* shift brv left, with i = number of bits shifted */ + i = 0; + if (!(brv & 0xffffffff00000000ull)) { + i = 32; + brv <<= 32; + } + if (!(brv & 0xffff000000000000ull)) { + i += 16; + brv <<= 16; + } + if (!(brv & 0xff00000000000000ull)) { + i += 8; + brv <<= 8; + } + if (!(brv & 0xf000000000000000ull)) { + i += 4; + brv <<= 4; + } + if (!(brv & 0xc000000000000000ull)) { + i += 2; + brv <<= 2; + } + if (!(brv & 0x8000000000000000ull)) { + i += 1; + brv <<= 1; + } + erv = (64 + 0x3fe) + p10->e - i; + if (erv <= 0 && nd > 19) + goto many_digits; /* denormal: may need to look at all digits */ + bhi = brv >> 32; + blo = brv & 0xffffffffull; + /* Unsigned 32-bit ints lie in [0,2^32-1] and */ + /* unsigned 64-bit ints lie in [0, 2^64-1]. The product of two unsigned */ + /* 32-bit ints is <= 2^64 - 2*2^32-1 + 1 = 2^64 - 1 - 2*(2^32 - 1), so */ + /* we can add two unsigned 32-bit ints to the product of two such ints, */ + /* and 64 bits suffice to contain the result. */ + t01 = bhi * p10->b1; + t10 = blo * p10->b0 + (t01 & 0xffffffffull); + t00 = bhi * p10->b0 + (t01 >> 32) + (t10 >> 32); + if (t00 & 0x8000000000000000ull) { + if ((t00 & 0x3ff) && (~t00 & 0x3fe)) { /* unambiguous result? */ + if (nd > 19 && ((t00 + (1< 19 && ((t00 + (1<b2; + t11 = blo * p10->b1 + (t02 & 0xffffffffull); + bexact = 1; + if (e1 < 0 || e1 > 41 || (t10 | t11) & 0xffffffffull || nd > 19) + bexact = 0; + tlo = (t10 & 0xffffffffull) + (t02 >> 32) + (t11 >> 32); + if (!bexact && (tlo + 0x10) >> 32 > tlo >> 32) + goto many_digits; + t00 += tlo >> 32; + if (t00 & 0x8000000000000000ull) { + if (erv <= 0) { /* denormal result */ + if (nd >= 20 || !((tlo & 0xfffffff0) | (t00 & 0x3ff))) + goto many_digits; + denormal: + if (erv <= -52) { +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto undfl; + case 2: goto tiniest; + } +#endif + if (erv < -52 || !(t00 & 0x7fffffffffffffffull)) + goto undfl; + goto tiniest; + } + tg = 1ull << (11 - erv); + t00 &= ~(tg - 1); /* clear low bits */ +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround_den; + case 2: goto roundup_den; + } +#endif + if (t00 & tg) { +#ifdef Honor_FLT_ROUNDS + roundup_den: +#endif + t00 += tg << 1; + if (!(t00 & 0x8000000000000000ull)) { + if (++erv > 0) + goto smallest_normal; + t00 = 0x8000000000000000ull; + } + } +#ifdef Honor_FLT_ROUNDS + noround_den: +#endif + LLval(&rv) = t00 >> (12 - erv); + Set_errno(ERANGE); + goto ret; + } + if (bexact) { +#ifdef SET_INEXACT + if (!(t00 & 0x7ff) && !(tlo & 0xffffffffull)) { + bc.inexact = 0; + goto noround; + } +#endif +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 2: + if (t00 & 0x7ff) + goto roundup; + case 0: goto noround; + } +#endif + if (t00 & 0x400 && (tlo & 0xffffffff) | (t00 & 0xbff)) + goto roundup; + goto noround; + } + if ((tlo & 0xfffffff0) | (t00 & 0x3ff) + && (nd <= 19 || ((t00 + (1ull << i)) & 0xfffffffffffffc00ull) + == (t00 & 0xfffffffffffffc00ull))) { + /* Unambiguous result. */ + /* If nd > 19, then incrementing the 19th digit */ + /* does not affect rv. */ +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround; + case 2: goto roundup; + } +#endif + if (t00 & 0x400) { /* round up */ + roundup: + t00 += 0x800; + if (!(t00 & 0x8000000000000000ull)) { + /* rounded up to a power of 2 */ + if (erv >= 0x7fe) + goto ovfl; + terv = erv + 1; + LLval(&rv) = terv << 52; + goto ret; + } + } + noround: + if (erv >= 0x7ff) + goto ovfl; + terv = erv; + LLval(&rv) = (terv << 52) | ((t00 & 0x7ffffffffffff800ull) >> 11); + goto ret; + } + } + else { + if (erv <= 1) { /* denormal result */ + if (nd >= 20 || !((tlo & 0xfffffff0) | (t00 & 0x1ff))) + goto many_digits; + denormal1: + if (erv <= -51) { +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto undfl; + case 2: goto tiniest; + } +#endif + if (erv < -51 || !(t00 & 0x3fffffffffffffffull)) + goto undfl; + tiniest: + LLval(&rv) = 1; + Set_errno(ERANGE); + goto ret; + } + tg = 1ull << (11 - erv); +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround1_den; + case 2: goto roundup1_den; + } +#endif + if (t00 & tg) { +#ifdef Honor_FLT_ROUNDS + roundup1_den: +#endif + if (0x8000000000000000ull & (t00 += (tg<<1)) && erv == 1) { + + smallest_normal: + LLval(&rv) = 0x0010000000000000ull; + goto ret; + } + } +#ifdef Honor_FLT_ROUNDS + noround1_den: +#endif + if (erv <= -52) + goto undfl; + LLval(&rv) = t00 >> (12 - erv); + Set_errno(ERANGE); + goto ret; + } + if (bexact) { +#ifdef SET_INEXACT + if (!(t00 & 0x3ff) && !(tlo & 0xffffffffull)) { + bc.inexact = 0; + goto noround1; + } +#endif +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 2: + if (t00 & 0x3ff) + goto roundup1; + case 0: goto noround1; + } +#endif + if (t00 & 0x200 && (t00 & 0x5ff || tlo)) + goto roundup1; + goto noround1; + } + if ((tlo & 0xfffffff0) | (t00 & 0x1ff) + && (nd <= 19 || ((t00 + (1ull << i)) & 0x7ffffffffffffe00ull) + == (t00 & 0x7ffffffffffffe00ull))) { + /* Unambiguous result. */ +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: goto noround1; + case 2: goto roundup1; + } +#endif + if (t00 & 0x200) { /* round up */ + roundup1: + t00 += 0x400; + if (!(t00 & 0x4000000000000000ull)) { + /* rounded up to a power of 2 */ + if (erv >= 0x7ff) + goto ovfl; + terv = erv; + LLval(&rv) = terv << 52; + goto ret; + } + } + noround1: + if (erv >= 0x800) + goto ovfl; + terv = erv - 1; + LLval(&rv) = (terv << 52) | ((t00 & 0x3ffffffffffffc00ull) >> 10); + goto ret; + } + } + many_digits: + Debug(++dtoa_stats[2]); + if (nd > 17) { + if (nd > 18) { + yz /= 100; + e1 += 2; + } + else { + yz /= 10; + e1 += 1; + } + y = yz / 100000000; + } + else if (nd > 9) { + i = nd - 9; + y = (yz >> i) / pfive[i-1]; + } + else + y = yz; + dval(&rv) = yz; +#endif /*}*/ + +#ifdef IEEE_Arith +#ifdef Avoid_Underflow + bc.scale = 0; +#endif +#endif /*IEEE_Arith*/ + + /* Get starting approximation = rv * 10**e1 */ + + if (e1 > 0) { + if ((i = e1 & 15)) + dval(&rv) *= tens[i]; + if (e1 &= ~15) { + if (e1 > DBL_MAX_10_EXP) { + ovfl: + /* Can't trust HUGE_VAL */ +#ifdef IEEE_Arith +#ifdef Honor_FLT_ROUNDS + switch(bc.rounding) { + case 0: /* toward 0 */ + case 3: /* toward -infinity */ + word0(&rv) = Big0; + word1(&rv) = Big1; + break; + default: + word0(&rv) = Exp_mask; + word1(&rv) = 0; + } +#else /*Honor_FLT_ROUNDS*/ + word0(&rv) = Exp_mask; + word1(&rv) = 0; +#endif /*Honor_FLT_ROUNDS*/ +#ifdef SET_INEXACT + /* set overflow bit */ + dval(&rv0) = 1e300; + dval(&rv0) *= dval(&rv0); +#endif +#else /*IEEE_Arith*/ + word0(&rv) = Big0; + word1(&rv) = Big1; +#endif /*IEEE_Arith*/ + range_err: + if (bd0) { + Bfree(bb MTb); + Bfree(bd MTb); + Bfree(bs MTb); + Bfree(bd0 MTb); + Bfree(delta MTb); + } + Set_errno(ERANGE); + goto ret; + } + e1 >>= 4; + for(j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) + dval(&rv) *= bigtens[j]; + /* The last multiplication could overflow. */ + word0(&rv) -= P*Exp_msk1; + dval(&rv) *= bigtens[j]; + if ((z = word0(&rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-P)) + goto ovfl; + if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { + /* set to largest number */ + /* (Can't trust DBL_MAX) */ + word0(&rv) = Big0; + word1(&rv) = Big1; + } + else + word0(&rv) += P*Exp_msk1; + } + } + else if (e1 < 0) { + e1 = -e1; + if ((i = e1 & 15)) + dval(&rv) /= tens[i]; + if (e1 >>= 4) { + if (e1 >= 1 << n_bigtens) + goto undfl; +#ifdef Avoid_Underflow + if (e1 & Scale_Bit) + bc.scale = 2*P; + for(j = 0; e1 > 0; j++, e1 >>= 1) + if (e1 & 1) + dval(&rv) *= tinytens[j]; + if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask) + >> Exp_shift)) > 0) { + /* scaled rv is denormal; clear j low bits */ + if (j >= 32) { + if (j > 54) + goto undfl; + word1(&rv) = 0; + if (j >= 53) + word0(&rv) = (P+2)*Exp_msk1; + else + word0(&rv) &= 0xffffffff << (j-32); + } + else + word1(&rv) &= 0xffffffff << j; + } +#else + for(j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) + dval(&rv) *= tinytens[j]; + /* The last multiplication could underflow. */ + dval(&rv0) = dval(&rv); + dval(&rv) *= tinytens[j]; + if (!dval(&rv)) { + dval(&rv) = 2.*dval(&rv0); + dval(&rv) *= tinytens[j]; +#endif + if (!dval(&rv)) { + undfl: + dval(&rv) = 0.; +#ifdef Honor_FLT_ROUNDS + if (bc.rounding == 2) + word1(&rv) = 1; +#endif + goto range_err; + } +#ifndef Avoid_Underflow + word0(&rv) = Tiny0; + word1(&rv) = Tiny1; + /* The refinement below will clean + * this approximation up. + */ + } +#endif + } + } + + /* Now the hard part -- adjusting rv to the correct value.*/ + + /* Put digits into bd: true value = bd * 10^e */ + + bc.nd = nd - nz1; +#ifndef NO_STRTOD_BIGCOMP + bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */ + /* to silence an erroneous warning about bc.nd0 */ + /* possibly not being initialized. */ + if (nd > strtod_diglim) { + /* ASSERT(strtod_diglim >= 18); 18 == one more than the */ + /* minimum number of decimal digits to distinguish double values */ + /* in IEEE arithmetic. */ + i = j = 18; + if (i > nd0) + j += bc.dplen; + for(;;) { + if (--j < bc.dp1 && j >= bc.dp0) + j = bc.dp0 - 1; + if (s0[j] != '0') + break; + --i; + } + e += nd - i; + nd = i; + if (nd0 > nd) + nd0 = nd; + if (nd < 9) { /* must recompute y */ + y = 0; + for(i = 0; i < nd0; ++i) + y = 10*y + s0[i] - '0'; + for(j = bc.dp1; i < nd; ++i) + y = 10*y + s0[j++] - '0'; + } + } +#endif + bd0 = s2b(s0, nd0, nd, y, bc.dplen MTb); + + for(;;) { + bd = Balloc(bd0->k MTb); + Bcopy(bd, bd0); + bb = d2b(&rv, &bbe, &bbbits MTb); /* rv = bb * 2^bbe */ + bs = i2b(1 MTb); + + if (e >= 0) { + bb2 = bb5 = 0; + bd2 = bd5 = e; + } + else { + bb2 = bb5 = -e; + bd2 = bd5 = 0; + } + if (bbe >= 0) + bb2 += bbe; + else + bd2 -= bbe; + bs2 = bb2; +#ifdef Honor_FLT_ROUNDS + if (bc.rounding != 1) + bs2++; +#endif +#ifdef Avoid_Underflow + Lsb = LSB; + Lsb1 = 0; + j = bbe - bc.scale; + i = j + bbbits - 1; /* logb(rv) */ + j = P + 1 - bbbits; + if (i < Emin) { /* denormal */ + i = Emin - i; + j -= i; + if (i < 32) + Lsb <<= i; + else if (i < 52) + Lsb1 = Lsb << (i-32); + else + Lsb1 = Exp_mask; + } +#else /*Avoid_Underflow*/ +#ifdef Sudden_Underflow +#ifdef IBM + j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); +#else + j = P + 1 - bbbits; +#endif +#else /*Sudden_Underflow*/ + j = bbe; + i = j + bbbits - 1; /* logb(rv) */ + if (i < Emin) /* denormal */ + j += P - Emin; + else + j = P + 1 - bbbits; +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow*/ + bb2 += j; + bd2 += j; +#ifdef Avoid_Underflow + bd2 += bc.scale; +#endif + i = bb2 < bd2 ? bb2 : bd2; + if (i > bs2) + i = bs2; + if (i > 0) { + bb2 -= i; + bd2 -= i; + bs2 -= i; + } + if (bb5 > 0) { + bs = pow5mult(bs, bb5 MTb); + bb1 = mult(bs, bb MTb); + Bfree(bb MTb); + bb = bb1; + } + if (bb2 > 0) + bb = lshift(bb, bb2 MTb); + if (bd5 > 0) + bd = pow5mult(bd, bd5 MTb); + if (bd2 > 0) + bd = lshift(bd, bd2 MTb); + if (bs2 > 0) + bs = lshift(bs, bs2 MTb); + delta = diff(bb, bd MTb); + bc.dsign = delta->sign; + delta->sign = 0; + i = cmp(delta, bs); +#ifndef NO_STRTOD_BIGCOMP /*{*/ + if (bc.nd > nd && i <= 0) { + if (bc.dsign) { + /* Must use bigcomp(). */ + req_bigcomp = 1; + break; + } +#ifdef Honor_FLT_ROUNDS + if (bc.rounding != 1) { + if (i < 0) { + req_bigcomp = 1; + break; + } + } + else +#endif + i = -1; /* Discarded digits make delta smaller. */ + } +#endif /*}*/ +#ifdef Honor_FLT_ROUNDS /*{*/ + if (bc.rounding != 1) { + if (i < 0) { + /* Error is less than an ulp */ + if (!delta->x[0] && delta->wds <= 1) { + /* exact */ +#ifdef SET_INEXACT + bc.inexact = 0; +#endif + break; + } + if (bc.rounding) { + if (bc.dsign) { + adj.d = 1.; + goto apply_adj; + } + } + else if (!bc.dsign) { + adj.d = -1.; + if (!word1(&rv) + && !(word0(&rv) & Frac_mask)) { + y = word0(&rv) & Exp_mask; +#ifdef Avoid_Underflow + if (!bc.scale || y > 2*P*Exp_msk1) +#else + if (y) +#endif + { + delta = lshift(delta,Log2P MTb); + if (cmp(delta, bs) <= 0) + adj.d = -0.5; + } + } + apply_adj: +#ifdef Avoid_Underflow /*{*/ + if (bc.scale && (y = word0(&rv) & Exp_mask) + <= 2*P*Exp_msk1) + word0(&adj) += (2*P+1)*Exp_msk1 - y; +#else +#ifdef Sudden_Underflow + if ((word0(&rv) & Exp_mask) <= + P*Exp_msk1) { + word0(&rv) += P*Exp_msk1; + dval(&rv) += adj.d*ulp(dval(&rv)); + word0(&rv) -= P*Exp_msk1; + } + else +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow}*/ + dval(&rv) += adj.d*ulp(&rv); + } + break; + } + adj.d = ratio(delta, bs); + if (adj.d < 1.) + adj.d = 1.; + if (adj.d <= 0x7ffffffe) { + /* adj = rounding ? ceil(adj) : floor(adj); */ + y = adj.d; + if (y != adj.d) { + if (!((bc.rounding>>1) ^ bc.dsign)) + y++; + adj.d = y; + } + } +#ifdef Avoid_Underflow /*{*/ + if (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) + word0(&adj) += (2*P+1)*Exp_msk1 - y; +#else +#ifdef Sudden_Underflow + if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { + word0(&rv) += P*Exp_msk1; + adj.d *= ulp(dval(&rv)); + if (bc.dsign) + dval(&rv) += adj.d; + else + dval(&rv) -= adj.d; + word0(&rv) -= P*Exp_msk1; + goto cont; + } +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow}*/ + adj.d *= ulp(&rv); + if (bc.dsign) { + if (word0(&rv) == Big0 && word1(&rv) == Big1) + goto ovfl; + dval(&rv) += adj.d; + } + else + dval(&rv) -= adj.d; + goto cont; + } +#endif /*}Honor_FLT_ROUNDS*/ + + if (i < 0) { + /* Error is less than half an ulp -- check for + * special case of mantissa a power of two. + */ + if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask +#ifdef IEEE_Arith /*{*/ +#ifdef Avoid_Underflow + || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1 +#else + || (word0(&rv) & Exp_mask) <= Exp_msk1 +#endif +#endif /*}*/ + ) { +#ifdef SET_INEXACT + if (!delta->x[0] && delta->wds <= 1) + bc.inexact = 0; +#endif + break; + } + if (!delta->x[0] && delta->wds <= 1) { + /* exact result */ +#ifdef SET_INEXACT + bc.inexact = 0; +#endif + break; + } + delta = lshift(delta,Log2P MTb); + if (cmp(delta, bs) > 0) + goto drop_down; + break; + } + if (i == 0) { + /* exactly half-way between */ + if (bc.dsign) { + if ((word0(&rv) & Bndry_mask1) == Bndry_mask1 + && word1(&rv) == ( +#ifdef Avoid_Underflow + (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) + ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : +#endif + 0xffffffff)) { + /*boundary case -- increment exponent*/ + if (word0(&rv) == Big0 && word1(&rv) == Big1) + goto ovfl; + word0(&rv) = (word0(&rv) & Exp_mask) + + Exp_msk1 +#ifdef IBM + | Exp_msk1 >> 4 +#endif + ; + word1(&rv) = 0; +#ifdef Avoid_Underflow + bc.dsign = 0; +#endif + break; + } + } + else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) { + drop_down: + /* boundary case -- decrement exponent */ +#ifdef Sudden_Underflow /*{{*/ + L = word0(&rv) & Exp_mask; +#ifdef IBM + if (L < Exp_msk1) +#else +#ifdef Avoid_Underflow + if (L <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) +#else + if (L <= Exp_msk1) +#endif /*Avoid_Underflow*/ +#endif /*IBM*/ + { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + L -= Exp_msk1; +#else /*Sudden_Underflow}{*/ +#ifdef Avoid_Underflow + if (bc.scale) { + L = word0(&rv) & Exp_mask; + if (L <= (2*P+1)*Exp_msk1) { + if (L > (P+2)*Exp_msk1) + /* round even ==> */ + /* accept rv */ + break; + /* rv = smallest denormal */ + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + } +#endif /*Avoid_Underflow*/ + L = (word0(&rv) & Exp_mask) - Exp_msk1; +#endif /*Sudden_Underflow}}*/ + word0(&rv) = L | Bndry_mask1; + word1(&rv) = 0xffffffff; +#ifdef IBM + goto cont; +#else +#ifndef NO_STRTOD_BIGCOMP + if (bc.nd > nd) + goto cont; +#endif + break; +#endif + } +#ifndef ROUND_BIASED +#ifdef Avoid_Underflow + if (Lsb1) { + if (!(word0(&rv) & Lsb1)) + break; + } + else if (!(word1(&rv) & Lsb)) + break; +#else + if (!(word1(&rv) & LSB)) + break; +#endif +#endif + if (bc.dsign) +#ifdef Avoid_Underflow + dval(&rv) += sulp(&rv, &bc); +#else + dval(&rv) += ulp(&rv); +#endif +#ifndef ROUND_BIASED + else { +#ifdef Avoid_Underflow + dval(&rv) -= sulp(&rv, &bc); +#else + dval(&rv) -= ulp(&rv); +#endif +#ifndef Sudden_Underflow + if (!dval(&rv)) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } +#endif + } +#ifdef Avoid_Underflow + bc.dsign = 1 - bc.dsign; +#endif +#endif + break; + } + if ((aadj = ratio(delta, bs)) <= 2.) { + if (bc.dsign) + aadj = aadj1 = 1.; + else if (word1(&rv) || word0(&rv) & Bndry_mask) { +#ifndef Sudden_Underflow + if (word1(&rv) == Tiny1 && !word0(&rv)) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } +#endif + aadj = 1.; + aadj1 = -1.; + } + else { + /* special case -- power of FLT_RADIX to be */ + /* rounded down... */ + + if (aadj < 2./FLT_RADIX) + aadj = 1./FLT_RADIX; + else + aadj *= 0.5; + aadj1 = -aadj; + } + } + else { + aadj *= 0.5; + aadj1 = bc.dsign ? aadj : -aadj; +#ifdef Check_FLT_ROUNDS + switch(bc.rounding) { + case 2: /* towards +infinity */ + aadj1 -= 0.5; + break; + case 0: /* towards 0 */ + case 3: /* towards -infinity */ + aadj1 += 0.5; + } +#else + if (Flt_Rounds == 0) + aadj1 += 0.5; +#endif /*Check_FLT_ROUNDS*/ + } + y = word0(&rv) & Exp_mask; + + /* Check for overflow */ + + if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { + dval(&rv0) = dval(&rv); + word0(&rv) -= P*Exp_msk1; + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + if ((word0(&rv) & Exp_mask) >= + Exp_msk1*(DBL_MAX_EXP+Bias-P)) { + if (word0(&rv0) == Big0 && word1(&rv0) == Big1) + goto ovfl; + word0(&rv) = Big0; + word1(&rv) = Big1; + goto cont; + } + else + word0(&rv) += P*Exp_msk1; + } + else { +#ifdef Avoid_Underflow + if (bc.scale && y <= 2*P*Exp_msk1) { + if (aadj <= 0x7fffffff) { + if ((z = aadj) <= 0) + z = 1; + aadj = z; + aadj1 = bc.dsign ? aadj : -aadj; + } + dval(&aadj2) = aadj1; + word0(&aadj2) += (2*P+1)*Exp_msk1 - y; + aadj1 = dval(&aadj2); + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + if (rv.d == 0.) +#ifdef NO_STRTOD_BIGCOMP + goto undfl; +#else + { + req_bigcomp = 1; + break; + } +#endif + } + else { + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + } +#else +#ifdef Sudden_Underflow + if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) { + dval(&rv0) = dval(&rv); + word0(&rv) += P*Exp_msk1; + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; +#ifdef IBM + if ((word0(&rv) & Exp_mask) < P*Exp_msk1) +#else + if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) +#endif + { + if (word0(&rv0) == Tiny0 + && word1(&rv0) == Tiny1) { + if (bc.nd >nd) { + bc.uflchk = 1; + break; + } + goto undfl; + } + word0(&rv) = Tiny0; + word1(&rv) = Tiny1; + goto cont; + } + else + word0(&rv) -= P*Exp_msk1; + } + else { + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; + } +#else /*Sudden_Underflow*/ + /* Compute adj so that the IEEE rounding rules will + * correctly round rv + adj in some half-way cases. + * If rv * ulp(rv) is denormalized (i.e., + * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid + * trouble from bits lost to denormalization; + * example: 1.2e-307 . + */ + if (y <= (P-1)*Exp_msk1 && aadj > 1.) { + aadj1 = (double)(int)(aadj + 0.5); + if (!bc.dsign) + aadj1 = -aadj1; + } + adj.d = aadj1 * ulp(&rv); + dval(&rv) += adj.d; +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow*/ + } + z = word0(&rv) & Exp_mask; +#ifndef SET_INEXACT + if (bc.nd == nd) { +#ifdef Avoid_Underflow + if (!bc.scale) +#endif + if (y == z) { + /* Can we stop now? */ + L = (Long)aadj; + aadj -= L; + /* The tolerances below are conservative. */ + if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) { + if (aadj < .4999999 || aadj > .5000001) + break; + } + else if (aadj < .4999999/FLT_RADIX) + break; + } + } +#endif + cont: + Bfree(bb MTb); + Bfree(bd MTb); + Bfree(bs MTb); + Bfree(delta MTb); + } + Bfree(bb MTb); + Bfree(bd MTb); + Bfree(bs MTb); + Bfree(bd0 MTb); + Bfree(delta MTb); +#ifndef NO_STRTOD_BIGCOMP + if (req_bigcomp) { + bd0 = 0; + bc.e0 += nz1; + bigcomp(&rv, s0, &bc MTb); + y = word0(&rv) & Exp_mask; + if (y == Exp_mask) + goto ovfl; + if (y == 0 && rv.d == 0.) + goto undfl; + } +#endif +#ifdef Avoid_Underflow + if (bc.scale) { + word0(&rv0) = Exp_1 - 2*P*Exp_msk1; + word1(&rv0) = 0; + dval(&rv) *= dval(&rv0); +#ifndef NO_ERRNO + /* try to avoid the bug of testing an 8087 register value */ +#ifdef IEEE_Arith + if (!(word0(&rv) & Exp_mask)) +#else + if (word0(&rv) == 0 && word1(&rv) == 0) +#endif + Set_errno(ERANGE); +#endif + } +#endif /* Avoid_Underflow */ + ret: +#ifdef SET_INEXACT + if (bc.inexact) { + if (!(word0(&rv) & Exp_mask)) { + /* set underflow and inexact bits */ + dval(&rv0) = 1e-300; + dval(&rv0) *= dval(&rv0); + } + else if (!oldinexact) { + word0(&rv0) = Exp_1 + (70 << Exp_shift); + word1(&rv0) = 0; + dval(&rv0) += 1.; + } + } + else if (!oldinexact) + clear_inexact(); +#endif + if (se) + *se = (char *)s; + return sign ? -dval(&rv) : dval(&rv); + } + +#ifndef STRTOD_ONLY +#ifndef MULTIPLE_THREADS + static char *dtoa_result; +#endif + + static char * +rv_alloc(int i MTd) +{ + int j, k, *r; + + j = sizeof(ULong); + for(k = 0; + sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i; + j <<= 1) + k++; + r = (int*)Balloc(k MTa); + *r = k; + return +#ifndef MULTIPLE_THREADS + dtoa_result = +#endif + (char *)(r+1); + } + + static char * +nrv_alloc(const char *s, char *s0, size_t s0len, char **rve, int n MTd) +{ + char *rv, *t; + + if (!s0) + s0 = rv_alloc(n MTa); + else if (s0len <= n) { + rv = 0; + t = rv + n; + goto rve_chk; + } + t = rv = s0; + while((*t = *s++)) + ++t; + rve_chk: + if (rve) + *rve = t; + return rv; + } + +/* freedtoa(s) must be used to free values s returned by dtoa + * when MULTIPLE_THREADS is #defined. It should be used in all cases, + * but for consistency with earlier versions of dtoa, it is optional + * when MULTIPLE_THREADS is not defined. + */ + + void +freedtoa(char *s) +{ +#ifdef MULTIPLE_THREADS + ThInfo *TI = 0; +#endif + Bigint *b = (Bigint *)((int *)s - 1); + b->maxwds = 1 << (b->k = *(int*)b); + Bfree(b MTb); +#ifndef MULTIPLE_THREADS + if (s == dtoa_result) + dtoa_result = 0; +#endif + } + +/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. + * + * Inspired by "How to Print Floating-Point Numbers Accurately" by + * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. + * + * Modifications: + * 1. Rather than iterating, we use a simple numeric overestimate + * to determine k = floor(log10(d)). We scale relevant + * quantities using O(log2(k)) rather than O(k) multiplications. + * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't + * try to generate digits strictly left to right. Instead, we + * compute with fewer bits and propagate the carry if necessary + * when rounding the final digit up. This is often faster. + * 3. Under the assumption that input will be rounded nearest, + * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. + * That is, we allow equality in stopping tests when the + * round-nearest rule will give the same floating-point value + * as would satisfaction of the stopping test with strict + * inequality. + * 4. We remove common factors of powers of 2 from relevant + * quantities. + * 5. When converting floating-point integers less than 1e16, + * we use floating-point arithmetic rather than resorting + * to multiple-precision integers. + * 6. When asked to produce fewer than 15 digits, we first try + * to get by with floating-point arithmetic; we resort to + * multiple-precision integer arithmetic only if we cannot + * guarantee that the floating-point calculation has given + * the correctly rounded result. For k requested digits and + * "uniformly" distributed input, the probability is + * something like 10^(k-15) that we must resort to the Long + * calculation. + */ + + char * +dtoa_r(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve, char *buf, size_t blen) +{ + /* Arguments ndigits, decpt, sign are similar to those + of ecvt and fcvt; trailing zeros are suppressed from + the returned string. If not null, *rve is set to point + to the end of the return value. If d is +-Infinity or NaN, + then *decpt is set to 9999. + + mode: + 0 ==> shortest string that yields d when read in + and rounded to nearest. + 1 ==> like 0, but with Steele & White stopping rule; + e.g. with IEEE P754 arithmetic , mode 0 gives + 1e23 whereas mode 1 gives 9.999999999999999e22. + 2 ==> max(1,ndigits) significant digits. This gives a + return value similar to that of ecvt, except + that trailing zeros are suppressed. + 3 ==> through ndigits past the decimal point. This + gives a return value similar to that from fcvt, + except that trailing zeros are suppressed, and + ndigits can be negative. + 4,5 ==> similar to 2 and 3, respectively, but (in + round-nearest mode) with the tests of mode 0 to + possibly return a shorter string that rounds to d. + With IEEE arithmetic and compilation with + -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same + as modes 2 and 3 when FLT_ROUNDS != 1. + 6-9 ==> Debugging modes similar to mode - 4: don't try + fast floating-point estimate (if applicable). + + Values of mode other than 0-9 are treated as mode 0. + + When not NULL, buf is an output buffer of length blen, which must + be large enough to accommodate suppressed trailing zeros and a trailing + null byte. If blen is too small, rv = NULL is returned, in which case + if rve is not NULL, a subsequent call with blen >= (*rve - rv) + 1 + should succeed in returning buf. + + When buf is NULL, sufficient space is allocated for the return value, + which, when done using, the caller should pass to freedtoa(). + + USE_BF is automatically defined when neither NO_LONG_LONG nor NO_BF96 + is defined. + */ + +#ifdef MULTIPLE_THREADS + ThInfo *TI = 0; +#endif + int bbits, b2, b5, be, dig, i, ilim, ilim1, + j, j1, k, leftright, m2, m5, s2, s5, spec_case; +#ifndef Sudden_Underflow + int denorm; +#endif + Bigint *b, *b1, *delta, *mlo, *mhi, *S; + U u; + char *s; +#ifdef SET_INEXACT + int inexact, oldinexact; +#endif +#ifdef USE_BF96 /*{{*/ + BF96 *p10; + ULLong dbhi, dbits, dblo, den, hb, rb, rblo, res, res0, res3, reslo, sres, + sulp, tv0, tv1, tv2, tv3, ulp, ulplo, ulpmask, ures, ureslo, zb; + int eulp, k1, n2, ulpadj, ulpshift; +#else /*}{*/ +#ifndef Sudden_Underflow + ULong x; +#endif + Long L; + U d2, eps; + double ds; + int ieps, ilim0, k0, k_check, try_quick; +#ifndef No_leftright +#ifdef IEEE_Arith + U eps1; +#endif +#endif +#endif /*}}*/ +#ifdef Honor_FLT_ROUNDS /*{*/ + int Rounding; +#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */ + Rounding = Flt_Rounds; +#else /*}{*/ + Rounding = 1; + switch(fegetround()) { + case FE_TOWARDZERO: Rounding = 0; break; + case FE_UPWARD: Rounding = 2; break; + case FE_DOWNWARD: Rounding = 3; + } +#endif /*}}*/ +#endif /*}*/ + + u.d = dd; + if (word0(&u) & Sign_bit) { + /* set sign for everything, including 0's and NaNs */ + *sign = 1; + word0(&u) &= ~Sign_bit; /* clear sign bit */ + } + else + *sign = 0; + +#if defined(IEEE_Arith) + defined(VAX) +#ifdef IEEE_Arith + if ((word0(&u) & Exp_mask) == Exp_mask) +#else + if (word0(&u) == 0x8000) +#endif + { + /* Infinity or NaN */ + *decpt = 9999; +#ifdef IEEE_Arith + if (!word1(&u) && !(word0(&u) & 0xfffff)) + return nrv_alloc("Infinity", buf, blen, rve, 8 MTb); +#endif + return nrv_alloc("NaN", buf, blen, rve, 3 MTb); + } +#endif +#ifdef IBM + dval(&u) += 0; /* normalize */ +#endif + if (!dval(&u)) { + *decpt = 1; + return nrv_alloc("0", buf, blen, rve, 1 MTb); + } + +#ifdef SET_INEXACT +#ifndef USE_BF96 + try_quick = +#endif + oldinexact = get_inexact(); + inexact = 1; +#endif +#ifdef Honor_FLT_ROUNDS + if (Rounding >= 2) { + if (*sign) + Rounding = Rounding == 2 ? 0 : 2; + else + if (Rounding != 2) + Rounding = 0; + } +#endif +#ifdef USE_BF96 /*{{*/ + dbits = (u.LL & 0xfffffffffffffull) << 11; /* fraction bits */ + if ((be = u.LL >> 52)) /* biased exponent; nonzero ==> normal */ { + dbits |= 0x8000000000000000ull; + denorm = ulpadj = 0; + } + else { + denorm = 1; + ulpadj = be + 1; + dbits <<= 1; + if (!(dbits & 0xffffffff00000000ull)) { + dbits <<= 32; + be -= 32; + } + if (!(dbits & 0xffff000000000000ull)) { + dbits <<= 16; + be -= 16; + } + if (!(dbits & 0xff00000000000000ull)) { + dbits <<= 8; + be -= 8; + } + if (!(dbits & 0xf000000000000000ull)) { + dbits <<= 4; + be -= 4; + } + if (!(dbits & 0xc000000000000000ull)) { + dbits <<= 2; + be -= 2; + } + if (!(dbits & 0x8000000000000000ull)) { + dbits <<= 1; + be -= 1; + } + assert(be >= -51); + ulpadj -= be; + } + j = Lhint[be + 51]; + p10 = &pten[j]; + dbhi = dbits >> 32; + dblo = dbits & 0xffffffffull; + i = be - 0x3fe; + if (i < p10->e + || (i == p10->e && (dbhi < p10->b0 || (dbhi == p10->b0 && dblo < p10->b1)))) + --j; + k = j - 342; + + /* now 10^k <= dd < 10^(k+1) */ + +#else /*}{*/ + + b = d2b(&u, &be, &bbits MTb); +#ifdef Sudden_Underflow + i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); +#else + if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { +#endif + dval(&d2) = dval(&u); + word0(&d2) &= Frac_mask1; + word0(&d2) |= Exp_11; +#ifdef IBM + if (j = 11 - hi0bits(word0(&d2) & Frac_mask)) + dval(&d2) /= 1 << j; +#endif + + /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 + * log10(x) = log(x) / log(10) + * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) + * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) + * + * This suggests computing an approximation k to log10(d) by + * + * k = (i - Bias)*0.301029995663981 + * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); + * + * We want k to be too large rather than too small. + * The error in the first-order Taylor series approximation + * is in our favor, so we just round up the constant enough + * to compensate for any error in the multiplication of + * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, + * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, + * adding 1e-13 to the constant term more than suffices. + * Hence we adjust the constant term to 0.1760912590558. + * (We could get a more accurate k by invoking log10, + * but this is probably not worthwhile.) + */ + + i -= Bias; +#ifdef IBM + i <<= 2; + i += j; +#endif +#ifndef Sudden_Underflow + denorm = 0; + } + else { + /* d is denormalized */ + + i = bbits + be + (Bias + (P-1) - 1); + x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32) + : word1(&u) << (32 - i); + dval(&d2) = x; + word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ + i -= (Bias + (P-1) - 1) + 1; + denorm = 1; + } +#endif + ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; + k = (int)ds; + if (ds < 0. && ds != k) + k--; /* want k = floor(ds) */ + k_check = 1; + if (k >= 0 && k <= Ten_pmax) { + if (dval(&u) < tens[k]) + k--; + k_check = 0; + } + j = bbits - i - 1; + if (j >= 0) { + b2 = 0; + s2 = j; + } + else { + b2 = -j; + s2 = 0; + } + if (k >= 0) { + b5 = 0; + s5 = k; + s2 += k; + } + else { + b2 -= k; + b5 = -k; + s5 = 0; + } +#endif /*}}*/ + if (mode < 0 || mode > 9) + mode = 0; + +#ifndef USE_BF96 +#ifndef SET_INEXACT +#ifdef Check_FLT_ROUNDS + try_quick = Rounding == 1; +#endif +#endif /*SET_INEXACT*/ +#endif + + if (mode > 5) { + mode -= 4; +#ifndef USE_BF96 + try_quick = 0; +#endif + } + leftright = 1; + ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ + /* silence erroneous "gcc -Wall" warning. */ + switch(mode) { + case 0: + case 1: + i = 18; + ndigits = 0; + break; + case 2: + leftright = 0; + /* no break */ + case 4: + if (ndigits <= 0) + ndigits = 1; + ilim = ilim1 = i = ndigits; + break; + case 3: + leftright = 0; + /* no break */ + case 5: + i = ndigits + k + 1; + ilim = i; + ilim1 = i - 1; + if (i <= 0) + i = 1; + } + if (!buf) { + buf = rv_alloc(i MTb); + blen = sizeof(Bigint) + ((1 << ((int*)buf)[-1]) - 1)*sizeof(ULong) - sizeof(int); + } + else if (blen <= i) { + buf = 0; + if (rve) + *rve = buf + i; + return buf; + } + s = buf; + + /* Check for special case that d is a normalized power of 2. */ + + spec_case = 0; + if (mode < 2 || (leftright +#ifdef Honor_FLT_ROUNDS + && Rounding == 1 +#endif + )) { + if (!word1(&u) && !(word0(&u) & Bndry_mask) +#ifndef Sudden_Underflow + && word0(&u) & (Exp_mask & ~Exp_msk1) +#endif + ) { + /* The special case */ + spec_case = 1; + } + } + +#ifdef USE_BF96 /*{*/ + b = 0; + if (ilim < 0 && (mode == 3 || mode == 5)) { + S = mhi = 0; + goto no_digits; + } + i = 1; + j = 52 + 0x3ff - be; + ulpshift = 0; + ulplo = 0; + /* Can we do an exact computation with 64-bit integer arithmetic? */ + if (k < 0) { + if (k < -25) + goto toobig; + res = dbits >> 11; + n2 = pfivebits[k1 = -(k + 1)] + 53; + j1 = j; + if (n2 > 61) { + ulpshift = n2 - 61; + if (res & (ulpmask = (1ull << ulpshift) - 1)) + goto toobig; + j -= ulpshift; + res >>= ulpshift; + } + /* Yes. */ + res *= ulp = pfive[k1]; + if (ulpshift) { + ulplo = ulp; + ulp >>= ulpshift; + } + j += k; + if (ilim == 0) { + S = mhi = 0; + if (res > (5ull << j)) + goto one_digit; + goto no_digits; + } + goto no_div; + } + if (ilim == 0 && j + k >= 0) { + S = mhi = 0; + if ((dbits >> 11) > (pfive[k-1] << j)) + goto one_digit; + goto no_digits; + } + if (k <= dtoa_divmax && j + k >= 0) { + /* Another "yes" case -- we will use exact integer arithmetic. */ + use_exact: + Debug(++dtoa_stats[3]); + res = dbits >> 11; /* residual */ + ulp = 1; + if (k <= 0) + goto no_div; + j1 = j + k + 1; + den = pfive[k-i] << (j1 - i); + for(;;) { + dig = res / den; + *s++ = '0' + dig; + if (!(res -= dig*den)) { +#ifdef SET_INEXACT + inexact = 0; + oldinexact = 1; +#endif + goto retc; + } + if (ilim < 0) { + ures = den - res; + if (2*res <= ulp + && (spec_case ? 4*res <= ulp : (2*res < ulp || dig & 1))) + goto ulp_reached; + if (2*ures < ulp) + goto Roundup; + } + else if (i == ilim) { + switch(Rounding) { + case 0: goto retc; + case 2: goto Roundup; + } + ures = 2*res; + if (ures > den + || (ures == den && dig & 1) + || (spec_case && res <= ulp && 2*res >= ulp)) + goto Roundup; + goto retc; + } + if (j1 < ++i) { + res *= 10; + ulp *= 10; + } + else { + if (i > k) + break; + den = pfive[k-i] << (j1 - i); + } + } + no_div: + for(;;) { + dig = den = res >> j; + *s++ = '0' + dig; + if (!(res -= den << j)) { +#ifdef SET_INEXACT + inexact = 0; + oldinexact = 1; +#endif + goto retc; + } + if (ilim < 0) { + ures = (1ull << j) - res; + if (2*res <= ulp + && (spec_case ? 4*res <= ulp : (2*res < ulp || dig & 1))) { + ulp_reached: + if (ures < res + || (ures == res && dig & 1)) + goto Roundup; + goto retc; + } + if (2*ures < ulp) + goto Roundup; + } + --j; + if (i == ilim) { +#ifdef Honor_FLT_ROUNDS + switch(Rounding) { + case 0: goto retc; + case 2: goto Roundup; + } +#endif + hb = 1ull << j; + if (res & hb && (dig & 1 || res & (hb-1))) + goto Roundup; + if (spec_case && res <= ulp && 2*res >= ulp) { + Roundup: + while(*--s == '9') + if (s == buf) { + ++k; + *s++ = '1'; + goto ret1; + } + ++*s++; + goto ret1; + } + goto retc; + } + ++i; + res *= 5; + if (ulpshift) { + ulplo = 5*(ulplo & ulpmask); + ulp = 5*ulp + (ulplo >> ulpshift); + } + else + ulp *= 5; + } + } + toobig: + if (ilim > 28) + goto Fast_failed1; + /* Scale by 10^-k */ + p10 = &pten[342-k]; + tv0 = p10->b2 * dblo; /* rarely matters, but does, e.g., for 9.862818194192001e18 */ + tv1 = p10->b1 * dblo + (tv0 >> 32); + tv2 = p10->b2 * dbhi + (tv1 & 0xffffffffull); + tv3 = p10->b0 * dblo + (tv1>>32) + (tv2>>32); + res3 = p10->b1 * dbhi + (tv3 & 0xffffffffull); + res = p10->b0 * dbhi + (tv3>>32) + (res3>>32); + be += p10->e - 0x3fe; + eulp = j1 = be - 54 + ulpadj; + if (!(res & 0x8000000000000000ull)) { + --be; + res3 <<= 1; + res = (res << 1) | ((res3 & 0x100000000ull) >> 32); + } + res0 = res; /* save for Fast_failed */ +#if !defined(SET_INEXACT) && !defined(NO_DTOA_64) /*{*/ + if (ilim > 19) + goto Fast_failed; + Debug(++dtoa_stats[4]); + assert(be >= 0 && be <= 4); /* be = 0 is rare, but possible, e.g., for 1e20 */ + res >>= 4 - be; + ulp = p10->b0; /* ulp */ + ulp = (ulp << 29) | (p10->b1 >> 3); + /* scaled ulp = ulp * 2^(eulp - 60) */ + /* We maintain 61 bits of the scaled ulp. */ + if (ilim == 0) { + if (!(res & 0x7fffffffffffffeull) + || !((~res) & 0x7fffffffffffffeull)) + goto Fast_failed1; + S = mhi = 0; + if (res >= 0x5000000000000000ull) + goto one_digit; + goto no_digits; + } + rb = 1; /* upper bound on rounding error */ + for(;;++i) { + dig = res >> 60; + *s++ = '0' + dig; + res &= 0xfffffffffffffffull; + if (ilim < 0) { + ures = 0x1000000000000000ull - res; + if (eulp > 0) { + assert(eulp <= 4); + sulp = ulp << (eulp - 1); + if (res <= ures) { + if (res + rb > ures - rb) + goto Fast_failed; + if (res < sulp) + goto retc; + } + else { + if (res - rb <= ures + rb) + goto Fast_failed; + if (ures < sulp) + goto Roundup; + } + } + else { + zb = -(1ull << (eulp + 63)); + if (!(zb & res)) { + sres = res << (1 - eulp); + if (sres < ulp && (!spec_case || 2*sres < ulp)) { + if ((res+rb) << (1 - eulp) >= ulp) + goto Fast_failed; + if (ures < res) { + if (ures + rb >= res - rb) + goto Fast_failed; + goto Roundup; + } + if (ures - rb < res + rb) + goto Fast_failed; + goto retc; + } + } + if (!(zb & ures) && ures << -eulp < ulp) { + if (ures << (1 - eulp) < ulp) + goto Roundup; + goto Fast_failed; + } + } + } + else if (i == ilim) { + ures = 0x1000000000000000ull - res; + if (ures < res) { + if (ures <= rb || res - rb <= ures + rb) { + if (j + k >= 0 && k >= 0 && k <= 27) + goto use_exact1; + goto Fast_failed; + } +#ifdef Honor_FLT_ROUNDS + if (Rounding == 0) + goto retc; +#endif + goto Roundup; + } + if (res <= rb || ures - rb <= res + rb) { + if (j + k >= 0 && k >= 0 && k <= 27) { + use_exact1: + s = buf; + i = 1; + goto use_exact; + } + goto Fast_failed; + } +#ifdef Honor_FLT_ROUNDS + if (Rounding == 2) + goto Roundup; +#endif + goto retc; + } + rb *= 10; + if (rb >= 0x1000000000000000ull) + goto Fast_failed; + res *= 10; + ulp *= 5; + if (ulp & 0x8000000000000000ull) { + eulp += 4; + ulp >>= 3; + } + else { + eulp += 3; + ulp >>= 2; + } + } +#endif /*}*/ +#ifndef NO_BF96 + Fast_failed: +#endif + Debug(++dtoa_stats[5]); + s = buf; + i = 4 - be; + res = res0 >> i; + reslo = 0xffffffffull & res3; + if (i) + reslo = (res0 << (64 - i)) >> 32 | (reslo >> i); + rb = 0; + rblo = 4; /* roundoff bound */ + ulp = p10->b0; /* ulp */ + ulp = (ulp << 29) | (p10->b1 >> 3); + eulp = j1; + for(i = 1;;++i) { + dig = res >> 60; + *s++ = '0' + dig; + res &= 0xfffffffffffffffull; +#ifdef SET_INEXACT + if (!res && !reslo) { + if (!(res3 & 0xffffffffull)) { + inexact = 0; + oldinexact = 1; + } + goto retc; + } +#endif + if (ilim < 0) { + ures = 0x1000000000000000ull - res; + ureslo = 0; + if (reslo) { + ureslo = 0x100000000ull - reslo; + --ures; + } + if (eulp > 0) { + assert(eulp <= 4); + sulp = (ulp << (eulp - 1)) - rb; + if (res <= ures) { + if (res < sulp) { + if (res+rb < ures-rb) + goto retc; + } + } + else if (ures < sulp) { + if (res-rb > ures+rb) + goto Roundup; + } + goto Fast_failed1; + } + else { + zb = -(1ull << (eulp + 60)); + if (!(zb & (res + rb))) { + sres = (res - rb) << (1 - eulp); + if (sres < ulp && (!spec_case || 2*sres < ulp)) { + sres = res << (1 - eulp); + if ((j = eulp + 31) > 0) + sres += (rblo + reslo) >> j; + else + sres += (rblo + reslo) << -j; + if (sres + (rb << (1 - eulp)) >= ulp) + goto Fast_failed1; + if (sres >= ulp) + goto more96; + if (ures < res + || (ures == res && ureslo < reslo)) { + if (ures + rb >= res - rb) + goto Fast_failed1; + goto Roundup; + } + if (ures - rb <= res + rb) + goto Fast_failed1; + goto retc; + } + } + if (!(zb & ures) && (ures-rb) << (1 - eulp) < ulp) { + if ((ures + rb) << (1 - eulp) < ulp) + goto Roundup; + goto Fast_failed1; + } + } + } + else if (i == ilim) { + ures = 0x1000000000000000ull - res; + sres = ureslo = 0; + if (reslo) { + ureslo = 0x100000000ull - reslo; + --ures; + sres = (reslo + rblo) >> 31; + } + sres += 2*rb; + if (ures <= res) { + if (ures <=sres || res - ures <= sres) + goto Fast_failed1; +#ifdef Honor_FLT_ROUNDS + if (Rounding == 0) + goto retc; +#endif + goto Roundup; + } + if (res <= sres || ures - res <= sres) + goto Fast_failed1; +#ifdef Honor_FLT_ROUNDS + if (Rounding == 2) + goto Roundup; +#endif + goto retc; + } + more96: + rblo *= 10; + rb = 10*rb + (rblo >> 32); + rblo &= 0xffffffffull; + if (rb >= 0x1000000000000000ull) + goto Fast_failed1; + reslo *= 10; + res = 10*res + (reslo >> 32); + reslo &= 0xffffffffull; + ulp *= 5; + if (ulp & 0x8000000000000000ull) { + eulp += 4; + ulp >>= 3; + } + else { + eulp += 3; + ulp >>= 2; + } + } + Fast_failed1: + Debug(++dtoa_stats[6]); + S = mhi = mlo = 0; +#ifdef USE_BF96 + b = d2b(&u, &be, &bbits MTb); +#endif + s = buf; + i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)); + i -= Bias; + if (ulpadj) + i -= ulpadj - 1; + j = bbits - i - 1; + if (j >= 0) { + b2 = 0; + s2 = j; + } + else { + b2 = -j; + s2 = 0; + } + if (k >= 0) { + b5 = 0; + s5 = k; + s2 += k; + } + else { + b2 -= k; + b5 = -k; + s5 = 0; + } +#endif /*}*/ + +#ifdef Honor_FLT_ROUNDS + if (mode > 1 && Rounding != 1) + leftright = 0; +#endif + +#ifndef USE_BF96 /*{*/ + if (ilim >= 0 && ilim <= Quick_max && try_quick) { + + /* Try to get by with floating-point arithmetic. */ + + i = 0; + dval(&d2) = dval(&u); + j1 = -(k0 = k); + ilim0 = ilim; + ieps = 2; /* conservative */ + if (k > 0) { + ds = tens[k&0xf]; + j = k >> 4; + if (j & Bletch) { + /* prevent overflows */ + j &= Bletch - 1; + dval(&u) /= bigtens[n_bigtens-1]; + ieps++; + } + for(; j; j >>= 1, i++) + if (j & 1) { + ieps++; + ds *= bigtens[i]; + } + dval(&u) /= ds; + } + else if (j1 > 0) { + dval(&u) *= tens[j1 & 0xf]; + for(j = j1 >> 4; j; j >>= 1, i++) + if (j & 1) { + ieps++; + dval(&u) *= bigtens[i]; + } + } + if (k_check && dval(&u) < 1. && ilim > 0) { + if (ilim1 <= 0) + goto fast_failed; + ilim = ilim1; + k--; + dval(&u) *= 10.; + ieps++; + } + dval(&eps) = ieps*dval(&u) + 7.; + word0(&eps) -= (P-1)*Exp_msk1; + if (ilim == 0) { + S = mhi = 0; + dval(&u) -= 5.; + if (dval(&u) > dval(&eps)) + goto one_digit; + if (dval(&u) < -dval(&eps)) + goto no_digits; + goto fast_failed; + } +#ifndef No_leftright + if (leftright) { + /* Use Steele & White method of only + * generating digits needed. + */ + dval(&eps) = 0.5/tens[ilim-1] - dval(&eps); +#ifdef IEEE_Arith + if (j1 >= 307) { + eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */ + word0(&eps1) -= Exp_msk1 * (Bias+P-1); + dval(&eps1) *= tens[j1 & 0xf]; + for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++) + if (j & 1) + dval(&eps1) *= bigtens[i]; + if (eps.d < eps1.d) + eps.d = eps1.d; + if (10. - u.d < 10.*eps.d && eps.d < 1.) { + /* eps.d < 1. excludes trouble with the tiniest denormal */ + *s++ = '1'; + ++k; + goto ret1; + } + } +#endif + for(i = 0;;) { + L = dval(&u); + dval(&u) -= L; + *s++ = '0' + (int)L; + if (1. - dval(&u) < dval(&eps)) + goto bump_up; + if (dval(&u) < dval(&eps)) + goto retc; + if (++i >= ilim) + break; + dval(&eps) *= 10.; + dval(&u) *= 10.; + } + } + else { +#endif + /* Generate ilim digits, then fix them up. */ + dval(&eps) *= tens[ilim-1]; + for(i = 1;; i++, dval(&u) *= 10.) { + L = (Long)(dval(&u)); + if (!(dval(&u) -= L)) + ilim = i; + *s++ = '0' + (int)L; + if (i == ilim) { + if (dval(&u) > 0.5 + dval(&eps)) + goto bump_up; + else if (dval(&u) < 0.5 - dval(&eps)) + goto retc; + break; + } + } +#ifndef No_leftright + } +#endif + fast_failed: + s = buf; + dval(&u) = dval(&d2); + k = k0; + ilim = ilim0; + } + + /* Do we have a "small" integer? */ + + if (be >= 0 && k <= Int_max) { + /* Yes. */ + ds = tens[k]; + if (ndigits < 0 && ilim <= 0) { + S = mhi = 0; + if (ilim < 0 || dval(&u) <= 5*ds) + goto no_digits; + goto one_digit; + } + for(i = 1;; i++, dval(&u) *= 10.) { + L = (Long)(dval(&u) / ds); + dval(&u) -= L*ds; +#ifdef Check_FLT_ROUNDS + /* If FLT_ROUNDS == 2, L will usually be high by 1 */ + if (dval(&u) < 0) { + L--; + dval(&u) += ds; + } +#endif + *s++ = '0' + (int)L; + if (!dval(&u)) { +#ifdef SET_INEXACT + inexact = 0; +#endif + break; + } + if (i == ilim) { +#ifdef Honor_FLT_ROUNDS + if (mode > 1) + switch(Rounding) { + case 0: goto retc; + case 2: goto bump_up; + } +#endif + dval(&u) += dval(&u); +#ifdef ROUND_BIASED + if (dval(&u) >= ds) +#else + if (dval(&u) > ds || (dval(&u) == ds && L & 1)) +#endif + { + bump_up: + while(*--s == '9') + if (s == buf) { + k++; + *s = '0'; + break; + } + ++*s++; + } + break; + } + } + goto retc; + } + +#endif /*}*/ + m2 = b2; + m5 = b5; + mhi = mlo = 0; + if (leftright) { + i = +#ifndef Sudden_Underflow + denorm ? be + (Bias + (P-1) - 1 + 1) : +#endif +#ifdef IBM + 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3); +#else + 1 + P - bbits; +#endif + b2 += i; + s2 += i; + mhi = i2b(1 MTb); + } + if (m2 > 0 && s2 > 0) { + i = m2 < s2 ? m2 : s2; + b2 -= i; + m2 -= i; + s2 -= i; + } + if (b5 > 0) { + if (leftright) { + if (m5 > 0) { + mhi = pow5mult(mhi, m5 MTb); + b1 = mult(mhi, b MTb); + Bfree(b MTb); + b = b1; + } + if ((j = b5 - m5)) + b = pow5mult(b, j MTb); + } + else + b = pow5mult(b, b5 MTb); + } + S = i2b(1 MTb); + if (s5 > 0) + S = pow5mult(S, s5 MTb); + + if (spec_case) { + b2 += Log2P; + s2 += Log2P; + } + + /* Arrange for convenient computation of quotients: + * shift left if necessary so divisor has 4 leading 0 bits. + * + * Perhaps we should just compute leading 28 bits of S once + * and for all and pass them and a shift to quorem, so it + * can do shifts and ors to compute the numerator for q. + */ + i = dshift(S, s2); + b2 += i; + m2 += i; + s2 += i; + if (b2 > 0) + b = lshift(b, b2 MTb); + if (s2 > 0) + S = lshift(S, s2 MTb); +#ifndef USE_BF96 + if (k_check) { + if (cmp(b,S) < 0) { + k--; + b = multadd(b, 10, 0 MTb); /* we botched the k estimate */ + if (leftright) + mhi = multadd(mhi, 10, 0 MTb); + ilim = ilim1; + } + } +#endif + if (ilim <= 0 && (mode == 3 || mode == 5)) { + if (ilim < 0 || cmp(b,S = multadd(S,5,0 MTb)) <= 0) { + /* no digits, fcvt style */ + no_digits: + k = -1 - ndigits; + goto ret; + } + one_digit: + *s++ = '1'; + ++k; + goto ret; + } + if (leftright) { + if (m2 > 0) + mhi = lshift(mhi, m2 MTb); + + /* Compute mlo -- check for special case + * that d is a normalized power of 2. + */ + + mlo = mhi; + if (spec_case) { + mhi = Balloc(mhi->k MTb); + Bcopy(mhi, mlo); + mhi = lshift(mhi, Log2P MTb); + } + + for(i = 1;;i++) { + dig = quorem(b,S) + '0'; + /* Do we yet have the shortest decimal string + * that will round to d? + */ + j = cmp(b, mlo); + delta = diff(S, mhi MTb); + j1 = delta->sign ? 1 : cmp(b, delta); + Bfree(delta MTb); +#ifndef ROUND_BIASED + if (j1 == 0 && mode != 1 && !(word1(&u) & 1) +#ifdef Honor_FLT_ROUNDS + && (mode <= 1 || Rounding >= 1) +#endif + ) { + if (dig == '9') + goto round_9_up; + if (j > 0) + dig++; +#ifdef SET_INEXACT + else if (!b->x[0] && b->wds <= 1) + inexact = 0; +#endif + *s++ = dig; + goto ret; + } +#endif + if (j < 0 || (j == 0 && mode != 1 +#ifndef ROUND_BIASED + && !(word1(&u) & 1) +#endif + )) { + if (!b->x[0] && b->wds <= 1) { +#ifdef SET_INEXACT + inexact = 0; +#endif + goto accept_dig; + } +#ifdef Honor_FLT_ROUNDS + if (mode > 1) + switch(Rounding) { + case 0: goto accept_dig; + case 2: goto keep_dig; + } +#endif /*Honor_FLT_ROUNDS*/ + if (j1 > 0) { + b = lshift(b, 1 MTb); + j1 = cmp(b, S); +#ifdef ROUND_BIASED + if (j1 >= 0 /*)*/ +#else + if ((j1 > 0 || (j1 == 0 && dig & 1)) +#endif + && dig++ == '9') + goto round_9_up; + } + accept_dig: + *s++ = dig; + goto ret; + } + if (j1 > 0) { +#ifdef Honor_FLT_ROUNDS + if (!Rounding && mode > 1) + goto accept_dig; +#endif + if (dig == '9') { /* possible if i == 1 */ + round_9_up: + *s++ = '9'; + goto roundoff; + } + *s++ = dig + 1; + goto ret; + } +#ifdef Honor_FLT_ROUNDS + keep_dig: +#endif + *s++ = dig; + if (i == ilim) + break; + b = multadd(b, 10, 0 MTb); + if (mlo == mhi) + mlo = mhi = multadd(mhi, 10, 0 MTb); + else { + mlo = multadd(mlo, 10, 0 MTb); + mhi = multadd(mhi, 10, 0 MTb); + } + } + } + else + for(i = 1;; i++) { + dig = quorem(b,S) + '0'; + *s++ = dig; + if (!b->x[0] && b->wds <= 1) { +#ifdef SET_INEXACT + inexact = 0; +#endif + goto ret; + } + if (i >= ilim) + break; + b = multadd(b, 10, 0 MTb); + } + + /* Round off last digit */ + +#ifdef Honor_FLT_ROUNDS + if (mode > 1) + switch(Rounding) { + case 0: goto ret; + case 2: goto roundoff; + } +#endif + b = lshift(b, 1 MTb); + j = cmp(b, S); +#ifdef ROUND_BIASED + if (j >= 0) +#else + if (j > 0 || (j == 0 && dig & 1)) +#endif + { + roundoff: + while(*--s == '9') + if (s == buf) { + k++; + *s++ = '1'; + goto ret; + } + ++*s++; + } + ret: + Bfree(S MTb); + if (mhi) { + if (mlo && mlo != mhi) + Bfree(mlo MTb); + Bfree(mhi MTb); + } + retc: + while(s > buf && s[-1] == '0') + --s; + ret1: + if (b) + Bfree(b MTb); + *s = 0; + *decpt = k + 1; + if (rve) + *rve = s; +#ifdef SET_INEXACT + if (inexact) { + if (!oldinexact) { + word0(&u) = Exp_1 + (70 << Exp_shift); + word1(&u) = 0; + dval(&u) += 1.; + } + } + else if (!oldinexact) + clear_inexact(); +#endif + return buf; + } + + char * +dtoa(double dd, int mode, int ndigits, int *decpt, int *sign, char **rve) +{ + /* Sufficient space is allocated to the return value + to hold the suppressed trailing zeros. + See dtoa_r() above for details on the other arguments. + */ +#ifndef MULTIPLE_THREADS + if (dtoa_result) + freedtoa(dtoa_result); +#endif + return dtoa_r(dd, mode, ndigits, decpt, sign, rve, 0, 0); + } + +#endif /* STRTOD_ONLY */ +#ifdef __cplusplus +} +#endif diff --git a/nolibc/errlist.c b/nolibc/errlist.c new file mode 100644 index 0000000..f714a52 --- /dev/null +++ b/nolibc/errlist.c @@ -0,0 +1,64 @@ +/* This code is mostly an extract from OpenBSD sources, keeping only the needed + * errno values + * + * NOTE: the list of errors must be kept in sync with errno.h */ + +/* + * Copyright (c) 1982, 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +#include + +const char *const sys_errlist[] = { + "Undefined error: 0", /* ENOERROR */ + "No such file or directory", /* ENOENT */ + "Interrupted system call", /* EINTR */ + "Bad file descriptor", /* EBADF */ + "Cannot allocate memory", /* ENOMEM */ + "Device busy", /* EBUSY */ + "Invalid argument", /* EINVAL */ + "Too many open files", /* EMFILE */ + "Broken pipe", /* EPIPE */ + +/* math software */ + "Result too large", /* ERANGE */ + +/* non-blocking and interrupt i/o */ + "Resource temporarily unavailable", /* EAGAIN */ + +/* ipc/network software -- operational errors */ + "Connection reset by peer", /* ECONNRESET */ + + "Function not implemented", /* ENOSYS */ + /* EOVERFLOW */ + "Value too large to be stored in data type", +}; + +static_assert((sizeof sys_errlist/sizeof sys_errlist[0]) == NB_ERRORS, + "errlist.c and errno.h are out of sync"); diff --git a/nolibc/fprintf.c b/nolibc/fprintf.c new file mode 100644 index 0000000..948743f --- /dev/null +++ b/nolibc/fprintf.c @@ -0,0 +1,12 @@ +#include +#include + +int fprintf(FILE *restrict f, const char *restrict fmt, ...) +{ + int ret; + va_list ap; + va_start(ap, fmt); + ret = vfprintf(f, fmt, ap); + va_end(ap); + return ret; +} diff --git a/nolibc/include/_gilbraltar/byteorder.h b/nolibc/include/_gilbraltar/byteorder.h new file mode 100644 index 0000000..f521c93 --- /dev/null +++ b/nolibc/include/_gilbraltar/byteorder.h @@ -0,0 +1,16 @@ +#ifndef __FREESTANDING_BYTEORDER_H +#define __FREESTANDING_BYTEORDER_H + +#if !defined(__BYTE_ORDER__) +#error C compiler does not define __BYTE_ORDER__ +#endif + +#if defined(BYTE_ORDER) || defined(LITTLE_ENDIAN) || defined(BIG_ENDIAN) +#error BYTE_ORDER, LITTLE_ENDIAN or BIG_ENDIAN must not be defined here +#endif + +#define BYTE_ORDER __BYTE_ORDER__ +#define LITTLE_ENDIAN __ORDER_LITTLE_ENDIAN__ +#define BIG_ENDIAN __ORDER_BIG_ENDIAN__ + +#endif /* __FREESTANDING_BYTEORDER_H */ diff --git a/nolibc/include/_gilbraltar/overrides.h b/nolibc/include/_gilbraltar/overrides.h new file mode 100644 index 0000000..78a842d --- /dev/null +++ b/nolibc/include/_gilbraltar/overrides.h @@ -0,0 +1,13 @@ +#ifndef __FREESTANDING_OVERRIDES_H +#define __FREESTANDING_OVERRIDES_H + +#undef __FreeBSD__ +#undef __OpenBSD__ +#undef __gnu_linux__ +#undef __linux +#undef __linux__ +#undef linux + +#define __ocaml_solo5__ + +#endif /* __FREESTANDING_OVERRIDES_H */ diff --git a/nolibc/include/assert.h b/nolibc/include/assert.h new file mode 100644 index 0000000..54fd909 --- /dev/null +++ b/nolibc/include/assert.h @@ -0,0 +1,20 @@ +#ifndef _ASSERT_H +#define _ASSERT_H + +extern void _assert_fail(const char *, const char *, const char *) + __attribute__((noreturn)); + +#define _ASSERT_STR_EXPAND(y) #y +#define _ASSERT_STR(x) _ASSERT_STR_EXPAND(x) + +#define assert(e) \ + do { \ + if (!(e)) \ + _assert_fail(__FILE__, _ASSERT_STR(__LINE__), #e); \ + } while (0) + +#endif + +#ifndef static_assert +# define static_assert _Static_assert +#endif diff --git a/nolibc/include/ctype.h b/nolibc/include/ctype.h new file mode 100644 index 0000000..71aab00 --- /dev/null +++ b/nolibc/include/ctype.h @@ -0,0 +1,12 @@ +#ifndef _CTYPE_H +#define _CTYPE_H + +int isalpha(int); +int isdigit(int); +int isprint(int); +int isspace(int); +int isupper(int); +int isalnum(int); +int tolower(int); + +#endif diff --git a/nolibc/include/dirent.h b/nolibc/include/dirent.h new file mode 100644 index 0000000..3954b16 --- /dev/null +++ b/nolibc/include/dirent.h @@ -0,0 +1,12 @@ +#ifndef _DIRENT_H +#define _DIRENT_H + +typedef int DIR; +int closedir(DIR *); +DIR *opendir(const char *); +struct dirent { + char *d_name; +}; +struct dirent *readdir(DIR *); + +#endif diff --git a/nolibc/include/endian.h b/nolibc/include/endian.h new file mode 100644 index 0000000..eb74e36 --- /dev/null +++ b/nolibc/include/endian.h @@ -0,0 +1,45 @@ +#ifndef _ENDIAN_H +#define _ENDIAN_H + +#include <_gilbraltar/byteorder.h> +#include + +#define bswap16(x) __builtin_bswap16(x) +#define bswap32(x) __builtin_bswap32(x) +#define bswap64(x) __builtin_bswap64(x) + +#if BYTE_ORDER == LITTLE_ENDIAN + +#define htobe16(x) bswap16(x) +#define htobe32(x) bswap32(x) +#define htobe64(x) bswap64(x) +#define htole16(x) (uint16_t)(x) +#define htole32(x) (uint32_t)(x) +#define htole64(x) (uint64_t)(x) + +#define be16toh(x) bswap16(x) +#define be32toh(x) bswap32(x) +#define be64toh(x) bswap64(x) +#define le16toh(x) (uint16_t)(x) +#define le32toh(x) (uint32_t)(x) +#define le64toh(x) (uint64_t)(x) + +#else /* BYTE_ORDER != LITTLE_ENDIAN */ + +#define htobe16(x) (uint16_t)(x) +#define htobe32(x) (uint32_t)(x) +#define htobe64(x) (uint64_t)(x) +#define htole16(x) bswap16(x) +#define htole32(x) bswap32(x) +#define htole64(x) bswap64(x) + +#define be16toh(x) (uint16_t)(x) +#define be32toh(x) (uint32_t)(x) +#define be64toh(x) (uint64_t)(x) +#define le16toh(x) bswap16(x) +#define le32toh(x) bswap32(x) +#define le64toh(x) bswap64(x) + +#endif /* BYTE_ORDER == LITTLE_ENDIAN */ + +#endif /* _ENDIAN_H */ diff --git a/nolibc/include/errno.h b/nolibc/include/errno.h new file mode 100644 index 0000000..eb99d80 --- /dev/null +++ b/nolibc/include/errno.h @@ -0,0 +1,26 @@ +#ifndef _ERRNO_H +#define _ERRNO_H + +extern int errno; + +/* This list of errors must be kept in sync with errlist.c */ + +#define ENOERROR 0 /* Actual error codes should be > 0 */ + +#define ENOENT 1 +#define EINTR 2 +#define EBADF 3 +#define ENOMEM 4 +#define EBUSY 5 +#define EINVAL 6 +#define EMFILE 7 +#define EPIPE 8 +#define ERANGE 9 +#define EAGAIN 10 +#define ECONNRESET 11 +#define ENOSYS 12 +#define EOVERFLOW 13 + +#define NB_ERRORS 14 + +#endif diff --git a/nolibc/include/fcntl.h b/nolibc/include/fcntl.h new file mode 100644 index 0000000..568b65d --- /dev/null +++ b/nolibc/include/fcntl.h @@ -0,0 +1,18 @@ +#ifndef _FCNTL_H +#define _FCNTL_H + +int fcntl(int, int, ...); +int open(const char *, int, ...); + +/* The following values are taken from: + * https://github.com/openbsd/src/blob/master/sys/sys/fcntl.h + */ +#define O_RDONLY 0x0000 /* open for reading only */ +#define O_WRONLY 0x0001 /* open for writing only */ +#define O_RDWR 0x0002 /* open for reading and writing */ +#define O_APPEND 0x0008 /* set append mode */ +#define O_CREAT 0x0200 /* create if nonexistent */ +#define O_TRUNC 0x0400 /* truncate to zero length */ +#define O_EXCL 0x0800 /* error if already exists */ + +#endif diff --git a/nolibc/include/features.h b/nolibc/include/features.h new file mode 100644 index 0000000..0d82a76 --- /dev/null +++ b/nolibc/include/features.h @@ -0,0 +1,6 @@ +#ifndef _FEATURES_H +#define _FEATURES_H + +/* No features, isn't that nice? */ + +#endif diff --git a/nolibc/include/inttypes.h b/nolibc/include/inttypes.h new file mode 100644 index 0000000..7220150 --- /dev/null +++ b/nolibc/include/inttypes.h @@ -0,0 +1,122 @@ +#ifndef _INTTYPES_H +#define _INTTYPES_H + +#include + +#if !defined(UINTPTR_MAX) || !defined(UINT64_MAX) +#error UINTPTR_MAX and UINT64_MAX must be defined here +#endif + +#if UINTPTR_MAX == UINT64_MAX +#define __PRI64 "l" +#define __PRIPTR "l" +#else +#define __PRI64 "ll" +#define __PRIPTR "" +#endif + +#define PRId8 "d" +#define PRId16 "d" +#define PRId32 "d" +#define PRId64 __PRI64 "d" + +#define PRIdLEAST8 "d" +#define PRIdLEAST16 "d" +#define PRIdLEAST32 "d" +#define PRIdLEAST64 __PRI64 "d" + +#define PRIdFAST8 "d" +#define PRIdFAST16 "d" +#define PRIdFAST32 "d" +#define PRIdFAST64 __PRI64 "d" + +#define PRIi8 "i" +#define PRIi16 "i" +#define PRIi32 "i" +#define PRIi64 __PRI64 "i" + +#define PRIiLEAST8 "i" +#define PRIiLEAST16 "i" +#define PRIiLEAST32 "i" +#define PRIiLEAST64 __PRI64 "i" + +#define PRIiFAST8 "i" +#define PRIiFAST16 "i" +#define PRIiFAST32 "i" +#define PRIiFAST64 __PRI64 "i" + +#define PRIo8 "o" +#define PRIo16 "o" +#define PRIo32 "o" +#define PRIo64 __PRI64 "o" + +#define PRIoLEAST8 "o" +#define PRIoLEAST16 "o" +#define PRIoLEAST32 "o" +#define PRIoLEAST64 __PRI64 "o" + +#define PRIoFAST8 "o" +#define PRIoFAST16 "o" +#define PRIoFAST32 "o" +#define PRIoFAST64 __PRI64 "o" + +#define PRIu8 "u" +#define PRIu16 "u" +#define PRIu32 "u" +#define PRIu64 __PRI64 "u" + +#define PRIuLEAST8 "u" +#define PRIuLEAST16 "u" +#define PRIuLEAST32 "u" +#define PRIuLEAST64 __PRI64 "u" + +#define PRIuFAST8 "u" +#define PRIuFAST16 "u" +#define PRIuFAST32 "u" +#define PRIuFAST64 __PRI64 "u" + +#define PRIx8 "x" +#define PRIx16 "x" +#define PRIx32 "x" +#define PRIx64 __PRI64 "x" + +#define PRIxLEAST8 "x" +#define PRIxLEAST16 "x" +#define PRIxLEAST32 "x" +#define PRIxLEAST64 __PRI64 "x" + +#define PRIxFAST8 "x" +#define PRIxFAST16 "x" +#define PRIxFAST32 "x" +#define PRIxFAST64 __PRI64 "x" + +#define PRIX8 "X" +#define PRIX16 "X" +#define PRIX32 "X" +#define PRIX64 __PRI64 "X" + +#define PRIXLEAST8 "X" +#define PRIXLEAST16 "X" +#define PRIXLEAST32 "X" +#define PRIXLEAST64 __PRI64 "X" + +#define PRIXFAST8 "X" +#define PRIXFAST16 "X" +#define PRIXFAST32 "X" +#define PRIXFAST64 __PRI64 "X" + +#define PRIdMAX __PRI64 "d" +#define PRIiMAX __PRI64 "i" +#define PRIoMAX __PRI64 "o" +#define PRIuMAX __PRI64 "u" +#define PRIxMAX __PRI64 "x" +#define PRIXMAX __PRI64 "X" + +#define PRIdPTR __PRIPTR "d" +#define PRIiPTR __PRIPTR "i" +#define PRIoPTR __PRIPTR "o" +#define PRIuPTR __PRIPTR "u" +#define PRIxPTR __PRIPTR "x" +#define PRIXPTR __PRIPTR "X" + +#endif diff --git a/nolibc/include/limits.h b/nolibc/include/limits.h new file mode 100644 index 0000000..ee74def --- /dev/null +++ b/nolibc/include/limits.h @@ -0,0 +1,23 @@ +#ifndef _LIMITS_H +#define _LIMITS_H + +#define INT_MAX 0x7fffffff +#define INT_MIN (-1-0x7fffffff) +#define UINT_MAX 0xffffffffU +#define SHRT_MAX 0x7fff +#define SHRT_MIN (-1-0x7fff) +#define USHRT_MAX 0xffff +#if defined(__x86_64__) || defined(__aarch64__) +#define LONG_MAX 0x7fffffffffffffffL +#define LLONG_MAX 0x7fffffffffffffffLL +#else +#error Unsupported architecture +#endif +#define LONG_MIN (-LONG_MAX-1) +#define LLONG_MIN (-LLONG_MAX-1) +#define ULONG_MAX (2UL*LONG_MAX+1) +#define NL_ARGMAX 9 +#define UCHAR_MAX 255 +#define CHAR_BIT 8 + +#endif diff --git a/nolibc/include/math.h b/nolibc/include/math.h new file mode 100644 index 0000000..a228a4f --- /dev/null +++ b/nolibc/include/math.h @@ -0,0 +1 @@ +#include diff --git a/nolibc/include/pthread.h b/nolibc/include/pthread.h new file mode 100644 index 0000000..ea7b565 --- /dev/null +++ b/nolibc/include/pthread.h @@ -0,0 +1,57 @@ +#ifndef _PTHREAD_H +#define _PTHREAD_H + +#include +#include + +typedef unsigned long int pthread_t; +typedef int cpu_set_t; + +int pthread_getaffinity_np(pthread_t, size_t, cpu_set_t *); + +pthread_t pthread_self(void); + +typedef int pthread_attr_t; + +int pthread_create(pthread_t *, const pthread_attr_t *, void *(*)(void *), void *); +int pthread_join(pthread_t, void **); +int pthread_attr_init(pthread_attr_t *); +void pthread_cleanup_push(void (*)(void *), void *); +void pthread_cleanup_pop(int); + +typedef int pthread_mutex_t; +typedef int pthread_cond_t; + +int pthread_mutex_lock(pthread_mutex_t *); +int pthread_mutex_trylock(pthread_mutex_t *); +int pthread_mutex_unlock(pthread_mutex_t *); + +#define PTHREAD_MUTEX_INITIALIZER 0 +#define PTHREAD_COND_INITIALIZER 0 + +int pthread_sigmask(int, const sigset_t *, sigset_t *); +int pthread_detach(pthread_t); +int pthread_equal(pthread_t, pthread_t); + +typedef int pthread_mutexattr_t; + +int pthread_mutexattr_init(pthread_mutexattr_t *); +int pthread_mutexattr_settype(pthread_mutexattr_t *, int); + +#define PTHREAD_MUTEX_ERRORCHECK 0 + +int pthread_mutex_init(pthread_mutex_t *, const pthread_mutexattr_t *); +int pthread_mutexattr_destroy(pthread_mutexattr_t *); +int pthread_mutex_destroy(pthread_mutex_t *); + +typedef int pthread_condattr_t; + +int pthread_condattr_init(pthread_condattr_t *); +int pthread_cond_init(pthread_cond_t *, const pthread_condattr_t *); + +int pthread_cond_wait(pthread_cond_t *, pthread_mutex_t *); +int pthread_cond_broadcast(pthread_cond_t *); +int pthread_cond_signal(pthread_cond_t *); +int pthread_cond_destroy(pthread_cond_t *); + +#endif diff --git a/nolibc/include/sched.h b/nolibc/include/sched.h new file mode 100644 index 0000000..e5fa930 --- /dev/null +++ b/nolibc/include/sched.h @@ -0,0 +1,8 @@ +#ifndef _SCHED_H +#define _SCHED_H + +typedef int cpu_set_t; + +#define CPU_ZERO (x) 0 + +#endif diff --git a/nolibc/include/setjmp.h b/nolibc/include/setjmp.h new file mode 100644 index 0000000..4d079b5 --- /dev/null +++ b/nolibc/include/setjmp.h @@ -0,0 +1,5 @@ +#include + +void longjmp(int, int) __attribute__ ((__noreturn__)); + +#define setjmp(buf) 0 diff --git a/nolibc/include/signal.h b/nolibc/include/signal.h new file mode 100644 index 0000000..c798f62 --- /dev/null +++ b/nolibc/include/signal.h @@ -0,0 +1,27 @@ +#ifndef _SIGNAL_H +#define _SIGNAL_H + +/* + * The following definitions are required not only to build the OCaml runtime + * but also the freestanding version of GMP used by Mirage. + * Note though that Solo5 does not implement signals, so we should not trigger a + * situation where these values are really used. + */ + +typedef int jmp_buf; +int setjmp(jmp_buf); +void (*signal(int sig, void (*func)(int)))(int); +#define SIG_DFL 0 +#define SIG_IGN 0 +#define SIG_ERR 0 +#define SIG_BLOCK 0 +#define SIG_SETMASK 0 + +#define SIGFPE 1 +int raise(int); + +typedef int sigset_t; +int sigfillset(sigset_t *); +int sigwait(const sigset_t *restrict set, int *restrict sig); + +#endif diff --git a/nolibc/include/stdio.h b/nolibc/include/stdio.h new file mode 100644 index 0000000..0754a18 --- /dev/null +++ b/nolibc/include/stdio.h @@ -0,0 +1,42 @@ +#ifndef _STDIO_H +#define _STDIO_H + +#include +#include + +struct _FILE; +typedef struct _FILE { + size_t (*write)(struct _FILE *f, const char *, size_t); + char *wpos; + char *wend; +} FILE; +int fflush(FILE *); +int fprintf(FILE *, const char *, ...); +int printf(const char *, ...); +int rename(const char *, const char *); +extern FILE *stdout; +extern FILE *stderr; +int sscanf(const char *, const char *, ...); +int snprintf(char *, size_t, const char *, ...); +int vfprintf(FILE *, const char *, va_list); +int vsnprintf(char *, size_t, const char *, va_list); +/* + * The following definitions are not required by the OCaml runtime, but are + * needed to build the freestanding version of GMP used by Mirage. + */ +#define EOF (-1) +extern FILE *stdin; +size_t fread(void *, size_t, size_t, FILE *); +int getc(FILE *); +int ungetc(int, FILE *); +size_t fwrite(const void *, size_t, size_t, FILE *); +int fputc(int, FILE *); +int putc(int, FILE *); +int ferror(FILE *); +int fputs(const char *, FILE *); +FILE *fopen(const char *, const char *); +int fclose(FILE *); +int puts(const char *); +int putchar(int); + +#endif diff --git a/nolibc/include/stdlib.h b/nolibc/include/stdlib.h new file mode 100644 index 0000000..e794974 --- /dev/null +++ b/nolibc/include/stdlib.h @@ -0,0 +1,39 @@ +#ifndef _STDLIB_H +#define _STDLIB_H + +#include + +void abort(void) __attribute__((noreturn)); +void exit(int) __attribute__((noreturn)); +void *malloc(size_t); +void free(void *); +void *calloc(size_t, size_t); +void *realloc(void *, size_t); +int posix_memalign(void **, size_t, size_t); + +struct mallinfo { + size_t arena; /* non-mmapped space allocated from system */ + size_t ordblks; /* number of free chunks */ + size_t smblks; /* always 0 */ + size_t hblks; /* always 0 */ + size_t hblkhd; /* space in mmapped regions */ + size_t usmblks; /* maximum total allocated space */ + size_t fsmblks; /* always 0 */ + size_t uordblks; /* total allocated space */ + size_t fordblks; /* total free space */ + size_t keepcost; /* releasable (via malloc_trim) space */ +}; +struct mallinfo mallinfo(void); + +char *getenv(const char *); +char *secure_getenv(const char *); +int system(const char *); +double strtod(const char *, char **); +long strtol(const char *, char **, int); + +void qsort(void *base, size_t nmemb, size_t size, + int (*compare)(const void *, const void *)); + +char *mktemp(char *); + +#endif diff --git a/nolibc/include/string.h b/nolibc/include/string.h new file mode 100644 index 0000000..7dec8cd --- /dev/null +++ b/nolibc/include/string.h @@ -0,0 +1,29 @@ +#ifndef _STRING_H +#define _STRING_H + +#include + +int memcmp(const void *, const void *, size_t); +void *memchr(const void *, int, size_t); +void *memcpy(void *, const void *, size_t); +void *memmove(void *, const void *, size_t); +void *memset(void *, int, size_t); +int strcmp(const char *, const char *); +size_t strlen(const char *); +size_t strnlen(const char *, size_t); +char *strerror(int); +int strerror_r(int errnum, char *buf, size_t buflen); +/* + * The following definitions are not required by the OCaml runtime, but are + * needed to build the freestanding version of GMP used by Mirage. + */ +char *strncpy(char *, const char *, size_t); +char *strcpy(char *, const char *); +char *strchr(const char *, int); +char *strstr(const char *, const char *); +/* + * The following definitions are required for the OCaml bytecode runtime. + */ +int strncmp(const char*, const char*, size_t); + +#endif diff --git a/nolibc/include/sys/ioctl.h b/nolibc/include/sys/ioctl.h new file mode 100644 index 0000000..541e4d5 --- /dev/null +++ b/nolibc/include/sys/ioctl.h @@ -0,0 +1,4 @@ +#ifndef _SYS_IOCTL_H +#define _SYS_IOCTL_H + +#endif diff --git a/nolibc/include/sys/mman.h b/nolibc/include/sys/mman.h new file mode 100644 index 0000000..5554ebd --- /dev/null +++ b/nolibc/include/sys/mman.h @@ -0,0 +1,26 @@ +#ifndef _MMAP_H +#define _MMAP_H + +#include +#include + +void *mmap(void *addr, size_t len, int prot, int flags, int fildes, off_t off); + +#define PROT_NONE 0 +#define PROT_READ 1 +#define PROT_WRITE 2 + +#define MAP_SHARED 0x01 +#define MAP_PRIVATE 0x02 +#define MAP_FIXED 0x10 +#define MAP_ANONYMOUS 0x20 +#define MAP_ANON MAP_ANONYMOUS + +// the MAP_FAILED comply with the mmap manual page +#define MAP_FAILED (void*)-1 + +#define OCAML_SOLO5_PAGESIZE (1 << 12) + +int munmap(void *addr, size_t len); + +#endif diff --git a/nolibc/include/sys/param.h b/nolibc/include/sys/param.h new file mode 100644 index 0000000..6e9f31a --- /dev/null +++ b/nolibc/include/sys/param.h @@ -0,0 +1,6 @@ +#ifndef _SYS_PARAM_H +#define _SYS_PARAM_H + +#include <_solo5/byteorder.h> + +#endif /* _SYS_PARAM_H */ diff --git a/nolibc/include/sys/stat.h b/nolibc/include/sys/stat.h new file mode 100644 index 0000000..cf4d4a5 --- /dev/null +++ b/nolibc/include/sys/stat.h @@ -0,0 +1,20 @@ +#ifndef _SYS_STAT_H +#define _SYS_STAT_H + +#include + +struct stat { + int st_mode; + int st_size; +}; +#define S_IFDIR 0 +#define S_IFMT 0 +#define S_IFREG 0 +#define S_ISREG(x) (0) +#define S_IRUSR 0 +#define S_IWUSR 0 +int stat(const char *, struct stat *); +int mkdir(const char *, mode_t); +int fstat(int, struct stat *); + +#endif diff --git a/nolibc/include/sys/time.h b/nolibc/include/sys/time.h new file mode 100644 index 0000000..f39c30f --- /dev/null +++ b/nolibc/include/sys/time.h @@ -0,0 +1,16 @@ +#ifndef _SYS_TIME_H +#define _SYS_TIME_H + +typedef long time_t; +typedef long suseconds_t; +struct timeval { + time_t tv_sec; + suseconds_t tv_usec; +}; +struct timezone { + int tz_minuteswest; + int tz_dsttime; +}; +int gettimeofday(struct timeval *tv, struct timezone *tz); + +#endif diff --git a/nolibc/include/sys/times.h b/nolibc/include/sys/times.h new file mode 100644 index 0000000..2fa128c --- /dev/null +++ b/nolibc/include/sys/times.h @@ -0,0 +1,13 @@ +#ifndef _SYS_TIMES_H +#define _SYS_TIMES_H + +typedef int clock_t; +struct tms { + clock_t tms_utime; + clock_t tms_stime; + clock_t tms_cutime; + clock_t tms_cstime; +}; +clock_t times(struct tms *buf); + +#endif diff --git a/nolibc/include/sys/types.h b/nolibc/include/sys/types.h new file mode 100644 index 0000000..af8bcac --- /dev/null +++ b/nolibc/include/sys/types.h @@ -0,0 +1,13 @@ +#ifndef _SYS_TYPES_H +#define _SYS_TYPES_H + +#include +#include + +typedef int pid_t; +typedef int off_t; +typedef int ssize_t; +typedef int mode_t; +typedef int useconds_t; + +#endif diff --git a/nolibc/include/sys/wait.h b/nolibc/include/sys/wait.h new file mode 100644 index 0000000..d60e52c --- /dev/null +++ b/nolibc/include/sys/wait.h @@ -0,0 +1,4 @@ +#ifndef _SYS_WAIT_H +#define _SYS_WAIT_H + +#endif diff --git a/nolibc/include/time.h b/nolibc/include/time.h new file mode 120000 index 0000000..a05acff --- /dev/null +++ b/nolibc/include/time.h @@ -0,0 +1 @@ +sys/time.h \ No newline at end of file diff --git a/nolibc/include/unistd.h b/nolibc/include/unistd.h new file mode 100644 index 0000000..e3c0188 --- /dev/null +++ b/nolibc/include/unistd.h @@ -0,0 +1,26 @@ +#ifndef _UNISTD_H +#define _UNISTD_H + +#include + +int chdir(const char *); +int close(int); +char *getcwd(char *, size_t); +pid_t getpid(void); +pid_t getppid(void); +int isatty(int); +off_t lseek(int, off_t, int); /* SEEK_ */ +ssize_t read(int, void *, size_t); +ssize_t write(int, const void *, size_t); +ssize_t readlink(const char *, char *, size_t); +int unlink(const char *); +int rmdir(const char *); +int usleep(useconds_t); +int ftruncate(int, off_t); +long sysconf(int); +int execv(const char *, char *const []); + +#define _SC_PAGESIZE 1 +#define _SC_PAGE_SIZE _SC_PAGESIZE + +#endif diff --git a/nolibc/memchr.c b/nolibc/memchr.c new file mode 100644 index 0000000..4daff7b --- /dev/null +++ b/nolibc/memchr.c @@ -0,0 +1,23 @@ +#include +#include +#include + +#define SS (sizeof(size_t)) +#define ALIGN (sizeof(size_t)-1) +#define ONES ((size_t)-1/UCHAR_MAX) +#define HIGHS (ONES * (UCHAR_MAX/2+1)) +#define HASZERO(x) ((x)-ONES & ~(x) & HIGHS) + +void *memchr(const void *src, int c, size_t n) +{ + const unsigned char *s = src; + c = (unsigned char)c; + for (; ((uintptr_t)s & ALIGN) && n && *s != c; s++, n--); + if (n && *s != c) { + const size_t *w; + size_t k = ONES * c; + for (w = (const void *)s; n>=SS && !HASZERO(*w^k); w++, n-=SS); + for (s = (const void *)w; n && *s != c; s++, n--); + } + return n ? (void *)s : 0; +} diff --git a/nolibc/memcmp.c b/nolibc/memcmp.c new file mode 100644 index 0000000..bdbce9f --- /dev/null +++ b/nolibc/memcmp.c @@ -0,0 +1,8 @@ +#include + +int memcmp(const void *vl, const void *vr, size_t n) +{ + const unsigned char *l=vl, *r=vr; + for (; n && *l == *r; n--, l++, r++); + return n ? *l-*r : 0; +} diff --git a/nolibc/memcpy.c b/nolibc/memcpy.c new file mode 100644 index 0000000..06e8874 --- /dev/null +++ b/nolibc/memcpy.c @@ -0,0 +1,124 @@ +#include +#include +#include + +void *memcpy(void *restrict dest, const void *restrict src, size_t n) +{ + unsigned char *d = dest; + const unsigned char *s = src; + +#ifdef __GNUC__ + +#if __BYTE_ORDER == __LITTLE_ENDIAN +#define LS >> +#define RS << +#else +#define LS << +#define RS >> +#endif + + typedef uint32_t __attribute__((__may_alias__)) u32; + uint32_t w, x; + + for (; (uintptr_t)s % 4 && n; n--) *d++ = *s++; + + if ((uintptr_t)d % 4 == 0) { + for (; n>=16; s+=16, d+=16, n-=16) { + *(u32 *)(d+0) = *(u32 *)(s+0); + *(u32 *)(d+4) = *(u32 *)(s+4); + *(u32 *)(d+8) = *(u32 *)(s+8); + *(u32 *)(d+12) = *(u32 *)(s+12); + } + if (n&8) { + *(u32 *)(d+0) = *(u32 *)(s+0); + *(u32 *)(d+4) = *(u32 *)(s+4); + d += 8; s += 8; + } + if (n&4) { + *(u32 *)(d+0) = *(u32 *)(s+0); + d += 4; s += 4; + } + if (n&2) { + *d++ = *s++; *d++ = *s++; + } + if (n&1) { + *d = *s; + } + return dest; + } + + if (n >= 32) switch ((uintptr_t)d % 4) { + case 1: + w = *(u32 *)s; + *d++ = *s++; + *d++ = *s++; + *d++ = *s++; + n -= 3; + for (; n>=17; s+=16, d+=16, n-=16) { + x = *(u32 *)(s+1); + *(u32 *)(d+0) = (w LS 24) | (x RS 8); + w = *(u32 *)(s+5); + *(u32 *)(d+4) = (x LS 24) | (w RS 8); + x = *(u32 *)(s+9); + *(u32 *)(d+8) = (w LS 24) | (x RS 8); + w = *(u32 *)(s+13); + *(u32 *)(d+12) = (x LS 24) | (w RS 8); + } + break; + case 2: + w = *(u32 *)s; + *d++ = *s++; + *d++ = *s++; + n -= 2; + for (; n>=18; s+=16, d+=16, n-=16) { + x = *(u32 *)(s+2); + *(u32 *)(d+0) = (w LS 16) | (x RS 16); + w = *(u32 *)(s+6); + *(u32 *)(d+4) = (x LS 16) | (w RS 16); + x = *(u32 *)(s+10); + *(u32 *)(d+8) = (w LS 16) | (x RS 16); + w = *(u32 *)(s+14); + *(u32 *)(d+12) = (x LS 16) | (w RS 16); + } + break; + case 3: + w = *(u32 *)s; + *d++ = *s++; + n -= 1; + for (; n>=19; s+=16, d+=16, n-=16) { + x = *(u32 *)(s+3); + *(u32 *)(d+0) = (w LS 8) | (x RS 24); + w = *(u32 *)(s+7); + *(u32 *)(d+4) = (x LS 8) | (w RS 24); + x = *(u32 *)(s+11); + *(u32 *)(d+8) = (w LS 8) | (x RS 24); + w = *(u32 *)(s+15); + *(u32 *)(d+12) = (x LS 8) | (w RS 24); + } + break; + } + if (n&16) { + *d++ = *s++; *d++ = *s++; *d++ = *s++; *d++ = *s++; + *d++ = *s++; *d++ = *s++; *d++ = *s++; *d++ = *s++; + *d++ = *s++; *d++ = *s++; *d++ = *s++; *d++ = *s++; + *d++ = *s++; *d++ = *s++; *d++ = *s++; *d++ = *s++; + } + if (n&8) { + *d++ = *s++; *d++ = *s++; *d++ = *s++; *d++ = *s++; + *d++ = *s++; *d++ = *s++; *d++ = *s++; *d++ = *s++; + } + if (n&4) { + *d++ = *s++; *d++ = *s++; *d++ = *s++; *d++ = *s++; + } + if (n&2) { + *d++ = *s++; *d++ = *s++; + } + if (n&1) { + *d = *s; + } + return dest; +#endif + + for (; n; n--) *d++ = *s++; + return dest; +} diff --git a/nolibc/memmove.c b/nolibc/memmove.c new file mode 100644 index 0000000..27f670e --- /dev/null +++ b/nolibc/memmove.c @@ -0,0 +1,36 @@ +#include +#include + +#define WT size_t +#define WS (sizeof(WT)) + +void *memmove(void *dest, const void *src, size_t n) +{ + char *d = dest; + const char *s = src; + + if (d==s) return d; + if (s+n <= d || d+n <= s) return memcpy(d, s, n); + + if (d=WS; n-=WS, d+=WS, s+=WS) *(WT *)d = *(WT *)s; + } + for (; n; n--) *d++ = *s++; + } else { + if ((uintptr_t)s % WS == (uintptr_t)d % WS) { + while ((uintptr_t)(d+n) % WS) { + if (!n--) return dest; + d[n] = s[n]; + } + while (n>=WS) n-=WS, *(WT *)(d+n) = *(WT *)(s+n); + } + while (n) n--, d[n] = s[n]; + } + + return dest; +} diff --git a/nolibc/memset.c b/nolibc/memset.c new file mode 100644 index 0000000..f438b07 --- /dev/null +++ b/nolibc/memset.c @@ -0,0 +1,86 @@ +#include +#include + +void *memset(void *dest, int c, size_t n) +{ + unsigned char *s = dest; + size_t k; + + /* Fill head and tail with minimal branching. Each + * conditional ensures that all the subsequently used + * offsets are well-defined and in the dest region. */ + + if (!n) return dest; + s[0] = s[n-1] = c; + if (n <= 2) return dest; + s[1] = s[n-2] = c; + s[2] = s[n-3] = c; + if (n <= 6) return dest; + s[3] = s[n-4] = c; + if (n <= 8) return dest; + + /* Advance pointer to align it at a 4-byte boundary, + * and truncate n to a multiple of 4. The previous code + * already took care of any head/tail that get cut off + * by the alignment. */ + + k = -(uintptr_t)s & 3; + s += k; + n -= k; + n &= -4; + +#ifdef __GNUC__ + typedef uint32_t __attribute__((__may_alias__)) u32; + typedef uint64_t __attribute__((__may_alias__)) u64; + + u32 c32 = ((u32)-1)/255 * (unsigned char)c; + + /* In preparation to copy 32 bytes at a time, aligned on + * an 8-byte bounary, fill head/tail up to 28 bytes each. + * As in the initial byte-based head/tail fill, each + * conditional below ensures that the subsequent offsets + * are valid (e.g. !(n<=24) implies n>=28). */ + + *(u32 *)(s+0) = c32; + *(u32 *)(s+n-4) = c32; + if (n <= 8) return dest; + *(u32 *)(s+4) = c32; + *(u32 *)(s+8) = c32; + *(u32 *)(s+n-12) = c32; + *(u32 *)(s+n-8) = c32; + if (n <= 24) return dest; + *(u32 *)(s+12) = c32; + *(u32 *)(s+16) = c32; + *(u32 *)(s+20) = c32; + *(u32 *)(s+24) = c32; + *(u32 *)(s+n-28) = c32; + *(u32 *)(s+n-24) = c32; + *(u32 *)(s+n-20) = c32; + *(u32 *)(s+n-16) = c32; + + /* Align to a multiple of 8 so we can fill 64 bits at a time, + * and avoid writing the same bytes twice as much as is + * practical without introducing additional branching. */ + + k = 24 + ((uintptr_t)s & 4); + s += k; + n -= k; + + /* If this loop is reached, 28 tail bytes have already been + * filled, so any remainder when n drops below 32 can be + * safely ignored. */ + + u64 c64 = c32 | ((u64)c32 << 32); + for (; n >= 32; n-=32, s+=32) { + *(u64 *)(s+0) = c64; + *(u64 *)(s+8) = c64; + *(u64 *)(s+16) = c64; + *(u64 *)(s+24) = c64; + } +#else + /* Pure C fallback with no aliasing violations. */ + for (; n; n--, s++) *s = c; +#endif + + return dest; +} diff --git a/nolibc/mmap.c b/nolibc/mmap.c new file mode 100644 index 0000000..3f99fc0 --- /dev/null +++ b/nolibc/mmap.c @@ -0,0 +1,77 @@ +#include +#include +#include + +#include + +void *mmap(void *addr, size_t len, int prot, int flags, int fildes, off_t off) { + + /* man page for mmap says: + * If addr is NULL, then the kernel chooses the (page-aligned) address at + * which to create the mapping; this is the most portable method of creating a + * new mapping. + * + * For our purpose (Solo5 & OCaml), OCaml might use a NULL addr and force us to + * use posix_memalign. + * OCaml calls mmap with a non-null address and with the MAP_FIXED flag only + * on already reserved memory to commit or decommit that memory block, ie to + * set its protection to PROT_READ|PROT_WRITE or to PROT_NONE, in the + * caml_mem_commit and caml_mem_decommit functions. + * So we accept this particular case without allocating memory that would leak + * since the OCaml code base simply ignores the returned value (as MAP_FIXED + * enforces the returned value to be either addr or MAP_FAILED). + * + * The OCaml runtime uses [mmap()] only to allocate memory, so only + * [fildes == 1] is handled. + */ + (void)prot; // unused argument + + if (fildes != -1) { + printf("mmap: file descriptor is unsupported.\n"); + abort(); + } + if (!(flags & MAP_ANONYMOUS) || off != 0) { + printf("mmap: only MAP_ANONYMOUS (and offset is 0) is supported.\n"); + abort(); + } + + void *ptr = NULL; + + if (addr == NULL) { + /* posix_memalign doesn't modify ptr on error: ptr will still be NULL and + * so we will return MAP_FAILED with no need to check explicitly the value + * returned by posix_memalign */ + posix_memalign(&ptr, OCAML_SOLO5_PAGESIZE, len); + } else { + if ((flags & MAP_FIXED) != 0) { + /* Case where mmap is called to commit or decommit already reserved + * memory. Since we ignore prot, we can simply let it go through */ + return addr; + } else { + /* We cannot handle this case */ + errno = EINVAL; + } + } + + if (ptr == NULL) { + return MAP_FAILED; + } else { + return ptr; + } +} + +int munmap(void *addr, size_t length) +{ + (void)length; // unused argument + + /* man page for munmap says: + * The address addr must be a multiple of the page size (but length need not be). + */ + if ((uintptr_t)addr & OCAML_SOLO5_PAGESIZE != 0) { + errno = EINVAL; + return -1; + } + + free(addr); + return 0; +} diff --git a/nolibc/printf.c b/nolibc/printf.c new file mode 100644 index 0000000..cebfe40 --- /dev/null +++ b/nolibc/printf.c @@ -0,0 +1,12 @@ +#include +#include + +int printf(const char *restrict fmt, ...) +{ + int ret; + va_list ap; + va_start(ap, fmt); + ret = vfprintf(stdout, fmt, ap); + va_end(ap); + return ret; +} diff --git a/nolibc/puts.c b/nolibc/puts.c new file mode 100644 index 0000000..98a5fb8 --- /dev/null +++ b/nolibc/puts.c @@ -0,0 +1,17 @@ +#include +#include + +extern void solo5_console_write(const char *, size_t); + +int puts(const char *s) +{ + size_t len = strlen(s); + solo5_console_write(s, len); + return (int)(len); // We should never have a string length above MAX_INT, do we? +} + +int putchar(int chr) +{ + solo5_console_write((char *) &chr, 1); + return (1); +} diff --git a/nolibc/snprintf.c b/nolibc/snprintf.c new file mode 100644 index 0000000..771503b --- /dev/null +++ b/nolibc/snprintf.c @@ -0,0 +1,13 @@ +#include +#include + +int snprintf(char *restrict s, size_t n, const char *restrict fmt, ...) +{ + int ret; + va_list ap; + va_start(ap, fmt); + ret = vsnprintf(s, n, fmt, ap); + va_end(ap); + return ret; +} + diff --git a/nolibc/stpncpy.c b/nolibc/stpncpy.c new file mode 100644 index 0000000..5d5d95a --- /dev/null +++ b/nolibc/stpncpy.c @@ -0,0 +1,27 @@ +#include +#include +#include + +#define ALIGN (sizeof(size_t)-1) +#define ONES ((size_t)-1/UCHAR_MAX) +#define HIGHS (ONES * (UCHAR_MAX/2+1)) +#define HASZERO(x) ((x)-ONES & ~(x) & HIGHS) + +char *__stpncpy(char *restrict d, const char *restrict s, size_t n) +{ + size_t *wd; + const size_t *ws; + + if (((uintptr_t)s & ALIGN) == ((uintptr_t)d & ALIGN)) { + for (; ((uintptr_t)s & ALIGN) && n && (*d=*s); n--, s++, d++); + if (!n || !*s) goto tail; + wd=(void *)d; ws=(const void *)s; + for (; n>=sizeof(size_t) && !HASZERO(*ws); + n-=sizeof(size_t), ws++, wd++) *wd = *ws; + d=(void *)wd; s=(const void *)ws; + } + for (; n && (*d=*s); n--, s++, d++); +tail: + memset(d, 0, n); + return d; +} diff --git a/nolibc/strchr.c b/nolibc/strchr.c new file mode 100644 index 0000000..bfae8f9 --- /dev/null +++ b/nolibc/strchr.c @@ -0,0 +1,9 @@ +#include + +char *__strchrnul(const char *, int); + +char *strchr(const char *s, int c) +{ + char *r = __strchrnul(s, c); + return *(unsigned char *)r == (unsigned char)c ? r : 0; +} diff --git a/nolibc/strchrnul.c b/nolibc/strchrnul.c new file mode 100644 index 0000000..e28c4f5 --- /dev/null +++ b/nolibc/strchrnul.c @@ -0,0 +1,23 @@ +#include +#include +#include + +#define ALIGN (sizeof(size_t)) +#define ONES ((size_t)-1/UCHAR_MAX) +#define HIGHS (ONES * (UCHAR_MAX/2+1)) +#define HASZERO(x) ((x)-ONES & ~(x) & HIGHS) + +char *__strchrnul(const char *s, int c) +{ + size_t *w, k; + + c = (unsigned char)c; + if (!c) return (char *)s + strlen(s); + + for (; (uintptr_t)s % ALIGN; s++) + if (!*s || *(unsigned char *)s == c) return (char *)s; + k = ONES * c; + for (w = (void *)s; !HASZERO(*w) && !HASZERO(*w^k); w++); + for (s = (void *)w; *s && *(unsigned char *)s != c; s++); + return (char *)s; +} diff --git a/nolibc/strcmp.c b/nolibc/strcmp.c new file mode 100644 index 0000000..808bd83 --- /dev/null +++ b/nolibc/strcmp.c @@ -0,0 +1,7 @@ +#include + +int strcmp(const char *l, const char *r) +{ + for (; *l==*r && *l; l++, r++); + return *(unsigned char *)l - *(unsigned char *)r; +} diff --git a/nolibc/strerror_r.c b/nolibc/strerror_r.c new file mode 100644 index 0000000..620fa14 --- /dev/null +++ b/nolibc/strerror_r.c @@ -0,0 +1,19 @@ +#include +#include +#include + +extern const char *const sys_errlist[]; + +int strerror_r(int num, char *buf, size_t buflen) +{ + if (num < 0 || num >= NB_ERRORS) { + errno = EINVAL; + return EINVAL; + } + if (snprintf(buf, buflen, "%s", sys_errlist[num]) >= (int)buflen) { + errno = ERANGE; + return ERANGE; + } + + return 0; +} diff --git a/nolibc/strlen.c b/nolibc/strlen.c new file mode 100644 index 0000000..929ddcb --- /dev/null +++ b/nolibc/strlen.c @@ -0,0 +1,18 @@ +#include +#include +#include + +#define ALIGN (sizeof(size_t)) +#define ONES ((size_t)-1/UCHAR_MAX) +#define HIGHS (ONES * (UCHAR_MAX/2+1)) +#define HASZERO(x) ((x)-ONES & ~(x) & HIGHS) + +size_t strlen(const char *s) +{ + const char *a = s; + const size_t *w; + for (; (uintptr_t)s % ALIGN; s++) if (!*s) return s-a; + for (w = (const void *)s; !HASZERO(*w); w++); + for (s = (const void *)w; *s; s++); + return s-a; +} diff --git a/nolibc/strncmp.c b/nolibc/strncmp.c new file mode 100644 index 0000000..e228843 --- /dev/null +++ b/nolibc/strncmp.c @@ -0,0 +1,9 @@ +#include + +int strncmp(const char *_l, const char *_r, size_t n) +{ + const unsigned char *l=(void *)_l, *r=(void *)_r; + if (!n--) return 0; + for (; *l && *r && n && *l == *r ; l++, r++, n--); + return *l - *r; +} diff --git a/nolibc/strncpy.c b/nolibc/strncpy.c new file mode 100644 index 0000000..441ba03 --- /dev/null +++ b/nolibc/strncpy.c @@ -0,0 +1,9 @@ +#include + +char *__stpncpy(char *, const char *, size_t); + +char *strncpy(char *restrict d, const char *restrict s, size_t n) +{ + __stpncpy(d, s, n); + return d; +} diff --git a/nolibc/strnlen.c b/nolibc/strnlen.c new file mode 100644 index 0000000..9f90a18 --- /dev/null +++ b/nolibc/strnlen.c @@ -0,0 +1,20 @@ +#include +#include +#include + +#define ALIGN (sizeof(size_t)) +#define ONES ((size_t)-1/UCHAR_MAX) +#define HIGHS (ONES * (UCHAR_MAX/2+1)) +#define HASZERO(x) ((x)-ONES & ~(x) & HIGHS) + +size_t strnlen(const char *s, size_t maxlen) +{ + const char *a = s; + const size_t *w; + size_t over = maxlen; + for (; ((uintptr_t)s % ALIGN) && over; s++, over--) if (!*s) return s-a; + for (w = (const void *)s; over>ALIGN && !HASZERO(*w); w++,over-=ALIGN); + for (s = (const void *)w; *s && over; s++, over--); + if (over) return s-a; + else return maxlen; +} diff --git a/nolibc/strstr.c b/nolibc/strstr.c new file mode 100644 index 0000000..cd06912 --- /dev/null +++ b/nolibc/strstr.c @@ -0,0 +1,155 @@ +#include +#include + +static char *twobyte_strstr(const unsigned char *h, const unsigned char *n) +{ + uint16_t nw = n[0]<<8 | n[1], hw = h[0]<<8 | h[1]; + for (h++; *h && hw != nw; hw = hw<<8 | *++h); + return *h ? (char *)h-1 : 0; +} + +static char *threebyte_strstr(const unsigned char *h, const unsigned char *n) +{ + uint32_t nw = n[0]<<24 | n[1]<<16 | n[2]<<8; + uint32_t hw = h[0]<<24 | h[1]<<16 | h[2]<<8; + for (h+=2; *h && hw != nw; hw = (hw|*++h)<<8); + return *h ? (char *)h-2 : 0; +} + +static char *fourbyte_strstr(const unsigned char *h, const unsigned char *n) +{ + uint32_t nw = n[0]<<24 | n[1]<<16 | n[2]<<8 | n[3]; + uint32_t hw = h[0]<<24 | h[1]<<16 | h[2]<<8 | h[3]; + for (h+=3; *h && hw != nw; hw = hw<<8 | *++h); + return *h ? (char *)h-3 : 0; +} + +#define MAX(a,b) ((a)>(b)?(a):(b)) +#define MIN(a,b) ((a)<(b)?(a):(b)) + +#define BITOP(a,b,op) \ + ((a)[(size_t)(b)/(8*sizeof *(a))] op (size_t)1<<((size_t)(b)%(8*sizeof *(a)))) + +static char *twoway_strstr(const unsigned char *h, const unsigned char *n) +{ + const unsigned char *z; + size_t l, ip, jp, k, p, ms, p0, mem, mem0; + size_t byteset[32 / sizeof(size_t)] = { 0 }; + size_t shift[256]; + + /* Computing length of needle and fill shift table */ + for (l=0; n[l] && h[l]; l++) + BITOP(byteset, n[l], |=), shift[n[l]] = l+1; + if (n[l]) return 0; /* hit the end of h */ + + /* Compute maximal suffix */ + ip = -1; jp = 0; k = p = 1; + while (jp+k n[jp+k]) { + jp += k; + k = 1; + p = jp - ip; + } else { + ip = jp++; + k = p = 1; + } + } + ms = ip; + p0 = p; + + /* And with the opposite comparison */ + ip = -1; jp = 0; k = p = 1; + while (jp+k ms+1) ms = ip; + else p = p0; + + /* Periodic needle? */ + if (memcmp(n, n+p, ms+1)) { + mem0 = 0; + p = MAX(ms, l-ms-1) + 1; + } else mem0 = l-p; + mem = 0; + + /* Initialize incremental end-of-haystack pointer */ + z = h; + + /* Search loop */ + for (;;) { + /* Update incremental end-of-haystack pointer */ + if (z-h < l) { + /* Fast estimate for MIN(l,63) */ + size_t grow = l | 63; + const unsigned char *z2 = memchr(z, 0, grow); + if (z2) { + z = z2; + if (z-h < l) return 0; + } else z += grow; + } + + /* Check last byte first; advance by shift on mismatch */ + if (BITOP(byteset, h[l-1], &)) { + k = l-shift[h[l-1]]; + //printf("adv by %zu (on %c) at [%s] (%zu;l=%zu)\n", k, h[l-1], h, shift[h[l-1]], l); + if (k) { + if (mem0 && mem && k < p) k = l-p; + h += k; + mem = 0; + continue; + } + } else { + h += l; + mem = 0; + continue; + } + + /* Compare right half */ + for (k=MAX(ms+1,mem); n[k] && n[k] == h[k]; k++); + if (n[k]) { + h += k-ms; + mem = 0; + continue; + } + /* Compare left half */ + for (k=ms+1; k>mem && n[k-1] == h[k-1]; k--); + if (k <= mem) return (char *)h; + h += p; + mem = mem0; + } +} + +char *strstr(const char *h, const char *n) +{ + /* Return immediately on empty needle */ + if (!n[0]) return (char *)h; + + /* Use faster algorithms for short needles */ + h = strchr(h, *n); + if (!h || !n[1]) return (char *)h; + if (!h[1]) return 0; + if (!n[2]) return twobyte_strstr((void *)h, (void *)n); + if (!h[2]) return 0; + if (!n[3]) return threebyte_strstr((void *)h, (void *)n); + if (!h[3]) return 0; + if (!n[4]) return fourbyte_strstr((void *)h, (void *)n); + + return twoway_strstr((void *)h, (void *)n); +} diff --git a/nolibc/strtol.c b/nolibc/strtol.c new file mode 100644 index 0000000..cfa03de --- /dev/null +++ b/nolibc/strtol.c @@ -0,0 +1,150 @@ +/* $OpenBSD: strtol.c,v 1.11 2015/09/13 08:31:48 guenther Exp $ */ +/* + * Copyright (c) 1990 The Regents of the University of California. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +#include +#include +#include + +/* + * Convert a string to a long integer. + * + * Ignores `locale' stuff. Assumes that the upper and lower case + * alphabets and digits are each contiguous. + */ +long +strtol(const char *nptr, char **endptr, int base) +{ + const char *s; + long acc, cutoff; + int c; + int neg, any, cutlim; + + /* + * Ensure that base is between 2 and 36 inclusive, or the special + * value of 0. + */ + if (base < 0 || base == 1 || base > 36) { + if (endptr != 0) + *endptr = (char *)nptr; + errno = EINVAL; + return 0; + } + + /* + * Skip white space and pick up leading +/- sign if any. + * If base is 0, allow 0x for hex and 0 for octal, else + * assume decimal; if base is already 16, allow 0x. + */ + s = nptr; + do { + c = (unsigned char) *s++; + } while (isspace(c)); + if (c == '-') { + neg = 1; + c = *s++; + } else { + neg = 0; + if (c == '+') + c = *s++; + } + if ((base == 0 || base == 16) && + c == '0' && (*s == 'x' || *s == 'X')) { + c = s[1]; + s += 2; + base = 16; + } + if (base == 0) + base = c == '0' ? 8 : 10; + + /* + * Compute the cutoff value between legal numbers and illegal + * numbers. That is the largest legal value, divided by the + * base. An input number that is greater than this value, if + * followed by a legal input character, is too big. One that + * is equal to this value may be valid or not; the limit + * between valid and invalid numbers is then based on the last + * digit. For instance, if the range for longs is + * [-2147483648..2147483647] and the input base is 10, + * cutoff will be set to 214748364 and cutlim to either + * 7 (neg==0) or 8 (neg==1), meaning that if we have accumulated + * a value > 214748364, or equal but the next digit is > 7 (or 8), + * the number is too big, and we will return a range error. + * + * Set any if any `digits' consumed; make it negative to indicate + * overflow. + */ + cutoff = neg ? LONG_MIN : LONG_MAX; + cutlim = cutoff % base; + cutoff /= base; + if (neg) { + if (cutlim > 0) { + cutlim -= base; + cutoff += 1; + } + cutlim = -cutlim; + } + for (acc = 0, any = 0;; c = (unsigned char) *s++) { + if (isdigit(c)) + c -= '0'; + else if (isalpha(c)) + c -= isupper(c) ? 'A' - 10 : 'a' - 10; + else + break; + if (c >= base) + break; + if (any < 0) + continue; + if (neg) { + if (acc < cutoff || (acc == cutoff && c > cutlim)) { + any = -1; + acc = LONG_MIN; + errno = ERANGE; + } else { + any = 1; + acc *= base; + acc -= c; + } + } else { + if (acc > cutoff || (acc == cutoff && c > cutlim)) { + any = -1; + acc = LONG_MAX; + errno = ERANGE; + } else { + any = 1; + acc *= base; + acc += c; + } + } + } + if (endptr != 0) + *endptr = (char *) (any ? s - 1 : nptr); + return (acc); +} diff --git a/nolibc/stubs.c b/nolibc/stubs.c new file mode 100644 index 0000000..bf189e3 --- /dev/null +++ b/nolibc/stubs.c @@ -0,0 +1,152 @@ +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#define STUB_ABORT(function) \ + int __unsup_##function(void) __asm__(#function) __attribute__((noreturn)); \ + int __unsup_##function(void) \ + { \ + printf("STUB: abort: %s() called\n", #function); \ + abort(); \ + } + +/* + * Warnings are deliberately disabled here to reduce unnecessary verbosity under + * normal operation. To enable, replace "called = 1" with "called = 0" and + * rebuild. + */ +#define STUB_WARN_ONCE(type, function, ret) \ + type __unsup_##function(void) __asm__(#function); \ + type __unsup_##function(void) \ + { \ + static int called = 1; \ + if (!called) {\ + printf("STUB: %s() called\n", #function); \ + called = 1; \ + } \ + errno = ENOSYS; \ + return ret; \ + } + +#define STUB_IGNORE(type, function, ret) \ + type __unsup_##function(void) __asm__(#function); \ + type __unsup_##function(void) \ + { \ + errno = ENOSYS; \ + return ret; \ + } + +/* stdio.h */ +STUB_WARN_ONCE(int, fflush, 0); +STUB_ABORT(rename); +STUB_ABORT(sscanf); /* Used only for parsing OCAMLRUNPARAM, never called */ +/* + * The following stubs are not required by the OCaml runtime, but are + * needed to build the freestanding version of GMP used by Mirage. + */ +STUB_WARN_ONCE(int, fread, 0); +STUB_WARN_ONCE(int, getc, EOF); +STUB_WARN_ONCE(int, ungetc, EOF); +STUB_WARN_ONCE(int, fwrite, 0); +STUB_WARN_ONCE(int, fputc, EOF); +STUB_WARN_ONCE(int, fputs, EOF); +STUB_WARN_ONCE(int, putc, EOF); +STUB_WARN_ONCE(int, ferror, 1); +STUB_WARN_ONCE(int, fopen, 1); +STUB_WARN_ONCE(int, fclose, 1); + +/* stdlib.h */ +STUB_WARN_ONCE(char *, getenv, NULL); +STUB_WARN_ONCE(char *, secure_getenv, NULL); +STUB_ABORT(system); + +/* unistd.h */ +STUB_WARN_ONCE(int, chdir, -1); +STUB_ABORT(close); +STUB_ABORT(getcwd); +STUB_WARN_ONCE(pid_t, getpid, 2); +STUB_WARN_ONCE(pid_t, getppid, 1); +STUB_IGNORE(int, isatty, 0); +STUB_IGNORE(off_t, lseek, -1); +STUB_ABORT(read); +STUB_IGNORE(int, readlink, -1); +STUB_ABORT(unlink); +STUB_ABORT(rmdir); +STUB_ABORT(ftruncate); +STUB_ABORT(execv); + +/* dirent.h */ +STUB_WARN_ONCE(int, closedir, -1); +STUB_WARN_ONCE(void *, opendir, NULL); +STUB_WARN_ONCE(struct dirent *, readdir, NULL); + +/* fcntl.h */ +STUB_ABORT(fcntl); +STUB_WARN_ONCE(int, open, -1); + +/* signal.h */ +STUB_IGNORE(int, setjmp, 0); +STUB_ABORT(signal); +/* + * The following stubs are not required by the OCaml runtime, but are + * needed to build the freestanding version of GMP used by Mirage. + */ +STUB_ABORT(raise); + +/* string.h */ +STUB_ABORT(strerror); + +/* sys/stat.h */ +STUB_WARN_ONCE(int, stat, -1); +STUB_ABORT(mkdir); + +/* pthread.h */ +STUB_IGNORE(int, pthread_join, 0); +STUB_IGNORE(int, pthread_create, EAGAIN); +STUB_IGNORE(int, pthread_attr_init, 0); +STUB_ABORT(pthread_cleanup_push); +STUB_ABORT(pthread_cleanup_pop); + +/* above that line, for OCaml 5, those are only required (i guess) for the configure step */ +STUB_IGNORE(int, pthread_mutex_lock, 0); +STUB_IGNORE(int, pthread_mutex_trylock, 0); +STUB_IGNORE(int, pthread_mutex_unlock, 0); +STUB_IGNORE(int, pthread_mutex_destroy, 0); +STUB_IGNORE(int, pthread_mutex_init, 0); + +STUB_IGNORE(int, pthread_mutexattr_init, 0); +STUB_IGNORE(int, pthread_mutexattr_destroy, 0); +STUB_IGNORE(int, pthread_mutexattr_settype, 0); + +STUB_IGNORE(int, pthread_sigmask, 0); + +STUB_IGNORE(int, pthread_equal, 1); + +STUB_IGNORE(int, pthread_condattr_init, 0); +/* pthread_condattr_destroy: not used by Ocaml 5 (pthread_condattr_init is only used in + ocaml/runtime/platform.c with a function local variable as argument) + */ + +STUB_IGNORE(int, pthread_cond_init, 0); +STUB_IGNORE(int, pthread_cond_destroy, 0); +/* it's possible to create a [Stdlib.Condition.t] but an execution path exists + * where we don't really use it. However, OCaml will try to destroy this + * [Stdlib.Condition.t] and we must ignore such execution path which is still + * safe for unikernels (with one core). The real issue with [pthread_cond_*] is + * when we would like to suspend the execution with [pthread_cond_wait] but + * [pthread_cond_init] and [pthread_cond_destroy] are safe to just ignore. */ +STUB_ABORT(pthread_cond_wait); +STUB_ABORT(pthread_cond_signal); +STUB_IGNORE(int, pthread_cond_broadcast, 0); +STUB_ABORT(pthread_self); +STUB_ABORT(pthread_detach); + +STUB_IGNORE(int, sigfillset, 0); +STUB_ABORT(sigwait); +STUB_ABORT(usleep); diff --git a/nolibc/sysconf.c b/nolibc/sysconf.c new file mode 100644 index 0000000..81297ec --- /dev/null +++ b/nolibc/sysconf.c @@ -0,0 +1,11 @@ +#include +#include + +long sysconf(int x) { + switch (x) { + case _SC_PAGESIZE: /* _SC_PAGE_SIZE */ + return OCAML_SOLO5_PAGESIZE; + default: + return -1; + } +} diff --git a/nolibc/sysdeps.c b/nolibc/sysdeps.c new file mode 100644 index 0000000..2ed6b7c --- /dev/null +++ b/nolibc/sysdeps.c @@ -0,0 +1,47 @@ +#include +#include +#include +#include +#include + +int errno; + +extern void gilbraltar_serial_write(const char *, size_t); +extern void gilbraltar_serial_puts(const char *); + +static size_t console_write(FILE *f __attribute__((unused)), const char *str, size_t len) { + gilbraltar_serial_write(str, len); + return (len); +} + +static FILE console = { .write = console_write }; +FILE *stderr = &console; +FILE *stdout = &console; + +ssize_t write(int fd, const void *buf, size_t count) { + if (fd == 1 || fd == 2) { + gilbraltar_serial_write(buf, count); + return (count); + } + errno = ENOSYS; + return (-1); +} + +void exit(int status) { + while (1) + __asm__ __volatile("wfi"); +} + +void abort(void) { + gilbraltar_serial_puts("Aborted\r\n"); + + while (1) + __asm__ __volatile("wfi"); +} + +#if defined(__aarch64__) +int __getauxval(int unused) { + errno = ENOENT; + return (0); +} +#endif diff --git a/nolibc/vfprintf.c b/nolibc/vfprintf.c new file mode 100644 index 0000000..9e886a0 --- /dev/null +++ b/nolibc/vfprintf.c @@ -0,0 +1,650 @@ +#include +#include +#include +#include +#include +#include +#include +#include +#include + +/* Some useful macros */ + +#define MAX(a,b) ((a)>(b) ? (a) : (b)) +#define MIN(a,b) ((a)<(b) ? (a) : (b)) + +/* Convenient bit representation for modifier flags, which all fall + * within 31 codepoints of the space character. */ + +#define ALT_FORM (1U<<'#'-' ') +#define ZERO_PAD (1U<<'0'-' ') +#define LEFT_ADJ (1U<<'-'-' ') +#define PAD_POS (1U<<' '-' ') +#define MARK_POS (1U<<'+'-' ') +#define GROUPED (1U<<'\''-' ') + +#define FLAGMASK (ALT_FORM|ZERO_PAD|LEFT_ADJ|PAD_POS|MARK_POS|GROUPED) + +#if UINT_MAX == ULONG_MAX +#define LONG_IS_INT +#endif + +#if SIZE_MAX != ULONG_MAX || UINTMAX_MAX != ULLONG_MAX +#define ODD_TYPES +#endif + +/* State machine to accept length modifiers + conversion specifiers. + * Result is 0 on failure, or an argument type to pop on success. */ + +enum { + BARE, LPRE, LLPRE, HPRE, HHPRE, BIGLPRE, + ZTPRE, JPRE, + STOP, + PTR, INT, UINT, ULLONG, +#ifndef LONG_IS_INT + LONG, ULONG, +#else +#define LONG INT +#define ULONG UINT +#endif + SHORT, USHORT, CHAR, UCHAR, +#ifdef ODD_TYPES + LLONG, SIZET, IMAX, UMAX, PDIFF, UIPTR, +#else +#define LLONG ULLONG +#define SIZET ULONG +#define IMAX LLONG +#define UMAX ULLONG +#define PDIFF LONG +#define UIPTR ULONG +#endif + DBL, LDBL, + NOARG, + MAXSTATE +}; + +#define S(x) [(x)-'A'] + +static const unsigned char states[]['z'-'A'+1] = { + { /* 0: bare types */ + S('d') = INT, S('i') = INT, + S('o') = UINT, S('u') = UINT, S('x') = UINT, S('X') = UINT, + S('e') = DBL, S('f') = DBL, S('g') = DBL, S('a') = DBL, + S('E') = DBL, S('F') = DBL, S('G') = DBL, S('A') = DBL, + S('c') = CHAR, S('C') = INT, + S('s') = PTR, S('S') = PTR, S('p') = UIPTR, S('n') = PTR, + S('m') = NOARG, + S('l') = LPRE, S('h') = HPRE, S('L') = BIGLPRE, + S('z') = ZTPRE, S('j') = JPRE, S('t') = ZTPRE, + }, { /* 1: l-prefixed */ + S('d') = LONG, S('i') = LONG, + S('o') = ULONG, S('u') = ULONG, S('x') = ULONG, S('X') = ULONG, + S('e') = DBL, S('f') = DBL, S('g') = DBL, S('a') = DBL, + S('E') = DBL, S('F') = DBL, S('G') = DBL, S('A') = DBL, + S('c') = INT, S('s') = PTR, S('n') = PTR, + S('l') = LLPRE, + }, { /* 2: ll-prefixed */ + S('d') = LLONG, S('i') = LLONG, + S('o') = ULLONG, S('u') = ULLONG, + S('x') = ULLONG, S('X') = ULLONG, + S('n') = PTR, + }, { /* 3: h-prefixed */ + S('d') = SHORT, S('i') = SHORT, + S('o') = USHORT, S('u') = USHORT, + S('x') = USHORT, S('X') = USHORT, + S('n') = PTR, + S('h') = HHPRE, + }, { /* 4: hh-prefixed */ + S('d') = CHAR, S('i') = CHAR, + S('o') = UCHAR, S('u') = UCHAR, + S('x') = UCHAR, S('X') = UCHAR, + S('n') = PTR, + }, { /* 5: L-prefixed */ + S('e') = LDBL, S('f') = LDBL, S('g') = LDBL, S('a') = LDBL, + S('E') = LDBL, S('F') = LDBL, S('G') = LDBL, S('A') = LDBL, + S('n') = PTR, + }, { /* 6: z- or t-prefixed (assumed to be same size) */ + S('d') = PDIFF, S('i') = PDIFF, + S('o') = SIZET, S('u') = SIZET, + S('x') = SIZET, S('X') = SIZET, + S('n') = PTR, + }, { /* 7: j-prefixed */ + S('d') = IMAX, S('i') = IMAX, + S('o') = UMAX, S('u') = UMAX, + S('x') = UMAX, S('X') = UMAX, + S('n') = PTR, + } +}; + +#define OOB(x) ((unsigned)(x)-'A' > 'z'-'A') + +union arg +{ + uintmax_t i; + long double f; + void *p; +}; + +static void pop_arg(union arg *arg, int type, va_list *ap) +{ + /* Give the compiler a hint for optimizing the switch. */ + if ((unsigned)type > MAXSTATE) return; + switch (type) { + case PTR: arg->p = va_arg(*ap, void *); + break; case INT: arg->i = va_arg(*ap, int); + break; case UINT: arg->i = va_arg(*ap, unsigned int); +#ifndef LONG_IS_INT + break; case LONG: arg->i = va_arg(*ap, long); + break; case ULONG: arg->i = va_arg(*ap, unsigned long); +#endif + break; case ULLONG: arg->i = va_arg(*ap, unsigned long long); + break; case SHORT: arg->i = (short)va_arg(*ap, int); + break; case USHORT: arg->i = (unsigned short)va_arg(*ap, int); + break; case CHAR: arg->i = (signed char)va_arg(*ap, int); + break; case UCHAR: arg->i = (unsigned char)va_arg(*ap, int); +#ifdef ODD_TYPES + break; case LLONG: arg->i = va_arg(*ap, long long); + break; case SIZET: arg->i = va_arg(*ap, size_t); + break; case IMAX: arg->i = va_arg(*ap, intmax_t); + break; case UMAX: arg->i = va_arg(*ap, uintmax_t); + break; case PDIFF: arg->i = va_arg(*ap, ptrdiff_t); + break; case UIPTR: arg->i = (uintptr_t)va_arg(*ap, void *); +#endif + break; case DBL: arg->f = va_arg(*ap, double); + break; case LDBL: arg->f = va_arg(*ap, long double); + } +} + +static void out(FILE *f, const char *s, size_t l) +{ + f->write(f, s, l); +} + +static void pad(FILE *f, char c, int w, int l, int fl) +{ + char pad[256]; + if (fl & (LEFT_ADJ | ZERO_PAD) || l >= w) return; + l = w - l; + memset(pad, c, l>sizeof pad ? sizeof pad : l); + for (; l >= sizeof pad; l -= sizeof pad) + out(f, pad, sizeof pad); + out(f, pad, l); +} + +static const char xdigits[16] = { + "0123456789ABCDEF" +}; + +static char *fmt_x(uintmax_t x, char *s, int lower) +{ + for (; x; x>>=4) *--s = xdigits[(x&15)]|lower; + return s; +} + +static char *fmt_o(uintmax_t x, char *s) +{ + for (; x; x>>=3) *--s = '0' + (x&7); + return s; +} + +static char *fmt_u(uintmax_t x, char *s) +{ + unsigned long y; + for ( ; x>ULONG_MAX; x/=10) *--s = '0' + x%10; + for (y=x; y; y/=10) *--s = '0' + y%10; + return s; +} + +/* Do not override this check. The floating point printing code below + * depends on the float.h constants being right. If they are wrong, it + * may overflow the stack. */ +#if LDBL_MANT_DIG == 53 +typedef char compiler_defines_long_double_incorrectly[9-(int)sizeof(long double)]; +#endif + +static int fmt_fp(FILE *f, double y, int w, int p, int fl, int t) +{ + uint32_t big[(DBL_MANT_DIG+28)/29 + 1 // mantissa expansion + + (DBL_MAX_EXP+DBL_MANT_DIG+28+8)/9]; // exponent expansion + uint32_t *a, *d, *r, *z; + int e2=0, e, i, j, l; + char buf[9+DBL_MANT_DIG/4], *s; + const char *prefix="-0X+0X 0X-0x+0x 0x"; + int pl; + char ebuf0[3*sizeof(int)], *ebuf=&ebuf0[3*sizeof(int)], *estr; + + pl=1; + if (signbit(y)) { + y=-y; + } else if (fl & MARK_POS) { + prefix+=3; + } else if (fl & PAD_POS) { + prefix+=6; + } else prefix++, pl=0; + + if (!isfinite(y)) { + char *s = (t&32)?"inf":"INF"; + if (y!=y) s=(t&32)?"nan":"NAN"; + pad(f, ' ', w, 3+pl, fl&~ZERO_PAD); + out(f, prefix, pl); + out(f, s, 3); + pad(f, ' ', w, 3+pl, fl^LEFT_ADJ); + return MAX(w, 3+pl); + } + + y = frexp(y, &e2) * 2; + if (y) e2--; + + if ((t|32)=='a') { + double round = 8.0; + int re; + + if (t&32) prefix += 9; + pl += 2; + + if (p<0 || p>=DBL_MANT_DIG/4-1) re=0; + else re=DBL_MANT_DIG/4-1-p; + + if (re) { + while (re--) round*=16; + if (*prefix=='-') { + y=-y; + y-=round; + y+=round; + y=-y; + } else { + y+=round; + y-=round; + } + } + + estr=fmt_u(e2<0 ? -e2 : e2, ebuf); + if (estr==ebuf) *--estr='0'; + *--estr = (e2<0 ? '-' : '+'); + *--estr = t+('p'-'a'); + + s=buf; + do { + int x=y; + *s++=xdigits[x]|(t&32); + y=16*(y-x); + if (s-buf==1 && (y||p>0||(fl&ALT_FORM))) *s++='.'; + } while (y); + + if (p && s-buf-2 < p) + l = (p+2) + (ebuf-estr); + else + l = (s-buf) + (ebuf-estr); + + pad(f, ' ', w, pl+l, fl); + out(f, prefix, pl); + pad(f, '0', w, pl+l, fl^ZERO_PAD); + out(f, buf, s-buf); + pad(f, '0', l-(ebuf-estr)-(s-buf), 0, 0); + out(f, estr, ebuf-estr); + pad(f, ' ', w, pl+l, fl^LEFT_ADJ); + return MAX(w, pl+l); + } + if (p<0) p=6; + + if (y) y *= 0x1p28, e2-=28; + + if (e2<0) a=r=z=big; + else a=r=z=big+sizeof(big)/sizeof(*big) - DBL_MANT_DIG - 1; + + do { + *z = y; + y = 1000000000*(y-*z++); + } while (y); + + while (e2>0) { + uint32_t carry=0; + int sh=MIN(29,e2); + for (d=z-1; d>=a; d--) { + uint64_t x = ((uint64_t)*d<a && !z[-1]) z--; + e2-=sh; + } + while (e2<0) { + uint32_t carry=0, *b; + int sh=MIN(9,-e2), need=1+(p+DBL_MANT_DIG/3+8)/9; + for (d=a; d>sh) + carry; + carry = (1000000000>>sh) * rm; + } + if (!*a) a++; + if (carry) *z++ = carry; + /* Avoid (slow!) computation past requested precision */ + b = (t|32)=='f' ? r : a; + if (z-b > need) z = b+need; + e2+=sh; + } + + if (a=i; i*=10, e++); + else e=0; + + /* Perform rounding: j is precision after the radix (possibly neg) */ + j = p - ((t|32)!='f')*e - ((t|32)=='g' && p); + if (j < 9*(z-r-1)) { + uint32_t x; + /* We avoid C's broken division of negative numbers */ + d = r + 1 + ((j+9*DBL_MAX_EXP)/9 - DBL_MAX_EXP); + j += 9*DBL_MAX_EXP; + j %= 9; + for (i=10, j++; j<9; i*=10, j++); + x = *d % i; + /* Are there any significant digits past j? */ + if (x || d+1!=z) { + double round = 2/DBL_EPSILON; + double small; + if (*d/i & 1) round += 2; + if (x 999999999) { + *d--=0; + if (d=i; i*=10, e++); + } + } + if (z>d+1) z=d+1; + } + for (; z>a && !z[-1]; z--); + + if ((t|32)=='g') { + if (!p) p++; + if (p>e && e>=-4) { + t--; + p-=e+1; + } else { + t-=2; + p--; + } + if (!(fl&ALT_FORM)) { + /* Count trailing zeros in last place */ + if (z>a && z[-1]) for (i=10, j=0; z[-1]%i==0; i*=10, j++); + else j=9; + if ((t|32)=='f') + p = MIN(p,MAX(0,9*(z-r-1)-j)); + else + p = MIN(p,MAX(0,9*(z-r-1)+e-j)); + } + } + l = 1 + p + (p || (fl&ALT_FORM)); + if ((t|32)=='f') { + if (e>0) l+=e; + } else { + estr=fmt_u(e<0 ? -e : e, ebuf); + while(ebuf-estr<2) *--estr='0'; + *--estr = (e<0 ? '-' : '+'); + *--estr = t; + l += ebuf-estr; + } + + pad(f, ' ', w, pl+l, fl); + out(f, prefix, pl); + pad(f, '0', w, pl+l, fl^ZERO_PAD); + + if ((t|32)=='f') { + if (a>r) a=r; + for (d=a; d<=r; d++) { + char *s = fmt_u(*d, buf+9); + if (d!=a) while (s>buf) *--s='0'; + else if (s==buf+9) *--s='0'; + out(f, s, buf+9-s); + } + if (p || (fl&ALT_FORM)) out(f, ".", 1); + for (; d0; d++, p-=9) { + char *s = fmt_u(*d, buf+9); + while (s>buf) *--s='0'; + out(f, s, MIN(9,p)); + } + pad(f, '0', p+9, 9, 0); + } else { + if (z<=a) z=a+1; + for (d=a; d=0; d++) { + char *s = fmt_u(*d, buf+9); + if (s==buf+9) *--s='0'; + if (d!=a) while (s>buf) *--s='0'; + else { + out(f, s++, 1); + if (p>0||(fl&ALT_FORM)) out(f, ".", 1); + } + out(f, s, MIN(buf+9-s, p)); + p -= buf+9-s; + } + pad(f, '0', p+18, 18, 0); + out(f, estr, ebuf-estr); + } + + pad(f, ' ', w, pl+l, fl^LEFT_ADJ); + + return MAX(w, pl+l); +} + +static int getint(char **s) { + int i; + for (i=0; isdigit(**s); (*s)++) + i = 10*i + (**s-'0'); + return i; +} + +int printf_core(FILE *f, const char *fmt, va_list *ap, union arg *nl_arg, int *nl_type) +{ + char *a, *z, *s=(char *)fmt; + unsigned l10n=0, fl; + int w, p; + union arg arg; + int argpos; + unsigned st, ps; + int cnt=0, l=0; + int i; + char buf[sizeof(uintmax_t)*3+3+LDBL_MANT_DIG/4]; + const char *prefix; + int t, pl; + + for (;;) { + /* Update output count, end loop when fmt is exhausted */ + if (cnt >= 0) { + if (l > INT_MAX - cnt) { + errno = EOVERFLOW; + cnt = -1; + } else cnt += l; + } + if (!*s) break; + + /* Handle literal text and %% format specifiers */ + for (a=s; *s && *s!='%'; s++); + for (z=s; s[0]=='%' && s[1]=='%'; z++, s+=2); + l = z-a; + if (f) out(f, a, l); + if (l) continue; + + if (isdigit(s[1]) && s[2]=='$') { + l10n=1; + argpos = s[1]-'0'; + s+=3; + } else { + argpos = -1; + s++; + } + + /* Read modifier flags */ + for (fl=0; (unsigned)*s-' '<32 && (FLAGMASK&(1U<<*s-' ')); s++) + fl |= 1U<<*s-' '; + + /* Read field width */ + if (*s=='*') { + if (isdigit(s[1]) && s[2]=='$') { + l10n=1; + nl_type[s[1]-'0'] = INT; + w = nl_arg[s[1]-'0'].i; + s+=3; + } else if (!l10n) { + w = f ? va_arg(*ap, int) : 0; + s++; + } else return -1; + if (w<0) fl|=LEFT_ADJ, w=-w; + } else if ((w=getint(&s))<0) return -1; + + /* Read precision */ + if (*s=='.' && s[1]=='*') { + if (isdigit(s[2]) && s[3]=='$') { + nl_type[s[2]-'0'] = INT; + p = nl_arg[s[2]-'0'].i; + s+=4; + } else if (!l10n) { + p = f ? va_arg(*ap, int) : 0; + s+=2; + } else return -1; + } else if (*s=='.') { + s++; + p = getint(&s); + } else p = -1; + + /* Format specifier state machine */ + st=0; + do { + if (OOB(*s)) return -1; + ps=st; + st=states[st]S(*s++); + } while (st-1=0) return -1; + } else { + if (argpos>=0) nl_type[argpos]=st, arg=nl_arg[argpos]; + else if (f) pop_arg(&arg, st, ap); + else return 0; + } + + if (!f) continue; + + z = buf + sizeof(buf); + prefix = "-+ 0X0x"; + pl = 0; + t = s[-1]; + + /* Transform ls,lc -> S,C */ + if (ps && (t&15)==3) t&=~32; + + /* - and 0 flags are mutually exclusive */ + if (fl & LEFT_ADJ) fl &= ~ZERO_PAD; + + switch(t) { + case 'n': + switch(ps) { + case BARE: *(int *)arg.p = cnt; break; + case LPRE: *(long *)arg.p = cnt; break; + case LLPRE: *(long long *)arg.p = cnt; break; + case HPRE: *(unsigned short *)arg.p = cnt; break; + case HHPRE: *(unsigned char *)arg.p = cnt; break; + case ZTPRE: *(size_t *)arg.p = cnt; break; + case JPRE: *(uintmax_t *)arg.p = cnt; break; + } + continue; + case 'p': + p = MAX(p, 2*sizeof(void*)); + t = 'x'; + fl |= ALT_FORM; + case 'x': case 'X': + a = fmt_x(arg.i, z, t&32); + if (arg.i && (fl & ALT_FORM)) prefix+=(t>>4), pl=2; + if (0) { + case 'o': + a = fmt_o(arg.i, z); + if ((fl&ALT_FORM) && pINTMAX_MAX) { + arg.i=-arg.i; + } else if (fl & MARK_POS) { + prefix++; + } else if (fl & PAD_POS) { + prefix+=2; + } else pl=0; + case 'u': + a = fmt_u(arg.i, z); + } + if (p>=0) fl &= ~ZERO_PAD; + if (!arg.i && !p) { + a=z; + break; + } + p = MAX(p, z-a + !arg.i); + break; + case 'c': + *(a=z-(p=1))=arg.i; + fl &= ~ZERO_PAD; + break; + case 'm': + if (1) a = strerror(errno); else + case 's': + a = arg.p ? arg.p : "(null)"; + z = memchr(a, 0, p); + if (!z) z=a+p; + else p=z-a; + fl &= ~ZERO_PAD; + break; + case 'e': case 'f': case 'g': case 'a': + case 'E': case 'F': case 'G': case 'A': + l = fmt_fp(f, arg.f, w, p, fl, t); + continue; + } + + if (p < z-a) p = z-a; + if (w < pl+p) w = pl+p; + + pad(f, ' ', w, pl+p, fl); + out(f, prefix, pl); + pad(f, '0', w, pl+p, fl^ZERO_PAD); + pad(f, '0', p, z-a, 0); + out(f, a, z-a); + pad(f, ' ', w, pl+p, fl^LEFT_ADJ); + + l = w; + } + + if (f) return cnt; + if (!l10n) return 0; + + for (i=1; i<=NL_ARGMAX && nl_type[i]; i++) + pop_arg(nl_arg+i, nl_type[i], ap); + for (; i<=NL_ARGMAX && !nl_type[i]; i++); + if (i<=NL_ARGMAX) return -1; + return 1; +} + +int vfprintf(FILE *restrict f, const char *restrict fmt, va_list ap) +{ + va_list ap2; + int nl_type[NL_ARGMAX+1] = {0}; + union arg nl_arg[NL_ARGMAX+1]; + int ret; + + /* the copy allows passing va_list* even if va_list is an array */ + va_copy(ap2, ap); + if (printf_core(0, fmt, &ap2, nl_arg, nl_type) < 0) { + va_end(ap2); + return -1; + } + + ret = printf_core(f, fmt, &ap2, nl_arg, nl_type); + va_end(ap2); + return ret; +} diff --git a/nolibc/vsnprintf.c b/nolibc/vsnprintf.c new file mode 100644 index 0000000..b56bb7e --- /dev/null +++ b/nolibc/vsnprintf.c @@ -0,0 +1,41 @@ +#include +#include +#include +#include +#include + +static size_t sn_write(FILE *f, const char *s, size_t l) +{ + size_t k = f->wend - f->wpos; + if (k > l) k = l; + memcpy(f->wpos, s, k); + f->wpos += k; + /* pretend to succeed, but discard extra data */ + return l; +} + +int vsnprintf(char *restrict s, size_t n, const char *restrict fmt, va_list ap) +{ + int r; + char b; + FILE f = { .write = sn_write }; + + if (n-1 > INT_MAX-1) { + if (n) { + errno = EOVERFLOW; + return -1; + } + s = &b; + n = 1; + } + + /* Ensure pointers don't wrap if "infinite" n is passed in */ + if (n > (char *)0+SIZE_MAX-s-1) n = (char *)0+SIZE_MAX-s-1; + f.wpos = s; + f.wend = (s+n); + r = vfprintf(&f, fmt, ap); + + /* Null-terminate, overwriting last char if dest buffer is full */ + if (n) f.wpos[-(f.wpos == f.wend)] = 0; + return r; +} diff --git a/openlibm/.gitignore b/openlibm/.gitignore new file mode 100644 index 0000000..e7e0c44 --- /dev/null +++ b/openlibm/.gitignore @@ -0,0 +1,7 @@ +*.o +*~ +*.a +*.dll* +*.so* +*.dylib* +*.pc diff --git a/openlibm/.mailmap b/openlibm/.mailmap new file mode 100644 index 0000000..637106f --- /dev/null +++ b/openlibm/.mailmap @@ -0,0 +1,61 @@ +JuliaLang +JuliaLang + +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson +Jeff Bezanson + +Stefan Karpinski +Stefan Karpinski +Stefan Karpinski + +Viral B. Shah +Viral B. Shah +Viral B. Shah +Viral B. Shah + +George Xing +George Xing + +Stephan Boyer +Stephan Boyer +Stephan Boyer +Stephan Boyer + +Giuseppe Zingales +Giuseppe Zingales + +Jameson Nash +Jameson Nash +Jameson Nash + +Alan Edelman + +PlayMyCode +PlayMyCode + +Corey M. Hoffstein +Corey M. Hoffstein + +Stefan Kroboth + +Tim Holy +Tim Holy + +Patrick O'Leary + +Ivan Mantova + +Keno Fischer +Keno Fischer +Keno Fischer diff --git a/openlibm/.travis.yml b/openlibm/.travis.yml new file mode 100644 index 0000000..19e6b11 --- /dev/null +++ b/openlibm/.travis.yml @@ -0,0 +1,73 @@ +# We require a full (virtual) machine to load the kernel module for +# binfmt support, which is needed to test other architectures besides +# x86 using qemu user emulation. (This will not work in a container.) +sudo: required +dist: trusty +language: c + +script: + - make $FLAGS + - make check $FLAGS $TEST_FLAGS + - make clean && git status --ignored --porcelain && test -z "$(git status --ignored --porcelain)" + +matrix: + include: + - compiler: clang + os: linux + addons: + apt: + sources: + - ubuntu-toolchain-r-test + - llvm-toolchain-precise-3.7 + packages: + - clang-3.7 + env: FLAGS="CC=clang-3.7 CXX=clang++-3.7" + + - os: osx + env: FLAGS="CC=clang" + + - os: linux + env: FLAGS="CC=gcc" + + - os: linux + env: FLAGS="CC=gcc ARCH=i686" # implies -m32 -march=i686 + addons: + apt: + packages: + - gcc-multilib + + - os: linux + env: FLAGS="CC=aarch64-linux-gnu-gcc" TEST_FLAGS="LDFLAGS=-static" + addons: + apt: + packages: + - gcc-aarch64-linux-gnu + - libc6-dev-arm64-cross + - qemu-user-static + - binfmt-support + + - os: linux + env: FLAGS="CC=arm-linux-gnueabihf-gcc" TEST_FLAGS="LDFLAGS=-static" + addons: + apt: + packages: + - gcc-arm-linux-gnueabihf + - libc6-dev-armhf-cross + - qemu-user-static + - binfmt-support + + # This works, but only if qemu-user-static is >= v2.4. This is not the + # case on the default trusty images, so we add a PPA that has qemu 2.5 + - os: linux + env: FLAGS="CC=powerpc64le-linux-gnu-gcc" TEST_FLAGS="LDFLAGS=-static" + addons: + apt: + sources: + - sourceline: "ppa:gns3/qemu" + packages: + - gcc-powerpc64le-linux-gnu + - libc6-dev-ppc64el-cross + - qemu-user-static + - binfmt-support +notifications: + email: false diff --git a/openlibm/CMakeLists.txt b/openlibm/CMakeLists.txt new file mode 100755 index 0000000..81045e2 --- /dev/null +++ b/openlibm/CMakeLists.txt @@ -0,0 +1,576 @@ +cmake_minimum_required(VERSION 3.25) + +# Get version string from Make.inc +file(READ "${CMAKE_CURRENT_LIST_DIR}/Make.inc" MAKE_FILE) +string(REGEX MATCH "VERSION = ([0-9\.]+)" _ ${MAKE_FILE}) + +project(openlibm + VERSION ${CMAKE_MATCH_1} + LANGUAGES C ASM) + +option(BUILD_SHARED_LIBS "Build using shared libraries" ON) + +add_library("${PROJECT_NAME}") + +# Find the relevant folder depending on the architecture +set(OPENLIBM_ARCH_FOLDER ${CMAKE_SYSTEM_PROCESSOR}) +string(TOLOWER "${OPENLIBM_ARCH_FOLDER}" OPENLIBM_ARCH_FOLDER) + +if(${OPENLIBM_ARCH_FOLDER} STREQUAL "amd64" OR ${OPENLIBM_ARCH_FOLDER} STREQUAL "x86_64") + set(OPENLIBM_ARCH_FOLDER "amd64") +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "arm64" OR ${OPENLIBM_ARCH_FOLDER} STREQUAL "aarch64") + set(OPENLIBM_ARCH_FOLDER "aarch64") +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "armv7-a") + set(OPENLIBM_ARCH_FOLDER "arm") +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "x86" OR ${OPENLIBM_ARCH_FOLDER} STREQUAL "i686") + set(OPENLIBM_ARCH_FOLDER "i387") +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "powerpc") + set(OPENLIBM_ARCH_FOLDER "powerpc") +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "riscv64") + set(OPENLIBM_ARCH_FOLDER "riscv64") +else() + message(FATAL_ERROR "${PROJECT_NAME} not set up for detected architecture: ${OPENLIBM_ARCH_FOLDER}") +endif() + + +# Compile flags +list(APPEND C_ASM_COMPILE_FLAGS "-ffp-contract=off" "-fno-fast-math" "-fno-rounding-math" "-fno-math-errno") +list(APPEND C_ASM_COMPILE_FLAGS "-fPIC" "-std=c99" "-fno-builtin") +list(APPEND C_ASM_COMPILE_FLAGS "-Wall" "-Wno-implicit-function-declaration") +list(APPEND C_ASM_COMPILE_FLAGS "-DASSEMBLER" "-D__BSD_VISIBLE" "-O3") + +# Compiler-specific compile flags +if("${CMAKE_C_COMPILER_ID}" MATCHES "Clang") + list(APPEND C_ASM_COMPILE_FLAGS "-fno-strict-aliasing" "-ffp-exception-behavior=strict") +elseif("${CMAKE_C_COMPILER_ID}" STREQUAL "GNU") + list(APPEND C_ASM_COMPILE_FLAGS "-fno-gnu89-inline") +else() + message(FATAL_ERROR "${PROJECT_NAME} not set up to be compiled with ${CMAKE_C_COMPILER_ID}") +endif() + +# Architecture-specific compile flags - take advantage of sse on x86 +if(${OPENLIBM_ARCH_FOLDER} STREQUAL "i387") + list(APPEND C_ASM_COMPILE_FLAGS "-march=i686" "-m32" "-msse2" "-mfpmath=sse") +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "amd64") + list(APPEND C_ASM_COMPILE_FLAGS "-m64" "-msse2" "-mfpmath=sse") +endif() + +# Suppress warnings if requested +if(OPENLIBM_SUPPRESS_WARNINGS) + list(APPEND C_ASM_COMPILE_FLAGS "-w") +endif() + +# Add compile flags +target_compile_options("${PROJECT_NAME}" PUBLIC ${C_ASM_COMPILE_FLAGS}) + +# Project Source +set(PROJECT_SRC "${CMAKE_CURRENT_SOURCE_DIR}") + +# Common +list(APPEND OPENLIBM_C_SOURCE + # src + "${PROJECT_SRC}/src/common.c" + "${PROJECT_SRC}/src/e_acos.c" + "${PROJECT_SRC}/src/e_acosf.c" + "${PROJECT_SRC}/src/e_acosh.c" + "${PROJECT_SRC}/src/e_acoshf.c" + "${PROJECT_SRC}/src/e_asin.c" + "${PROJECT_SRC}/src/e_asinf.c" + "${PROJECT_SRC}/src/e_atan2.c" + "${PROJECT_SRC}/src/e_atan2f.c" + "${PROJECT_SRC}/src/e_atanh.c" + "${PROJECT_SRC}/src/e_atanhf.c" + "${PROJECT_SRC}/src/e_cosh.c" + "${PROJECT_SRC}/src/e_coshf.c" + "${PROJECT_SRC}/src/e_exp.c" + "${PROJECT_SRC}/src/e_expf.c" + "${PROJECT_SRC}/src/e_fmod.c" + "${PROJECT_SRC}/src/e_fmodf.c" + "${PROJECT_SRC}/src/e_hypot.c" + "${PROJECT_SRC}/src/e_hypotf.c" + "${PROJECT_SRC}/src/e_j0.c" + "${PROJECT_SRC}/src/e_j0f.c" + "${PROJECT_SRC}/src/e_j1.c" + "${PROJECT_SRC}/src/e_j1f.c" + "${PROJECT_SRC}/src/e_jn.c" + "${PROJECT_SRC}/src/e_jnf.c" + "${PROJECT_SRC}/src/e_lgamma.c" + "${PROJECT_SRC}/src/e_lgamma_r.c" + "${PROJECT_SRC}/src/e_lgammaf.c" + "${PROJECT_SRC}/src/e_lgammaf_r.c" + "${PROJECT_SRC}/src/e_log.c" + "${PROJECT_SRC}/src/e_log10.c" + "${PROJECT_SRC}/src/e_log10f.c" + "${PROJECT_SRC}/src/e_log2.c" + "${PROJECT_SRC}/src/e_log2f.c" + "${PROJECT_SRC}/src/e_logf.c" + "${PROJECT_SRC}/src/e_pow.c" + "${PROJECT_SRC}/src/e_powf.c" + "${PROJECT_SRC}/src/e_remainder.c" + "${PROJECT_SRC}/src/e_remainderf.c" + "${PROJECT_SRC}/src/e_rem_pio2.c" + "${PROJECT_SRC}/src/e_rem_pio2f.c" + "${PROJECT_SRC}/src/e_sinh.c" + "${PROJECT_SRC}/src/e_sinhf.c" + "${PROJECT_SRC}/src/e_sqrt.c" + "${PROJECT_SRC}/src/e_sqrtf.c" + "${PROJECT_SRC}/src/k_cos.c" + "${PROJECT_SRC}/src/k_exp.c" + "${PROJECT_SRC}/src/k_expf.c" + "${PROJECT_SRC}/src/k_rem_pio2.c" + "${PROJECT_SRC}/src/k_sin.c" + "${PROJECT_SRC}/src/k_tan.c" + "${PROJECT_SRC}/src/k_cosf.c" + "${PROJECT_SRC}/src/k_sinf.c" + "${PROJECT_SRC}/src/k_tanf.c" + "${PROJECT_SRC}/src/s_asinh.c" + "${PROJECT_SRC}/src/s_asinhf.c" + "${PROJECT_SRC}/src/s_atan.c" + "${PROJECT_SRC}/src/s_atanf.c" + "${PROJECT_SRC}/src/s_carg.c" + "${PROJECT_SRC}/src/s_cargf.c" + "${PROJECT_SRC}/src/s_cbrt.c" + "${PROJECT_SRC}/src/s_cbrtf.c" + "${PROJECT_SRC}/src/s_ceil.c" + "${PROJECT_SRC}/src/s_ceilf.c" + "${PROJECT_SRC}/src/s_copysign.c" + "${PROJECT_SRC}/src/s_copysignf.c" + "${PROJECT_SRC}/src/s_cos.c" + "${PROJECT_SRC}/src/s_cosf.c" + "${PROJECT_SRC}/src/s_csqrt.c" + "${PROJECT_SRC}/src/s_csqrtf.c" + "${PROJECT_SRC}/src/s_erf.c" + "${PROJECT_SRC}/src/s_erff.c" + "${PROJECT_SRC}/src/s_exp2.c" + "${PROJECT_SRC}/src/s_exp2f.c" + "${PROJECT_SRC}/src/s_expm1.c" + "${PROJECT_SRC}/src/s_expm1f.c" + "${PROJECT_SRC}/src/s_fabs.c" + "${PROJECT_SRC}/src/s_fabsf.c" + "${PROJECT_SRC}/src/s_fdim.c" + "${PROJECT_SRC}/src/s_floor.c" + "${PROJECT_SRC}/src/s_floorf.c" + "${PROJECT_SRC}/src/s_fmax.c" + "${PROJECT_SRC}/src/s_fmaxf.c" + "${PROJECT_SRC}/src/s_fmin.c" + "${PROJECT_SRC}/src/s_fminf.c" + "${PROJECT_SRC}/src/s_fpclassify.c" + "${PROJECT_SRC}/src/s_frexp.c" + "${PROJECT_SRC}/src/s_frexpf.c" + "${PROJECT_SRC}/src/s_ilogb.c" + "${PROJECT_SRC}/src/s_ilogbf.c" + "${PROJECT_SRC}/src/s_isinf.c" + "${PROJECT_SRC}/src/s_isfinite.c" + "${PROJECT_SRC}/src/s_isnormal.c" + "${PROJECT_SRC}/src/s_isnan.c" + "${PROJECT_SRC}/src/s_log1p.c" + "${PROJECT_SRC}/src/s_log1pf.c" + "${PROJECT_SRC}/src/s_logb.c" + "${PROJECT_SRC}/src/s_logbf.c" + "${PROJECT_SRC}/src/s_modf.c" + "${PROJECT_SRC}/src/s_modff.c" + "${PROJECT_SRC}/src/s_nextafter.c" + "${PROJECT_SRC}/src/s_nextafterf.c" + "${PROJECT_SRC}/src/s_nexttowardf.c" + "${PROJECT_SRC}/src/s_remquo.c" + "${PROJECT_SRC}/src/s_remquof.c" + "${PROJECT_SRC}/src/s_rint.c" + "${PROJECT_SRC}/src/s_rintf.c" + "${PROJECT_SRC}/src/s_round.c" + "${PROJECT_SRC}/src/s_roundf.c" + "${PROJECT_SRC}/src/s_scalbln.c" + "${PROJECT_SRC}/src/s_scalbn.c" + "${PROJECT_SRC}/src/s_scalbnf.c" + "${PROJECT_SRC}/src/s_signbit.c" + "${PROJECT_SRC}/src/s_signgam.c" + "${PROJECT_SRC}/src/s_sin.c" + "${PROJECT_SRC}/src/s_sincos.c" + "${PROJECT_SRC}/src/s_sinf.c" + "${PROJECT_SRC}/src/s_sincosf.c" + "${PROJECT_SRC}/src/s_tan.c" + "${PROJECT_SRC}/src/s_tanf.c" + "${PROJECT_SRC}/src/s_tanh.c" + "${PROJECT_SRC}/src/s_tanhf.c" + "${PROJECT_SRC}/src/s_tgammaf.c" + "${PROJECT_SRC}/src/s_trunc.c" + "${PROJECT_SRC}/src/s_truncf.c" + "${PROJECT_SRC}/src/s_cpow.c" + "${PROJECT_SRC}/src/s_cpowf.c" + "${PROJECT_SRC}/src/w_cabs.c" + "${PROJECT_SRC}/src/w_cabsf.c" + + "${PROJECT_SRC}/src/s_fma.c" + "${PROJECT_SRC}/src/s_fmaf.c" + "${PROJECT_SRC}/src/s_lrint.c" + "${PROJECT_SRC}/src/s_lrintf.c" + "${PROJECT_SRC}/src/s_lround.c" + "${PROJECT_SRC}/src/s_lroundf.c" + "${PROJECT_SRC}/src/s_llrint.c" + "${PROJECT_SRC}/src/s_llrintf.c" + "${PROJECT_SRC}/src/s_llround.c" + "${PROJECT_SRC}/src/s_llroundf.c" + "${PROJECT_SRC}/src/s_nearbyint.c" + + # C99 complex functions + "${PROJECT_SRC}/src/s_ccosh.c" + "${PROJECT_SRC}/src/s_ccoshf.c" + "${PROJECT_SRC}/src/s_cexp.c" + "${PROJECT_SRC}/src/s_cexpf.c" + "${PROJECT_SRC}/src/s_cimag.c" + "${PROJECT_SRC}/src/s_cimagf.c" + "${PROJECT_SRC}/src/s_conj.c" + "${PROJECT_SRC}/src/s_conjf.c" + "${PROJECT_SRC}/src/s_cproj.c" + "${PROJECT_SRC}/src/s_cprojf.c" + "${PROJECT_SRC}/src/s_creal.c" + "${PROJECT_SRC}/src/s_crealf.c" + "${PROJECT_SRC}/src/s_csinh.c" + "${PROJECT_SRC}/src/s_csinhf.c" + "${PROJECT_SRC}/src/s_ctanh.c" + "${PROJECT_SRC}/src/s_ctanhf.c" + "${PROJECT_SRC}/src/s_cacos.c" + "${PROJECT_SRC}/src/s_cacosf.c" + "${PROJECT_SRC}/src/s_cacosh.c" + "${PROJECT_SRC}/src/s_cacoshf.c" + "${PROJECT_SRC}/src/s_casin.c" + "${PROJECT_SRC}/src/s_casinf.c" + "${PROJECT_SRC}/src/s_casinh.c" + "${PROJECT_SRC}/src/s_casinhf.c" + "${PROJECT_SRC}/src/s_catan.c" + "${PROJECT_SRC}/src/s_catanf.c" + "${PROJECT_SRC}/src/s_catanh.c" + "${PROJECT_SRC}/src/s_catanhf.c" + "${PROJECT_SRC}/src/s_clog.c" + "${PROJECT_SRC}/src/s_clogf.c" + + # bsdsrc + "${PROJECT_SRC}/bsdsrc/b_exp.c" + "${PROJECT_SRC}/bsdsrc/b_log.c" + "${PROJECT_SRC}/bsdsrc/b_tgamma.c" +) + +if(NOT ${CMAKE_SYSTEM_NAME} STREQUAL "Windows") + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/src/s_nan.c" + ) +endif() + +# Determine if long double and double are the same size +include(CheckCSourceCompiles) +check_c_source_compiles(" +#include +#if (LDBL_MANT_DIG == DBL_MANT_DIG) +#error \"long double and double are the same size\" +#endif +int main(void ) { return 0; } +" LONG_DOUBLE_NOT_DOUBLE) + +# Add in long double functions for x86, x64 and aarch64 +if(LONG_DOUBLE_NOT_DOUBLE) + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/src/s_copysignl.c" + "${PROJECT_SRC}/src/s_fabsl.c" + "${PROJECT_SRC}/src/s_llrintl.c" + "${PROJECT_SRC}/src/s_lrintl.c" + "${PROJECT_SRC}/src/s_modfl.c" + + "${PROJECT_SRC}/src/e_acosl.c" + "${PROJECT_SRC}/src/e_asinl.c" + "${PROJECT_SRC}/src/e_atan2l.c" + "${PROJECT_SRC}/src/e_fmodl.c" + "${PROJECT_SRC}/src/s_fmaxl.c" + "${PROJECT_SRC}/src/s_fminl.c" + "${PROJECT_SRC}/src/s_ilogbl.c" + "${PROJECT_SRC}/src/e_hypotl.c" + "${PROJECT_SRC}/src/e_lgammal.c" + "${PROJECT_SRC}/src/e_remainderl.c" + "${PROJECT_SRC}/src/e_sqrtl.c" + "${PROJECT_SRC}/src/s_atanl.c" + "${PROJECT_SRC}/src/s_ceill.c" + "${PROJECT_SRC}/src/s_cosl.c" + "${PROJECT_SRC}/src/s_cprojl.c" + "${PROJECT_SRC}/src/s_csqrtl.c" + "${PROJECT_SRC}/src/s_floorl.c" + "${PROJECT_SRC}/src/s_fmal.c" + "${PROJECT_SRC}/src/s_frexpl.c" + "${PROJECT_SRC}/src/s_logbl.c" + "${PROJECT_SRC}/src/s_nexttoward.c" + "${PROJECT_SRC}/src/s_remquol.c" + "${PROJECT_SRC}/src/s_roundl.c" + "${PROJECT_SRC}/src/s_lroundl.c" + "${PROJECT_SRC}/src/s_llroundl.c" + "${PROJECT_SRC}/src/s_cpowl.c" + "${PROJECT_SRC}/src/s_cargl.c" + "${PROJECT_SRC}/src/s_sinl.c" + "${PROJECT_SRC}/src/s_sincosl.c" + "${PROJECT_SRC}/src/s_tanl.c" + "${PROJECT_SRC}/src/s_truncl.c" + "${PROJECT_SRC}/src/w_cabsl.c" + "${PROJECT_SRC}/src/s_nextafterl.c" + "${PROJECT_SRC}/src/s_rintl.c" + "${PROJECT_SRC}/src/s_scalbnl.c" + "${PROJECT_SRC}/src/polevll.c" + "${PROJECT_SRC}/src/s_casinl.c" + "${PROJECT_SRC}/src/s_ctanl.c" + "${PROJECT_SRC}/src/s_cimagl.c" + "${PROJECT_SRC}/src/s_conjl.c" + "${PROJECT_SRC}/src/s_creall.c" + "${PROJECT_SRC}/src/s_cacoshl.c" + "${PROJECT_SRC}/src/s_catanhl.c" + "${PROJECT_SRC}/src/s_casinhl.c" + "${PROJECT_SRC}/src/s_catanl.c" + "${PROJECT_SRC}/src/s_csinl.c" + "${PROJECT_SRC}/src/s_cacosl.c" + "${PROJECT_SRC}/src/s_cexpl.c" + "${PROJECT_SRC}/src/s_csinhl.c" + "${PROJECT_SRC}/src/s_ccoshl.c" + "${PROJECT_SRC}/src/s_clogl.c" + "${PROJECT_SRC}/src/s_ctanhl.c" + "${PROJECT_SRC}/src/s_ccosl.c" + "${PROJECT_SRC}/src/s_cbrtl.c" + ) +endif() + +if (LONG_DOUBLE_NOT_DOUBLE) + if (${OPENLIBM_ARCH_FOLDER} STREQUAL "i387" OR ${OPENLIBM_ARCH_FOLDER} STREQUAL "amd64") + list(APPEND OPENLIBM_C_SOURCE + # ld80 + "${PROJECT_SRC}/ld80/invtrig.c" + "${PROJECT_SRC}/ld80/e_acoshl.c" + "${PROJECT_SRC}/ld80/e_powl.c" + "${PROJECT_SRC}/ld80/k_tanl.c" + "${PROJECT_SRC}/ld80/s_exp2l.c" + "${PROJECT_SRC}/ld80/e_atanhl.c" + "${PROJECT_SRC}/ld80/e_lgammal_r.c" + "${PROJECT_SRC}/ld80/e_sinhl.c" + "${PROJECT_SRC}/ld80/s_asinhl.c" + "${PROJECT_SRC}/ld80/s_expm1l.c" + "${PROJECT_SRC}/ld80/e_coshl.c" + "${PROJECT_SRC}/ld80/e_log10l.c" + "${PROJECT_SRC}/ld80/e_tgammal.c" + "${PROJECT_SRC}/ld80/e_expl.c" + "${PROJECT_SRC}/ld80/e_log2l.c" + "${PROJECT_SRC}/ld80/k_cosl.c" + "${PROJECT_SRC}/ld80/s_log1pl.c" + "${PROJECT_SRC}/ld80/s_tanhl.c" + "${PROJECT_SRC}/ld80/e_logl.c" + "${PROJECT_SRC}/ld80/k_sinl.c" + "${PROJECT_SRC}/ld80/s_erfl.c" + ) + + if(NOT ${CMAKE_SYSTEM_NAME} STREQUAL "Windows") + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/ld80/s_nanl.c" + ) + endif() + else() + if(${OPENLIBM_ARCH_FOLDER} STREQUAL "aarch64") + list(APPEND OPENLIBM_C_SOURCE + # ld128 + "${PROJECT_SRC}/ld128/invtrig.c" + "${PROJECT_SRC}/ld128/e_acoshl.c" + "${PROJECT_SRC}/ld128/e_powl.c" + "${PROJECT_SRC}/ld128/k_tanl.c" + "${PROJECT_SRC}/ld128/s_exp2l.c" + "${PROJECT_SRC}/ld128/e_atanhl.c" + "${PROJECT_SRC}/ld128/e_lgammal_r.c" + "${PROJECT_SRC}/ld128/e_sinhl.c" + "${PROJECT_SRC}/ld128/s_asinhl.c" + "${PROJECT_SRC}/ld128/s_expm1l.c" + "${PROJECT_SRC}/ld128/e_coshl.c" + "${PROJECT_SRC}/ld128/e_log10l.c" + "${PROJECT_SRC}/ld128/e_tgammal.c" + "${PROJECT_SRC}/ld128/e_expl.c" + "${PROJECT_SRC}/ld128/e_log2l.c" + "${PROJECT_SRC}/ld128/k_cosl.c" + "${PROJECT_SRC}/ld128/s_log1pl.c" + "${PROJECT_SRC}/ld128/s_tanhl.c" + "${PROJECT_SRC}/ld128/e_logl.c" + "${PROJECT_SRC}/ld128/k_sinl.c" + "${PROJECT_SRC}/ld128/s_erfl.c" + ) + + if(NOT ${CMAKE_SYSTEM_NAME} STREQUAL "Windows") + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/ld128/s_nanl.c" + ) + endif() + endif() + endif() +endif() + +# Architecture-specific sources +if (${OPENLIBM_ARCH_FOLDER} STREQUAL "amd64") + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/amd64/fenv.c" + ) + + list(APPEND OPENLIBM_ASM_SOURCE + "${PROJECT_SRC}/amd64/e_remainder.S" + "${PROJECT_SRC}/amd64/e_remainderf.S" + "${PROJECT_SRC}/amd64/e_remainderl.S" + "${PROJECT_SRC}/amd64/e_sqrt.S" + "${PROJECT_SRC}/amd64/e_sqrtf.S" + "${PROJECT_SRC}/amd64/e_sqrtl.S" + "${PROJECT_SRC}/amd64/s_llrint.S" + "${PROJECT_SRC}/amd64/s_llrintf.S" + "${PROJECT_SRC}/amd64/s_llrintl.S" + "${PROJECT_SRC}/amd64/s_logbl.S" + "${PROJECT_SRC}/amd64/s_lrint.S" + "${PROJECT_SRC}/amd64/s_lrintf.S" + "${PROJECT_SRC}/amd64/s_lrintl.S" + "${PROJECT_SRC}/amd64/s_remquo.S" + "${PROJECT_SRC}/amd64/s_remquof.S" + "${PROJECT_SRC}/amd64/s_remquol.S" + "${PROJECT_SRC}/amd64/s_rintl.S" + "${PROJECT_SRC}/amd64/s_scalbn.S" + "${PROJECT_SRC}/amd64/s_scalbnf.S" + "${PROJECT_SRC}/amd64/s_scalbnl.S" + "${PROJECT_SRC}/amd64/e_fmod.S" + "${PROJECT_SRC}/amd64/e_fmodf.S" + "${PROJECT_SRC}/amd64/e_fmodl.S" + ) + +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "aarch64") + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/aarch64/fenv.c" + ) + +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "arm") + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/${OPENLIBM_ARCH_FOLDER}/fenv.c" + ) + +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "i387") + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/i387/fenv.c" + ) + + list(APPEND OPENLIBM_ASM_SOURCE + "${PROJECT_SRC}/i387/e_exp.S" + "${PROJECT_SRC}/i387/e_fmod.S" + "${PROJECT_SRC}/i387/e_log.S" + "${PROJECT_SRC}/i387/e_log10.S" + "${PROJECT_SRC}/i387/e_remainder.S" + "${PROJECT_SRC}/i387/e_sqrt.S" + "${PROJECT_SRC}/i387/s_ceil.S" + "${PROJECT_SRC}/i387/s_copysign.S" + "${PROJECT_SRC}/i387/s_floor.S" + "${PROJECT_SRC}/i387/s_llrint.S" + "${PROJECT_SRC}/i387/s_logb.S" + "${PROJECT_SRC}/i387/s_lrint.S" + "${PROJECT_SRC}/i387/s_remquo.S" + "${PROJECT_SRC}/i387/s_rint.S" + "${PROJECT_SRC}/i387/s_tan.S" + "${PROJECT_SRC}/i387/s_trunc.S" + + # float counterparts + "${PROJECT_SRC}/i387/e_log10f.S" + "${PROJECT_SRC}/i387/e_logf.S" + "${PROJECT_SRC}/i387/e_remainderf.S" + "${PROJECT_SRC}/i387/e_sqrtf.S" + "${PROJECT_SRC}/i387/s_ceilf.S" + "${PROJECT_SRC}/i387/s_copysignf.S" + "${PROJECT_SRC}/i387/s_floorf.S" + "${PROJECT_SRC}/i387/s_llrintf.S" + "${PROJECT_SRC}/i387/s_logbf.S" + "${PROJECT_SRC}/i387/s_lrintf.S" + "${PROJECT_SRC}/i387/s_remquof.S" + "${PROJECT_SRC}/i387/s_rintf.S" + "${PROJECT_SRC}/i387/s_truncf.S" + + # long double counterparts + "${PROJECT_SRC}/i387/e_remainderl.S" + "${PROJECT_SRC}/i387/e_sqrtl.S" + "${PROJECT_SRC}/i387/s_ceill.S" + "${PROJECT_SRC}/i387/s_copysignl.S" + "${PROJECT_SRC}/i387/s_floorl.S" + "${PROJECT_SRC}/i387/s_llrintl.S" + "${PROJECT_SRC}/i387/s_logbl.S" + "${PROJECT_SRC}/i387/s_lrintl.S" + "${PROJECT_SRC}/i387/s_remquol.S" + "${PROJECT_SRC}/i387/s_rintl.S" + "${PROJECT_SRC}/i387/s_truncl.S" + ) + + if(NOT ${CMAKE_SYSTEM_NAME} STREQUAL "Windows") + list(APPEND OPENLIBM_ASM_SOURCE + "${PROJECT_SRC}/i387/s_scalbn.S" + "${PROJECT_SRC}/i387/s_scalbnf.S" + "${PROJECT_SRC}/i387/s_scalbnl.S" + ) + endif() + +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "powerpc") + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/powerpc/fenv.c" + ) +elseif(${OPENLIBM_ARCH_FOLDER} STREQUAL "riscv64") + list(APPEND OPENLIBM_C_SOURCE + "${PROJECT_SRC}/riscv64/fenv.c") +else() + message(FATAL_ERROR "${PROJECT_NAME} CMake build is not set up for ${OPENLIBM_ARCH_FOLDER}") +endif() + + +# Filter out C implementation from compilation list if a native implementation exists +foreach(FILE_TO_REMOVE ${OPENLIBM_ASM_SOURCE}) + # Get filename and strip out extension + cmake_path(GET FILE_TO_REMOVE FILENAME FILENAME_TO_REMOVE) + cmake_path(REMOVE_EXTENSION FILENAME_TO_REMOVE OUTPUT_VARIABLE FILENAME_TO_REMOVE) + message(DEBUG "Filename to remove: ${FILENAME_TO_REMOVE}") + + # Go through files and remove one with the same name + foreach(CUR_FILE ${OPENLIBM_C_SOURCE}) + cmake_path(GET CUR_FILE FILENAME CUR_FILENAME) + cmake_path(REMOVE_EXTENSION CUR_FILENAME OUTPUT_VARIABLE CUR_FILENAME) + + if(${CUR_FILENAME} STREQUAL ${FILENAME_TO_REMOVE}) + list(REMOVE_ITEM OPENLIBM_C_SOURCE ${CUR_FILE}) + message(DEBUG "Removed source file from compilation list: ${CUR_FILE}") + break() + endif() + endforeach() +endforeach() + + +# Add sources +target_sources("${PROJECT_NAME}" PRIVATE ${OPENLIBM_C_SOURCE} + ${OPENLIBM_ASM_SOURCE} +) + + +# Include directories +list(APPEND OPENLIBM_INCLUDE_DIRS + "${PROJECT_SRC}" + "${PROJECT_SRC}/include" + "${PROJECT_SRC}/${OPENLIBM_ARCH_FOLDER}" + "${PROJECT_SRC}/src" +) + +if(${OPENLIBM_ARCH_FOLDER} STREQUAL "i387" OR ${OPENLIBM_ARCH_FOLDER} STREQUAL "amd64" OR ${OPENLIBM_ARCH_FOLDER} STREQUAL "powerpc") + list(APPEND OPENLIBM_INCLUDE_DIRS "${PROJECT_SRC}/ld80") +else() + if(${OPENLIBM_ARCH_FOLDER} STREQUAL "aarch64" OR ${OPENLIBM_ARCH_FOLDER} STREQUAL "riscv64") + list(APPEND OPENLIBM_INCLUDE_DIRS "${PROJECT_SRC}/ld128") + endif() +endif() + +target_include_directories("${PROJECT_NAME}" PUBLIC ${OPENLIBM_INCLUDE_DIRS}) + +file(GLOB PUBLIC_HEADERS "*.h" "include/*.h" "${OPENLIBM_ARCH_FOLDER}/*.h" "src/*.h") +set_target_properties("${PROJECT_NAME}" PROPERTIES PUBLIC_HEADER "${PUBLIC_HEADERS}") +install (TARGETS "${PROJECT_NAME}") + +# Can't use configure_file because openlibm.pc.in uses $var instead of CMake configure @var's +# Would rather string replace variables here instead of editing .pc.in, because editing .pc.in +# might build break autotools build. +file(READ "${PROJECT_SRC}/openlibm.pc.in" PC_FILE) +string(REPLACE "\${version}" ${CMAKE_PROJECT_VERSION} PC_FILE ${PC_FILE}) +string(PREPEND PC_FILE "prefix=${CMAKE_INSTALL_PREFIX} +includedir=\${prefix}/${CMAKE_INSTALL_INCLUDEDIR} +libdir=\${prefix}/${CMAKE_INSTALL_LIBDIR}\n +") +file(WRITE "${CMAKE_BINARY_DIR}/${PROJECT_NAME}.pc" ${PC_FILE}) +install(FILES "${CMAKE_BINARY_DIR}/${PROJECT_NAME}.pc" + DESTINATION "${CMAKE_INSTALL_LIBDIR}/pkgconfig") diff --git a/openlibm/LICENSE.md b/openlibm/LICENSE.md new file mode 100644 index 0000000..d76019e --- /dev/null +++ b/openlibm/LICENSE.md @@ -0,0 +1,115 @@ +## OpenLibm + +OpenLibm contains code that is covered by various licenses. + +The OpenLibm code derives from the FreeBSD msun and OpenBSD libm +implementations, which in turn derives from FDLIBM 5.3. As a result, it +has a number of fixes and updates that have accumulated over the years +in msun, and also optimized assembly versions of many functions. These +improvements are provided under the BSD and ISC licenses. The msun +library also includes work placed under the public domain, which is +noted in the individual files. Further work on making a standalone +OpenLibm library from msun, as part of the Julia project is covered +under the MIT license. The test files, test-double.c and test-float.c +are under the LGPL. + +## Parts copyrighted by the Julia project (MIT License) + +> Copyright (c) 2011-14 The Julia Project. +> https://github.com/JuliaMath/openlibm/graphs/contributors +> +> Permission is hereby granted, free of charge, to any person obtaining +> a copy of this software and associated documentation files (the +> "Software"), to deal in the Software without restriction, including +> without limitation the rights to use, copy, modify, merge, publish, +> distribute, sublicense, and/or sell copies of the Software, and to +> permit persons to whom the Software is furnished to do so, subject to +> the following conditions: +> +> The above copyright notice and this permission notice shall be +> included in all copies or substantial portions of the Software. +> +> THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +> EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +> MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +> NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE +> LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION +> OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION +> WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + +## Parts copyrighted by Stephen L. Moshier (ISC License) + +> Copyright (c) 2008 Stephen L. Moshier +> +> Permission to use, copy, modify, and distribute this software for any +> purpose with or without fee is hereby granted, provided that the above +> copyright notice and this permission notice appear in all copies. +> +> THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES +> WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF +> MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR +> ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES +> WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN +> ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF +> OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + +## FREEBSD MSUN (FreeBSD/2-clause BSD/Simplified BSD License) + +> Copyright 1992-2011 The FreeBSD Project. All rights reserved. +> +> Redistribution and use in source and binary forms, with or without +> modification, are permitted provided that the following conditions are +> met: +> +> 1. Redistributions of source code must retain the above copyright +> notice, this list of conditions and the following disclaimer. +> +> 2. Redistributions in binary form must reproduce the above copyright +> notice, this list of conditions and the following disclaimer in the +> documentation and/or other materials provided with the distribution. +> THIS SOFTWARE IS PROVIDED BY THE FREEBSD PROJECT ``AS IS'' AND ANY +> EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +> IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +> PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FREEBSD PROJECT OR +> CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +> EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +> PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +> PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +> LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +> NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +> SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +> +> The views and conclusions contained in the software and documentation +> are those of the authors and should not be interpreted as representing +> official policies, either expressed or implied, of the FreeBSD +> Project. + +## FDLIBM + +> Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. +> +> Developed at SunPro, a Sun Microsystems, Inc. business. +> Permission to use, copy, modify, and distribute this +> software is freely granted, provided that this notice +> is preserved. + +## Tests + +> Copyright (C) 1997, 1999 Free Software Foundation, Inc. +> This file is part of the GNU C Library. +> Contributed by Andreas Jaeger , 1997. +> +> The GNU C Library is free software; you can redistribute it and/or +> modify it under the terms of the GNU Lesser General Public +> License as published by the Free Software Foundation; either +> version 2.1 of the License, or (at your option) any later version. +> +> The GNU C Library is distributed in the hope that it will be useful, +> but WITHOUT ANY WARRANTY; without even the implied warranty of +> MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +> Lesser General Public License for more details. +> +> You should have received a copy of the GNU Lesser General Public +> License along with the GNU C Library; if not, write to the Free +> Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA +> 02111-1307 USA. diff --git a/openlibm/Make.inc b/openlibm/Make.inc new file mode 100644 index 0000000..df8fbf0 --- /dev/null +++ b/openlibm/Make.inc @@ -0,0 +1,190 @@ +# -*- mode: makefile-gmake -*- + +# Default build rule for any Makefile in this project: all +default: all + +OS := $(shell uname) +# Do not forget to bump SOMINOR when changing VERSION, +# and SOMAJOR when breaking ABI in a backward-incompatible way +VERSION = 0.8.0 +SOMAJOR = 4 +SOMINOR = 0 +DESTDIR = +prefix ?= /usr/local +bindir ?= $(prefix)/bin +libdir ?= $(prefix)/lib +includedir ?= $(prefix)/include + +ifeq ($(OS), FreeBSD) +pkgconfigdir ?= $(prefix)/libdata/pkgconfig +else +pkgconfigdir ?= $(libdir)/pkgconfig +endif + +# Build with Code Coverage +# Only test with Ubuntu + gcc + lcov, may not work for other platform. +# deps: https://github.com/linux-test-project/lcov +# You don't need to set this flag manually, `make coverage` will do it for you. +# Just Run: make clean && make coverage -j +CODE_COVERAGE ?= 0 + +USEGCC ?= 1 +USECLANG ?= 0 +TOOLPREFIX ?= + +ifneq (,$(findstring $(OS),Darwin FreeBSD OpenBSD)) +USEGCC ?= 0 +USECLANG ?= 1 +endif + +ifeq ($(ARCH),wasm32) +USECLANG = 1 +USEGCC = 0 +TOOLPREFIX = llvm- +endif + +AR := $(TOOLPREFIX)ar + +ifeq ($(USECLANG),1) +USEGCC ?= 0 +CC = clang +CFLAGS_add += -fno-builtin -fno-strict-aliasing +endif + +ifeq ($(USEGCC),1) +CC := $(TOOLPREFIX)gcc +CFLAGS_add += -fno-gnu89-inline -fno-builtin +endif + +ARCH ?= $(shell $(CC) -dumpmachine | sed "s/\([^-]*\).*$$/\1/") + +ifeq ($(ARCH),mingw32) +$(error "the mingw32 compiler you are using fails the openblas testsuite. please see the Julia README.windows.md document for a replacement") +endif + +# OS-specific stuff +ifeq ($(ARCH),arm64) +override ARCH := aarch64 +endif +ifeq ($(findstring arm,$(ARCH)),arm) +override ARCH := arm +MARCH ?= armv7-a+fp +CFLAGS_add += -mhard-float +endif +ifeq ($(findstring powerpc,$(ARCH)),powerpc) +override ARCH := powerpc +endif +ifeq ($(findstring ppc,$(ARCH)),ppc) +override ARCH := powerpc +endif +ifeq ($(findstring s390,$(ARCH)),s390) +override ARCH := s390 +endif +ifneq ($(filter $(ARCH),i386 i486 i586 i686 i387 i487 i587 i687),) +override ARCH := i387 +MARCH ?= i686 +endif +ifeq ($(ARCH),x86_64) +override ARCH := amd64 +endif +ifeq ($(findstring mips,$(ARCH)),mips) +override ARCH := mips +endif +ifeq ($(findstring riscv64,$(ARCH)),riscv64) +override ARCH := riscv64 +endif +ifeq ($(findstring loongarch64,$(ARCH)),loongarch64) +override ARCH := loongarch64 +endif + +# If CFLAGS does not contain a -O optimization flag, default to -O3 +ifeq ($(findstring -O,$(CFLAGS)),) +CFLAGS_add += -O3 +endif + +ifneq (,$(findstring MINGW,$(OS))) +override OS=WINNT +endif + +#keep these if statements separate +ifeq ($(OS), WINNT) +SHLIB_EXT = dll +SONAME_FLAG = +shlibdir = $(bindir) +else +ifeq ($(OS), Darwin) +SHLIB_EXT = dylib +SONAME_FLAG = -install_name +else +SHLIB_EXT = so +SONAME_FLAG = -soname +endif +CFLAGS_add += -fPIC +shlibdir = $(libdir) +endif + +# Add `-march` to our CFLAGS if it's defined +ifneq ($(MARCH),) +CFLAGS_arch += -march=$(MARCH) +endif + +ifeq ($(ARCH),i387) +CFLAGS_arch += -m32 +SFLAGS_arch += -m32 +LDFLAGS_arch += -m32 +endif + +ifeq ($(ARCH),amd64) +CFLAGS_arch += -m64 +SFLAGS_arch += -m64 +LDFLAGS_arch += -m64 +endif + +ifeq ($(ARCH),wasm32) +CFLAGS_arch += -ffreestanding -nostdlib -nostdinc --target=wasm32-unknown-unknown +endif + +# Add our "arch"-related FLAGS in. We separate arch-related flags out so that +# we can conveniently get at them for targets that don't want the rest of +# *FLAGS_add, such as the testing Makefile targets +CFLAGS_add += $(CFLAGS_arch) +SFLAGS_add += $(SFLAGS_arch) +LDFLAGS_add += $(LDFLAGS_arch) + +CFLAGS_add += -std=c99 -Wall -I$(OPENLIBM_HOME) -I$(OPENLIBM_HOME)/include -I$(OPENLIBM_HOME)/$(ARCH) -I$(OPENLIBM_HOME)/src -DASSEMBLER -D__BSD_VISIBLE -Wno-implicit-function-declaration +ifneq ($(filter $(ARCH),i387 amd64 powerpc),) +CFLAGS_add += -I$(OPENLIBM_HOME)/ld80 +else +ifneq ($(filter $(ARCH),aarch64 riscv64),) +CFLAGS_add += -I$(OPENLIBM_HOME)/ld128 +endif +endif + +ifneq ($(filter $(ARCH),i387 amd64),) +# Determines whether `long double` is the same as `double` on this arch. +# linux x86_64, for instance, `long double` is 80 bits wide, whereas on macOS aarch64, +# `long double` is the same as `double`. +LONG_DOUBLE_NOT_DOUBLE := 1 +else ifeq ($(ARCH), aarch64 riscv64) +ifeq ($(filter $(OS),Darwin WINNT),) +LONG_DOUBLE_NOT_DOUBLE := 1 +endif +endif + +ifeq ($(CODE_COVERAGE),1) +CFLAGS_add += -g -O0 --coverage +LDFLAGS_add += --coverage +endif # CODE_COVERAGE==1 + + +%.c.o: %.c + $(CC) $(CPPFLAGS) $(CFLAGS) $(CFLAGS_add) -c $< -o $@ + +%.S.o: %.S + $(CC) $(CPPFLAGS) $(SFLAGS) $(SFLAGS_add) $(filter -m% -B% -I% -D%,$(CFLAGS_add)) -c $< -o $@ + + +# Makefile debugging trick: +# call print-VARIABLE to see the runtime value of any variable +print-%: + @echo '$*=$($*)' diff --git a/openlibm/Makefile b/openlibm/Makefile new file mode 100644 index 0000000..17e03a0 --- /dev/null +++ b/openlibm/Makefile @@ -0,0 +1,137 @@ +OPENLIBM_HOME=$(abspath .) +include ./Make.inc + +SUBDIRS = src $(ARCH) bsdsrc +ifeq ($(LONG_DOUBLE_NOT_DOUBLE),1) +# Add ld80 directory on x86 and x64 +ifneq ($(filter $(ARCH),i387 amd64),) +SUBDIRS += ld80 +else +ifneq ($(filter $(ARCH),aarch64),) +SUBDIRS += ld128 +else +endif +endif +endif + +define INC_template +TEST=test +override CUR_SRCS = $(1)_SRCS +include $(1)/Make.files +SRCS += $$(addprefix $(1)/,$$($(1)_SRCS)) +endef + +DIR=test + +$(foreach dir,$(SUBDIRS),$(eval $(call INC_template,$(dir)))) + +DUPLICATE_NAMES = $(filter $(patsubst %.S,%,$($(ARCH)_SRCS)),$(patsubst %.c,%,$(src_SRCS))) +DUPLICATE_SRCS = $(addsuffix .c,$(DUPLICATE_NAMES)) + +OBJS = $(patsubst %.f,%.f.o,\ + $(patsubst %.S,%.S.o,\ + $(patsubst %.c,%.c.o,$(filter-out $(addprefix src/,$(DUPLICATE_SRCS)),$(SRCS))))) + +# If we're on windows, don't do versioned shared libraries. Also, generate an import library +# for the DLL. If we're on OSX, put the version number before the .dylib. Otherwise, +# put it after. +ifeq ($(OS), WINNT) +OLM_MAJOR_MINOR_SHLIB_EXT := $(SHLIB_EXT) +LDFLAGS_add += -Wl,--out-implib,libopenlibm.$(OLM_MAJOR_MINOR_SHLIB_EXT).a +else +ifeq ($(OS), Darwin) +OLM_MAJOR_MINOR_SHLIB_EXT := $(SOMAJOR).$(SOMINOR).$(SHLIB_EXT) +OLM_MAJOR_SHLIB_EXT := $(SOMAJOR).$(SHLIB_EXT) +else +OLM_MAJOR_MINOR_SHLIB_EXT := $(SHLIB_EXT).$(SOMAJOR).$(SOMINOR) +OLM_MAJOR_SHLIB_EXT := $(SHLIB_EXT).$(SOMAJOR) +endif +LDFLAGS_add += -Wl,$(SONAME_FLAG),libopenlibm.$(OLM_MAJOR_SHLIB_EXT) +endif + +.PHONY: all check test clean distclean \ + install install-static install-shared install-pkgconfig install-headers + + +OLM_LIBS := libopenlibm.a +ifneq ($(ARCH), wasm32) +OLM_LIBS += libopenlibm.$(OLM_MAJOR_MINOR_SHLIB_EXT) +endif + +all : $(OLM_LIBS) + +check test: test/test-double test/test-float + test/test-double + test/test-float + +libopenlibm.a: $(OBJS) + $(AR) -rcs libopenlibm.a $(OBJS) + +libopenlibm.$(OLM_MAJOR_MINOR_SHLIB_EXT): $(OBJS) + $(CC) -shared $(OBJS) $(LDFLAGS) $(LDFLAGS_add) -o $@ +ifneq ($(OS),WINNT) + ln -sf $@ libopenlibm.$(OLM_MAJOR_SHLIB_EXT) + ln -sf $@ libopenlibm.$(SHLIB_EXT) +endif + +test/test-double: libopenlibm.$(OLM_MAJOR_MINOR_SHLIB_EXT) + $(MAKE) -C test test-double + +test/test-float: libopenlibm.$(OLM_MAJOR_MINOR_SHLIB_EXT) + $(MAKE) -C test test-float + +COVERAGE_DIR:=cov-html +COVERAGE_FILE:=$(COVERAGE_DIR)/libopenlibm.info +# Gen cov report with: make clean && make coverage -j +coverage: clean-coverage + mkdir $(COVERAGE_DIR) + $(MAKE) test CODE_COVERAGE=1 + lcov -d amd64 -d bsdsrc -d ld80 -d src \ + --rc lcov_branch_coverage=1 --capture --output-file $(COVERAGE_FILE) + genhtml --legend --branch-coverage \ + --title "Openlibm commit `git rev-parse HEAD`" \ + --output-directory $(COVERAGE_DIR)/ \ + $(COVERAGE_FILE) + +# Zero coverage statistics and Delete report +clean-coverage: + -lcov -d amd64 -d bsdsrc -d ld80 -d src --zerocounters + rm -f ./*/*.gcda + rm -rf $(COVERAGE_DIR)/ + +clean: clean-coverage + rm -f aarch64/*.o amd64/*.o arm/*.o bsdsrc/*.o i387/*.o loongarch64/*.o ld80/*.o ld128/*.o src/*.o powerpc/*.o mips/*.o s390/*.o riscv64/*.o + rm -f libopenlibm.a libopenlibm.*$(SHLIB_EXT)* + rm -f ./*/*.gcno + $(MAKE) -C test clean + +openlibm.pc: openlibm.pc.in Make.inc Makefile + echo "version=${VERSION}" > openlibm.pc + echo "libdir=$(DESTDIR)$(libdir)" >> openlibm.pc + echo "includedir=$(DESTDIR)$(includedir)/openlibm" >> openlibm.pc + cat openlibm.pc.in >> openlibm.pc + +install-static: libopenlibm.a + mkdir -p $(DESTDIR)$(libdir) + cp -RpP -f libopenlibm.a $(DESTDIR)$(libdir)/ + +install-shared: libopenlibm.$(OLM_MAJOR_MINOR_SHLIB_EXT) + mkdir -p $(DESTDIR)$(shlibdir) +ifeq ($(OS), WINNT) + mkdir -p $(DESTDIR)$(libdir) + cp -RpP -f libopenlibm.*$(SHLIB_EXT) $(DESTDIR)$(shlibdir)/ + cp -RpP -f libopenlibm.*$(SHLIB_EXT).a $(DESTDIR)$(libdir)/ +else + cp -RpP -f libopenlibm.*$(SHLIB_EXT)* $(DESTDIR)$(shlibdir)/ +endif + +install-pkgconfig: openlibm.pc + mkdir -p $(DESTDIR)$(pkgconfigdir) + cp -RpP -f openlibm.pc $(DESTDIR)$(pkgconfigdir)/ + +install-headers: + mkdir -p $(DESTDIR)$(includedir)/openlibm + cp -RpP -f include/*.h $(DESTDIR)$(includedir)/openlibm + cp -RpP -f src/*.h $(DESTDIR)$(includedir)/openlibm + +install: install-static install-shared install-pkgconfig install-headers diff --git a/openlibm/README.md b/openlibm/README.md new file mode 100644 index 0000000..d543a3b --- /dev/null +++ b/openlibm/README.md @@ -0,0 +1,71 @@ +# OpenLibm + +[![codecov](https://codecov.io/gh/JuliaMath/openlibm/graph/badge.svg?token=eTAdN7d9cg)](https://codecov.io/gh/JuliaMath/openlibm) + +[OpenLibm](https://openlibm.org/) is an effort to have a high quality, portable, standalone +C mathematical library ([`libm`](http://en.wikipedia.org/wiki/libm)). +It can be used standalone in applications and programming language +implementations. + +The project was born out of a need to have a good `libm` for the +[Julia programming language](http://www.julialang.org) that worked +consistently across compilers and operating systems, and in 32-bit and +64-bit environments. + +## Platform support + +OpenLibm builds on Linux, macOS, Windows, FreeBSD, OpenBSD, NetBSD, and +DragonFly BSD. It builds with both GCC and clang. Although largely +tested and widely used on the x86 and x86-64 architectures, OpenLibm +also supports arm, aarch64, ppc64le, mips, wasm32, riscv, s390(x) and +loongarch64. + +## Build instructions + +### GNU Make + +1. Use GNU Make to build OpenLibm. This is `make` on most systems, but `gmake` on BSDs. +2. Use `make USEGCC=1` to build with GCC. This is the default on + Linux and Windows. +3. Use `make USECLANG=1` to build with clang. This is the default on OS X, FreeBSD, + and OpenBSD. +4. Use `make ARCH=wasm32` to build the wasm32 library with clang. +5. Architectures are auto-detected. Use `make ARCH=i386` to force a + build for i386. Other supported architectures are i486, i586, and + i686. GCC 4.8 is the minimum requirement for correct codegen on + older 32-bit architectures. + + +**Cross Build** +Take `riscv64` as example: +1. install `qemu-riscv64-static`, `gcc-riscv64-linux-gnu` +2. Cross build: +```sh +ARCH=riscv64 +TRIPLE=$ARCH-linux-gnu +make ARCH=$ARCH TOOLPREFIX=$TRIPLE- -j +make -C test ARCH=$ARCH TOOLPREFIX=$TRIPLE- -j +``` + +3. Run test with qemu: +```sh +qemu-$ARCH-static -L . -L /usr/$TRIPLE/ test/test-float +qemu-$ARCH-static -L . -L /usr/$TRIPLE/ test/test-double +``` + + +### CMake + +1. Create build directory with `mkdir build` and navigate into it with `cd build`. +2. Run CMake to configure project and generate native build system with `cmake /path/to/openlibm/` +or generate project with build system of choice e.g. `cmake /path/to/openlib/ -G "MinGW Makefiles"`. +3. Build with the build system with `cmake --build .`. + +Default CMake configuration builds a shared library, this can easily be configured using +[BUILD_SHARED_LIBS](https://cmake.org/cmake/help/latest/variable/BUILD_SHARED_LIBS.html) +configuration option. + + +## Acknowledgements + +PowerPC support for openlibm was graciously sponsored by IBM. diff --git a/openlibm/aarch64/Make.files b/openlibm/aarch64/Make.files new file mode 100644 index 0000000..483a7cc --- /dev/null +++ b/openlibm/aarch64/Make.files @@ -0,0 +1 @@ +$(CUR_SRCS) = fenv.c diff --git a/openlibm/aarch64/fenv.c b/openlibm/aarch64/fenv.c new file mode 100644 index 0000000..8a1ca57 --- /dev/null +++ b/openlibm/aarch64/fenv.c @@ -0,0 +1,51 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/arm/fenv.c,v 1.3 2011/10/16 05:37:56 das Exp $ + */ + +#include + +#ifdef __GNUC_GNU_INLINE__ +#error "This file must be compiled with C99 'inline' semantics" +#endif + +/* + * Hopefully the system ID byte is immutable, so it's valid to use + * this as a default environment. + */ +const fenv_t __fe_dfl_env = 0; + +extern inline int feclearexcept(int __excepts); +extern inline int fegetexceptflag(fexcept_t *__flagp, int __excepts); +extern inline int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +extern inline int feraiseexcept(int __excepts); +extern inline int fetestexcept(int __excepts); +extern inline int fegetround(void); +extern inline int fesetround(int __round); +extern inline int fegetenv(fenv_t *__envp); +extern inline int feholdexcept(fenv_t *__envp); +extern inline int fesetenv(const fenv_t *__envp); +extern inline int feupdateenv(const fenv_t *__envp); diff --git a/openlibm/amd64/Make.files b/openlibm/amd64/Make.files new file mode 100644 index 0000000..662071c --- /dev/null +++ b/openlibm/amd64/Make.files @@ -0,0 +1,7 @@ +$(CUR_SRCS) = fenv.c e_remainder.S e_remainderf.S e_remainderl.S \ + e_sqrt.S e_sqrtf.S e_sqrtl.S \ + s_llrint.S s_llrintf.S s_llrintl.S \ + s_logbl.S s_lrint.S s_lrintf.S s_lrintl.S \ + s_remquo.S s_remquof.S s_remquol.S \ + s_rintl.S s_scalbn.S s_scalbnf.S s_scalbnl.S \ + e_fmod.S e_fmodf.S e_fmodl.S diff --git a/openlibm/amd64/bsd_asm.h b/openlibm/amd64/bsd_asm.h new file mode 100644 index 0000000..b9c815b --- /dev/null +++ b/openlibm/amd64/bsd_asm.h @@ -0,0 +1,110 @@ +/*- + * Copyright (c) 1990 The Regents of the University of California. + * All rights reserved. + * + * This code is derived from software contributed to Berkeley by + * William Jolitz. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * from: @(#)DEFS.h 5.1 (Berkeley) 4/23/90 + * $FreeBSD: src/sys/amd64/include/asm.h,v 1.18 2007/08/22 04:26:07 jkoshy Exp $ + */ + +#ifndef _BSD_ASM_H_ +#define _BSD_ASM_H_ + +#ifdef __APPLE__ +#include "../i387/osx_asm.h" +#define CNAME(x) EXT(x) +#else +#include "bsd_cdefs.h" + +#ifdef PIC +#define PIC_PLT(x) x@PLT +#define PIC_GOT(x) x@GOTPCREL(%rip) +#else +#define PIC_PLT(x) x +#define PIC_GOT(x) x +#endif + +/* + * CNAME and HIDENAME manage the relationship between symbol names in C + * and the equivalent assembly language names. CNAME is given a name as + * it would be used in a C program. It expands to the equivalent assembly + * language name. HIDENAME is given an assembly-language name, and expands + * to a possibly-modified form that will be invisible to C programs. + */ +#define CNAME(csym) csym +#define HIDENAME(asmsym) .asmsym + +#define _START_ENTRY .p2align 4,0x90 + +#if defined(__ELF__) +#define _ENTRY(x) .text; _START_ENTRY; \ + .globl CNAME(x); .type CNAME(x),@function; CNAME(x): +#define END(x) .size x, . - x + +#elif defined(_WIN32) +#ifndef _MSC_VER +#define END(x) .end +#define _START_ENTRY_WIN .text; _START_ENTRY +#else +#define END(x) end +#define _START_ENTRY_WIN .code; _START_ENTRY +#endif +#define _ENTRY(x) _START_ENTRY_WIN; \ + .globl CNAME(x); .section .drectve; .ascii " -export:", #x; \ + .section .text; .def CNAME(x); .scl 2; .type 32; .endef; CNAME(x): +#endif + +#ifdef PROF +#define ALTENTRY(x) _ENTRY(x); \ + pushq %rbp; movq %rsp,%rbp; \ + call PIC_PLT(HIDENAME(mcount)); \ + popq %rbp; \ + jmp 9f +#define ENTRY(x) _ENTRY(x); \ + pushq %rbp; movq %rsp,%rbp; \ + call PIC_PLT(HIDENAME(mcount)); \ + popq %rbp; \ + 9: +#else +#define ALTENTRY(x) _ENTRY(x) +#define ENTRY(x) _ENTRY(x) +#endif + + +#define RCSID(x) .text; .asciz x + +#undef __FBSDID +#if !defined(lint) && !defined(STRIP_FBSDID) +#define __FBSDID(s) .ident s +#else +#define __FBSDID(s) /* nothing */ +#endif /* not lint and not STRIP_FBSDID */ + +#endif +#endif /* !_BSD_ASM_H_ */ diff --git a/openlibm/amd64/bsd_fpu.h b/openlibm/amd64/bsd_fpu.h new file mode 100644 index 0000000..513b345 --- /dev/null +++ b/openlibm/amd64/bsd_fpu.h @@ -0,0 +1,218 @@ +/*- + * Copyright (c) 1990 The Regents of the University of California. + * All rights reserved. + * + * This code is derived from software contributed to Berkeley by + * William Jolitz. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * from: @(#)npx.h 5.3 (Berkeley) 1/18/91 + * $FreeBSD: src/sys/x86/include/fpu.h,v 1.1 2012/03/16 20:24:30 tijl Exp $ + */ + +/* + * Floating Point Data Structures and Constants + * W. Jolitz 1/90 + */ + +#ifndef _BSD_FPU_H_ +#define _BSD_FPU_H_ + +#include "types-compat.h" + +/* Environment information of floating point unit. */ +struct env87 { + int32_t en_cw; /* control word (16bits) */ + int32_t en_sw; /* status word (16bits) */ + int32_t en_tw; /* tag word (16bits) */ + int32_t en_fip; /* fp instruction pointer */ + uint16_t en_fcs; /* fp code segment selector */ + uint16_t en_opcode; /* opcode last executed (11 bits) */ + int32_t en_foo; /* fp operand offset */ + int32_t en_fos; /* fp operand segment selector */ +}; + +/* Contents of each x87 floating point accumulator. */ +struct fpacc87 { + uint8_t fp_bytes[10]; +}; + +/* Floating point context. (i386 fnsave/frstor) */ +struct save87 { + struct env87 sv_env; /* floating point control/status */ + struct fpacc87 sv_ac[8]; /* accumulator contents, 0-7 */ + uint8_t sv_pad0[4]; /* saved status word (now unused) */ + /* + * Bogus padding for emulators. Emulators should use their own + * struct and arrange to store into this struct (ending here) + * before it is inspected for ptracing or for core dumps. Some + * emulators overwrite the whole struct. We have no good way of + * knowing how much padding to leave. Leave just enough for the + * GPL emulator's i387_union (176 bytes total). + */ + uint8_t sv_pad[64]; /* padding; used by emulators */ +}; + +/* Contents of each SSE extended accumulator. */ +struct xmmacc { + uint8_t xmm_bytes[16]; +}; + +/* Contents of the upper 16 bytes of each AVX extended accumulator. */ +struct ymmacc { + uint8_t ymm_bytes[16]; +}; + +/* Rename structs below depending on machine architecture. */ +#ifdef __i386__ +#define __envxmm32 envxmm +#else +#define __envxmm32 envxmm32 +#define __envxmm64 envxmm +#endif + +struct __envxmm32 { + uint16_t en_cw; /* control word (16bits) */ + uint16_t en_sw; /* status word (16bits) */ + uint16_t en_tw; /* tag word (16bits) */ + uint16_t en_opcode; /* opcode last executed (11 bits) */ + uint32_t en_fip; /* fp instruction pointer */ + uint16_t en_fcs; /* fp code segment selector */ + uint16_t en_pad0; /* padding */ + uint32_t en_foo; /* fp operand offset */ + uint16_t en_fos; /* fp operand segment selector */ + uint16_t en_pad1; /* padding */ + uint32_t en_mxcsr; /* SSE control/status register */ + uint32_t en_mxcsr_mask; /* valid bits in mxcsr */ +}; + +struct __envxmm64 { + uint16_t en_cw; /* control word (16bits) */ + uint16_t en_sw; /* status word (16bits) */ + uint8_t en_tw; /* tag word (8bits) */ + uint8_t en_zero; + uint16_t en_opcode; /* opcode last executed (11 bits ) */ + uint64_t en_rip; /* fp instruction pointer */ + uint64_t en_rdp; /* fp operand pointer */ + uint32_t en_mxcsr; /* SSE control/status register */ + uint32_t en_mxcsr_mask; /* valid bits in mxcsr */ +}; + +/* Floating point context. (i386 fxsave/fxrstor) */ +struct savexmm { + struct __envxmm32 sv_env; + struct { + struct fpacc87 fp_acc; + uint8_t fp_pad[6]; /* padding */ + } sv_fp[8]; + struct xmmacc sv_xmm[8]; + uint8_t sv_pad[224]; +} __attribute__ ((aligned(16))); + +#ifdef __i386__ +union savefpu { + struct save87 sv_87; + struct savexmm sv_xmm; +}; +#else +/* Floating point context. (amd64 fxsave/fxrstor) */ +struct savefpu { + struct __envxmm64 sv_env; + struct { + struct fpacc87 fp_acc; + uint8_t fp_pad[6]; /* padding */ + } sv_fp[8]; + struct xmmacc sv_xmm[16]; + uint8_t sv_pad[96]; +} __attribute__ ((aligned(16))); +#endif + +struct xstate_hdr { + uint64_t xstate_bv; + uint8_t xstate_rsrv0[16]; + uint8_t xstate_rsrv[40]; +}; + +struct savexmm_xstate { + struct xstate_hdr sx_hd; + struct ymmacc sx_ymm[16]; +}; + +struct savexmm_ymm { + struct __envxmm32 sv_env; + struct { + struct fpacc87 fp_acc; + int8_t fp_pad[6]; /* padding */ + } sv_fp[8]; + struct xmmacc sv_xmm[16]; + uint8_t sv_pad[96]; + struct savexmm_xstate sv_xstate; +} __attribute__ ((aligned(16))); + +struct savefpu_xstate { + struct xstate_hdr sx_hd; + struct ymmacc sx_ymm[16]; +}; + +struct savefpu_ymm { + struct __envxmm64 sv_env; + struct { + struct fpacc87 fp_acc; + int8_t fp_pad[6]; /* padding */ + } sv_fp[8]; + struct xmmacc sv_xmm[16]; + uint8_t sv_pad[96]; + struct savefpu_xstate sv_xstate; +} __attribute__ ((aligned(64))); + +#undef __envxmm32 +#undef __envxmm64 + +/* + * The hardware default control word for i387's and later coprocessors is + * 0x37F, giving: + * + * round to nearest + * 64-bit precision + * all exceptions masked. + * + * FreeBSD/i386 uses 53 bit precision for things like fadd/fsub/fsqrt etc + * because of the difference between memory and fpu register stack arguments. + * If its using an intermediate fpu register, it has 80/64 bits to work + * with. If it uses memory, it has 64/53 bits to work with. However, + * gcc is aware of this and goes to a fair bit of trouble to make the + * best use of it. + * + * This is mostly academic for AMD64, because the ABI prefers the use + * SSE2 based math. For FreeBSD/amd64, we go with the default settings. + */ +#define __INITIAL_FPUCW__ 0x037F +#define __INITIAL_FPUCW_I386__ 0x127F +#define __INITIAL_NPXCW__ __INITIAL_FPUCW_I386__ +#define __INITIAL_MXCSR__ 0x1F80 +#define __INITIAL_MXCSR_MASK__ 0xFFBF + +#endif /* !_BSD_FPU_H_ */ diff --git a/openlibm/amd64/bsd_ieeefp.h b/openlibm/amd64/bsd_ieeefp.h new file mode 100644 index 0000000..6103d50 --- /dev/null +++ b/openlibm/amd64/bsd_ieeefp.h @@ -0,0 +1,272 @@ +/*- + * Copyright (c) 2003 Peter Wemm. + * Copyright (c) 1990 Andrew Moore, Talke Studio + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * from: @(#) ieeefp.h 1.0 (Berkeley) 9/23/93 + * $FreeBSD: src/sys/amd64/include/ieeefp.h,v 1.14 2005/04/12 23:12:00 jhb Exp $ + */ + +/* + * IEEE floating point type and constant definitions. + */ + +#ifndef _BSD_IEEEFP_H_ +#define _BSD_IEEEFP_H_ + +/* + * FP rounding modes + */ +typedef enum { + FP_RN=0, /* round to nearest */ + FP_RM, /* round down to minus infinity */ + FP_RP, /* round up to plus infinity */ + FP_RZ /* truncate */ +} fp_rnd_t; + +/* + * FP precision modes + */ +typedef enum { + FP_PS=0, /* 24 bit (single-precision) */ + FP_PRS, /* reserved */ + FP_PD, /* 53 bit (double-precision) */ + FP_PE /* 64 bit (extended-precision) */ +} fp_prec_t; + +#define fp_except_t int + +/* + * FP exception masks + */ +#define FP_X_INV 0x01 /* invalid operation */ +#define FP_X_DNML 0x02 /* denormal */ +#define FP_X_DZ 0x04 /* zero divide */ +#define FP_X_OFL 0x08 /* overflow */ +#define FP_X_UFL 0x10 /* underflow */ +#define FP_X_IMP 0x20 /* (im)precision */ +#define FP_X_STK 0x40 /* stack fault */ + +/* + * FP registers + */ +#define FP_MSKS_REG 0 /* exception masks */ +#define FP_PRC_REG 0 /* precision */ +#define FP_RND_REG 0 /* direction */ +#define FP_STKY_REG 1 /* sticky flags */ + +/* + * FP register bit field masks + */ +#define FP_MSKS_FLD 0x3f /* exception masks field */ +#define FP_PRC_FLD 0x300 /* precision control field */ +#define FP_RND_FLD 0xc00 /* round control field */ +#define FP_STKY_FLD 0x3f /* sticky flags field */ + +/* + * SSE mxcsr register bit field masks + */ +#define SSE_STKY_FLD 0x3f /* exception flags */ +#define SSE_DAZ_FLD 0x40 /* Denormals are zero */ +#define SSE_MSKS_FLD 0x1f80 /* exception masks field */ +#define SSE_RND_FLD 0x6000 /* rounding control */ +#define SSE_FZ_FLD 0x8000 /* flush to zero on underflow */ + +/* + * FP register bit field offsets + */ +#define FP_MSKS_OFF 0 /* exception masks offset */ +#define FP_PRC_OFF 8 /* precision control offset */ +#define FP_RND_OFF 10 /* round control offset */ +#define FP_STKY_OFF 0 /* sticky flags offset */ + +/* + * SSE mxcsr register bit field offsets + */ +#define SSE_STKY_OFF 0 /* exception flags offset */ +#define SSE_DAZ_OFF 6 /* DAZ exception mask offset */ +#define SSE_MSKS_OFF 7 /* other exception masks offset */ +#define SSE_RND_OFF 13 /* rounding control offset */ +#define SSE_FZ_OFF 15 /* flush to zero offset */ + +#if (defined(__GNUCLIKE_ASM) && defined(__CC_SUPPORTS___INLINE__)) || defined(_WIN32) \ + && !defined(__cplusplus) + +#define __fldenv(addr) __asm __volatile("fldenv %0" : : "m" (*(addr))) +#define __fnstenv(addr) __asm __volatile("fnstenv %0" : "=m" (*(addr))) +#define __fldcw(addr) __asm __volatile("fldcw %0" : : "m" (*(addr))) +#define __fnstcw(addr) __asm __volatile("fnstcw %0" : "=m" (*(addr))) +#define __fnstsw(addr) __asm __volatile("fnstsw %0" : "=m" (*(addr))) +#define __ldmxcsr(addr) __asm __volatile("ldmxcsr %0" : : "m" (*(addr))) +#define __stmxcsr(addr) __asm __volatile("stmxcsr %0" : "=m" (*(addr))) + +/* + * General notes about conflicting SSE vs FP status bits. + * This code assumes that software will not fiddle with the control + * bits of the SSE and x87 in such a way to get them out of sync and + * still expect this to work. Break this at your peril. + * Because I based this on the i386 port, the x87 state is used for + * the fpget*() functions, and is shadowed into the SSE state for + * the fpset*() functions. For dual source fpget*() functions, I + * merge the two together. I think. + */ + +/* Set rounding control */ +static __inline__ fp_rnd_t +__fpgetround(void) +{ + unsigned short _cw; + + __fnstcw(&_cw); + return ((_cw & FP_RND_FLD) >> FP_RND_OFF); +} + +static __inline__ fp_rnd_t +__fpsetround(fp_rnd_t _m) +{ + unsigned short _cw; + unsigned int _mxcsr; + fp_rnd_t _p; + + __fnstcw(&_cw); + _p = (_cw & FP_RND_FLD) >> FP_RND_OFF; + _cw &= ~FP_RND_FLD; + _cw |= (_m << FP_RND_OFF) & FP_RND_FLD; + __fldcw(&_cw); + __stmxcsr(&_mxcsr); + _mxcsr &= ~SSE_RND_FLD; + _mxcsr |= (_m << SSE_RND_OFF) & SSE_RND_FLD; + __ldmxcsr(&_mxcsr); + return (_p); +} + +/* + * Set precision for fadd/fsub/fsqrt etc x87 instructions + * There is no equivalent SSE mode or control. + */ +static __inline__ fp_prec_t +__fpgetprec(void) +{ + unsigned short _cw; + + __fnstcw(&_cw); + return ((_cw & FP_PRC_FLD) >> FP_PRC_OFF); +} + +static __inline__ fp_prec_t +__fpsetprec(fp_rnd_t _m) +{ + unsigned short _cw; + fp_prec_t _p; + + __fnstcw(&_cw); + _p = (_cw & FP_PRC_FLD) >> FP_PRC_OFF; + _cw &= ~FP_PRC_FLD; + _cw |= (_m << FP_PRC_OFF) & FP_PRC_FLD; + __fldcw(&_cw); + return (_p); +} + +/* + * Look at the exception masks + * Note that x87 masks are inverse of the fp*() functions + * API. ie: mask = 1 means disable for x87 and SSE, but + * for the fp*() api, mask = 1 means enabled. + */ +static __inline__ fp_except_t +__fpgetmask(void) +{ + unsigned short _cw; + + __fnstcw(&_cw); + return ((~_cw) & FP_MSKS_FLD); +} + +static __inline__ fp_except_t +__fpsetmask(fp_except_t _m) +{ + unsigned short _cw; + unsigned int _mxcsr; + fp_except_t _p; + + __fnstcw(&_cw); + _p = (~_cw) & FP_MSKS_FLD; + _cw &= ~FP_MSKS_FLD; + _cw |= (~_m) & FP_MSKS_FLD; + __fldcw(&_cw); + __stmxcsr(&_mxcsr); + /* XXX should we clear non-ieee SSE_DAZ_FLD and SSE_FZ_FLD ? */ + _mxcsr &= ~SSE_MSKS_FLD; + _mxcsr |= ((~_m) << SSE_MSKS_OFF) & SSE_MSKS_FLD; + __ldmxcsr(&_mxcsr); + return (_p); +} + +/* See which sticky exceptions are pending, and reset them */ +static __inline__ fp_except_t +__fpgetsticky(void) +{ + unsigned short _sw; + unsigned int _mxcsr; + fp_except_t _ex; + + __fnstsw(&_sw); + _ex = _sw & FP_STKY_FLD; + __stmxcsr(&_mxcsr); + _ex |= _mxcsr & SSE_STKY_FLD; + return (_ex); +} + +#endif /* __GNUCLIKE_ASM && __CC_SUPPORTS___INLINE__ && !__cplusplus */ + +#if !defined(__IEEEFP_NOINLINES__) && !defined(__cplusplus) \ + && defined(__GNUCLIKE_ASM) && defined(__CC_SUPPORTS___INLINE__) + +#define fpgetround() __fpgetround() +#define fpsetround(_m) __fpsetround(_m) +#define fpgetprec() __fpgetprec() +#define fpsetprec(_m) __fpsetprec(_m) +#define fpgetmask() __fpgetmask() +#define fpsetmask(_m) __fpsetmask(_m) +#define fpgetsticky() __fpgetsticky() + +/* Suppress prototypes in the MI header. */ +#define _IEEEFP_INLINED_ 1 + +#else /* !__IEEEFP_NOINLINES__ && !__cplusplus && __GNUCLIKE_ASM + && __CC_SUPPORTS___INLINE__ */ + +/* Augment the userland declarations */ +__BEGIN_DECLS +extern fp_prec_t fpgetprec(void); +extern fp_prec_t fpsetprec(fp_prec_t); +__END_DECLS + +#endif /* !__IEEEFP_NOINLINES__ && !__cplusplus && __GNUCLIKE_ASM + && __CC_SUPPORTS___INLINE__ */ + +#endif /* !_BSD_IEEEFP_H_ */ diff --git a/openlibm/amd64/e_fmod.S b/openlibm/amd64/e_fmod.S new file mode 100644 index 0000000..d2c8ecd --- /dev/null +++ b/openlibm/amd64/e_fmod.S @@ -0,0 +1,56 @@ +/* + * Copyright (c) 1993,94 Winning Strategies, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by Winning Strategies, Inc. + * 4. The name of the author may not be used to endorse or promote products + * derived from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/* + * Based on the i387 version written by: + * J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc. + */ + +#include + +ENTRY(fmod) + movsd %xmm0,-8(%rsp) + movsd %xmm1,-16(%rsp) + fldl -16(%rsp) + fldl -8(%rsp) +1: fprem + fstsw %ax + testw $0x400,%ax + jne 1b + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 + fstp %st + ret +END(fmod) + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/e_fmodf.S b/openlibm/amd64/e_fmodf.S new file mode 100644 index 0000000..b045e73 --- /dev/null +++ b/openlibm/amd64/e_fmodf.S @@ -0,0 +1,26 @@ +/* + * Based on the i387 version written by J.T. Conklin . + * Public domain. + */ + +#include + +ENTRY(fmodf) + movss %xmm0,-4(%rsp) + movss %xmm1,-8(%rsp) + flds -8(%rsp) + flds -4(%rsp) +1: fprem + fstsw %ax + testw $0x400,%ax + jne 1b + fstps -4(%rsp) + movss -4(%rsp),%xmm0 + fstp %st + ret +END(fmodf) + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/e_fmodl.S b/openlibm/amd64/e_fmodl.S new file mode 100644 index 0000000..cab539d --- /dev/null +++ b/openlibm/amd64/e_fmodl.S @@ -0,0 +1,52 @@ +/* + * Copyright (c) 1993,94 Winning Strategies, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by Winning Strategies, Inc. + * 4. The name of the author may not be used to endorse or promote products + * derived from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/* + * Based on the i387 version written by: + * J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc. + */ + +#include + +ENTRY(fmodl) + fldt 24(%rsp) + fldt 8(%rsp) +1: fprem + fstsw %ax + testw $0x400,%ax + jne 1b + fstp %st(1) + ret +END(fmodl) + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/e_remainder.S b/openlibm/amd64/e_remainder.S new file mode 100644 index 0000000..a0b4900 --- /dev/null +++ b/openlibm/amd64/e_remainder.S @@ -0,0 +1,30 @@ +/* + * Based on the i387 version written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include + +//RCSID("from: FreeBSD: src/lib/msun/i387/e_remainder.S,v 1.8 2005/02/04 14:08:32 das Exp") +//__FBSDID("$FreeBSD: src/lib/msun/amd64/e_remainder.S,v 1.2 2011/01/07 16:13:12 kib Exp $") + +ENTRY(remainder) + movsd %xmm0,-8(%rsp) + movsd %xmm1,-16(%rsp) + fldl -16(%rsp) + fldl -8(%rsp) +1: fprem1 + fstsw %ax + testw $0x400,%ax + jne 1b + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 + fstp %st + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/e_remainderf.S b/openlibm/amd64/e_remainderf.S new file mode 100644 index 0000000..c63e97e --- /dev/null +++ b/openlibm/amd64/e_remainderf.S @@ -0,0 +1,29 @@ +/* + * Based on the i387 version written by J.T. Conklin . + * Public domain. + */ + +#include + +//RCSID("from: $NetBSD: e_remainderf.S,v 1.2 1995/05/08 23:49:47 jtc Exp $") +//__FBSDID("$FreeBSD: src/lib/msun/amd64/e_remainderf.S,v 1.2 2011/01/07 16:13:12 kib Exp $") + +ENTRY(remainderf) + movss %xmm0,-4(%rsp) + movss %xmm1,-8(%rsp) + flds -8(%rsp) + flds -4(%rsp) +1: fprem1 + fstsw %ax + testw $0x400,%ax + jne 1b + fstps -4(%rsp) + movss -4(%rsp),%xmm0 + fstp %st + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/e_remainderl.S b/openlibm/amd64/e_remainderl.S new file mode 100644 index 0000000..5f21b93 --- /dev/null +++ b/openlibm/amd64/e_remainderl.S @@ -0,0 +1,35 @@ +/* + * Based on the i387 version written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/amd64/e_remainderl.S,v 1.2 2011/01/07 16:13:12 kib Exp $") + +ENTRY(remainderl) +#ifndef _WIN64 + fldt 24(%rsp) + fldt 8(%rsp) +#else + fldt (%r8) + fldt (%rdx) +#endif +1: fprem1 + fstsw %ax + testw $0x400,%ax + jne 1b + fstp %st(1) +#ifdef _WIN64 + mov %rcx,%rax + movq $0x0,0x8(%rcx) + fstpt (%rcx) +#endif + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/e_sqrt.S b/openlibm/amd64/e_sqrt.S new file mode 100644 index 0000000..a44e41f --- /dev/null +++ b/openlibm/amd64/e_sqrt.S @@ -0,0 +1,40 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/e_sqrt.S,v 1.4 2011/01/07 16:13:12 kib Exp $") + +ENTRY(sqrt) + sqrtsd %xmm0, %xmm0 + ret +END(sqrt) + + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/e_sqrtf.S b/openlibm/amd64/e_sqrtf.S new file mode 100644 index 0000000..f74175b --- /dev/null +++ b/openlibm/amd64/e_sqrtf.S @@ -0,0 +1,39 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/e_sqrtf.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(sqrtf) + sqrtss %xmm0, %xmm0 + ret +END(sqrtf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/e_sqrtl.S b/openlibm/amd64/e_sqrtl.S new file mode 100644 index 0000000..6e7eac0 --- /dev/null +++ b/openlibm/amd64/e_sqrtl.S @@ -0,0 +1,46 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/e_sqrtl.S,v 1.2 2011/01/07 16:13:12 kib Exp $") + +ENTRY(sqrtl) +#ifndef _WIN64 + fldt 8(%rsp) + fsqrt +#else + fldt (%rdx) + fsqrt + mov %rcx,%rax + movq $0x0,0x8(%rcx) + fstpt (%rcx) +#endif + ret + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/fenv.c b/openlibm/amd64/fenv.c new file mode 100644 index 0000000..ddf7dba --- /dev/null +++ b/openlibm/amd64/fenv.c @@ -0,0 +1,162 @@ +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/amd64/fenv.c,v 1.8 2011/10/21 06:25:31 das Exp $ + */ + +#include "bsd_fpu.h" +#include "math_private.h" + +#ifdef _WIN32 +#define __fenv_static OLM_DLLEXPORT +#endif +#include + +#ifdef __GNUC_GNU_INLINE__ +#error "This file must be compiled with C99 'inline' semantics" +#endif + +const fenv_t __fe_dfl_env = { + { 0xffff0000 | __INITIAL_FPUCW__, + 0xffff0000, + 0xffffffff, + { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff } + }, + __INITIAL_MXCSR__ +}; + +extern inline OLM_DLLEXPORT int feclearexcept(int __excepts); +extern inline OLM_DLLEXPORT int fegetexceptflag(fexcept_t *__flagp, int __excepts); + +OLM_DLLEXPORT int +fesetexceptflag(const fexcept_t *flagp, int excepts) +{ + fenv_t env; + + __fnstenv(&env.__x87); + env.__x87.__status &= ~excepts; + env.__x87.__status |= *flagp & excepts; + __fldenv(env.__x87); + + __stmxcsr(&env.__mxcsr); + env.__mxcsr &= ~excepts; + env.__mxcsr |= *flagp & excepts; + __ldmxcsr(env.__mxcsr); + + return (0); +} + +OLM_DLLEXPORT int +feraiseexcept(int excepts) +{ + fexcept_t ex = excepts; + + fesetexceptflag(&ex, excepts); + __fwait(); + return (0); +} + +extern inline OLM_DLLEXPORT int fetestexcept(int __excepts); +extern inline OLM_DLLEXPORT int fegetround(void); +extern inline OLM_DLLEXPORT int fesetround(int __round); + +OLM_DLLEXPORT int +fegetenv(fenv_t *envp) +{ + + __fnstenv(&envp->__x87); + __stmxcsr(&envp->__mxcsr); + /* + * fnstenv masks all exceptions, so we need to restore the + * control word to avoid this side effect. + */ + __fldcw(envp->__x87.__control); + return (0); +} + +OLM_DLLEXPORT int +feholdexcept(fenv_t *envp) +{ + uint32_t mxcsr; + + __stmxcsr(&mxcsr); + __fnstenv(&envp->__x87); + __fnclex(); + envp->__mxcsr = mxcsr; + mxcsr &= ~FE_ALL_EXCEPT; + mxcsr |= FE_ALL_EXCEPT << _SSE_EMASK_SHIFT; + __ldmxcsr(mxcsr); + return (0); +} + +extern inline OLM_DLLEXPORT int fesetenv(const fenv_t *__envp); + +OLM_DLLEXPORT int +feupdateenv(const fenv_t *envp) +{ + uint32_t mxcsr; + uint16_t status; + + __fnstsw(&status); + __stmxcsr(&mxcsr); + fesetenv(envp); + feraiseexcept((mxcsr | status) & FE_ALL_EXCEPT); + return (0); +} + +int +feenableexcept(int mask) +{ + uint32_t mxcsr, omask; + uint16_t control; + + mask &= FE_ALL_EXCEPT; + __fnstcw(&control); + __stmxcsr(&mxcsr); + omask = ~(control | mxcsr >> _SSE_EMASK_SHIFT) & FE_ALL_EXCEPT; + control &= ~mask; + __fldcw(control); + mxcsr &= ~(mask << _SSE_EMASK_SHIFT); + __ldmxcsr(mxcsr); + return (omask); +} + +int +fedisableexcept(int mask) +{ + uint32_t mxcsr, omask; + uint16_t control; + + mask &= FE_ALL_EXCEPT; + __fnstcw(&control); + __stmxcsr(&mxcsr); + omask = ~(control | mxcsr >> _SSE_EMASK_SHIFT) & FE_ALL_EXCEPT; + control |= mask; + __fldcw(control); + mxcsr |= mask << _SSE_EMASK_SHIFT; + __ldmxcsr(mxcsr); + return (omask); +} diff --git a/openlibm/amd64/s_llrint.S b/openlibm/amd64/s_llrint.S new file mode 100644 index 0000000..d7a0f74 --- /dev/null +++ b/openlibm/amd64/s_llrint.S @@ -0,0 +1,12 @@ +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_llrint.S,v 1.3 2011/02/04 21:54:06 kib Exp $") + +ENTRY(llrint) + cvtsd2si %xmm0, %rax + ret +END(llrint) + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_llrintf.S b/openlibm/amd64/s_llrintf.S new file mode 100644 index 0000000..f5d39b3 --- /dev/null +++ b/openlibm/amd64/s_llrintf.S @@ -0,0 +1,12 @@ +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_llrintf.S,v 1.3 2011/02/04 21:54:06 kib Exp $") + +ENTRY(llrintf) + cvtss2si %xmm0, %rax + ret +END(llrintf) + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_llrintl.S b/openlibm/amd64/s_llrintl.S new file mode 100644 index 0000000..12f2d33 --- /dev/null +++ b/openlibm/amd64/s_llrintl.S @@ -0,0 +1,45 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_llrintl.S,v 1.2 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(llrintl) +#ifndef _WIN64 + fldt 8(%rsp) +#else + fldt (%rcx) +#endif + subq $8,%rsp + fistpll (%rsp) + popq %rax + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_logbl.S b/openlibm/amd64/s_logbl.S new file mode 100644 index 0000000..d22afeb --- /dev/null +++ b/openlibm/amd64/s_logbl.S @@ -0,0 +1,29 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_logbl.S,v 1.4 2011/01/07 16:13:12 kib Exp $") + +ENTRY(logbl) +#ifndef _WIN64 + fldt 8(%rsp) +#else + fldt (%rdx) +#endif + fxtract + fstp %st +#ifdef _WIN64 + mov %rcx,%rax + movq $0x0,0x8(%rcx) + fstpt (%rcx) +#endif + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_lrint.S b/openlibm/amd64/s_lrint.S new file mode 100644 index 0000000..9e1b917 --- /dev/null +++ b/openlibm/amd64/s_lrint.S @@ -0,0 +1,44 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_lrint.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(lrint) +#ifndef _WIN64 + cvtsd2si %xmm0, %rax +#else + cvtsd2si %xmm0, %eax +#endif + ret +END(lrint) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_lrintf.S b/openlibm/amd64/s_lrintf.S new file mode 100644 index 0000000..8e0b0c2 --- /dev/null +++ b/openlibm/amd64/s_lrintf.S @@ -0,0 +1,44 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_lrintf.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(lrintf) +#ifndef _WIN64 + cvtss2si %xmm0, %rax +#else + cvtss2si %xmm0, %eax +#endif + ret +END(lrintf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_lrintl.S b/openlibm/amd64/s_lrintl.S new file mode 100644 index 0000000..288c0bb --- /dev/null +++ b/openlibm/amd64/s_lrintl.S @@ -0,0 +1,45 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_lrintl.S,v 1.2 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(lrintl) +#ifndef _WIN64 + fldt 8(%rsp) +#else + fldt (%rcx) +#endif + subq $8,%rsp + fistpll (%rsp) + popq %rax + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_remquo.S b/openlibm/amd64/s_remquo.S new file mode 100644 index 0000000..8ef8425 --- /dev/null +++ b/openlibm/amd64/s_remquo.S @@ -0,0 +1,76 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* + * Based on public-domain remainder routine by J.T. Conklin . + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_remquo.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(remquo) + movsd %xmm0,-8(%rsp) + movsd %xmm1,-16(%rsp) + fldl -16(%rsp) + fldl -8(%rsp) +1: fprem1 + fstsw %ax + btw $10,%ax + jc 1b + fstp %st(1) +/* Extract the three low-order bits of the quotient from C0,C3,C1. */ + shrl $6,%eax + movl %eax,%ecx + andl $0x108,%eax + rorl $7,%eax + orl %eax,%ecx + roll $4,%eax + orl %ecx,%eax + andl $7,%eax +/* Negate the quotient bits if x*y<0. Avoid using an unpredictable branch. */ + movl -12(%rsp),%ecx + xorl -4(%rsp),%ecx + sarl $16,%ecx + sarl $16,%ecx + xorl %ecx,%eax + andl $1,%ecx + addl %ecx,%eax +/* Store the quotient and return. */ +#ifndef _WIN64 + movl %eax,(%rdi) +#else + movl %eax,(%r8) +#endif + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 + ret +END(remquo) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_remquof.S b/openlibm/amd64/s_remquof.S new file mode 100644 index 0000000..129a807 --- /dev/null +++ b/openlibm/amd64/s_remquof.S @@ -0,0 +1,76 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* + * Based on public-domain remainder routine by J.T. Conklin . + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_remquof.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(remquof) + movss %xmm0,-4(%rsp) + movss %xmm1,-8(%rsp) + flds -8(%rsp) + flds -4(%rsp) +1: fprem1 + fstsw %ax + btw $10,%ax + jc 1b + fstp %st(1) +/* Extract the three low-order bits of the quotient from C0,C3,C1. */ + shrl $6,%eax + movl %eax,%ecx + andl $0x108,%eax + rorl $7,%eax + orl %eax,%ecx + roll $4,%eax + orl %ecx,%eax + andl $7,%eax +/* Negate the quotient bits if x*y<0. Avoid using an unpredictable branch. */ + movl -8(%rsp),%ecx + xorl -4(%rsp),%ecx + sarl $16,%ecx + sarl $16,%ecx + xorl %ecx,%eax + andl $1,%ecx + addl %ecx,%eax +/* Store the quotient and return. */ +#ifndef _WIN64 + movl %eax,(%rdi) +#else + movl %eax,(%r8) +#endif + fstps -4(%rsp) + movss -4(%rsp),%xmm0 + ret +END(remquof) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_remquol.S b/openlibm/amd64/s_remquol.S new file mode 100644 index 0000000..344e1fb --- /dev/null +++ b/openlibm/amd64/s_remquol.S @@ -0,0 +1,81 @@ +/*- + * Copyright (c) 2005-2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* + * Based on public-domain remainder routine by J.T. Conklin . + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_remquol.S,v 1.2 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(remquol) +#ifndef _WIN64 + fldt 24(%rsp) + fldt 8(%rsp) +#else + fldt (%r8) + fldt (%rdx) + mov %rcx,%r8 +#endif +1: fprem1 + fstsw %ax + btw $10,%ax + jc 1b + fstp %st(1) +/* Extract the three low-order bits of the quotient from C0,C3,C1. */ + shrl $6,%eax + movl %eax,%ecx + andl $0x108,%eax + rorl $7,%eax + orl %eax,%ecx + roll $4,%eax + orl %ecx,%eax + andl $7,%eax +/* Negate the quotient bits if x*y<0. Avoid using an unpredictable branch. */ + movl 32(%rsp),%ecx + xorl 16(%rsp),%ecx + movsx %cx,%ecx + sarl $16,%ecx + sarl $16,%ecx + xorl %ecx,%eax + andl $1,%ecx + addl %ecx,%eax +/* Store the quotient and return. */ +#ifndef _WIN64 + movl %eax,(%rdi) +#else + movl %eax,(%r9) + mov %r8,%rax + movq $0x0,0x8(%r8) + fstpt (%r8) +#endif + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_rintl.S b/openlibm/amd64/s_rintl.S new file mode 100644 index 0000000..479e836 --- /dev/null +++ b/openlibm/amd64/s_rintl.S @@ -0,0 +1,26 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include + +ENTRY(rintl) +#ifndef _WIN64 + fldt 8(%rsp) + frndint +#else + fldt (%rdx) + frndint + mov %rcx,%rax + movq $0x0,0x8(%rcx) + fstpt (%rcx) +#endif + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_scalbn.S b/openlibm/amd64/s_scalbn.S new file mode 100644 index 0000000..9d4152b --- /dev/null +++ b/openlibm/amd64/s_scalbn.S @@ -0,0 +1,55 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_scalbn.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(scalbn) + movsd %xmm0,-8(%rsp) +#ifndef _WIN64 + movl %edi,-12(%rsp) +#else + movl %edx,-12(%rsp) +#endif + fildl -12(%rsp) + fldl -8(%rsp) + fscale + fstp %st(1) + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 + ret +#ifndef _WIN64 +END(scalbn) +.globl CNAME(ldexp) +#else +.globl CNAME(ldexp); .section .drectve; .ascii " -export:ldexp" +#endif +.set CNAME(ldexp),CNAME(scalbn) + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_scalbnf.S b/openlibm/amd64/s_scalbnf.S new file mode 100644 index 0000000..75b4bb2 --- /dev/null +++ b/openlibm/amd64/s_scalbnf.S @@ -0,0 +1,55 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_scalbnf.S,v 1.4 2011/01/07 16:13:12 kib Exp $") + +ENTRY(scalbnf) + movss %xmm0,-8(%rsp) +#ifndef _WIN64 + movl %edi,-4(%rsp) +#else + movl %edx,-4(%rsp) +#endif + fildl -4(%rsp) + flds -8(%rsp) + fscale + fstp %st(1) + fstps -8(%rsp) + movss -8(%rsp),%xmm0 + ret +#ifndef _WIN64 +END(scalbnf) +.globl CNAME(ldexpf) +#else +.globl CNAME(ldexpf); .section .drectve; .ascii " -export:ldexpf" +#endif +.set CNAME(ldexpf),CNAME(scalbnf) + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/amd64/s_scalbnl.S b/openlibm/amd64/s_scalbnl.S new file mode 100644 index 0000000..fa0d2bf --- /dev/null +++ b/openlibm/amd64/s_scalbnl.S @@ -0,0 +1,40 @@ +/* + * Based on code written by J.T. Conklin . + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/amd64/s_scalbnl.S,v 1.3 2011/01/07 16:13:12 kib Exp $") +/* //RCSID("$NetBSD: s_scalbnf.S,v 1.4 1999/01/02 05:15:40 kristerw Exp $") */ + +ENTRY(scalbnl) +#ifndef _WIN64 + movl %edi,-4(%rsp) + fildl -4(%rsp) + fldt 8(%rsp) +#else + mov %r8,%rax + movl %eax,-4(%rsp) + fildl -4(%rsp) + fldt (%rdx) +#endif + fscale + fstp %st(1) +#ifdef _WIN64 + mov %rcx,%rax + movq $0x0,0x8(%rcx) + fstpt (%rcx) +#endif + ret +#ifndef _WIN64 +END(scalbnl) +.globl CNAME(ldexpl) +#else +.globl CNAME(ldexpl); .section .drectve; .ascii " -export:ldexpl" +#endif +.set CNAME(ldexpl),CNAME(scalbnl) + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/arm/Make.files b/openlibm/arm/Make.files new file mode 100644 index 0000000..483a7cc --- /dev/null +++ b/openlibm/arm/Make.files @@ -0,0 +1 @@ +$(CUR_SRCS) = fenv.c diff --git a/openlibm/arm/fenv.c b/openlibm/arm/fenv.c new file mode 100644 index 0000000..c9abf14 --- /dev/null +++ b/openlibm/arm/fenv.c @@ -0,0 +1,52 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/arm/fenv.c,v 1.3 2011/10/16 05:37:56 das Exp $ + */ + +#define __fenv_static +#include + +#ifdef __GNUC_GNU_INLINE__ +#error "This file must be compiled with C99 'inline' semantics" +#endif + +/* + * Hopefully the system ID byte is immutable, so it's valid to use + * this as a default environment. + */ +const fenv_t __fe_dfl_env = 0; + +extern inline int feclearexcept(int __excepts); +extern inline int fegetexceptflag(fexcept_t *__flagp, int __excepts); +extern inline int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +extern inline int feraiseexcept(int __excepts); +extern inline int fetestexcept(int __excepts); +extern inline int fegetround(void); +extern inline int fesetround(int __round); +extern inline int fegetenv(fenv_t *__envp); +extern inline int feholdexcept(fenv_t *__envp); +extern inline int fesetenv(const fenv_t *__envp); +extern inline int feupdateenv(const fenv_t *__envp); diff --git a/openlibm/bsdsrc/Make.files b/openlibm/bsdsrc/Make.files new file mode 100644 index 0000000..6777fe2 --- /dev/null +++ b/openlibm/bsdsrc/Make.files @@ -0,0 +1 @@ +$(CUR_SRCS) += b_exp.c b_log.c b_tgamma.c diff --git a/openlibm/bsdsrc/b_exp.c b/openlibm/bsdsrc/b_exp.c new file mode 100644 index 0000000..6af8dd7 --- /dev/null +++ b/openlibm/bsdsrc/b_exp.c @@ -0,0 +1,172 @@ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* @(#)exp.c 8.1 (Berkeley) 6/4/93 */ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/bsdsrc/b_exp.c,v 1.9 2011/10/16 05:37:20 das Exp $"); + +#include + +/* EXP(X) + * RETURN THE EXPONENTIAL OF X + * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS) + * CODED IN C BY K.C. NG, 1/19/85; + * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86. + * + * Required system supported functions: + * scalb(x,n) + * copysign(x,y) + * finite(x) + * + * Method: + * 1. Argument Reduction: given the input x, find r and integer k such + * that + * x = k*ln2 + r, |r| <= 0.5*ln2 . + * r will be represented as r := z+c for better accuracy. + * + * 2. Compute exp(r) by + * + * exp(r) = 1 + r + r*R1/(2-R1), + * where + * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))). + * + * 3. exp(x) = 2^k * exp(r) . + * + * Special cases: + * exp(INF) is INF, exp(NaN) is NaN; + * exp(-INF)= 0; + * for finite argument, only exp(0)=1 is exact. + * + * Accuracy: + * exp(x) returns the exponential of x nearly rounded. In a test run + * with 1,156,000 random arguments on a VAX, the maximum observed + * error was 0.869 ulps (units in the last place). + */ + +#include "mathimpl.h" + +static const double p1 = 0x1.555555555553ep-3; +static const double p2 = -0x1.6c16c16bebd93p-9; +static const double p3 = 0x1.1566aaf25de2cp-14; +static const double p4 = -0x1.bbd41c5d26bf1p-20; +static const double p5 = 0x1.6376972bea4d0p-25; +static const double ln2hi = 0x1.62e42fee00000p-1; +static const double ln2lo = 0x1.a39ef35793c76p-33; +static const double lnhuge = 0x1.6602b15b7ecf2p9; +static const double lntiny = -0x1.77af8ebeae354p9; +static const double invln2 = 0x1.71547652b82fep0; + +#if 0 +OLM_DLLEXPORT double exp(x) +double x; +{ + double z,hi,lo,c; + int k; + +#if !defined(vax)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(vax)&&!defined(tahoe) */ + if( x <= lnhuge ) { + if( x >= lntiny ) { + + /* argument reduction : x --> x - k*ln2 */ + + k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */ + + /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */ + + hi=x-k*ln2hi; + x=hi-(lo=k*ln2lo); + + /* return 2^k*[1+x+x*c/(2+c)] */ + z=x*x; + c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); + return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k); + + } + /* end of x > lntiny */ + + else + /* exp(-big#) underflows to zero */ + if(finite(x)) return(scalb(1.0,-5000)); + + /* exp(-INF) is zero */ + else return(0.0); + } + /* end of x < lnhuge */ + + else + /* exp(INF) is INF, exp(+big#) overflows to INF */ + return( finite(x) ? scalb(1.0,5000) : x); +} +#endif + +/* returns exp(r = x + c) for |c| < |x| with no overlap. */ + +double __exp__D(x, c) +double x, c; +{ + double z,hi,lo; + int k; + + if (x != x) /* x is NaN */ + return(x); + if ( x <= lnhuge ) { + if ( x >= lntiny ) { + + /* argument reduction : x --> x - k*ln2 */ + z = invln2*x; + k = z + copysign(.5, x); + + /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */ + + hi=(x-k*ln2hi); /* Exact. */ + x= hi - (lo = k*ln2lo-c); + /* return 2^k*[1+x+x*c/(2+c)] */ + z=x*x; + c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); + c = (x*c)/(2.0-c); + + return scalbn(1.+(hi-(lo - c)), k); + } + /* end of x > lntiny */ + + else + /* exp(-big#) underflows to zero */ + if(isfinite(x)) return(scalbn(1.0,-5000)); + + /* exp(-INF) is zero */ + else return(0.0); + } + /* end of x < lnhuge */ + + else + /* exp(INF) is INF, exp(+big#) overflows to INF */ + return( isfinite(x) ? scalbn(1.0,5000) : x); +} diff --git a/openlibm/bsdsrc/b_log.c b/openlibm/bsdsrc/b_log.c new file mode 100644 index 0000000..c20d290 --- /dev/null +++ b/openlibm/bsdsrc/b_log.c @@ -0,0 +1,466 @@ +/* + * Copyright (c) 1992, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* @(#)log.c 8.2 (Berkeley) 11/30/93 */ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/bsdsrc/b_log.c,v 1.9 2008/02/22 02:26:51 das Exp $"); + +#include + +#include "mathimpl.h" + +/* Table-driven natural logarithm. + * + * This code was derived, with minor modifications, from: + * Peter Tang, "Table-Driven Implementation of the + * Logarithm in IEEE Floating-Point arithmetic." ACM Trans. + * Math Software, vol 16. no 4, pp 378-400, Dec 1990). + * + * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256, + * where F = j/128 for j an integer in [0, 128]. + * + * log(2^m) = log2_hi*m + log2_tail*m + * since m is an integer, the dominant term is exact. + * m has at most 10 digits (for subnormal numbers), + * and log2_hi has 11 trailing zero bits. + * + * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h + * logF_hi[] + 512 is exact. + * + * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ... + * the leading term is calculated to extra precision in two + * parts, the larger of which adds exactly to the dominant + * m and F terms. + * There are two cases: + * 1. when m, j are non-zero (m | j), use absolute + * precision for the leading term. + * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1). + * In this case, use a relative precision of 24 bits. + * (This is done differently in the original paper) + * + * Special cases: + * 0 return signalling -Inf + * neg return signalling NaN + * +Inf return +Inf +*/ + +#define N 128 + +/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128. + * Used for generation of extend precision logarithms. + * The constant 35184372088832 is 2^45, so the divide is exact. + * It ensures correct reading of logF_head, even for inaccurate + * decimal-to-binary conversion routines. (Everybody gets the + * right answer for integers less than 2^53.) + * Values for log(F) were generated using error < 10^-57 absolute + * with the bc -l package. +*/ +static double A1 = .08333333333333178827; +static double A2 = .01250000000377174923; +static double A3 = .002232139987919447809; +static double A4 = .0004348877777076145742; + +static double logF_head[N+1] = { + 0., + .007782140442060381246, + .015504186535963526694, + .023167059281547608406, + .030771658666765233647, + .038318864302141264488, + .045809536031242714670, + .053244514518837604555, + .060624621816486978786, + .067950661908525944454, + .075223421237524235039, + .082443669210988446138, + .089612158689760690322, + .096729626458454731618, + .103796793681567578460, + .110814366340264314203, + .117783035656430001836, + .124703478501032805070, + .131576357788617315236, + .138402322859292326029, + .145182009844575077295, + .151916042025732167530, + .158605030176659056451, + .165249572895390883786, + .171850256926518341060, + .178407657472689606947, + .184922338493834104156, + .191394852999565046047, + .197825743329758552135, + .204215541428766300668, + .210564769107350002741, + .216873938300523150246, + .223143551314024080056, + .229374101064877322642, + .235566071312860003672, + .241719936886966024758, + .247836163904594286577, + .253915209980732470285, + .259957524436686071567, + .265963548496984003577, + .271933715484010463114, + .277868451003087102435, + .283768173130738432519, + .289633292582948342896, + .295464212893421063199, + .301261330578199704177, + .307025035294827830512, + .312755710004239517729, + .318453731118097493890, + .324119468654316733591, + .329753286372579168528, + .335355541920762334484, + .340926586970454081892, + .346466767346100823488, + .351976423156884266063, + .357455888922231679316, + .362905493689140712376, + .368325561158599157352, + .373716409793814818840, + .379078352934811846353, + .384411698910298582632, + .389716751140440464951, + .394993808240542421117, + .400243164127459749579, + .405465108107819105498, + .410659924985338875558, + .415827895143593195825, + .420969294644237379543, + .426084395310681429691, + .431173464818130014464, + .436236766774527495726, + .441274560805140936281, + .446287102628048160113, + .451274644139630254358, + .456237433481874177232, + .461175715122408291790, + .466089729924533457960, + .470979715219073113985, + .475845904869856894947, + .480688529345570714212, + .485507815781602403149, + .490303988045525329653, + .495077266798034543171, + .499827869556611403822, + .504556010751912253908, + .509261901790523552335, + .513945751101346104405, + .518607764208354637958, + .523248143765158602036, + .527867089620485785417, + .532464798869114019908, + .537041465897345915436, + .541597282432121573947, + .546132437597407260909, + .550647117952394182793, + .555141507540611200965, + .559615787935399566777, + .564070138285387656651, + .568504735352689749561, + .572919753562018740922, + .577315365035246941260, + .581691739635061821900, + .586049045003164792433, + .590387446602107957005, + .594707107746216934174, + .599008189645246602594, + .603290851438941899687, + .607555250224322662688, + .611801541106615331955, + .616029877215623855590, + .620240409751204424537, + .624433288012369303032, + .628608659422752680256, + .632766669570628437213, + .636907462236194987781, + .641031179420679109171, + .645137961373620782978, + .649227946625615004450, + .653301272011958644725, + .657358072709030238911, + .661398482245203922502, + .665422632544505177065, + .669430653942981734871, + .673422675212350441142, + .677398823590920073911, + .681359224807238206267, + .685304003098281100392, + .689233281238557538017, + .693147180560117703862 +}; + +static double logF_tail[N+1] = { + 0., + -.00000000000000543229938420049, + .00000000000000172745674997061, + -.00000000000001323017818229233, + -.00000000000001154527628289872, + -.00000000000000466529469958300, + .00000000000005148849572685810, + -.00000000000002532168943117445, + -.00000000000005213620639136504, + -.00000000000001819506003016881, + .00000000000006329065958724544, + .00000000000008614512936087814, + -.00000000000007355770219435028, + .00000000000009638067658552277, + .00000000000007598636597194141, + .00000000000002579999128306990, + -.00000000000004654729747598444, + -.00000000000007556920687451336, + .00000000000010195735223708472, + -.00000000000017319034406422306, + -.00000000000007718001336828098, + .00000000000010980754099855238, + -.00000000000002047235780046195, + -.00000000000008372091099235912, + .00000000000014088127937111135, + .00000000000012869017157588257, + .00000000000017788850778198106, + .00000000000006440856150696891, + .00000000000016132822667240822, + -.00000000000007540916511956188, + -.00000000000000036507188831790, + .00000000000009120937249914984, + .00000000000018567570959796010, + -.00000000000003149265065191483, + -.00000000000009309459495196889, + .00000000000017914338601329117, + -.00000000000001302979717330866, + .00000000000023097385217586939, + .00000000000023999540484211737, + .00000000000015393776174455408, + -.00000000000036870428315837678, + .00000000000036920375082080089, + -.00000000000009383417223663699, + .00000000000009433398189512690, + .00000000000041481318704258568, + -.00000000000003792316480209314, + .00000000000008403156304792424, + -.00000000000034262934348285429, + .00000000000043712191957429145, + -.00000000000010475750058776541, + -.00000000000011118671389559323, + .00000000000037549577257259853, + .00000000000013912841212197565, + .00000000000010775743037572640, + .00000000000029391859187648000, + -.00000000000042790509060060774, + .00000000000022774076114039555, + .00000000000010849569622967912, + -.00000000000023073801945705758, + .00000000000015761203773969435, + .00000000000003345710269544082, + -.00000000000041525158063436123, + .00000000000032655698896907146, + -.00000000000044704265010452446, + .00000000000034527647952039772, + -.00000000000007048962392109746, + .00000000000011776978751369214, + -.00000000000010774341461609578, + .00000000000021863343293215910, + .00000000000024132639491333131, + .00000000000039057462209830700, + -.00000000000026570679203560751, + .00000000000037135141919592021, + -.00000000000017166921336082431, + -.00000000000028658285157914353, + -.00000000000023812542263446809, + .00000000000006576659768580062, + -.00000000000028210143846181267, + .00000000000010701931762114254, + .00000000000018119346366441110, + .00000000000009840465278232627, + -.00000000000033149150282752542, + -.00000000000018302857356041668, + -.00000000000016207400156744949, + .00000000000048303314949553201, + -.00000000000071560553172382115, + .00000000000088821239518571855, + -.00000000000030900580513238244, + -.00000000000061076551972851496, + .00000000000035659969663347830, + .00000000000035782396591276383, + -.00000000000046226087001544578, + .00000000000062279762917225156, + .00000000000072838947272065741, + .00000000000026809646615211673, + -.00000000000010960825046059278, + .00000000000002311949383800537, + -.00000000000058469058005299247, + -.00000000000002103748251144494, + -.00000000000023323182945587408, + -.00000000000042333694288141916, + -.00000000000043933937969737844, + .00000000000041341647073835565, + .00000000000006841763641591466, + .00000000000047585534004430641, + .00000000000083679678674757695, + -.00000000000085763734646658640, + .00000000000021913281229340092, + -.00000000000062242842536431148, + -.00000000000010983594325438430, + .00000000000065310431377633651, + -.00000000000047580199021710769, + -.00000000000037854251265457040, + .00000000000040939233218678664, + .00000000000087424383914858291, + .00000000000025218188456842882, + -.00000000000003608131360422557, + -.00000000000050518555924280902, + .00000000000078699403323355317, + -.00000000000067020876961949060, + .00000000000016108575753932458, + .00000000000058527188436251509, + -.00000000000035246757297904791, + -.00000000000018372084495629058, + .00000000000088606689813494916, + .00000000000066486268071468700, + .00000000000063831615170646519, + .00000000000025144230728376072, + -.00000000000017239444525614834 +}; + +#if 0 +OLM_DLLEXPORT double +#ifdef _ANSI_SOURCE +log(double x) +#else +log(x) double x; +#endif +{ + int m, j; + double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0; + volatile double u1; + + /* Catch special cases */ + if (x <= 0) + if (x == zero) /* log(0) = -Inf */ + return (-one/zero); + else /* log(neg) = NaN */ + return (zero/zero); + else if (!finite(x)) + return (x+x); /* x = NaN, Inf */ + + /* Argument reduction: 1 <= g < 2; x/2^m = g; */ + /* y = F*(1 + f/F) for |f| <= 2^-8 */ + + m = logb(x); + g = ldexp(x, -m); + if (m == -1022) { + j = logb(g), m += j; + g = ldexp(g, -j); + } + j = N*(g-1) + .5; + F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */ + f = g - F; + + /* Approximate expansion for log(1+f/F) ~= u + q */ + g = 1/(2*F+f); + u = 2*f*g; + v = u*u; + q = u*v*(A1 + v*(A2 + v*(A3 + v*A4))); + + /* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8, + * u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits. + * It also adds exactly to |m*log2_hi + log_F_head[j] | < 750 + */ + if (m | j) + u1 = u + 513, u1 -= 513; + + /* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero; + * u1 = u to 24 bits. + */ + else + u1 = u, TRUNC(u1); + u2 = (2.0*(f - F*u1) - u1*f) * g; + /* u1 + u2 = 2f/(2F+f) to extra precision. */ + + /* log(x) = log(2^m*F*(1+f/F)) = */ + /* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */ + /* (exact) + (tiny) */ + + u1 += m*logF_head[N] + logF_head[j]; /* exact */ + u2 = (u2 + logF_tail[j]) + q; /* tiny */ + u2 += logF_tail[N]*m; + return (u1 + u2); +} +#endif + +/* + * Extra precision variant, returning struct {double a, b;}; + * log(x) = a+b to 63 bits, with a rounded to 26 bits. + */ +struct Double +#ifdef _ANSI_SOURCE +__log__D(double x) +#else +__log__D(x) double x; +#endif +{ + int m, j; + double F, f, g, q, u, v, u2; + volatile double u1; + struct Double r; + + /* Argument reduction: 1 <= g < 2; x/2^m = g; */ + /* y = F*(1 + f/F) for |f| <= 2^-8 */ + + m = logb(x); + g = ldexp(x, -m); + if (m == -1022) { + j = logb(g), m += j; + g = ldexp(g, -j); + } + j = N*(g-1) + .5; + F = (1.0/N) * j + 1; + f = g - F; + + g = 1/(2*F+f); + u = 2*f*g; + v = u*u; + q = u*v*(A1 + v*(A2 + v*(A3 + v*A4))); + if (m | j) + u1 = u + 513, u1 -= 513; + else + u1 = u, TRUNC(u1); + u2 = (2.0*(f - F*u1) - u1*f) * g; + + u1 += m*logF_head[N] + logF_head[j]; + + u2 += logF_tail[j]; u2 += q; + u2 += logF_tail[N]*m; + r.a = u1 + u2; /* Only difference is here */ + TRUNC(r.a); + r.b = (u1 - r.a) + u2; + return (r); +} diff --git a/openlibm/bsdsrc/b_tgamma.c b/openlibm/bsdsrc/b_tgamma.c new file mode 100644 index 0000000..f3871de --- /dev/null +++ b/openlibm/bsdsrc/b_tgamma.c @@ -0,0 +1,319 @@ +/*- + * Copyright (c) 1992, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* @(#)gamma.c 8.1 (Berkeley) 6/4/93 */ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/bsdsrc/b_tgamma.c,v 1.10 2008/02/22 02:26:51 das Exp $"); + +/* + * This code by P. McIlroy, Oct 1992; + * + * The financial support of UUNET Communications Services is greatfully + * acknowledged. + */ + +#include +#include + +#include "mathimpl.h" + +/* METHOD: + * x < 0: Use reflection formula, G(x) = pi/(sin(pi*x)*x*G(x)) + * At negative integers, return NaN and raise invalid. + * + * x < 6.5: + * Use argument reduction G(x+1) = xG(x) to reach the + * range [1.066124,2.066124]. Use a rational + * approximation centered at the minimum (x0+1) to + * ensure monotonicity. + * + * x >= 6.5: Use the asymptotic approximation (Stirling's formula) + * adjusted for equal-ripples: + * + * log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + 1/x*P(1/(x*x)) + * + * Keep extra precision in multiplying (x-.5)(log(x)-1), to + * avoid premature round-off. + * + * Special values: + * -Inf: return NaN and raise invalid; + * negative integer: return NaN and raise invalid; + * other x ~< 177.79: return +-0 and raise underflow; + * +-0: return +-Inf and raise divide-by-zero; + * finite x ~> 171.63: return +Inf and raise overflow; + * +Inf: return +Inf; + * NaN: return NaN. + * + * Accuracy: tgamma(x) is accurate to within + * x > 0: error provably < 0.9ulp. + * Maximum observed in 1,000,000 trials was .87ulp. + * x < 0: + * Maximum observed error < 4ulp in 1,000,000 trials. + */ + +static double neg_gam(double); +static double small_gam(double); +static double smaller_gam(double); +static struct Double large_gam(double); +static struct Double ratfun_gam(double, double); + +/* + * Rational approximation, A0 + x*x*P(x)/Q(x), on the interval + * [1.066.., 2.066..] accurate to 4.25e-19. + */ +#define LEFT -.3955078125 /* left boundary for rat. approx */ +#define x0 .461632144968362356785 /* xmin - 1 */ + +#define a0_hi 0.88560319441088874992 +#define a0_lo -.00000000000000004996427036469019695 +#define P0 6.21389571821820863029017800727e-01 +#define P1 2.65757198651533466104979197553e-01 +#define P2 5.53859446429917461063308081748e-03 +#define P3 1.38456698304096573887145282811e-03 +#define P4 2.40659950032711365819348969808e-03 +#define Q0 1.45019531250000000000000000000e+00 +#define Q1 1.06258521948016171343454061571e+00 +#define Q2 -2.07474561943859936441469926649e-01 +#define Q3 -1.46734131782005422506287573015e-01 +#define Q4 3.07878176156175520361557573779e-02 +#define Q5 5.12449347980666221336054633184e-03 +#define Q6 -1.76012741431666995019222898833e-03 +#define Q7 9.35021023573788935372153030556e-05 +#define Q8 6.13275507472443958924745652239e-06 +/* + * Constants for large x approximation (x in [6, Inf]) + * (Accurate to 2.8*10^-19 absolute) + */ +#define lns2pi_hi 0.418945312500000 +#define lns2pi_lo -.000006779295327258219670263595 +#define Pa0 8.33333333333333148296162562474e-02 +#define Pa1 -2.77777777774548123579378966497e-03 +#define Pa2 7.93650778754435631476282786423e-04 +#define Pa3 -5.95235082566672847950717262222e-04 +#define Pa4 8.41428560346653702135821806252e-04 +#define Pa5 -1.89773526463879200348872089421e-03 +#define Pa6 5.69394463439411649408050664078e-03 +#define Pa7 -1.44705562421428915453880392761e-02 + +static const double zero = 0., one = 1.0, tiny = 1e-300; + +OLM_DLLEXPORT double +tgamma(x) + double x; +{ + struct Double u; + + if (isgreaterequal(x, 6)) { + if(x > 171.63) + return (x / zero); + u = large_gam(x); + return(__exp__D(u.a, u.b)); + } else if (isgreaterequal(x, 1.0 + LEFT + x0)) + return (small_gam(x)); + else if (isgreater(x, 1.e-17)) + return (smaller_gam(x)); + else if (isgreater(x, -1.e-17)) { + if (x != 0.0) + u.a = one - tiny; /* raise inexact */ + return (one/x); + } else if (!isfinite(x)) + return (x - x); /* x is NaN or -Inf */ + else + return (neg_gam(x)); +} +/* + * Accurate to max(ulp(1/128) absolute, 2^-66 relative) error. + */ +static struct Double +large_gam(x) + double x; +{ + double z, p; + struct Double t, u, v; + + z = one/(x*x); + p = Pa0+z*(Pa1+z*(Pa2+z*(Pa3+z*(Pa4+z*(Pa5+z*(Pa6+z*Pa7)))))); + p = p/x; + + u = __log__D(x); + u.a -= one; + v.a = (x -= .5); + TRUNC(v.a); + v.b = x - v.a; + t.a = v.a*u.a; /* t = (x-.5)*(log(x)-1) */ + t.b = v.b*u.a + x*u.b; + /* return t.a + t.b + lns2pi_hi + lns2pi_lo + p */ + t.b += lns2pi_lo; t.b += p; + u.a = lns2pi_hi + t.b; u.a += t.a; + u.b = t.a - u.a; + u.b += lns2pi_hi; u.b += t.b; + return (u); +} +/* + * Good to < 1 ulp. (provably .90 ulp; .87 ulp on 1,000,000 runs.) + * It also has correct monotonicity. + */ +static double +small_gam(x) + double x; +{ + double y, ym1, t; + struct Double yy, r; + y = x - one; + ym1 = y - one; + if (y <= 1.0 + (LEFT + x0)) { + yy = ratfun_gam(y - x0, 0); + return (yy.a + yy.b); + } + r.a = y; + TRUNC(r.a); + yy.a = r.a - one; + y = ym1; + yy.b = r.b = y - yy.a; + /* Argument reduction: G(x+1) = x*G(x) */ + for (ym1 = y-one; ym1 > LEFT + x0; y = ym1--, yy.a--) { + t = r.a*yy.a; + r.b = r.a*yy.b + y*r.b; + r.a = t; + TRUNC(r.a); + r.b += (t - r.a); + } + /* Return r*tgamma(y). */ + yy = ratfun_gam(y - x0, 0); + y = r.b*(yy.a + yy.b) + r.a*yy.b; + y += yy.a*r.a; + return (y); +} +/* + * Good on (0, 1+x0+LEFT]. Accurate to 1ulp. + */ +static double +smaller_gam(x) + double x; +{ + double t, d; + struct Double r, xx; + if (x < x0 + LEFT) { + t = x, TRUNC(t); + d = (t+x)*(x-t); + t *= t; + xx.a = (t + x), TRUNC(xx.a); + xx.b = x - xx.a; xx.b += t; xx.b += d; + t = (one-x0); t += x; + d = (one-x0); d -= t; d += x; + x = xx.a + xx.b; + } else { + xx.a = x, TRUNC(xx.a); + xx.b = x - xx.a; + t = x - x0; + d = (-x0 -t); d += x; + } + r = ratfun_gam(t, d); + d = r.a/x, TRUNC(d); + r.a -= d*xx.a; r.a -= d*xx.b; r.a += r.b; + return (d + r.a/x); +} +/* + * returns (z+c)^2 * P(z)/Q(z) + a0 + */ +static struct Double +ratfun_gam(z, c) + double z, c; +{ + double p, q; + struct Double r, t; + + q = Q0 +z*(Q1+z*(Q2+z*(Q3+z*(Q4+z*(Q5+z*(Q6+z*(Q7+z*Q8))))))); + p = P0 + z*(P1 + z*(P2 + z*(P3 + z*P4))); + + /* return r.a + r.b = a0 + (z+c)^2*p/q, with r.a truncated to 26 bits. */ + p = p/q; + t.a = z, TRUNC(t.a); /* t ~= z + c */ + t.b = (z - t.a) + c; + t.b *= (t.a + z); + q = (t.a *= t.a); /* t = (z+c)^2 */ + TRUNC(t.a); + t.b += (q - t.a); + r.a = p, TRUNC(r.a); /* r = P/Q */ + r.b = p - r.a; + t.b = t.b*p + t.a*r.b + a0_lo; + t.a *= r.a; /* t = (z+c)^2*(P/Q) */ + r.a = t.a + a0_hi, TRUNC(r.a); + r.b = ((a0_hi-r.a) + t.a) + t.b; + return (r); /* r = a0 + t */ +} + +static double +neg_gam(x) + double x; +{ + int sgn = 1; + struct Double lg, lsine; + double y, z; + + y = ceil(x); + if (y == x) /* Negative integer. */ + return ((x - x) / zero); + z = y - x; + if (z > 0.5) + z = one - z; + y = 0.5 * y; + if (y == ceil(y)) + sgn = -1; + if (z < .25) + z = sin(M_PI*z); + else + z = cos(M_PI*(0.5-z)); + /* Special case: G(1-x) = Inf; G(x) may be nonzero. */ + if (x < -170) { + if (x < -190) + return ((double)sgn*tiny*tiny); + y = one - x; /* exact: 128 < |x| < 255 */ + lg = large_gam(y); + lsine = __log__D(M_PI/z); /* = TRUNC(log(u)) + small */ + lg.a -= lsine.a; /* exact (opposite signs) */ + lg.b -= lsine.b; + y = -(lg.a + lg.b); + z = (y + lg.a) + lg.b; + y = __exp__D(y, z); + if (sgn < 0) y = -y; + return (y); + } + y = one-x; + if (one-y == x) + y = tgamma(y); + else /* 1-x is inexact */ + y = -x*tgamma(-x); + if (sgn < 0) y = -y; + return (M_PI / (y*z)); +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(tgamma, tgammal); +#endif diff --git a/openlibm/bsdsrc/mathimpl.h b/openlibm/bsdsrc/mathimpl.h new file mode 100644 index 0000000..983c4eb --- /dev/null +++ b/openlibm/bsdsrc/mathimpl.h @@ -0,0 +1,70 @@ +/* + * Copyright (c) 1988, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * @(#)mathimpl.h 8.1 (Berkeley) 6/4/93 + * $FreeBSD: src/lib/msun/bsdsrc/mathimpl.h,v 1.7 2005/11/18 05:03:12 bde Exp $ + */ + +#ifndef _MATHIMPL_H_ +#define _MATHIMPL_H_ + +#include "cdefs-compat.h" +#include "math_private.h" + +/* + * TRUNC() is a macro that sets the trailing 27 bits in the mantissa of an + * IEEE double variable to zero. It must be expression-like for syntactic + * reasons, and we implement this expression using an inline function + * instead of a pure macro to avoid depending on the gcc feature of + * statement-expressions. + */ +#define TRUNC(d) (_b_trunc(&(d))) + +static __inline void +_b_trunc(volatile double *_dp) +{ + //VBS + //u_int32_t _lw; + u_int32_t _lw; + + GET_LOW_WORD(_lw, *_dp); + SET_LOW_WORD(*_dp, _lw & 0xf8000000); +} + +struct Double { + double a; + double b; +}; + +/* + * Functions internal to the math package, yet not static. + */ +double __exp__D(double, double); +struct Double __log__D(double); + +#endif /* !_MATHIMPL_H_ */ diff --git a/openlibm/docs/CNAME b/openlibm/docs/CNAME new file mode 100644 index 0000000..60f23f5 --- /dev/null +++ b/openlibm/docs/CNAME @@ -0,0 +1 @@ +openlibm.org \ No newline at end of file diff --git a/openlibm/docs/images/arrow-down.png b/openlibm/docs/images/arrow-down.png new file mode 100644 index 0000000000000000000000000000000000000000..5c55c6a8c9edfaa47379862d770304c36c3ac7ff GIT binary patch literal 216 zcmeAS@N?(olHy`uVBq!ia0vp^JU}eW!3HFke0{SLNX_?jaSYLzn4I9i%II*Xp^aIh zpz+6!8``B?P5)0c^x#?E7OdXC_y6D5zw1+Ygru)Ji1RWzykR(WyifLD&pJjGw#n?P zLqkH=Y}vm3H~*pZ^K<_6Lqu1mGH{74&_2}6eISp?=$Y`s3cD`%ef7U|_uU`DGt*!YlC@Am|DD>an&JK*_ z<>mi__UCKux;y>4Pqor7j|)IU*M9Gw z-IGbu2m_ZdUGO1GBT$h55cdP|c_4ld#Or}LA6*>)0_L))J+G2e00000NkvXXu0mjf DP-vTT literal 0 HcmV?d00001 diff --git a/openlibm/docs/index.html b/openlibm/docs/index.html new file mode 100644 index 0000000..2926cc8 --- /dev/null +++ b/openlibm/docs/index.html @@ -0,0 +1,93 @@ + + + + + + OpenLibm + + + + + + + +
+
+

OpenLibm

+

A high quality system independent, portable, open source libm implementation

+ + + +

This project is maintained by the Julia Project

+ + +
+
+

+OpenLibm

+ +

OpenLibm is an effort to have a high quality, portable, standalone +C mathematical library (libm). +It can be used standalone in applications and programming language +implementations.

+ +

The project was born out of a need to have a good libm for the +Julia programming langage that worked +consistently across compilers and operating systems, and in 32-bit and +64-bit environments.

+ +

+History

+ +

The OpenLibm code derives from the FreeBSD +msun and OpenBSD +libm +implementations, which in turn derive from FDLIBM +5.3. Over and above that, OpenLibm itself has received a number of patches to make it platform independent and portable.

+ +

+Platform support

+ +

OpenLibm builds on Linux, macOS, Windows, FreeBSD, OpenBSD, NetBSD, and +DragonFly BSD. It builds with both GCC and clang. Although largely +tested and widely used on the x86 and x86-64 architectures, OpenLibm +also supports arm, aarch64, ppc64le, mips, wasm32, and s390(x). + +

+Other relevant projects

+ +
    +
  1. MUSL The libm library in the musl-libc project
    2. +
  2. FDLIBM: Freely Distributable Math Library
    3. +
  3. FreeBSD msun: FreeBSD's math library
    4. +
  4. CRlibm: Correctly Rounded mathematical library
    5. +
+ +

+Acknowledgements

+ +

PowerPC support for OpenLibm was graciously sponsored by IBM. + + +

+ +
+ + + + + + diff --git a/openlibm/docs/javascripts/scale.fix.js b/openlibm/docs/javascripts/scale.fix.js new file mode 100644 index 0000000..08716c0 --- /dev/null +++ b/openlibm/docs/javascripts/scale.fix.js @@ -0,0 +1,20 @@ +fixScale = function(doc) { + + var addEvent = 'addEventListener', + type = 'gesturestart', + qsa = 'querySelectorAll', + scales = [1, 1], + meta = qsa in doc ? doc[qsa]('meta[name=viewport]') : []; + + function fix() { + meta.content = 'width=device-width,minimum-scale=' + scales[0] + ',maximum-scale=' + scales[1]; + doc.removeEventListener(type, fix, true); + } + + if ((meta = meta[meta.length - 1]) && addEvent in doc) { + fix(); + scales = [.25, 1.6]; + doc[addEvent](type, fix, true); + } + +}; \ No newline at end of file diff --git a/openlibm/docs/params.json b/openlibm/docs/params.json new file mode 100644 index 0000000..cd0a5ed --- /dev/null +++ b/openlibm/docs/params.json @@ -0,0 +1 @@ +{"name":"OpenLibm","tagline":"A high quality system independent, portable, open source libm implementation","body":"## OpenLibm\r\n\r\n[OpenLibm](http://www.openlibm.org) is an effort to have a high quality, portable, standalone\r\nC mathematical library ([`libm`](http://en.wikipedia.org/wiki/libm)).\r\nIt can be used standalone in applications and programming language\r\nimplementations.\r\n\r\nThe project was born out of a need to have a good `libm` for the\r\n[Julia programming langage](http://www.julialang.org) that worked\r\nconsistently across compilers and operating systems, and in 32-bit and\r\n64-bit environments.\r\n\r\n### History\r\n\r\nThe OpenLibm code derives from the [FreeBSD\r\nmsun](http://svnweb.freebsd.org/base/head/lib/msun/) and [OpenBSD\r\nlibm](http://cvsweb.openbsd.org/cgi-bin/cvsweb/src/lib/libm/src/)\r\nimplementations, which in turn derives from [FDLIBM\r\n5.3](http://www.netlib.org/fdlibm/). As a result, it includes a number\r\nof fixes and updates to FDLIBM that have accumulated over the years in\r\n`msun`, and optimized versions of many functions.\r\n\r\n### Platform support\r\n\r\nOpenLibm builds on Linux, Mac OS X, and Windows, and with little\r\neffort, should build on FreeBSD as well. It builds with both GCC and\r\nclang. Although largely tested on x86, it also includes experimental\r\nsupport for ARM. The original `msun` also includes support for mips,\r\nsparc64, powerpc, ia64, and alpha. These are present in the OpenLibm\r\nsource tree, but no attempt has been made to build any of these.\r\n\r\n### Build instructions\r\n\r\n1. `make` or `make USEGCC=1` to build with GCC. This is the default on\r\n Linux and Windows.\r\n2. `make USECLANG=1` to build with clang. This is the default on OS X.\r\n","google":"UA-28835595-4","note":"Don't delete this file! It's used internally to help with page regeneration."} \ No newline at end of file diff --git a/openlibm/docs/stylesheets/pygment_trac.css b/openlibm/docs/stylesheets/pygment_trac.css new file mode 100644 index 0000000..c6a6452 --- /dev/null +++ b/openlibm/docs/stylesheets/pygment_trac.css @@ -0,0 +1,69 @@ +.highlight { background: #ffffff; } +.highlight .c { color: #999988; font-style: italic } /* Comment */ +.highlight .err { color: #a61717; background-color: #e3d2d2 } /* Error */ +.highlight .k { font-weight: bold } /* Keyword */ +.highlight .o { font-weight: bold } /* Operator */ +.highlight .cm { color: #999988; font-style: italic } /* Comment.Multiline */ +.highlight .cp { color: #999999; font-weight: bold } /* Comment.Preproc */ +.highlight .c1 { color: #999988; font-style: italic } /* Comment.Single */ +.highlight .cs { color: #999999; font-weight: bold; font-style: italic } /* Comment.Special */ +.highlight .gd { color: #000000; background-color: #ffdddd } /* Generic.Deleted */ +.highlight .gd .x { color: #000000; background-color: #ffaaaa } /* Generic.Deleted.Specific */ +.highlight .ge { font-style: italic } /* Generic.Emph */ +.highlight .gr { color: #aa0000 } /* Generic.Error */ +.highlight .gh { color: #999999 } /* Generic.Heading */ +.highlight .gi { color: #000000; background-color: #ddffdd } /* Generic.Inserted */ +.highlight .gi .x { color: #000000; background-color: #aaffaa } /* Generic.Inserted.Specific */ +.highlight .go { color: #888888 } /* Generic.Output */ +.highlight .gp { color: #555555 } /* Generic.Prompt */ +.highlight .gs { font-weight: bold } /* Generic.Strong */ +.highlight .gu { color: #800080; font-weight: bold; } /* Generic.Subheading */ +.highlight .gt { color: #aa0000 } /* Generic.Traceback */ +.highlight .kc { font-weight: bold } /* Keyword.Constant */ +.highlight .kd { font-weight: bold } /* Keyword.Declaration */ +.highlight .kn { font-weight: bold } /* Keyword.Namespace */ +.highlight .kp { font-weight: bold } /* Keyword.Pseudo */ +.highlight .kr { font-weight: bold } /* Keyword.Reserved */ +.highlight .kt { color: #445588; font-weight: bold } /* Keyword.Type */ +.highlight .m { color: #009999 } /* Literal.Number */ +.highlight .s { color: #d14 } /* Literal.String */ +.highlight .na { color: #008080 } /* Name.Attribute */ +.highlight .nb { color: #0086B3 } /* Name.Builtin */ +.highlight .nc { color: #445588; font-weight: bold } /* Name.Class */ +.highlight .no { color: #008080 } /* Name.Constant */ +.highlight .ni { color: #800080 } /* Name.Entity */ +.highlight .ne { color: #990000; font-weight: bold } /* Name.Exception */ +.highlight .nf { color: #990000; font-weight: bold } /* Name.Function */ +.highlight .nn { color: #555555 } /* Name.Namespace */ +.highlight .nt { color: #000080 } /* Name.Tag */ +.highlight .nv { color: #008080 } /* Name.Variable */ +.highlight .ow { font-weight: bold } /* Operator.Word */ +.highlight .w { color: #bbbbbb } /* Text.Whitespace */ +.highlight .mf { color: #009999 } /* Literal.Number.Float */ +.highlight .mh { color: #009999 } /* Literal.Number.Hex */ +.highlight .mi { color: #009999 } /* Literal.Number.Integer */ +.highlight .mo { color: #009999 } /* Literal.Number.Oct */ +.highlight .sb { color: #d14 } /* Literal.String.Backtick */ +.highlight .sc { color: #d14 } /* Literal.String.Char */ +.highlight .sd { color: #d14 } /* Literal.String.Doc */ +.highlight .s2 { color: #d14 } /* Literal.String.Double */ +.highlight .se { color: #d14 } /* Literal.String.Escape */ +.highlight .sh { color: #d14 } /* Literal.String.Heredoc */ +.highlight .si { color: #d14 } /* Literal.String.Interpol */ +.highlight .sx { color: #d14 } /* Literal.String.Other */ +.highlight .sr { color: #009926 } /* Literal.String.Regex */ +.highlight .s1 { color: #d14 } /* Literal.String.Single */ +.highlight .ss { color: #990073 } /* Literal.String.Symbol */ +.highlight .bp { color: #999999 } /* Name.Builtin.Pseudo */ +.highlight .vc { color: #008080 } /* Name.Variable.Class */ +.highlight .vg { color: #008080 } /* Name.Variable.Global */ +.highlight .vi { color: #008080 } /* Name.Variable.Instance */ +.highlight .il { color: #009999 } /* Literal.Number.Integer.Long */ + +.type-csharp .highlight .k { color: #0000FF } +.type-csharp .highlight .kt { color: #0000FF } +.type-csharp .highlight .nf { color: #000000; font-weight: normal } +.type-csharp .highlight .nc { color: #2B91AF } +.type-csharp .highlight .nn { color: #000000 } +.type-csharp .highlight .s { color: #A31515 } +.type-csharp .highlight .sc { color: #A31515 } diff --git a/openlibm/docs/stylesheets/styles.css b/openlibm/docs/stylesheets/styles.css new file mode 100644 index 0000000..647f08d --- /dev/null +++ b/openlibm/docs/stylesheets/styles.css @@ -0,0 +1,423 @@ +@import url(https://fonts.googleapis.com/css?family=Arvo:400,700,400italic); + +/* MeyerWeb Reset */ + +html, body, div, span, applet, object, iframe, +h1, h2, h3, h4, h5, h6, p, blockquote, pre, +a, abbr, acronym, address, big, cite, code, +del, dfn, em, img, ins, kbd, q, s, samp, +small, strike, strong, sub, sup, tt, var, +b, u, i, center, +dl, dt, dd, ol, ul, li, +fieldset, form, label, legend, +table, caption, tbody, tfoot, thead, tr, th, td, +article, aside, canvas, details, embed, +figure, figcaption, footer, header, hgroup, +menu, nav, output, ruby, section, summary, +time, mark, audio, video { + margin: 0; + padding: 0; + border: 0; + font: inherit; + vertical-align: baseline; +} + + +/* Base text styles */ + +body { + padding:10px 50px 0 0; + font-family:"Helvetica Neue", Helvetica, Arial, sans-serif; + font-size: 14px; + color: #232323; + background-color: #FBFAF7; + margin: 0; + line-height: 1.8em; + -webkit-font-smoothing: antialiased; + +} + +h1, h2, h3, h4, h5, h6 { + color:#232323; + margin:36px 0 10px; +} + +p, ul, ol, table, dl { + margin:0 0 22px; +} + +h1, h2, h3 { + font-family: Arvo, Monaco, serif; + line-height:1.3; + font-weight: normal; +} + +h1,h2, h3 { + display: block; + border-bottom: 1px solid #ccc; + padding-bottom: 5px; +} + +h1 { + font-size: 30px; +} + +h2 { + font-size: 24px; +} + +h3 { + font-size: 18px; +} + +h4, h5, h6 { + font-family: Arvo, Monaco, serif; + font-weight: 700; +} + +a { + color:#C30000; + font-weight:200; + text-decoration:none; +} + +a:hover { + text-decoration: underline; +} + +a small { + font-size: 12px; +} + +em { + font-style: italic; +} + +strong { + font-weight:700; +} + +ul { + list-style-position: inside; + list-style: disc; + padding-left: 25px; +} + +ol { + list-style-position: inside; + list-style: decimal; + padding-left: 25px; +} + +blockquote { + margin: 0; + padding: 0 0 0 20px; + font-style: italic; +} + +dl, dt, dd, dl p { + font-color: #444; +} + +dl dt { + font-weight: bold; +} + +dl dd { + padding-left: 20px; + font-style: italic; +} + +dl p { + padding-left: 20px; + font-style: italic; +} + +hr { + border:0; + background:#ccc; + height:1px; + margin:0 0 24px; +} + +/* Images */ + +img { + position: relative; + margin: 0 auto; + max-width: 650px; + padding: 5px; + margin: 10px 0 32px 0; + border: 1px solid #ccc; +} + +p img { + display: inline; + margin: 0; + padding: 0; + vertical-align: middle; + text-align: center; + border: none; +} + +/* Code blocks */ + +code, pre { + font-family: Monaco, "Bitstream Vera Sans Mono", "Lucida Console", Terminal, monospace; + color:#000; + font-size:14px; +} + +pre { + padding: 4px 12px; + background: #FDFEFB; + border-radius:4px; + border:1px solid #D7D8C8; + overflow: auto; + overflow-y: hidden; + margin-bottom: 32px; +} + + +/* Tables */ + +table { + width:100%; +} + +table { + border: 1px solid #ccc; + margin-bottom: 32px; + text-align: left; + } + +th { + font-family: 'Arvo', Helvetica, Arial, sans-serif; + font-size: 18px; + font-weight: normal; + padding: 10px; + background: #232323; + color: #FDFEFB; + } + +td { + padding: 10px; + background: #ccc; + } + + +/* Wrapper */ +.wrapper { + width:960px; +} + + +/* Header */ + +header { + background-color: #171717; + color: #FDFDFB; + width:170px; + float:left; + position:fixed; + border: 1px solid #000; + -webkit-border-top-right-radius: 4px; + -webkit-border-bottom-right-radius: 4px; + -moz-border-radius-topright: 4px; + -moz-border-radius-bottomright: 4px; + border-top-right-radius: 4px; + border-bottom-right-radius: 4px; + padding: 34px 25px 22px 50px; + margin: 30px 25px 0 0; + -webkit-font-smoothing: antialiased; +} + +p.header { + font-size: 16px; +} + +h1.header { + font-family: Arvo, sans-serif; + font-size: 30px; + font-weight: 300; + line-height: 1.3em; + border-bottom: none; + margin-top: 0; +} + + +h1.header, a.header, a.name, header a{ + color: #fff; +} + +a.header { + text-decoration: underline; +} + +a.name { + white-space: nowrap; +} + +header ul { + list-style:none; + padding:0; +} + +header li { + list-style-type: none; + width:132px; + height:15px; + margin-bottom: 12px; + line-height: 1em; + padding: 6px 6px 6px 7px; + + background: #AF0011; + background: -moz-linear-gradient(top, #AF0011 0%, #820011 100%); + background: -webkit-gradient(linear, left top, left bottom, color-stop(0%,#f8f8f8), color-stop(100%,#dddddd)); + background: -webkit-linear-gradient(top, #AF0011 0%,#820011 100%); + background: -o-linear-gradient(top, #AF0011 0%,#820011 100%); + background: -ms-linear-gradient(top, #AF0011 0%,#820011 100%); + background: linear-gradient(top, #AF0011 0%,#820011 100%); + + border-radius:4px; + border:1px solid #0D0D0D; + + -webkit-box-shadow: inset 0px 1px 1px 0 rgba(233,2,38, 1); + box-shadow: inset 0px 1px 1px 0 rgba(233,2,38, 1); + +} + +header li:hover { + background: #C3001D; + background: -moz-linear-gradient(top, #C3001D 0%, #950119 100%); + background: -webkit-gradient(linear, left top, left bottom, color-stop(0%,#f8f8f8), color-stop(100%,#dddddd)); + background: -webkit-linear-gradient(top, #C3001D 0%,#950119 100%); + background: -o-linear-gradient(top, #C3001D 0%,#950119 100%); + background: -ms-linear-gradient(top, #C3001D 0%,#950119 100%); + background: linear-gradient(top, #C3001D 0%,#950119 100%); +} + +a.buttons { + -webkit-font-smoothing: antialiased; + background: url(../images/arrow-down.png) no-repeat; + font-weight: normal; + text-shadow: rgba(0, 0, 0, 0.4) 0 -1px 0; + padding: 2px 2px 2px 22px; + height: 30px; +} + +a.github { + background: url(../images/octocat-small.png) no-repeat 1px; +} + +a.buttons:hover { + color: #fff; + text-decoration: none; +} + + +/* Section - for main page content */ + +section { + width:650px; + float:right; + padding-bottom:50px; +} + + +/* Footer */ + +footer { + width:170px; + float:left; + position:fixed; + bottom:10px; + padding-left: 50px; +} + +@media print, screen and (max-width: 960px) { + + div.wrapper { + width:auto; + margin:0; + } + + header, section, footer { + float:none; + position:static; + width:auto; + } + + footer { + border-top: 1px solid #ccc; + margin:0 84px 0 50px; + padding:0; + } + + header { + padding-right:320px; + } + + section { + padding:20px 84px 20px 50px; + margin:0 0 20px; + } + + header a small { + display:inline; + } + + header ul { + position:absolute; + right:130px; + top:84px; + } +} + +@media print, screen and (max-width: 720px) { + body { + word-wrap:break-word; + } + + header { + padding:10px 20px 0; + margin-right: 0; + } + + section { + padding:10px 0 10px 20px; + margin:0 0 30px; + } + + footer { + margin: 0 0 0 30px; + } + + header ul, header p.view { + position:static; + } +} + +@media print, screen and (max-width: 480px) { + + header ul li.download { + display:none; + } + + footer { + margin: 0 0 0 20px; + } + + footer a{ + display:block; + } + +} + +@media print { + body { + padding:0.4in; + font-size:12pt; + color:#444; + } +} \ No newline at end of file diff --git a/openlibm/i387/Make.files b/openlibm/i387/Make.files new file mode 100644 index 0000000..369c541 --- /dev/null +++ b/openlibm/i387/Make.files @@ -0,0 +1,21 @@ +$(CUR_SRCS) = e_exp.S e_fmod.S e_log.S e_log10.S \ + e_remainder.S e_sqrt.S s_ceil.S s_copysign.S \ + s_floor.S s_llrint.S s_logb.S s_lrint.S \ + s_remquo.S s_rint.S s_tan.S s_trunc.S + +ifneq ($(OS), WINNT) +$(CUR_SRCS) += s_scalbn.S s_scalbnf.S s_scalbnl.S +endif + +# float counterparts +$(CUR_SRCS)+= e_log10f.S e_logf.S e_remainderf.S \ + e_sqrtf.S s_ceilf.S s_copysignf.S s_floorf.S \ + s_llrintf.S s_logbf.S s_lrintf.S \ + s_remquof.S s_rintf.S s_truncf.S + +# long double counterparts +$(CUR_SRCS)+= e_remainderl.S e_sqrtl.S s_ceill.S s_copysignl.S \ + s_floorl.S s_llrintl.S \ + s_logbl.S s_lrintl.S s_remquol.S s_rintl.S s_truncl.S + +$(CUR_SRCS)+= fenv.c diff --git a/openlibm/i387/bsd_asm.h b/openlibm/i387/bsd_asm.h new file mode 100644 index 0000000..93ac617 --- /dev/null +++ b/openlibm/i387/bsd_asm.h @@ -0,0 +1,118 @@ +/*- + * Copyright (c) 1990 The Regents of the University of California. + * All rights reserved. + * + * This code is derived from software contributed to Berkeley by + * William Jolitz. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * from: @(#)DEFS.h 5.1 (Berkeley) 4/23/90 + * $FreeBSD: src/sys/i386/include/asm.h,v 1.14 2007/08/22 04:26:07 jkoshy Exp $ + */ + +#ifndef _MACHINE_ASM_H_ +#define _MACHINE_ASM_H_ + +#if defined(__APPLE__) +#include "osx_asm.h" +#define CNAME(x) EXT(x) +#else +#include "cdefs-compat.h" + +#ifdef PIC +#define PIC_PROLOGUE \ + pushl %ebx; \ + call 1f; \ +1: \ + popl %ebx; \ + addl $_GLOBAL_OFFSET_TABLE_+[.-1b],%ebx +#define PIC_EPILOGUE \ + popl %ebx +#define PIC_PLT(x) x@PLT +#define PIC_GOT(x) x@GOT(%ebx) +#else +#define PIC_PROLOGUE +#define PIC_EPILOGUE +#define PIC_PLT(x) x +#define PIC_GOT(x) x +#endif + +/* + * CNAME and HIDENAME manage the relationship between symbol names in C + * and the equivalent assembly language names. CNAME is given a name as + * it would be used in a C program. It expands to the equivalent assembly + * language name. HIDENAME is given an assembly-language name, and expands + * to a possibly-modified form that will be invisible to C programs. + */ + + +/* XXX should use .p2align 4,0x90 for -m486. */ +#define _START_ENTRY .p2align 2,0x90 + +#if defined(__ELF__) +#define CNAME(csym) csym +#define HIDENAME(asmsym) .asmsym +#define _ENTRY(x) .text; _START_ENTRY; \ + .globl CNAME(x); .type CNAME(x),@function; CNAME(x): +#define END(x) .size x, . - x +#elif defined(_WIN32) +#ifndef _MSC_VER +#define END(x) .end +#define _START_ENTRY_WIN .text; _START_ENTRY +#else +#define END(x) end +#define _START_ENTRY_WIN .code; _START_ENTRY +#endif +#define CNAME(csym) _##csym +#define HIDENAME(asmsym) .asmsym +#define _ENTRY(x) _START_ENTRY_WIN; \ + .globl CNAME(x); .section .drectve; .ascii " -export:", #x; \ + .section .text; .def CNAME(x); .scl 2; .type 32; .endef; CNAME(x): +#endif + +#ifdef PROF +#define ALTENTRY(x) _ENTRY(x); \ + pushl %ebp; movl %esp,%ebp; \ + call PIC_PLT(HIDENAME(mcount)); \ + popl %ebp; \ + jmp 9f +#define ENTRY(x) _ENTRY(x); \ + pushl %ebp; movl %esp,%ebp; \ + call PIC_PLT(HIDENAME(mcount)); \ + popl %ebp; \ + 9: +#else +#define ALTENTRY(x) _ENTRY(x) +#define ENTRY(x) _ENTRY(x) +#endif + +#define RCSID(x) .text; .asciz x + +#undef __FBSDID +#define __FBSDID(s) /* nothing */ + +#endif +#endif /* !_MACHINE_ASM_H_ */ diff --git a/openlibm/i387/bsd_ieeefp.h b/openlibm/i387/bsd_ieeefp.h new file mode 100644 index 0000000..79c7bf3 --- /dev/null +++ b/openlibm/i387/bsd_ieeefp.h @@ -0,0 +1,265 @@ +/*- + * Copyright (c) 2003 Peter Wemm. + * Copyright (c) 1990 Andrew Moore, Talke Studio + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the University of + * California, Berkeley and its contributors. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * from: @(#) ieeefp.h 1.0 (Berkeley) 9/23/93 + * $FreeBSD$ + */ + +#ifndef _MACHINE_IEEEFP_H_ +#define _MACHINE_IEEEFP_H_ + +/* + * Deprecated historical FPU control interface + * + * IEEE floating point type, constant and function definitions. + * XXX: FP*FLD and FP*OFF are undocumented pollution. + */ + +/* VBS + +#ifndef _SYS_CDEFS_H_ +#error this file needs sys/cdefs.h as a prerequisite +#endif + +*/ + +/* + * Rounding modes. + */ +typedef enum { + FP_RN=0, /* round to nearest */ + FP_RM, /* round down towards minus infinity */ + FP_RP, /* round up towards plus infinity */ + FP_RZ /* truncate */ +} fp_rnd_t; + +/* + * Precision (i.e., rounding precision) modes. + */ +typedef enum { + FP_PS=0, /* 24 bit (single-precision) */ + FP_PRS, /* reserved */ + FP_PD, /* 53 bit (double-precision) */ + FP_PE /* 64 bit (extended-precision) */ +} fp_prec_t; + +#define fp_except_t int + +/* + * Exception bit masks. + */ +#define FP_X_INV 0x01 /* invalid operation */ +#define FP_X_DNML 0x02 /* denormal */ +#define FP_X_DZ 0x04 /* zero divide */ +#define FP_X_OFL 0x08 /* overflow */ +#define FP_X_UFL 0x10 /* underflow */ +#define FP_X_IMP 0x20 /* (im)precision */ +#define FP_X_STK 0x40 /* stack fault */ + +/* + * FPU control word bit-field masks. + */ +#define FP_MSKS_FLD 0x3f /* exception masks field */ +#define FP_PRC_FLD 0x300 /* precision control field */ +#define FP_RND_FLD 0xc00 /* rounding control field */ + +/* + * FPU status word bit-field masks. + */ +#define FP_STKY_FLD 0x3f /* sticky flags field */ + +/* + * FPU control word bit-field offsets (shift counts). + */ +#define FP_MSKS_OFF 0 /* exception masks offset */ +#define FP_PRC_OFF 8 /* precision control offset */ +#define FP_RND_OFF 10 /* rounding control offset */ + +/* + * FPU status word bit-field offsets (shift counts). + */ +#define FP_STKY_OFF 0 /* sticky flags offset */ + +//VBS +//#ifdef __GNUCLIKE_ASM + +#define __fldcw(addr) __asm __volatile("fldcw %0" : : "m" (*(addr))) +#define __fldenv(addr) __asm __volatile("fldenv %0" : : "m" (*(addr))) +#define __fnclex() __asm __volatile("fnclex") +#define __fnstcw(addr) __asm __volatile("fnstcw %0" : "=m" (*(addr))) +#define __fnstenv(addr) __asm __volatile("fnstenv %0" : "=m" (*(addr))) +#define __fnstsw(addr) __asm __volatile("fnstsw %0" : "=m" (*(addr))) + +/* + * Load the control word. Be careful not to trap if there is a currently + * unmasked exception (ones that will become freshly unmasked are not a + * problem). This case must be handled by a save/restore of the + * environment or even of the full x87 state. Accessing the environment + * is very inefficient, so only do it when necessary. + */ +static __inline void +__fnldcw(unsigned short _cw, unsigned short _newcw) +{ + struct { + unsigned _cw; + unsigned _other[6]; + } _env; + unsigned short _sw; + + if ((_cw & FP_MSKS_FLD) != FP_MSKS_FLD) { + __fnstsw(&_sw); + if (((_sw & ~_cw) & FP_STKY_FLD) != 0) { + __fnstenv(&_env); + _env._cw = _newcw; + __fldenv(&_env); + return; + } + } + __fldcw(&_newcw); +} + +static __inline fp_rnd_t +fpgetround(void) +{ + unsigned short _cw; + + __fnstcw(&_cw); + return ((fp_rnd_t)((_cw & FP_RND_FLD) >> FP_RND_OFF)); +} + +static __inline fp_rnd_t +fpsetround(fp_rnd_t _m) +{ + fp_rnd_t _p; + unsigned short _cw, _newcw; + + __fnstcw(&_cw); + _p = (fp_rnd_t)((_cw & FP_RND_FLD) >> FP_RND_OFF); + _newcw = _cw & ~FP_RND_FLD; + _newcw |= (_m << FP_RND_OFF) & FP_RND_FLD; + __fnldcw(_cw, _newcw); + return (_p); +} + +//static __inline fp_prec_t +OLM_DLLEXPORT fp_prec_t +fpgetprec(void) +{ + unsigned short _cw; + + __fnstcw(&_cw); + return ((fp_prec_t)((_cw & FP_PRC_FLD) >> FP_PRC_OFF)); +} + +//static __inline fp_prec_t +OLM_DLLEXPORT fp_prec_t +fpsetprec(fp_prec_t _m) +{ + fp_prec_t _p; + unsigned short _cw, _newcw; + + __fnstcw(&_cw); + _p = (fp_prec_t)((_cw & FP_PRC_FLD) >> FP_PRC_OFF); + _newcw = _cw & ~FP_PRC_FLD; + _newcw |= (_m << FP_PRC_OFF) & FP_PRC_FLD; + __fnldcw(_cw, _newcw); + return (_p); +} + +/* + * Get or set the exception mask. + * Note that the x87 mask bits are inverted by the API -- a mask bit of 1 + * means disable for x87 and SSE, but for fp*mask() it means enable. + */ + +static __inline fp_except_t +fpgetmask(void) +{ + unsigned short _cw; + + __fnstcw(&_cw); + return ((~_cw & FP_MSKS_FLD) >> FP_MSKS_OFF); +} + +static __inline fp_except_t +fpsetmask(fp_except_t _m) +{ + fp_except_t _p; + unsigned short _cw, _newcw; + + __fnstcw(&_cw); + _p = (~_cw & FP_MSKS_FLD) >> FP_MSKS_OFF; + _newcw = _cw & ~FP_MSKS_FLD; + _newcw |= (~_m << FP_MSKS_OFF) & FP_MSKS_FLD; + __fnldcw(_cw, _newcw); + return (_p); +} + +static __inline fp_except_t +fpgetsticky(void) +{ + unsigned _ex; + unsigned short _sw; + + __fnstsw(&_sw); + _ex = (_sw & FP_STKY_FLD) >> FP_STKY_OFF; + return ((fp_except_t)_ex); +} + +static __inline fp_except_t +fpresetsticky(fp_except_t _m) +{ + struct { + unsigned _cw; + unsigned _sw; + unsigned _other[5]; + } _env; + fp_except_t _p; + + _m &= FP_STKY_FLD >> FP_STKY_OFF; + _p = fpgetsticky(); + if ((_p & ~_m) == _p) + return (_p); + if ((_p & ~_m) == 0) { + __fnclex(); + return (_p); + } + __fnstenv(&_env); + _env._sw &= ~_m; + __fldenv(&_env); + return (_p); +} + +//#endif /* __GNUCLIKE_ASM */ + +#endif /* !_MACHINE_IEEEFP_H_ */ diff --git a/openlibm/i387/bsd_npx.h b/openlibm/i387/bsd_npx.h new file mode 100644 index 0000000..78c5cbe --- /dev/null +++ b/openlibm/i387/bsd_npx.h @@ -0,0 +1,160 @@ +/*- + * Copyright (c) 1990 The Regents of the University of California. + * All rights reserved. + * + * This code is derived from software contributed to Berkeley by + * William Jolitz. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * from: @(#)npx.h 5.3 (Berkeley) 1/18/91 + * $FreeBSD: src/sys/i386/include/npx.h,v 1.29.2.1 2006/07/01 00:57:55 davidxu Exp $ + */ + +/* + * 287/387 NPX Coprocessor Data Structures and Constants + * W. Jolitz 1/90 + */ + +#ifndef _MACHINE_NPX_H_ +#define _MACHINE_NPX_H_ + +/* Environment information of floating point unit */ +struct env87 { + long en_cw; /* control word (16bits) */ + long en_sw; /* status word (16bits) */ + long en_tw; /* tag word (16bits) */ + long en_fip; /* floating point instruction pointer */ + unsigned short en_fcs; /* floating code segment selector */ + unsigned short en_opcode; /* opcode last executed (11 bits ) */ + long en_foo; /* floating operand offset */ + long en_fos; /* floating operand segment selector */ +}; + +/* Contents of each floating point accumulator */ +struct fpacc87 { +#ifdef dontdef /* too unportable */ + unsigned long fp_mantlo; /* mantissa low (31:0) */ + unsigned long fp_manthi; /* mantissa high (63:32) */ + int fp_exp:15; /* exponent */ + int fp_sgn:1; /* mantissa sign */ +#else + unsigned char fp_bytes[10]; +#endif +}; + +/* Floating point context */ +struct save87 { + struct env87 sv_env; /* floating point control/status */ + struct fpacc87 sv_ac[8]; /* accumulator contents, 0-7 */ + unsigned char sv_pad0[4]; /* padding for (now unused) saved status word */ + /* + * Bogus padding for emulators. Emulators should use their own + * struct and arrange to store into this struct (ending here) + * before it is inspected for ptracing or for core dumps. Some + * emulators overwrite the whole struct. We have no good way of + * knowing how much padding to leave. Leave just enough for the + * GPL emulator's i387_union (176 bytes total). + */ + unsigned char sv_pad[64]; /* padding; used by emulators */ +}; + +struct envxmm { + uint16_t en_cw; /* control word (16bits) */ + uint16_t en_sw; /* status word (16bits) */ + uint16_t en_tw; /* tag word (16bits) */ + uint16_t en_opcode; /* opcode last executed (11 bits ) */ + uint32_t en_fip; /* floating point instruction pointer */ + uint16_t en_fcs; /* floating code segment selector */ + uint16_t en_pad0; /* padding */ + uint32_t en_foo; /* floating operand offset */ + uint16_t en_fos; /* floating operand segment selector */ + uint16_t en_pad1; /* padding */ + uint32_t en_mxcsr; /* SSE sontorol/status register */ + uint32_t en_mxcsr_mask; /* valid bits in mxcsr */ +}; + +/* Contents of each SSE extended accumulator */ +struct xmmacc { + unsigned char xmm_bytes[16]; +}; + +struct savexmm { + struct envxmm sv_env; + struct { + struct fpacc87 fp_acc; + unsigned char fp_pad[6]; /* padding */ + } sv_fp[8]; + struct xmmacc sv_xmm[8]; + unsigned char sv_pad[224]; +} __attribute__((__aligned__(16))); + +union savefpu { + struct save87 sv_87; + struct savexmm sv_xmm; +}; + +/* + * The hardware default control word for i387's and later coprocessors is + * 0x37F, giving: + * + * round to nearest + * 64-bit precision + * all exceptions masked. + * + * We modify the affine mode bit and precision bits in this to give: + * + * affine mode for 287's (if they work at all) (1 in bitfield 1<<12) + * 53-bit precision (2 in bitfield 3<<8) + * + * 64-bit precision often gives bad results with high level languages + * because it makes the results of calculations depend on whether + * intermediate values are stored in memory or in FPU registers. + */ +#define __INITIAL_NPXCW__ 0x127F +#define __INITIAL_MXCSR__ 0x1F80 + +#ifdef _KERNEL + +#define IO_NPX 0x0F0 /* Numeric Coprocessor */ +#define IO_NPXSIZE 16 /* 80387/80487 NPX registers */ + +#define IRQ_NPX 13 + +/* full reset on some systems, NOP on others */ +#define npx_full_reset() outb(IO_NPX + 1, 0) + +int npxdna(void); +void npxdrop(void); +void npxexit(struct thread *td); +int npxformat(void); +int npxgetregs(struct thread *td, union savefpu *addr); +void npxinit(unsigned short control); +void npxsave(union savefpu *addr); +void npxsetregs(struct thread *td, union savefpu *addr); +int npxtrap(void); +#endif + +#endif /* !_MACHINE_NPX_H_ */ \ No newline at end of file diff --git a/openlibm/i387/e_exp.S b/openlibm/i387/e_exp.S new file mode 100644 index 0000000..0f03f9e --- /dev/null +++ b/openlibm/i387/e_exp.S @@ -0,0 +1,76 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include + +/* e^x = 2^(x * log2(e)) */ + +ENTRY(exp) + /* + * If x is +-Inf, then the subtraction would give Inf-Inf = NaN. + * Avoid this. Also avoid it if x is NaN for convenience. + */ + movl 8(%esp),%eax + andl $0x7fffffff,%eax + cmpl $0x7ff00000,%eax + jae x_Inf_or_NaN + + fldl 4(%esp) + + /* + * Extended precision is needed to reduce the maximum error from + * hundreds of ulps to less than 1 ulp. Switch to it if necessary. + * We may as well set the rounding mode to to-nearest and mask traps + * if we switch. + */ + fstcw 4(%esp) + movl 4(%esp),%eax + andl $0x0300,%eax + cmpl $0x0300,%eax /* RC == 0 && PC == 3? */ + je 1f /* jump if mode is good */ + movl $0x137f,8(%esp) + fldcw 8(%esp) +1: + fldl2e + fmulp /* x * log2(e) */ + fst %st(1) + frndint /* int(x * log2(e)) */ + fst %st(2) + fsubrp /* fract(x * log2(e)) */ + f2xm1 /* 2^(fract(x * log2(e))) - 1 */ + fld1 + faddp /* 2^(fract(x * log2(e))) */ + fscale /* e^x */ + fstp %st(1) + je 1f + fldcw 4(%esp) +1: + ret + +x_Inf_or_NaN: + /* + * Return 0 if x is -Inf. Otherwise just return x; when x is Inf + * this gives Inf, and when x is a NaN this gives the same result + * as (x + x) (x quieted). + */ + cmpl $0xfff00000,8(%esp) + jne x_not_minus_Inf + cmpl $0,4(%esp) + jne x_not_minus_Inf + fldz + ret + +x_not_minus_Inf: + fldl 4(%esp) + ret +END(exp) + + // + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_fmod.S b/openlibm/i387/e_fmod.S new file mode 100644 index 0000000..44e52e5 --- /dev/null +++ b/openlibm/i387/e_fmod.S @@ -0,0 +1,25 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_fmod.S,v 1.11 2011/01/07 16:13:12 kib Exp $") + +ENTRY(fmod) + fldl 12(%esp) + fldl 4(%esp) +1: fprem + fstsw %ax + sahf + jp 1b + fstp %st(1) + ret +END(fmod) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_log.S b/openlibm/i387/e_log.S new file mode 100644 index 0000000..ebd6ae7 --- /dev/null +++ b/openlibm/i387/e_log.S @@ -0,0 +1,21 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_log.S,v 1.10 2011/01/07 16:13:12 kib Exp $") + +ENTRY(log) + fldln2 + fldl 4(%esp) + fyl2x + ret +END(log) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_log10.S b/openlibm/i387/e_log10.S new file mode 100644 index 0000000..b559a74 --- /dev/null +++ b/openlibm/i387/e_log10.S @@ -0,0 +1,21 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_log10.S,v 1.10 2011/01/07 16:13:12 kib Exp $") + +ENTRY(log10) + fldlg2 + fldl 4(%esp) + fyl2x + ret +END(log10) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_log10f.S b/openlibm/i387/e_log10f.S new file mode 100644 index 0000000..afdf1b0 --- /dev/null +++ b/openlibm/i387/e_log10f.S @@ -0,0 +1,22 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_log10f.S,v 1.4 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: e_log10f.S,v 1.1 1996/07/03 16:50:22 jtc Exp $") */ + +ENTRY(log10f) + fldlg2 + flds 4(%esp) + fyl2x + ret +END(log10f) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_logf.S b/openlibm/i387/e_logf.S new file mode 100644 index 0000000..af06fd8 --- /dev/null +++ b/openlibm/i387/e_logf.S @@ -0,0 +1,21 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_logf.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: e_logf.S,v 1.2 1996/07/06 00:15:45 jtc Exp $") */ + +ENTRY(logf) + fldln2 + flds 4(%esp) + fyl2x + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_remainder.S b/openlibm/i387/e_remainder.S new file mode 100644 index 0000000..2aa3113 --- /dev/null +++ b/openlibm/i387/e_remainder.S @@ -0,0 +1,25 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_remainder.S,v 1.11 2011/01/07 16:13:12 kib Exp $") + +ENTRY(remainder) + fldl 12(%esp) + fldl 4(%esp) +1: fprem1 + fstsw %ax + sahf + jp 1b + fstp %st(1) + ret +END(remainder) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_remainderf.S b/openlibm/i387/e_remainderf.S new file mode 100644 index 0000000..2b7b597 --- /dev/null +++ b/openlibm/i387/e_remainderf.S @@ -0,0 +1,26 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_remainderf.S,v 1.4 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: e_remainderf.S,v 1.2 1995/05/08 23:49:47 jtc Exp $") */ + +ENTRY(remainderf) + flds 8(%esp) + flds 4(%esp) +1: fprem1 + fstsw %ax + sahf + jp 1b + fstp %st(1) + ret +END(remainderf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_remainderl.S b/openlibm/i387/e_remainderl.S new file mode 100644 index 0000000..04d460b --- /dev/null +++ b/openlibm/i387/e_remainderl.S @@ -0,0 +1,25 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_remainderl.S,v 1.2 2011/01/07 16:13:12 kib Exp $") + +ENTRY(remainderl) + fldt 16(%esp) + fldt 4(%esp) +1: fprem1 + fstsw %ax + sahf + jp 1b + fstp %st(1) + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_sqrt.S b/openlibm/i387/e_sqrt.S new file mode 100644 index 0000000..5cd45b0 --- /dev/null +++ b/openlibm/i387/e_sqrt.S @@ -0,0 +1,37 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_sqrt.S,v 1.10 2011/01/07 16:13:12 kib Exp $") + +ENTRY(sqrt) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + andw $0xfeff,%dx /* Set precision field to 64 bits (53 bit mantissa). + We assume it's set to 0b11 (extended precision), + so zeroing out the low bit of the precision field, + will correctly set the precision */ + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldl 8(%ebp) + fsqrt + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(sqrt) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_sqrtf.S b/openlibm/i387/e_sqrtf.S new file mode 100644 index 0000000..05fb77f --- /dev/null +++ b/openlibm/i387/e_sqrtf.S @@ -0,0 +1,21 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_sqrtf.S,v 1.4 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: e_sqrtf.S,v 1.2 1995/05/08 23:50:14 jtc Exp $") */ + +ENTRY(sqrtf) + flds 4(%esp) + fsqrt + ret +END(sqrtf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/e_sqrtl.S b/openlibm/i387/e_sqrtl.S new file mode 100644 index 0000000..5317f95 --- /dev/null +++ b/openlibm/i387/e_sqrtl.S @@ -0,0 +1,19 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/e_sqrtl.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(sqrtl) + fldt 4(%esp) + fsqrt + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/fenv.c b/openlibm/i387/fenv.c new file mode 100644 index 0000000..6afe766 --- /dev/null +++ b/openlibm/i387/fenv.c @@ -0,0 +1,226 @@ +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/i387/fenv.c,v 1.8 2011/10/21 06:25:31 das Exp $ + */ + +#include "cdefs-compat.h" +#include "types-compat.h" +#include "math_private.h" +#include "i387/bsd_npx.h" + +#define __fenv_static +#include + +#ifdef __GNUC_GNU_INLINE__ +#error "This file must be compiled with C99 'inline' semantics" +#endif + +const fenv_t __fe_dfl_env = { + __INITIAL_NPXCW__, + 0x0000, + 0x0000, + 0x1f80, + 0xffffffff, + { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff } +}; + +enum __sse_support __has_sse = +#ifdef __SSE__ + __SSE_YES; +#else + __SSE_UNK; +#endif + +#define getfl(x) __asm __volatile("pushfl\n\tpopl %0" : "=mr" (*(x))) +#define setfl(x) __asm __volatile("pushl %0\n\tpopfl" : : "g" (x)) +#define cpuid_dx(x) __asm __volatile("pushl %%ebx\n\tmovl $1, %%eax\n\t" \ + "cpuid\n\tpopl %%ebx" \ + : "=d" (*(x)) : : "eax", "ecx") + +/* + * Test for SSE support on this processor. We need to do this because + * we need to use ldmxcsr/stmxcsr to get correct results if any part + * of the program was compiled to use SSE floating-point, but we can't + * use SSE on older processors. + */ +int +__test_sse(void) +{ + int flag, nflag; + int dx_features; + + /* Am I a 486? */ + getfl(&flag); + nflag = flag ^ 0x200000; + setfl(nflag); + getfl(&nflag); + if (flag != nflag) { + /* Not a 486, so CPUID should work. */ + cpuid_dx(&dx_features); + if (dx_features & 0x2000000) { + __has_sse = __SSE_YES; + return (1); + } + } + __has_sse = __SSE_NO; + return (0); +} + +extern inline OLM_DLLEXPORT int feclearexcept(int __excepts); +extern inline OLM_DLLEXPORT int fegetexceptflag(fexcept_t *__flagp, int __excepts); + +OLM_DLLEXPORT int +fesetexceptflag(const fexcept_t *flagp, int excepts) +{ + fenv_t env; + uint32_t mxcsr; + + __fnstenv(&env); + env.__status &= ~excepts; + env.__status |= *flagp & excepts; + __fldenv(env); + + if (__HAS_SSE()) { + __stmxcsr(&mxcsr); + mxcsr &= ~excepts; + mxcsr |= *flagp & excepts; + __ldmxcsr(mxcsr); + } + + return (0); +} + +OLM_DLLEXPORT int +feraiseexcept(int excepts) +{ + fexcept_t ex = excepts; + + fesetexceptflag(&ex, excepts); + __fwait(); + return (0); +} + +extern inline OLM_DLLEXPORT int fetestexcept(int __excepts); +extern inline OLM_DLLEXPORT int fegetround(void); +extern inline OLM_DLLEXPORT int fesetround(int __round); + +int +fegetenv(fenv_t *envp) +{ + uint32_t mxcsr; + + __fnstenv(envp); + /* + * fnstenv masks all exceptions, so we need to restore + * the old control word to avoid this side effect. + */ + __fldcw(envp->__control); + if (__HAS_SSE()) { + __stmxcsr(&mxcsr); + __set_mxcsr(*envp, mxcsr); + } + return (0); +} + +int +feholdexcept(fenv_t *envp) +{ + uint32_t mxcsr; + + __fnstenv(envp); + __fnclex(); + if (__HAS_SSE()) { + __stmxcsr(&mxcsr); + __set_mxcsr(*envp, mxcsr); + mxcsr &= ~FE_ALL_EXCEPT; + mxcsr |= FE_ALL_EXCEPT << _SSE_EMASK_SHIFT; + __ldmxcsr(mxcsr); + } + return (0); +} + +extern inline OLM_DLLEXPORT int fesetenv(const fenv_t *__envp); + +OLM_DLLEXPORT int +feupdateenv(const fenv_t *envp) +{ + uint32_t mxcsr; + uint16_t status; + + __fnstsw(&status); + if (__HAS_SSE()) + __stmxcsr(&mxcsr); + else + mxcsr = 0; + fesetenv(envp); + feraiseexcept((mxcsr | status) & FE_ALL_EXCEPT); + return (0); +} + +int +feenableexcept(int mask) +{ + uint32_t mxcsr, omask; + uint16_t control; + + mask &= FE_ALL_EXCEPT; + __fnstcw(&control); + if (__HAS_SSE()) + __stmxcsr(&mxcsr); + else + mxcsr = 0; + omask = ~(control | mxcsr >> _SSE_EMASK_SHIFT) & FE_ALL_EXCEPT; + control &= ~mask; + __fldcw(control); + if (__HAS_SSE()) { + mxcsr &= ~(mask << _SSE_EMASK_SHIFT); + __ldmxcsr(mxcsr); + } + return (omask); +} + +int +fedisableexcept(int mask) +{ + uint32_t mxcsr, omask; + uint16_t control; + + mask &= FE_ALL_EXCEPT; + __fnstcw(&control); + if (__HAS_SSE()) + __stmxcsr(&mxcsr); + else + mxcsr = 0; + omask = ~(control | mxcsr >> _SSE_EMASK_SHIFT) & FE_ALL_EXCEPT; + control |= mask; + __fldcw(control); + if (__HAS_SSE()) { + mxcsr |= mask << _SSE_EMASK_SHIFT; + __ldmxcsr(mxcsr); + } + return (omask); +} diff --git a/openlibm/i387/invtrig.c b/openlibm/i387/invtrig.c new file mode 100644 index 0000000..4afd832 --- /dev/null +++ b/openlibm/i387/invtrig.c @@ -0,0 +1,86 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/invtrig.c,v 1.1 2008/08/02 03:56:22 das Exp $"); + +#include + +#define STRUCT_DECLS +#include "invtrig.h" + +/* + * asinl() and acosl() + */ +const LONGDOUBLE +pS0 = { 0xaaaaaaaaaaaaaaa8ULL, 0x3ffcU }, /* 1.66666666666666666631e-01L */ +pS1 = { 0xd5271b6699b48bfaULL, 0xbffdU }, /* -4.16313987993683104320e-01L */ +pS2 = { 0xbcf67ca9e9f669cfULL, 0x3ffdU }, /* 3.69068046323246813704e-01L */ +pS3 = { 0x8b7baa3d15f9830dULL, 0xbffcU }, /* -1.36213932016738603108e-01L */ +pS4 = { 0x92154b093a3bff1cULL, 0x3ff9U }, /* 1.78324189708471965733e-02L */ +pS5 = { 0xe5dd76401964508cULL, 0xbff2U }, /* -2.19216428382605211588e-04L */ +pS6 = { 0xee69c5b0fdb76951ULL, 0xbfedU }, /* -7.10526623669075243183e-06L */ +qS1 = { 0xbcaa2159c01436a0ULL, 0xc000U }, /* -2.94788392796209867269e+00L */ +qS2 = { 0xd17a73d1e1564c29ULL, 0x4000U }, /* 3.27309890266528636716e+00L */ +qS3 = { 0xd767e411c9cf4c2cULL, 0xbfffU }, /* -1.68285799854822427013e+00L */ +qS4 = { 0xc809c0dfb9b0d0b7ULL, 0x3ffdU }, /* 3.90699412641738801874e-01L */ +qS5 = { 0x80c3a2197c8ced57ULL, 0xbffaU }; /* -3.14365703596053263322e-02L */ + +/* + * atanl() + */ +const LONGDOUBLE atanhi[] = { + { 0xed63382b0dda7b45ULL, 0x3ffdU }, /* 4.63647609000806116202e-01L */ + { 0xc90fdaa22168c235ULL, 0x3ffeU }, /* 7.85398163397448309628e-01L */ + { 0xfb985e940fb4d900ULL, 0x3ffeU }, /* 9.82793723247329067960e-01L */ + { 0xc90fdaa22168c235ULL, 0x3fffU }, /* 1.57079632679489661926e+00L */ +}; + +const LONGDOUBLE atanlo[] = { + { 0xdfc88bd978751a07ULL, 0x3fbcU }, /* 1.18469937025062860669e-20L */ + { 0xece675d1fc8f8cbbULL, 0xbfbcU }, /* -1.25413940316708300586e-20L */ + { 0xf10f5e197793c283ULL, 0x3fbdU }, /* 2.55232234165405176172e-20L */ + { 0xece675d1fc8f8cbbULL, 0xbfbdU }, /* -2.50827880633416601173e-20L */ +}; + +const LONGDOUBLE aT[] = { + { 0xaaaaaaaaaaaaaa9fULL, 0x3ffdU }, /* 3.33333333333333333017e-01L */ + { 0xcccccccccccc62bcULL, 0xbffcU }, /* -1.99999999999999632011e-01L */ + { 0x9249249248b81e3fULL, 0x3ffcU }, /* 1.42857142857046531280e-01L */ + { 0xe38e38e3316f3de5ULL, 0xbffbU }, /* -1.11111111100562372733e-01L */ + { 0xba2e8b8dc280726aULL, 0x3ffbU }, /* 9.09090902935647302252e-02L */ + { 0x9d89d5b4c6847ec4ULL, 0xbffbU }, /* -7.69230552476207730353e-02L */ + { 0x8888461d3099c677ULL, 0x3ffbU }, /* 6.66661718042406260546e-02L */ + { 0xf0e8ee0f5328dc29ULL, 0xbffaU }, /* -5.88158892835030888692e-02L */ + { 0xd73ea84d24bae54aULL, 0x3ffaU }, /* 5.25499891539726639379e-02L */ + { 0xc08fa381dcd9213aULL, 0xbffaU }, /* -4.70119845393155721494e-02L */ + { 0xa54a26f4095f2a3aULL, 0x3ffaU }, /* 4.03539201366454414072e-02L */ + { 0xeea2d8d059ef3ad6ULL, 0xbff9U }, /* -2.91303858419364158725e-02L */ + { 0xcc82292ab894b051ULL, 0x3ff8U }, /* 1.24822046299269234080e-02L */ +}; + +const LONGDOUBLE +pi_lo = { 0xece675d1fc8f8cbbULL, 0xbfbeU }; /* -5.01655761266833202345e-20L */ diff --git a/openlibm/i387/osx_asm.h b/openlibm/i387/osx_asm.h new file mode 100644 index 0000000..284224c --- /dev/null +++ b/openlibm/i387/osx_asm.h @@ -0,0 +1,408 @@ +/* + * Copyright (c) 2000 Apple Computer, Inc. All rights reserved. + * + * @APPLE_OSREFERENCE_LICENSE_HEADER_START@ + * + * This file contains Original Code and/or Modifications of Original Code + * as defined in and that are subject to the Apple Public Source License + * Version 2.0 (the 'License'). You may not use this file except in + * compliance with the License. The rights granted to you under the License + * may not be used to create, or enable the creation or redistribution of, + * unlawful or unlicensed copies of an Apple operating system, or to + * circumvent, violate, or enable the circumvention or violation of, any + * terms of an Apple operating system software license agreement. + * + * Please obtain a copy of the License at + * http://www.opensource.apple.com/apsl/ and read it before using this file. + * + * The Original Code and all software distributed under the License are + * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER + * EXPRESS OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES, + * INCLUDING WITHOUT LIMITATION, ANY WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT. + * Please see the License for the specific language governing rights and + * limitations under the License. + * + * @APPLE_OSREFERENCE_LICENSE_HEADER_END@ + */ +/* + * @OSF_COPYRIGHT@ + */ +/* + * Mach Operating System + * Copyright (c) 1991,1990,1989 Carnegie Mellon University + * All Rights Reserved. + * + * Permission to use, copy, modify and distribute this software and its + * documentation is hereby granted, provided that both the copyright + * notice and this permission notice appear in all copies of the + * software, derivative works or modified versions, and any portions + * thereof, and that both notices appear in supporting documentation. + * + * CARNEGIE MELLON ALLOWS FREE USE OF THIS SOFTWARE IN ITS "AS IS" + * CONDITION. CARNEGIE MELLON DISCLAIMS ANY LIABILITY OF ANY KIND FOR + * ANY DAMAGES WHATSOEVER RESULTING FROM THE USE OF THIS SOFTWARE. + * + * Carnegie Mellon requests users of this software to return to + * + * Software Distribution Coordinator or Software.Distribution@CS.CMU.EDU + * School of Computer Science + * Carnegie Mellon University + * Pittsburgh PA 15213-3890 + * + * any improvements or extensions that they make and grant Carnegie Mellon + * the rights to redistribute these changes. + */ + +#ifndef _I386_ASM_H_ +#define _I386_ASM_H_ + +#ifdef _KERNEL +#include +#endif /* _KERNEL */ + +#ifdef MACH_KERNEL +#include +#else /* !MACH_KERNEL */ +#define MACH_KDB 0 +#endif /* !MACH_KERNEL */ + + +#if defined(MACH_KERNEL) || defined(_KERNEL) +#include +#endif /* MACH_KERNEL || _KERNEL */ + +#if defined(__i386__) + +#define S_PC (%esp) +#define S_ARG0 4(%esp) +#define S_ARG1 8(%esp) +#define S_ARG2 12(%esp) +#define S_ARG3 16(%esp) +#define S_ARG4 20(%esp) + +#define FRAME pushl %ebp; movl %esp, %ebp +#define EMARF leave + +#define B_LINK (%ebp) +#define B_PC 4(%ebp) +#define B_ARG0 8(%ebp) +#define B_ARG1 12(%ebp) +#define B_ARG2 16(%ebp) +#define B_ARG3 20(%ebp) + +#elif defined(__x86_64__) + +#define S_PC (%rsp) + +#define FRAME pushq %rbp; movq %rsp, %rbp +#define EMARF leave + +#define B_LINK (%rbp) +#define B_PC 8(%rbp) + +#else +#error unsupported architecture +#endif + +/* There is another definition of ALIGN for .c sources */ +#ifdef ASSEMBLER +#define ALIGN 4,0x90 +#endif /* ASSEMBLER */ + +#ifndef FALIGN +#define FALIGN ALIGN +#endif + +#define LB(x,n) n +#if __STDC__ +#ifndef __NO_UNDERSCORES__ +#define LCL(x) L ## x +#define EXT(x) _ ## x +#define LEXT(x) _ ## x ## : +#else +#define LCL(x) .L ## x +#define EXT(x) x +#define LEXT(x) x ## : +#endif +#define LBc(x,n) n ## : +#define LBb(x,n) n ## b +#define LBf(x,n) n ## f +#else /* __STDC__ */ +#ifndef __NO_UNDERSCORES__ +#define LCL(x) L/**/x +#define EXT(x) _/**/x +#define LEXT(x) _/**/x/**/: +#else /* __NO_UNDERSCORES__ */ +#define LCL(x) .L/**/x +#define EXT(x) x +#define LEXT(x) x/**/: +#endif /* __NO_UNDERSCORES__ */ +#define LBc(x,n) n/**/: +#define LBb(x,n) n/**/b +#define LBf(x,n) n/**/f +#endif /* __STDC__ */ + +#define SVC .byte 0x9a; .long 0; .word 0x7 + +#define RPC_SVC .byte 0x9a; .long 0; .word 0xf + +#define String .asciz +#define Value .word +#define Times(a,b) (a*b) +#define Divide(a,b) (a/b) + +#define INB inb %dx, %al +#define OUTB outb %al, %dx +#define INL inl %dx, %eax +#define OUTL outl %eax, %dx + +#define data16 .byte 0x66 +#define addr16 .byte 0x67 + +#if !GPROF +#define MCOUNT + +#elif defined(__SHARED__) +#define MCOUNT ; .data;\ + .align ALIGN;\ + LBc(x, 8) .long 0;\ + .text;\ + Gpush;\ + Gload;\ + leal Gotoff(LBb(x,8)),%edx;\ + Egaddr(%eax,_mcount_ptr);\ + Gpop;\ + call *(%eax); + +#else /* !GPROF, !__SHARED__ */ +#define MCOUNT ; call mcount; +#endif /* GPROF */ + +#ifdef __ELF__ +#define ELF_FUNC(x) .type x,@function +#define ELF_DATA(x) .type x,@object +#define ELF_SIZE(x,s) .size x,s +#else +#define ELF_FUNC(x) +#define ELF_DATA(x) +#define ELF_SIZE(x,s) +#endif + +#define Entry(x) .globl EXT(x); ELF_FUNC(EXT(x)); .align FALIGN; LEXT(x) +#define ENTRY(x) Entry(x) MCOUNT +#define ENTRY2(x,y) .globl EXT(x); .globl EXT(y); \ + ELF_FUNC(EXT(x)); ELF_FUNC(EXT(y)); \ + .align FALIGN; LEXT(x); LEXT(y) \ + MCOUNT +#if __STDC__ +#define ASENTRY(x) .globl x; .align FALIGN; x ## : ELF_FUNC(x) MCOUNT +#else +#define ASENTRY(x) .globl x; .align FALIGN; x: ELF_FUNC(x) MCOUNT +#endif /* __STDC__ */ + +#define DATA(x) .globl EXT(x); ELF_DATA(EXT(x)); .align ALIGN; LEXT(x) + +#define End(x) ELF_SIZE(x,.-x) +#define END(x) End(EXT(x)) +#define ENDDATA(x) END(x) +#define Enddata(x) End(x) + +/* + * ELF shared library accessor macros. + * Gpush saves the %ebx register used for the GOT address + * Gpop pops %ebx if we need a GOT + * Gload loads %ebx with the GOT address if shared libraries are used + * Gcall calls an external function. + * Gotoff allows you to reference local labels. + * Gotoff2 allows you to reference local labels with an index reg. + * Gotoff3 allows you to reference local labels with an index reg & size. + * Gaddr loads up a register with an address of an external item. + * Gstack is the number of bytes that Gpush pushes on the stack. + * + * Varients of the above with E or L prefixes do EXT(name) or LCL(name) + * respectively. + */ + +#ifndef __SHARED__ +#define Gpush +#define Gpop +#define Gload +#define Gcall(func) call func +#define Gotoff(lab) lab +#define Gotoff2(l,r) l(r) +#define Gotoff3(l,r,s) l(,r,s) +#define Gaddr(to,lab) movl $lab,to +#define Gcmp(lab,reg) cmpl $lab,reg +#define Gmemload(lab,reg) movl lab,reg +#define Gmemstore(reg,lab,tmp) movl reg,lab +#define Gstack 0 + +#else +#ifdef __ELF__ /* ELF shared libraries */ +#define Gpush pushl %ebx +#define Gpop popl %ebx +#define Gload call 9f; 9: popl %ebx; addl $_GLOBAL_OFFSET_TABLE_+[.-9b],%ebx +#define Gcall(func) call EXT(func)@PLT +#define Gotoff(lab) lab@GOTOFF(%ebx) +#define Gotoff2(l,r) l@GOTOFF(%ebx,r) +#define Gotoff3(l,r,s) l@GOTOFF(%ebx,r,s) +#define Gaddr(to,lab) movl lab@GOT(%ebx),to +#define Gcmp(lab,reg) cmpl reg,lab@GOT(%ebx) +#define Gmemload(lab,reg) movl lab@GOT(%ebx),reg; movl (reg),reg +#define Gmemstore(reg,lab,tmp) movl lab@GOT(%ebx),tmp; movl reg,(tmp) +#define Gstack 4 + +#else /* ROSE shared libraries */ +#define Gpush +#define Gpop +#define Gload +#define Gcall(func) call *9f; .data; .align ALIGN; 9: .long func; .text +#define Gotoff(lab) lab +#define Gotoff2(l,r) l(r) +#define Gotoff3(l,r,s) l(,r,s) +#define Gaddr(to,lab) movl 9f,to; .data; .align ALIGN; 9: .long lab; .text +#define Gcmp(lab,reg) cmpl reg,9f; .data; .align ALIGN; 9: .long lab; .text +#define Gmemload(lab,reg) movl 9f,reg; movl (reg),reg; .data; .align ALIGN; 9: .long lab; .text +#define Gmemstore(reg,lab,tmp) movl 9f,tmp; movl reg,(tmp); .data; .align ALIGN; 9: .long lab; .text +#define Gstack 0 +#endif /* __ELF__ */ +#endif /* __SHARED__ */ + +/* Egotoff is not provided, since external symbols should not use @GOTOFF + relocations. */ +#define Egcall(func) Gcall(EXT(func)) +#define Egaddr(to,lab) Gaddr(to,EXT(lab)) +#define Egcmp(lab,reg) Gcmp(EXT(lab),reg) +#define Egmemload(lab,reg) Gmemload(EXT(lab),reg) +#define Egmemstore(reg,lab,tmp) Gmemstore(reg,EXT(lab),tmp) + +#define Lgotoff(lab) Gotoff(LCL(lab)) +#define Lgotoff2(l,r) Gotoff2(LCL(l),r) +#define Lgotoff3(l,r,s) Gotoff3(LCL(l),r,s) +#define Lgcmp(lab,reg) Gcmp(LCL(lab),reg) +#define Lgmemload(lab,reg) movl Lgotoff(lab),reg +#define Lgmemstore(reg,lab,tmp) movl reg,Lgotoff(lab) + +#ifdef ASSEMBLER +#if MACH_KDB +#include +/* + * This pseudo-assembler line is added so that there will be at least + * one N_SO entry in the symbol stable to define the current file name. + */ +#endif /* MACH_KDB */ + +#else /* NOT ASSEMBLER */ + +/* These defines are here for .c files that wish to reference global symbols + * within __asm__ statements. + */ +#ifndef __NO_UNDERSCORES__ +#define CC_SYM_PREFIX "_" +#else +#define CC_SYM_PREFIX "" +#endif /* __NO_UNDERSCORES__ */ +#endif /* ASSEMBLER */ + +/* + * The following macros make calls into C code. + * They dynamically align the stack to 16 bytes. + */ +#if defined(__i386__) +/* + * Arguments are moved (not pushed) onto the correctly aligned stack. + * NOTE: ESI is destroyed in the process, and hence cannot + * be directly used as a parameter. Users of this macro must + * independently preserve ESI (a non-volatile) if the routine is + * intended to be called from C, for instance. + */ + +#define CCALL(fn) \ + movl %esp, %esi ;\ + andl $0xFFFFFFF0, %esp ;\ + call EXT(fn) ;\ + movl %esi, %esp + +#define CCALL1(fn, arg1) \ + movl %esp, %esi ;\ + subl $4, %esp ;\ + andl $0xFFFFFFF0, %esp ;\ + movl arg1, (%esp) ;\ + call EXT(fn) ;\ + movl %esi, %esp + +#define CCALL2(fn, arg1, arg2) \ + movl %esp, %esi ;\ + subl $8, %esp ;\ + andl $0xFFFFFFF0, %esp ;\ + movl arg2, 4(%esp) ;\ + movl arg1, (%esp) ;\ + call EXT(fn) ;\ + movl %esi, %esp + +/* This variant exists to permit adjustment of the stack by "dtrace" */ +#define CCALL1WITHSP(fn, arg1) \ + movl %esp, %esi ;\ + subl $12, %esp ;\ + andl $0xFFFFFFF0, %esp ;\ + movl %esi, 8(%esp) ;\ + leal 8(%esp), %esi ;\ + movl %esi, 4(%esp) ;\ + movl arg1, (%esp) ;\ + call EXT(fn) ;\ + movl 8(%esp), %esp + +/* + * CCALL5 is used for callee functions with 3 arguments but + * where arg2 (a3:a2) and arg3 (a5:a4) are 64-bit values. + */ +#define CCALL5(fn, a1, a2, a3, a4, a5) \ + movl %esp, %esi ;\ + subl $20, %esp ;\ + andl $0xFFFFFFF0, %esp ;\ + movl a5, 16(%esp) ;\ + movl a4, 12(%esp) ;\ + movl a3, 8(%esp) ;\ + movl a2, 4(%esp) ;\ + movl a1, (%esp) ;\ + call EXT(fn) ;\ + movl %esi, %esp + +#elif defined(__x86_64__) + +/* This variant exists to permit adjustment of the stack by "dtrace" */ +#define CCALLWITHSP(fn) \ + mov %rsp, %r12 ;\ + sub $8, %rsp ;\ + and $0xFFFFFFFFFFFFFFF0, %rsp ;\ + mov %r12, (%rsp) ;\ + leaq (%rsp), %rsi ;\ + call EXT(fn) ;\ + mov (%rsp), %rsp + +#define CCALL(fn) \ + mov %rsp, %r12 ;\ + and $0xFFFFFFFFFFFFFFF0, %rsp ;\ + call EXT(fn) ;\ + mov %r12, %rsp + +#define CCALL1(fn, arg1) \ + mov arg1, %rdi ;\ + CCALL(fn) + +#define CCALL2(fn, arg1, arg2) \ + mov arg1, %rdi ;\ + CCALL(fn) + +#define CCALL3(fn, arg1, arg2, arg3) \ + mov arg1, %rdi ;\ + mov arg2, %rsi ;\ + mov arg3, %rdx ;\ + CCALL(fn) + +#else +#error unsupported architecture +#endif + +#endif /* _I386_ASM_H_ */ diff --git a/openlibm/i387/s_ceil.S b/openlibm/i387/s_ceil.S new file mode 100644 index 0000000..80de70a --- /dev/null +++ b/openlibm/i387/s_ceil.S @@ -0,0 +1,34 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include + +ENTRY(ceil) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0800,%dx /* round towards +oo */ + andw $0xfbff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldl 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(ceil) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_ceilf.S b/openlibm/i387/s_ceilf.S new file mode 100644 index 0000000..7ea898a --- /dev/null +++ b/openlibm/i387/s_ceilf.S @@ -0,0 +1,36 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_ceilf.S,v 1.4 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: s_ceilf.S,v 1.3 1995/05/08 23:52:44 jtc Exp $") */ + +ENTRY(ceilf) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0800,%dx /* round towards +oo */ + andw $0xfbff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + flds 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(ceilf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_ceill.S b/openlibm/i387/s_ceill.S new file mode 100644 index 0000000..838edd1 --- /dev/null +++ b/openlibm/i387/s_ceill.S @@ -0,0 +1,34 @@ +/* + * Based on code written by J.T. Conklin . + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_ceill.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(ceill) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0800,%dx /* round towards +oo */ + andw $0xfbff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldt 8(%ebp) /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(ceill) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_copysign.S b/openlibm/i387/s_copysign.S new file mode 100644 index 0000000..4386747 --- /dev/null +++ b/openlibm/i387/s_copysign.S @@ -0,0 +1,25 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_copysign.S,v 1.9 2011/01/07 16:13:12 kib Exp $") + +ENTRY(copysign) + movl 16(%esp),%edx + andl $0x80000000,%edx + movl 8(%esp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,8(%esp) + fldl 4(%esp) + ret +END(copysign) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_copysignf.S b/openlibm/i387/s_copysignf.S new file mode 100644 index 0000000..5d0169b --- /dev/null +++ b/openlibm/i387/s_copysignf.S @@ -0,0 +1,26 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_copysignf.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: s_copysignf.S,v 1.3 1995/05/08 23:53:25 jtc Exp $") */ + +ENTRY(copysignf) + movl 8(%esp),%edx + andl $0x80000000,%edx + movl 4(%esp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,4(%esp) + flds 4(%esp) + ret +END(copysignf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_copysignl.S b/openlibm/i387/s_copysignl.S new file mode 100644 index 0000000..1a9a06a --- /dev/null +++ b/openlibm/i387/s_copysignl.S @@ -0,0 +1,24 @@ +/* + * Based on code written by J.T. Conklin . + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_copysignl.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(copysignl) + movl 24(%esp),%edx + andl $0x8000,%edx + movl 12(%esp),%eax + andl $0x7fff,%eax + orl %edx,%eax + movl %eax,12(%esp) + fldt 4(%esp) + ret +END(copysignl) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_cos.S b/openlibm/i387/s_cos.S new file mode 100644 index 0000000..4e29ec3 --- /dev/null +++ b/openlibm/i387/s_cos.S @@ -0,0 +1,33 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_cos.S,v 1.9 2011/01/07 16:13:12 kib Exp $") + +ENTRY(cos) + fldl 4(%esp) + fcos + fnstsw %ax + andw $0x400,%ax + jnz 1f + ret +1: fldpi + fadd %st(0) + fxch %st(1) +2: fprem1 + fnstsw %ax + andw $0x400,%ax + jnz 2b + fstp %st(1) + fcos + ret +END(cos) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_floor.S b/openlibm/i387/s_floor.S new file mode 100644 index 0000000..13097eb --- /dev/null +++ b/openlibm/i387/s_floor.S @@ -0,0 +1,35 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_floor.S,v 1.10 2011/01/07 16:13:12 kib Exp $") + +ENTRY(floor) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0400,%dx /* round towards -oo */ + andw $0xf7ff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldl 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(floor) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_floorf.S b/openlibm/i387/s_floorf.S new file mode 100644 index 0000000..c3a4e09 --- /dev/null +++ b/openlibm/i387/s_floorf.S @@ -0,0 +1,36 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_floorf.S,v 1.4 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: s_floorf.S,v 1.3 1995/05/09 00:04:32 jtc Exp $") */ + +ENTRY(floorf) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0400,%dx /* round towards -oo */ + andw $0xf7ff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + flds 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(floorf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_floorl.S b/openlibm/i387/s_floorl.S new file mode 100644 index 0000000..949116f --- /dev/null +++ b/openlibm/i387/s_floorl.S @@ -0,0 +1,34 @@ +/* + * Based on code written by J.T. Conklin . + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_floorl.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(floorl) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0400,%dx /* round towards -oo */ + andw $0xf7ff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldt 8(%ebp) /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(floorl) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_llrint.S b/openlibm/i387/s_llrint.S new file mode 100644 index 0000000..97c292e --- /dev/null +++ b/openlibm/i387/s_llrint.S @@ -0,0 +1,43 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_llrint.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(llrint) + fldl 4(%esp) + subl $8,%esp + fistpll (%esp) + popl %eax + popl %edx + ret +END(llrint) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_llrintf.S b/openlibm/i387/s_llrintf.S new file mode 100644 index 0000000..447e77a --- /dev/null +++ b/openlibm/i387/s_llrintf.S @@ -0,0 +1,43 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_llrintf.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(llrintf) + flds 4(%esp) + subl $8,%esp + fistpll (%esp) + popl %eax + popl %edx + ret +END(llrintf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_llrintl.S b/openlibm/i387/s_llrintl.S new file mode 100644 index 0000000..ad6a7c9 --- /dev/null +++ b/openlibm/i387/s_llrintl.S @@ -0,0 +1,42 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_llrintl.S,v 1.2 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(llrintl) + fldt 4(%esp) + subl $8,%esp + fistpll (%esp) + popl %eax + popl %edx + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_logb.S b/openlibm/i387/s_logb.S new file mode 100644 index 0000000..d0fc5d6 --- /dev/null +++ b/openlibm/i387/s_logb.S @@ -0,0 +1,21 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_logb.S,v 1.10 2011/01/07 16:13:12 kib Exp $") + +ENTRY(logb) + fldl 4(%esp) + fxtract + fstp %st + ret +END(logb) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_logbf.S b/openlibm/i387/s_logbf.S new file mode 100644 index 0000000..3e3568c --- /dev/null +++ b/openlibm/i387/s_logbf.S @@ -0,0 +1,22 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_logbf.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: s_logbf.S,v 1.3 1995/05/09 00:15:12 jtc Exp $") */ + +ENTRY(logbf) + flds 4(%esp) + fxtract + fstp %st + ret +END(logbf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_logbl.S b/openlibm/i387/s_logbl.S new file mode 100644 index 0000000..6d2de64 --- /dev/null +++ b/openlibm/i387/s_logbl.S @@ -0,0 +1,20 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_logbl.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(logbl) + fldt 4(%esp) + fxtract + fstp %st + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_lrint.S b/openlibm/i387/s_lrint.S new file mode 100644 index 0000000..1e12539 --- /dev/null +++ b/openlibm/i387/s_lrint.S @@ -0,0 +1,42 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_lrint.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(lrint) + fldl 4(%esp) + subl $4,%esp + fistpl (%esp) + popl %eax + ret +END(lrint) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_lrintf.S b/openlibm/i387/s_lrintf.S new file mode 100644 index 0000000..b588c1a --- /dev/null +++ b/openlibm/i387/s_lrintf.S @@ -0,0 +1,42 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_lrintf.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(lrintf) + flds 4(%esp) + subl $4,%esp + fistpl (%esp) + popl %eax + ret +END(lrintf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_lrintl.S b/openlibm/i387/s_lrintl.S new file mode 100644 index 0000000..94cc6cb --- /dev/null +++ b/openlibm/i387/s_lrintl.S @@ -0,0 +1,41 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_lrintl.S,v 1.2 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(lrintl) + fldt 4(%esp) + subl $4,%esp + fistpl (%esp) + popl %eax + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_remquo.S b/openlibm/i387/s_remquo.S new file mode 100644 index 0000000..78a588d --- /dev/null +++ b/openlibm/i387/s_remquo.S @@ -0,0 +1,69 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* + * Based on public-domain remainder routine by J.T. Conklin . + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_remquo.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(remquo) + fldl 12(%esp) + fldl 4(%esp) +1: fprem1 + fstsw %ax + sahf + jp 1b + fstp %st(1) +/* Extract the three low-order bits of the quotient from C0,C3,C1. */ + shrl $6,%eax + movl %eax,%ecx + andl $0x108,%eax + rorl $7,%eax + orl %eax,%ecx + roll $4,%eax + orl %ecx,%eax + andl $7,%eax +/* Negate the quotient bits if x*y<0. Avoid using an unpredictable branch. */ + movl 16(%esp),%ecx + xorl 8(%esp),%ecx + sarl $16,%ecx + sarl $16,%ecx + xorl %ecx,%eax + andl $1,%ecx + addl %ecx,%eax +/* Store the quotient and return. */ + movl 20(%esp),%ecx + movl %eax,(%ecx) + ret +END(remquo) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_remquof.S b/openlibm/i387/s_remquof.S new file mode 100644 index 0000000..8f532c3 --- /dev/null +++ b/openlibm/i387/s_remquof.S @@ -0,0 +1,69 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* + * Based on public-domain remainder routine by J.T. Conklin . + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_remquof.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(remquof) + flds 8(%esp) + flds 4(%esp) +1: fprem1 + fstsw %ax + sahf + jp 1b + fstp %st(1) +/* Extract the three low-order bits of the quotient from C0,C3,C1. */ + shrl $6,%eax + movl %eax,%ecx + andl $0x108,%eax + rorl $7,%eax + orl %eax,%ecx + roll $4,%eax + orl %ecx,%eax + andl $7,%eax +/* Negate the quotient bits if x*y<0. Avoid using an unpredictable branch. */ + movl 8(%esp),%ecx + xorl 4(%esp),%ecx + sarl $16,%ecx + sarl $16,%ecx + xorl %ecx,%eax + andl $1,%ecx + addl %ecx,%eax +/* Store the quotient and return. */ + movl 12(%esp),%ecx + movl %eax,(%ecx) + ret +END(remquof) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_remquol.S b/openlibm/i387/s_remquol.S new file mode 100644 index 0000000..b89563c --- /dev/null +++ b/openlibm/i387/s_remquol.S @@ -0,0 +1,69 @@ +/*- + * Copyright (c) 2005-2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* + * Based on public-domain remainder routine by J.T. Conklin . + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_remquol.S,v 1.2 2011/01/07 16:13:12 kib Exp $"); + +ENTRY(remquol) + fldt 16(%esp) + fldt 4(%esp) +1: fprem1 + fstsw %ax + sahf + jp 1b + fstp %st(1) +/* Extract the three low-order bits of the quotient from C0,C3,C1. */ + shrl $6,%eax + movl %eax,%ecx + andl $0x108,%eax + rorl $7,%eax + orl %eax,%ecx + roll $4,%eax + orl %ecx,%eax + andl $7,%eax +/* Negate the quotient bits if x*y<0. Avoid using an unpredictable branch. */ + movl 24(%esp),%ecx + xorl 12(%esp),%ecx + movsx %cx,%ecx + sarl $16,%ecx + sarl $16,%ecx + xorl %ecx,%eax + andl $1,%ecx + addl %ecx,%eax +/* Store the quotient and return. */ + movl 28(%esp),%ecx + movl %eax,(%ecx) + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_rint.S b/openlibm/i387/s_rint.S new file mode 100644 index 0000000..a8109cd --- /dev/null +++ b/openlibm/i387/s_rint.S @@ -0,0 +1,20 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_rint.S,v 1.9 2011/01/07 16:13:12 kib Exp $") + +ENTRY(rint) + fldl 4(%esp) + frndint + ret +END(rint) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_rintf.S b/openlibm/i387/s_rintf.S new file mode 100644 index 0000000..184a16f --- /dev/null +++ b/openlibm/i387/s_rintf.S @@ -0,0 +1,21 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_rintf.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: s_rintf.S,v 1.3 1995/05/09 00:17:22 jtc Exp $") */ + +ENTRY(rintf) + flds 4(%esp) + frndint + ret +END(rintf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_rintl.S b/openlibm/i387/s_rintl.S new file mode 100644 index 0000000..8727322 --- /dev/null +++ b/openlibm/i387/s_rintl.S @@ -0,0 +1,19 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_rintl.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(rintl) + fldt 4(%esp) + frndint + ret + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_scalbn.S b/openlibm/i387/s_scalbn.S new file mode 100644 index 0000000..d690ff1 --- /dev/null +++ b/openlibm/i387/s_scalbn.S @@ -0,0 +1,23 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_scalbn.S,v 1.10 2011/01/07 16:13:12 kib Exp $") + +ENTRY(scalbn) + fildl 12(%esp) + fldl 4(%esp) + fscale + fstp %st(1) + ret +END(scalbn) + +.globl CNAME(ldexp) +.set CNAME(ldexp),CNAME(scalbn) +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_scalbnf.S b/openlibm/i387/s_scalbnf.S new file mode 100644 index 0000000..7f4a2bc --- /dev/null +++ b/openlibm/i387/s_scalbnf.S @@ -0,0 +1,26 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_scalbnf.S,v 1.4 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: s_scalbnf.S,v 1.4 1999/01/02 05:15:40 kristerw Exp $") */ + +ENTRY(scalbnf) + fildl 8(%esp) + flds 4(%esp) + fscale + fstp %st(1) /* bug fix for fp stack overflow */ + ret +END(scalbnf) + +.globl CNAME(ldexpf) +.set CNAME(ldexpf),CNAME(scalbnf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_scalbnl.S b/openlibm/i387/s_scalbnl.S new file mode 100644 index 0000000..5d359eb --- /dev/null +++ b/openlibm/i387/s_scalbnl.S @@ -0,0 +1,26 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_scalbnl.S,v 1.3 2011/01/07 16:13:12 kib Exp $"); +/* RCSID("$NetBSD: s_scalbnf.S,v 1.4 1999/01/02 05:15:40 kristerw Exp $") */ + +ENTRY(scalbnl) + fildl 16(%esp) + fldt 4(%esp) + fscale + fstp %st(1) + ret +END(scalbnl) + +.globl CNAME(ldexpl) +.set CNAME(ldexpl),CNAME(scalbnl) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_sin.S b/openlibm/i387/s_sin.S new file mode 100644 index 0000000..6b71455 --- /dev/null +++ b/openlibm/i387/s_sin.S @@ -0,0 +1,33 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_sin.S,v 1.9 2011/01/07 16:13:12 kib Exp $") + +ENTRY(sin) + fldl 4(%esp) + fsin + fnstsw %ax + andw $0x400,%ax + jnz 1f + ret +1: fldpi + fadd %st(0) + fxch %st(1) +2: fprem1 + fnstsw %ax + andw $0x400,%ax + jnz 2b + fstp %st(1) + fsin + ret +END(sin) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_tan.S b/openlibm/i387/s_tan.S new file mode 100644 index 0000000..7b25c3a --- /dev/null +++ b/openlibm/i387/s_tan.S @@ -0,0 +1,35 @@ +/* + * Written by: + * J.T. Conklin (jtc@netbsd.org) + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_tan.S,v 1.9 2011/01/07 16:13:12 kib Exp $") + +ENTRY(tan) + fldl 4(%esp) + fptan + fnstsw %ax + andw $0x400,%ax + jnz 1f + fstp %st(0) + ret +1: fldpi + fadd %st(0) + fxch %st(1) +2: fprem1 + fstsw %ax + andw $0x400,%ax + jnz 2b + fstp %st(1) + fptan + fstp %st(0) + ret +END(tan) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_trunc.S b/openlibm/i387/s_trunc.S new file mode 100644 index 0000000..5422770 --- /dev/null +++ b/openlibm/i387/s_trunc.S @@ -0,0 +1,33 @@ +/* + * Based on code written by J.T. Conklin . + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_trunc.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(trunc) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0c00,%dx /* round towards -oo */ + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldl 8(%ebp) /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(trunc) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_truncf.S b/openlibm/i387/s_truncf.S new file mode 100644 index 0000000..c9d32bb --- /dev/null +++ b/openlibm/i387/s_truncf.S @@ -0,0 +1,33 @@ +/* + * Based on code written by J.T. Conklin . + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_truncf.S,v 1.4 2011/01/07 16:13:12 kib Exp $") + +ENTRY(truncf) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0c00,%dx /* round towards -oo */ + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + flds 8(%ebp) /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(truncf) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/i387/s_truncl.S b/openlibm/i387/s_truncl.S new file mode 100644 index 0000000..7152638 --- /dev/null +++ b/openlibm/i387/s_truncl.S @@ -0,0 +1,33 @@ +/* + * Based on code written by J.T. Conklin . + * Public domain. + */ + +#include +//__FBSDID("$FreeBSD: src/lib/msun/i387/s_truncl.S,v 1.3 2011/01/07 16:13:12 kib Exp $") + +ENTRY(truncl) + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0c00,%dx /* round towards -oo */ + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldt 8(%ebp) /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave + ret +END(truncl) + + +/* Enable stack protection */ +#if defined(__ELF__) +.section .note.GNU-stack,"",%progbits +#endif diff --git a/openlibm/include/openlibm.h b/openlibm/include/openlibm.h new file mode 100644 index 0000000..d851945 --- /dev/null +++ b/openlibm/include/openlibm.h @@ -0,0 +1,8 @@ +#ifndef OPENLIBM_H +#define OPENLIBM_H + +#include +#include +#include + +#endif /* !OPENLIBM_H */ diff --git a/openlibm/include/openlibm_complex.h b/openlibm/include/openlibm_complex.h new file mode 100644 index 0000000..7afc992 --- /dev/null +++ b/openlibm/include/openlibm_complex.h @@ -0,0 +1,179 @@ +/* $OpenBSD: complex.h,v 1.5 2014/03/16 18:38:30 guenther Exp $ */ +/* + * Copyright (c) 2008 Martynas Venckus + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#ifdef OPENLIBM_USE_HOST_COMPLEX_H +#include +#else /* !OPENLIBM_USE_HOST_COMPLEX_H */ + +#ifndef OPENLIBM_COMPLEX_H +#define OPENLIBM_COMPLEX_H + +#define complex _Complex + +#define _Complex_I 1.0fi +#define I _Complex_I + +/* + * Macros that can be used to construct complex values. + * + * The C99 standard intends x+I*y to be used for this, but x+I*y is + * currently unusable in general since gcc introduces many overflow, + * underflow, sign and efficiency bugs by rewriting I*y as + * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product. + * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted + * to -0.0+I*0.0. + * + * In C11, a CMPLX(x,y) macro was added to circumvent this limitation, + * and gcc 4.7 added a __builtin_complex feature to simplify implementation + * of CMPLX in libc, so we can take advantage of these features if they + * are available. Clang simply allows complex values to be constructed + * using a compound literal. + * + * If __builtin_complex is not available, resort to using inline + * functions instead. These can unfortunately not be used to construct + * compile-time constants. + * + * C99 specifies that complex numbers have the same representation as + * an array of two elements, where the first element is the real part + * and the second element is the imaginary part. + */ + +#ifdef __clang__ +# define CMPLXF(x, y) ((float complex){x, y}) +# define CMPLX(x, y) ((double complex){x, y}) +# define CMPLXL(x, y) ((long double complex){x, y}) +#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 7)) && !defined(__INTEL_COMPILER) +# define CMPLXF(x,y) __builtin_complex ((float) (x), (float) (y)) +# define CMPLX(x,y) __builtin_complex ((double) (x), (double) (y)) +# define CMPLXL(x,y) __builtin_complex ((long double) (x), (long double) (y)) +#else +static inline float complex +CMPLXF(float x, float y) +{ + union { + float a[2]; + float complex f; + } z = {{ x, y }}; + + return (z.f); +} + +static inline double complex +CMPLX(double x, double y) +{ + union { + double a[2]; + double complex f; + } z = {{ x, y }}; + + return (z.f); +} + +static inline long double complex +CMPLXL(long double x, long double y) +{ + union { + long double a[2]; + long double complex f; + } z = {{ x, y }}; + + return (z.f); +} +#endif + +/* + * Double versions of C99 functions + */ +double complex cacos(double complex); +double complex casin(double complex); +double complex catan(double complex); +double complex ccos(double complex); +double complex csin(double complex); +double complex ctan(double complex); +double complex cacosh(double complex); +double complex casinh(double complex); +double complex catanh(double complex); +double complex ccosh(double complex); +double complex csinh(double complex); +double complex ctanh(double complex); +double complex cexp(double complex); +double complex clog(double complex); +double cabs(double complex); +double complex cpow(double complex, double complex); +double complex csqrt(double complex); +double carg(double complex); +double cimag(double complex); +double complex conj(double complex); +double complex cproj(double complex); +double creal(double complex); + +/* + * Float versions of C99 functions + */ +float complex cacosf(float complex); +float complex casinf(float complex); +float complex catanf(float complex); +float complex ccosf(float complex); +float complex csinf(float complex); +float complex ctanf(float complex); +float complex cacoshf(float complex); +float complex casinhf(float complex); +float complex catanhf(float complex); +float complex ccoshf(float complex); +float complex csinhf(float complex); +float complex ctanhf(float complex); +float complex cexpf(float complex); +float complex clogf(float complex); +float cabsf(float complex); +float complex cpowf(float complex, float complex); +float complex csqrtf(float complex); +float cargf(float complex); +float cimagf(float complex); +float complex conjf(float complex); +float complex cprojf(float complex); +float crealf(float complex); + +/* + * Long double versions of C99 functions + */ +long double complex cacosl(long double complex); +long double complex casinl(long double complex); +long double complex catanl(long double complex); +long double complex ccosl(long double complex); +long double complex csinl(long double complex); +long double complex ctanl(long double complex); +long double complex cacoshl(long double complex); +long double complex casinhl(long double complex); +long double complex catanhl(long double complex); +long double complex ccoshl(long double complex); +long double complex csinhl(long double complex); +long double complex ctanhl(long double complex); +long double complex cexpl(long double complex); +long double complex clogl(long double complex); +long double cabsl(long double complex); +long double complex cpowl(long double complex, + long double complex); +long double complex csqrtl(long double complex); +long double cargl(long double complex); +long double cimagl(long double complex); +long double complex conjl(long double complex); +long double complex cprojl(long double complex); +long double creall(long double complex); + +#endif /* !OPENLIBM_COMPLEX_H */ + +#endif /* OPENLIBM_USE_HOST_COMPLEX_H */ diff --git a/openlibm/include/openlibm_defs.h b/openlibm/include/openlibm_defs.h new file mode 100644 index 0000000..8a6fa6b --- /dev/null +++ b/openlibm/include/openlibm_defs.h @@ -0,0 +1,14 @@ +#ifndef OPENLIBM_DEFS_H_ +#define OPENLIBM_DEFS_H_ + +#ifdef _WIN32 +# ifdef IMPORT_EXPORTS +# define OLM_DLLEXPORT __declspec(dllimport) +# else +# define OLM_DLLEXPORT __declspec(dllexport) +# endif +#else +#define OLM_DLLEXPORT __attribute__ ((visibility("default"))) +#endif + +#endif // OPENLIBM_DEFS_H_ diff --git a/openlibm/include/openlibm_fenv.h b/openlibm/include/openlibm_fenv.h new file mode 100644 index 0000000..145e960 --- /dev/null +++ b/openlibm/include/openlibm_fenv.h @@ -0,0 +1,25 @@ +#ifdef OPENLIBM_USE_HOST_FENV_H +#include +#else /* !OPENLIBM_USE_HOST_FENV_H */ + +#if defined(__aarch64__) || defined(__arm__) +#include +#elif defined(__x86_64__) +#include +#elif defined(__i386__) +#include +#elif defined(__powerpc__) || defined(__POWERPC__) +#include +#elif defined(__mips__) +#include +#elif defined(__s390__) +#include +#elif defined(__riscv) +#include +#elif defined(__loongarch64) +#include +#else +#error "Unsupported platform" +#endif + +#endif /* OPENLIBM_USE_HOST_FENV_H */ diff --git a/openlibm/include/openlibm_fenv_amd64.h b/openlibm/include/openlibm_fenv_amd64.h new file mode 100644 index 0000000..c6db210 --- /dev/null +++ b/openlibm/include/openlibm_fenv_amd64.h @@ -0,0 +1,223 @@ +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/amd64/fenv.h,v 1.8 2011/10/10 15:43:09 das Exp $ + */ + +#ifndef _FENV_H_ +#define _FENV_H_ + +#include +#include "cdefs-compat.h" +#include "types-compat.h" + +#ifndef __fenv_static +#define __fenv_static static +#endif + +typedef struct { + struct { + uint32_t __control; + uint32_t __status; + uint32_t __tag; + char __other[16]; + } __x87; + uint32_t __mxcsr; +} fenv_t; + +typedef uint16_t fexcept_t; + +/* Exception flags */ +#define FE_INVALID 0x01 +#define FE_DENORMAL 0x02 +#define FE_DIVBYZERO 0x04 +#define FE_OVERFLOW 0x08 +#define FE_UNDERFLOW 0x10 +#define FE_INEXACT 0x20 +#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_DENORMAL | FE_INEXACT | \ + FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW) + +/* Rounding modes */ +#define FE_TONEAREST 0x0000 +#define FE_DOWNWARD 0x0400 +#define FE_UPWARD 0x0800 +#define FE_TOWARDZERO 0x0c00 +#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \ + FE_UPWARD | FE_TOWARDZERO) + +/* + * As compared to the x87 control word, the SSE unit's control word + * has the rounding control bits offset by 3 and the exception mask + * bits offset by 7. + */ +#define _SSE_ROUND_SHIFT 3 +#define _SSE_EMASK_SHIFT 7 + +__BEGIN_DECLS + +/* Default floating-point environment */ +extern const fenv_t __fe_dfl_env; +#define FE_DFL_ENV (&__fe_dfl_env) + +#define __fldcw(__cw) __asm __volatile("fldcw %0" : : "m" (__cw)) +#define __fldenv(__env) __asm __volatile("fldenv %0" : : "m" (__env)) +#define __fldenvx(__env) __asm __volatile("fldenv %0" : : "m" (__env) \ + : "st", "st(1)", "st(2)", "st(3)", "st(4)", \ + "st(5)", "st(6)", "st(7)") +#define __fnclex() __asm __volatile("fnclex") +#define __fnstenv(__env) __asm __volatile("fnstenv %0" : "=m" (*(__env))) +#define __fnstcw(__cw) __asm __volatile("fnstcw %0" : "=m" (*(__cw))) +#define __fnstsw(__sw) __asm __volatile("fnstsw %0" : "=am" (*(__sw))) +#define __fwait() __asm __volatile("fwait") +#define __ldmxcsr(__csr) __asm __volatile("ldmxcsr %0" : : "m" (__csr)) +#define __stmxcsr(__csr) __asm __volatile("stmxcsr %0" : "=m" (*(__csr))) + +__fenv_static __attribute__((always_inline)) inline int +feclearexcept(int __excepts) +{ + fenv_t __env; + + if (__excepts == FE_ALL_EXCEPT) { + __fnclex(); + } else { + __fnstenv(&__env.__x87); + __env.__x87.__status &= ~__excepts; + __fldenv(__env.__x87); + } + __stmxcsr(&__env.__mxcsr); + __env.__mxcsr &= ~__excepts; + __ldmxcsr(__env.__mxcsr); + return (0); +} + +__fenv_static inline int +fegetexceptflag(fexcept_t *__flagp, int __excepts) +{ + uint32_t __mxcsr; + uint16_t __status; + + __stmxcsr(&__mxcsr); + __fnstsw(&__status); + *__flagp = (__mxcsr | __status) & __excepts; + return (0); +} + +OLM_DLLEXPORT int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +OLM_DLLEXPORT int feraiseexcept(int __excepts); + +__fenv_static __attribute__((always_inline)) inline int +fetestexcept(int __excepts) +{ + uint32_t __mxcsr; + uint16_t __status; + + __stmxcsr(&__mxcsr); + __fnstsw(&__status); + return ((__status | __mxcsr) & __excepts); +} + +__fenv_static inline int +fegetround(void) +{ + uint16_t __control; + + /* + * We assume that the x87 and the SSE unit agree on the + * rounding mode. Reading the control word on the x87 turns + * out to be about 5 times faster than reading it on the SSE + * unit on an Opteron 244. + */ + __fnstcw(&__control); + return (__control & _ROUND_MASK); +} + +__fenv_static inline int +fesetround(int __round) +{ + uint32_t __mxcsr; + uint16_t __control; + + if (__round & ~_ROUND_MASK) + return (-1); + + __fnstcw(&__control); + __control &= ~_ROUND_MASK; + __control |= __round; + __fldcw(__control); + + __stmxcsr(&__mxcsr); + __mxcsr &= ~(_ROUND_MASK << _SSE_ROUND_SHIFT); + __mxcsr |= __round << _SSE_ROUND_SHIFT; + __ldmxcsr(__mxcsr); + + return (0); +} + +OLM_DLLEXPORT int fegetenv(fenv_t *__envp); +OLM_DLLEXPORT int feholdexcept(fenv_t *__envp); + +__fenv_static inline int +fesetenv(const fenv_t *__envp) +{ + + /* + * XXX Using fldenvx() instead of fldenv() tells the compiler that this + * instruction clobbers the i387 register stack. This happens because + * we restore the tag word from the saved environment. Normally, this + * would happen anyway and we wouldn't care, because the ABI allows + * function calls to clobber the i387 regs. However, fesetenv() is + * inlined, so we need to be more careful. + */ + __fldenvx(__envp->__x87); + __ldmxcsr(__envp->__mxcsr); + return (0); +} + +OLM_DLLEXPORT int feupdateenv(const fenv_t *__envp); + +#if __BSD_VISIBLE + +OLM_DLLEXPORT int feenableexcept(int __mask); +OLM_DLLEXPORT int fedisableexcept(int __mask); + +/* We currently provide no external definition of fegetexcept(). */ +static inline int +fegetexcept(void) +{ + uint16_t __control; + + /* + * We assume that the masks for the x87 and the SSE unit are + * the same. + */ + __fnstcw(&__control); + return (~__control & FE_ALL_EXCEPT); +} + +#endif /* __BSD_VISIBLE */ + +__END_DECLS + +#endif /* !_FENV_H_ */ diff --git a/openlibm/include/openlibm_fenv_arm.h b/openlibm/include/openlibm_fenv_arm.h new file mode 100644 index 0000000..ff1946f --- /dev/null +++ b/openlibm/include/openlibm_fenv_arm.h @@ -0,0 +1,230 @@ +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/arm/fenv.h,v 1.6 2011/10/10 15:43:09 das Exp $ + */ + +#ifndef _FENV_H_ +#define _FENV_H_ + +#include + +#include "cdefs-compat.h" + +#ifndef __fenv_static +#define __fenv_static static +#endif + +typedef uint32_t fenv_t; +typedef uint32_t fexcept_t; + +/* Exception flags */ +#define FE_INVALID 0x0001 +#define FE_DIVBYZERO 0x0002 +#define FE_OVERFLOW 0x0004 +#define FE_UNDERFLOW 0x0008 +#define FE_INEXACT 0x0010 +#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_INEXACT | \ + FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW) + +/* Rounding modes */ +#define FE_TONEAREST 0x0000 +#define FE_TOWARDZERO 0x0001 +#define FE_UPWARD 0x0002 +#define FE_DOWNWARD 0x0003 +#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \ + FE_UPWARD | FE_TOWARDZERO) +__BEGIN_DECLS + +/* Default floating-point environment */ +extern const fenv_t __fe_dfl_env; +#define FE_DFL_ENV (&__fe_dfl_env) + +/* We need to be able to map status flag positions to mask flag positions */ +#define _FPUSW_SHIFT 16 +#define _ENABLE_MASK (FE_ALL_EXCEPT << _FPUSW_SHIFT) + +#if defined(__aarch64__) +#define __rfs(__fpsr) __asm __volatile("mrs %0,fpsr" : "=r" (*(__fpsr))) +#define __wfs(__fpsr) __asm __volatile("msr fpsr,%0" : : "r" (__fpsr)) +/* Test for hardware support for ARM floating point operations, explicitly +checking for float and double support, see "ARM C Language Extensions", 6.5.1 */ +#elif defined(__ARM_FP) && (__ARM_FP & 0x0C) != 0 +#define __rfs(__fpsr) __asm __volatile("vmrs %0,fpscr" : "=&r" (*(__fpsr))) +#define __wfs(__fpsr) __asm __volatile("vmsr fpscr,%0" : : "r" (__fpsr)) +#else +#define __rfs(__fpsr) (*(__fpsr) = 0) +#define __wfs(__fpsr) +#endif + +__fenv_static inline int +feclearexcept(int __excepts) +{ + fexcept_t __fpsr; + + __rfs(&__fpsr); + __fpsr &= ~__excepts; + __wfs(__fpsr); + return (0); +} + +__fenv_static inline int +fegetexceptflag(fexcept_t *__flagp, int __excepts) +{ + fexcept_t __fpsr; + + __rfs(&__fpsr); + *__flagp = __fpsr & __excepts; + return (0); +} + +__fenv_static inline int +fesetexceptflag(const fexcept_t *__flagp, int __excepts) +{ + fexcept_t __fpsr; + + __rfs(&__fpsr); + __fpsr &= ~__excepts; + __fpsr |= *__flagp & __excepts; + __wfs(__fpsr); + return (0); +} + +__fenv_static inline int +feraiseexcept(int __excepts) +{ + fexcept_t __ex = __excepts; + + fesetexceptflag(&__ex, __excepts); /* XXX */ + return (0); +} + +__fenv_static inline int +fetestexcept(int __excepts) +{ + fexcept_t __fpsr; + + __rfs(&__fpsr); + return (__fpsr & __excepts); +} + +__fenv_static inline int +fegetround(void) +{ + + /* + * Apparently, the rounding mode is specified as part of the + * instruction format on ARM, so the dynamic rounding mode is + * indeterminate. Some FPUs may differ. + */ + return (-1); +} + +__fenv_static inline int +fesetround(int __round) +{ + + return (-1); +} + +__fenv_static inline int +fegetenv(fenv_t *__envp) +{ + + __rfs(__envp); + return (0); +} + +__fenv_static inline int +feholdexcept(fenv_t *__envp) +{ + fenv_t __env; + + __rfs(&__env); + *__envp = __env; + __env &= ~(FE_ALL_EXCEPT | _ENABLE_MASK); + __wfs(__env); + return (0); +} + +__fenv_static inline int +fesetenv(const fenv_t *__envp) +{ + + __wfs(*__envp); + return (0); +} + +__fenv_static inline int +feupdateenv(const fenv_t *__envp) +{ + fexcept_t __fpsr; + + __rfs(&__fpsr); + __wfs(*__envp); + feraiseexcept(__fpsr & FE_ALL_EXCEPT); + return (0); +} + +#if __BSD_VISIBLE + +/* We currently provide no external definitions of the functions below. */ + +static inline int +feenableexcept(int __mask) +{ + fenv_t __old_fpsr, __new_fpsr; + + __rfs(&__old_fpsr); + __new_fpsr = __old_fpsr | (__mask & FE_ALL_EXCEPT) << _FPUSW_SHIFT; + __wfs(__new_fpsr); + return ((__old_fpsr >> _FPUSW_SHIFT) & FE_ALL_EXCEPT); +} + +static inline int +fedisableexcept(int __mask) +{ + fenv_t __old_fpsr, __new_fpsr; + + __rfs(&__old_fpsr); + __new_fpsr = __old_fpsr & ~((__mask & FE_ALL_EXCEPT) << _FPUSW_SHIFT); + __wfs(__new_fpsr); + return ((__old_fpsr >> _FPUSW_SHIFT) & FE_ALL_EXCEPT); +} + +static inline int +fegetexcept(void) +{ + fenv_t __fpsr; + + __rfs(&__fpsr); + return ((__fpsr & _ENABLE_MASK) >> _FPUSW_SHIFT); +} + +#endif /* __BSD_VISIBLE */ + +__END_DECLS + +#endif /* !_FENV_H_ */ diff --git a/openlibm/include/openlibm_fenv_i387.h b/openlibm/include/openlibm_fenv_i387.h new file mode 100644 index 0000000..ec4eb87 --- /dev/null +++ b/openlibm/include/openlibm_fenv_i387.h @@ -0,0 +1,260 @@ +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/i387/fenv.h,v 1.8 2011/10/10 15:43:09 das Exp $ + */ + +#ifndef _FENV_H_ +#define _FENV_H_ + +#include "openlibm_defs.h" +#include "cdefs-compat.h" +#include "types-compat.h" + +#ifndef __fenv_static +#define __fenv_static static +#endif + +/* + * To preserve binary compatibility with FreeBSD 5.3, we pack the + * mxcsr into some reserved fields, rather than changing sizeof(fenv_t). + */ +typedef struct { + uint16_t __control; + uint16_t __mxcsr_hi; + uint16_t __status; + uint16_t __mxcsr_lo; + uint32_t __tag; + char __other[16]; +} fenv_t; + +#define __get_mxcsr(env) (((env).__mxcsr_hi << 16) | \ + ((env).__mxcsr_lo)) +#define __set_mxcsr(env, x) do { \ + (env).__mxcsr_hi = (uint32_t)(x) >> 16; \ + (env).__mxcsr_lo = (uint16_t)(x); \ +} while (0) + +typedef uint16_t fexcept_t; + +/* Exception flags */ +#define FE_INVALID 0x01 +#define FE_DENORMAL 0x02 +#define FE_DIVBYZERO 0x04 +#define FE_OVERFLOW 0x08 +#define FE_UNDERFLOW 0x10 +#define FE_INEXACT 0x20 +#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_DENORMAL | FE_INEXACT | \ + FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW) + +/* Rounding modes */ +#define FE_TONEAREST 0x0000 +#define FE_DOWNWARD 0x0400 +#define FE_UPWARD 0x0800 +#define FE_TOWARDZERO 0x0c00 +#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \ + FE_UPWARD | FE_TOWARDZERO) + +/* + * As compared to the x87 control word, the SSE unit's control word + * has the rounding control bits offset by 3 and the exception mask + * bits offset by 7. + */ +#define _SSE_ROUND_SHIFT 3 +#define _SSE_EMASK_SHIFT 7 + +__BEGIN_DECLS + +/* After testing for SSE support once, we cache the result in __has_sse. */ +enum __sse_support { __SSE_YES, __SSE_NO, __SSE_UNK }; +OLM_DLLEXPORT extern enum __sse_support __has_sse; +OLM_DLLEXPORT int __test_sse(void); +#ifdef __SSE__ +#define __HAS_SSE() 1 +#else +#define __HAS_SSE() (__has_sse == __SSE_YES || \ + (__has_sse == __SSE_UNK && __test_sse())) +#endif + +/* Default floating-point environment */ +OLM_DLLEXPORT extern const fenv_t __fe_dfl_env; +#define FE_DFL_ENV (&__fe_dfl_env) + +#define __fldcw(__cw) __asm __volatile("fldcw %0" : : "m" (__cw)) +#define __fldenv(__env) __asm __volatile("fldenv %0" : : "m" (__env)) +#define __fldenvx(__env) __asm __volatile("fldenv %0" : : "m" (__env) \ + : "st", "st(1)", "st(2)", "st(3)", "st(4)", \ + "st(5)", "st(6)", "st(7)") +#define __fnclex() __asm __volatile("fnclex") +#define __fnstenv(__env) __asm __volatile("fnstenv %0" : "=m" (*(__env))) +#define __fnstcw(__cw) __asm __volatile("fnstcw %0" : "=m" (*(__cw))) +#define __fnstsw(__sw) __asm __volatile("fnstsw %0" : "=am" (*(__sw))) +#define __fwait() __asm __volatile("fwait") +#define __ldmxcsr(__csr) __asm __volatile("ldmxcsr %0" : : "m" (__csr)) +#define __stmxcsr(__csr) __asm __volatile("stmxcsr %0" : "=m" (*(__csr))) + +__fenv_static inline int +feclearexcept(int __excepts) +{ + fenv_t __env; + uint32_t __mxcsr; + + if (__excepts == FE_ALL_EXCEPT) { + __fnclex(); + } else { + __fnstenv(&__env); + __env.__status &= ~__excepts; + __fldenv(__env); + } + if (__HAS_SSE()) { + __stmxcsr(&__mxcsr); + __mxcsr &= ~__excepts; + __ldmxcsr(__mxcsr); + } + return (0); +} + +__fenv_static inline int +fegetexceptflag(fexcept_t *__flagp, int __excepts) +{ + uint32_t __mxcsr; + uint16_t __status; + + __fnstsw(&__status); + if (__HAS_SSE()) + __stmxcsr(&__mxcsr); + else + __mxcsr = 0; + *__flagp = (__mxcsr | __status) & __excepts; + return (0); +} + +OLM_DLLEXPORT int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +OLM_DLLEXPORT int feraiseexcept(int __excepts); + +__fenv_static inline int +fetestexcept(int __excepts) +{ + uint32_t __mxcsr; + uint16_t __status; + + __fnstsw(&__status); + if (__HAS_SSE()) + __stmxcsr(&__mxcsr); + else + __mxcsr = 0; + return ((__status | __mxcsr) & __excepts); +} + +__fenv_static inline int +fegetround(void) +{ + uint16_t __control; + + /* + * We assume that the x87 and the SSE unit agree on the + * rounding mode. Reading the control word on the x87 turns + * out to be about 5 times faster than reading it on the SSE + * unit on an Opteron 244. + */ + __fnstcw(&__control); + return (__control & _ROUND_MASK); +} + +__fenv_static inline int +fesetround(int __round) +{ + uint32_t __mxcsr; + uint16_t __control; + + if (__round & ~_ROUND_MASK) + return (-1); + + __fnstcw(&__control); + __control &= ~_ROUND_MASK; + __control |= __round; + __fldcw(__control); + + if (__HAS_SSE()) { + __stmxcsr(&__mxcsr); + __mxcsr &= ~(_ROUND_MASK << _SSE_ROUND_SHIFT); + __mxcsr |= __round << _SSE_ROUND_SHIFT; + __ldmxcsr(__mxcsr); + } + + return (0); +} + +OLM_DLLEXPORT int fegetenv(fenv_t *__envp); +OLM_DLLEXPORT int feholdexcept(fenv_t *__envp); + +__fenv_static inline int +fesetenv(const fenv_t *__envp) +{ + fenv_t __env = *__envp; + uint32_t __mxcsr; + + __mxcsr = __get_mxcsr(__env); + __set_mxcsr(__env, 0xffffffff); + /* + * XXX Using fldenvx() instead of fldenv() tells the compiler that this + * instruction clobbers the i387 register stack. This happens because + * we restore the tag word from the saved environment. Normally, this + * would happen anyway and we wouldn't care, because the ABI allows + * function calls to clobber the i387 regs. However, fesetenv() is + * inlined, so we need to be more careful. + */ + __fldenvx(__env); + if (__HAS_SSE()) + __ldmxcsr(__mxcsr); + return (0); +} + +OLM_DLLEXPORT int feupdateenv(const fenv_t *__envp); + +#if __BSD_VISIBLE + +OLM_DLLEXPORT int feenableexcept(int __mask); +OLM_DLLEXPORT int fedisableexcept(int __mask); + +/* We currently provide no external definition of fegetexcept(). */ +static inline int +fegetexcept(void) +{ + uint16_t __control; + + /* + * We assume that the masks for the x87 and the SSE unit are + * the same. + */ + __fnstcw(&__control); + return (~__control & FE_ALL_EXCEPT); +} + +#endif /* __BSD_VISIBLE */ + +__END_DECLS + +#endif /* !_FENV_H_ */ diff --git a/openlibm/include/openlibm_fenv_loongarch64.h b/openlibm/include/openlibm_fenv_loongarch64.h new file mode 100644 index 0000000..cfaf020 --- /dev/null +++ b/openlibm/include/openlibm_fenv_loongarch64.h @@ -0,0 +1,226 @@ +/*- + * Copyright (c) 2023 Yifan An + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef _FENV_H_ +#define _FENV_H_ + +#include +#include "cdefs-compat.h" + +#ifndef __fenv_static +#define __fenv_static static +#endif + +typedef uint32_t fenv_t; +typedef uint32_t fexcept_t; + +/* Exception flags */ +#define FE_INVALID 0x100000 +#define FE_DIVBYZERO 0x080000 +#define FE_OVERFLOW 0x040000 +#define FE_UNDERFLOW 0x020000 +#define FE_INEXACT 0x010000 +#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_INEXACT | \ + FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW) + +/* Rounding modes */ +#define FE_TONEAREST 0x0000 +#define FE_TOWARDZERO 0x0100 +#define FE_DOWNWARD 0x0200 +#define FE_UPWARD 0x0300 +#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \ + FE_UPWARD | FE_TOWARDZERO) + +__BEGIN_DECLS + +/* Default floating-point environment */ +extern const fenv_t __fe_dfl_env; +#define FE_DFL_ENV (&__fe_dfl_env) + +#define _FPU_MASK_V 0x10 +#define _FPU_MASK_Z 0x08 +#define _FPU_MASK_O 0x04 +#define _FPU_MASK_U 0x02 +#define _FPU_MASK_I 0x01 + +#define _FPUSW_SHIFT 16 +#define _ENABLE_MASK (_FPU_MASK_V | _FPU_MASK_Z | _FPU_MASK_O | _FPU_MASK_U | _FPU_MASK_I) + +#define __rfs(__fpsr) __asm __volatile("movfcsr2gr %0,$r0" : "=r"(__fpsr)) +#define __wfs(__fpsr) __asm __volatile("movgr2fcsr $r0,%0" : : "r"(__fpsr)) + +__fenv_static inline int +feclearexcept(int __excepts) +{ + fexcept_t __fpsr; + + __rfs(__fpsr); + __fpsr &= ~__excepts; + __wfs(__fpsr); + return (0); +} + +__fenv_static inline int +fegetexceptflag(fexcept_t *__flagp, int __excepts) +{ + fexcept_t __fpsr; + + __rfs(__fpsr); + *__flagp = __fpsr & __excepts; + return (0); +} + +__fenv_static inline int +fesetexceptflag(const fexcept_t *__flagp, int __excepts) +{ + fexcept_t __fpsr; + + __rfs(__fpsr); + __fpsr &= ~__excepts; + __fpsr |= *__flagp & __excepts; + __wfs(__fpsr); + return (0); +} + +__fenv_static inline int +feraiseexcept(int __excepts) +{ + fexcept_t __ex = __excepts; + + fesetexceptflag(&__ex, __excepts); /* XXX */ + return (0); +} + +__fenv_static inline int +fetestexcept(int __excepts) +{ + fexcept_t __fpsr; + + __rfs(__fpsr); + return (__fpsr & __excepts); +} + +__fenv_static inline int +fegetround(void) +{ + fexcept_t __fpsr; + + __rfs(__fpsr); + return __fpsr & _ROUND_MASK; +} + +__fenv_static inline int +fesetround(int __round) +{ + fexcept_t __fpsr; + if ((__round & ~_ROUND_MASK) != 0) + return 1; + + __rfs(__fpsr); + __fpsr &= ~_ROUND_MASK; + __fpsr |= __round; + __wfs(__fpsr); + + return (0); +} + +__fenv_static inline int +fegetenv(fenv_t *__envp) +{ + __rfs(*__envp); + return (0); +} + +__fenv_static inline int +feholdexcept(fenv_t *__envp) +{ + fenv_t __env; + + __rfs(__env); + *__envp = __env; + __env &= ~(FE_ALL_EXCEPT | _FPU_MASK_V | _FPU_MASK_Z | _FPU_MASK_O | _FPU_MASK_U | _FPU_MASK_I); + __wfs(__env); + return (0); +} + +__fenv_static inline int +fesetenv(const fenv_t *__envp) +{ + __wfs(*__envp); + return (0); +} + +__fenv_static inline int +feupdateenv(const fenv_t *__envp) +{ + fexcept_t __fpsr; + + __rfs(__fpsr); + __wfs(*__envp); + feraiseexcept(__fpsr & FE_ALL_EXCEPT); + return (0); +} + +#if __BSD_VISIBLE + +static inline int +feenableexcept(int __mask) +{ + fenv_t __old_fpsr, __new_fpsr; + + __rfs(__new_fpsr); + __old_fpsr = (__new_fpsr & _ENABLE_MASK) << _FPUSW_SHIFT; + __new_fpsr |= (__mask & FE_ALL_EXCEPT) >> _FPUSW_SHIFT; + __wfs(__new_fpsr); + return __old_fpsr; +} + +static inline int +fedisableexcept(int __mask) +{ + fenv_t __old_fpsr, __new_fpsr; + + __rfs(__new_fpsr); + __old_fpsr = (__new_fpsr & _ENABLE_MASK) << _FPUSW_SHIFT; + __new_fpsr &= ~((__mask & FE_ALL_EXCEPT) >> _FPUSW_SHIFT); + __wfs(__new_fpsr); + return __old_fpsr; +} + +static inline int +fegetexcept(void) +{ + fenv_t __fpsr; + + __rfs(__fpsr); + return ((__fpsr & _ENABLE_MASK) << _FPUSW_SHIFT); +} + +#endif /* __BSD_VISIBLE */ + +__END_DECLS + +#endif /* !_FENV_H_ */ \ No newline at end of file diff --git a/openlibm/include/openlibm_fenv_mips.h b/openlibm/include/openlibm_fenv_mips.h new file mode 100644 index 0000000..980252f --- /dev/null +++ b/openlibm/include/openlibm_fenv_mips.h @@ -0,0 +1,278 @@ +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + */ + +#ifndef _FENV_H_ +#define _FENV_H_ + +#include +#include "cdefs-compat.h" + +#ifndef __fenv_static +#define __fenv_static static +#endif + +typedef uint32_t fenv_t; +typedef uint32_t fexcept_t; + +/* Exception flags */ +#ifdef __mips_soft_float +#define _FPUSW_SHIFT 16 +#define FE_INVALID 0x0001 +#define FE_DIVBYZERO 0x0002 +#define FE_OVERFLOW 0x0004 +#define FE_UNDERFLOW 0x0008 +#define FE_INEXACT 0x0010 +#else +#define _FCSR_CAUSE_SHIFT 10 +#define FE_INVALID 0x0040 +#define FE_DIVBYZERO 0x0020 +#define FE_OVERFLOW 0x0010 +#define FE_UNDERFLOW 0x0008 +#define FE_INEXACT 0x0004 +#endif +#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_INEXACT | \ + FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW) + +/* Rounding modes */ +#define FE_TONEAREST 0x0000 +#define FE_TOWARDZERO 0x0001 +#define FE_UPWARD 0x0002 +#define FE_DOWNWARD 0x0003 +#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \ + FE_UPWARD | FE_TOWARDZERO) +__BEGIN_DECLS + +/* Default floating-point environment */ +extern const fenv_t __fe_dfl_env; +#define FE_DFL_ENV (&__fe_dfl_env) + +/* We need to be able to map status flag positions to mask flag positions */ +#define _ENABLE_SHIFT 5 +#define _ENABLE_MASK (FE_ALL_EXCEPT << _ENABLE_SHIFT) + +#ifndef __mips_soft_float +#define __cfc1(__fcsr) __asm __volatile("cfc1 %0, $31" : "=r" (__fcsr)) +#define __ctc1(__fcsr) __asm __volatile("ctc1 %0, $31" :: "r" (__fcsr)) +#endif + +#ifdef __mips_soft_float +int feclearexcept(int __excepts); +int fegetexceptflag(fexcept_t *__flagp, int __excepts); +int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +int feraiseexcept(int __excepts); +int fetestexcept(int __excepts); +int fegetround(void); +int fesetround(int __round); +int fegetenv(fenv_t *__envp); +int feholdexcept(fenv_t *__envp); +int fesetenv(const fenv_t *__envp); +int feupdateenv(const fenv_t *__envp); +#else +__fenv_static inline int +feclearexcept(int __excepts) +{ + fexcept_t fcsr; + + __excepts &= FE_ALL_EXCEPT; + __cfc1(fcsr); + fcsr &= ~(__excepts | (__excepts << _FCSR_CAUSE_SHIFT)); + __ctc1(fcsr); + + return (0); +} + +__fenv_static inline int +fegetexceptflag(fexcept_t *__flagp, int __excepts) +{ + fexcept_t fcsr; + + __excepts &= FE_ALL_EXCEPT; + __cfc1(fcsr); + *__flagp = fcsr & __excepts; + + return (0); +} + +__fenv_static inline int +fesetexceptflag(const fexcept_t *__flagp, int __excepts) +{ + fexcept_t fcsr; + + __excepts &= FE_ALL_EXCEPT; + __cfc1(fcsr); + fcsr &= ~__excepts; + fcsr |= *__flagp & __excepts; + __ctc1(fcsr); + + return (0); +} + +__fenv_static inline int +feraiseexcept(int __excepts) +{ + fexcept_t fcsr; + + __excepts &= FE_ALL_EXCEPT; + __cfc1(fcsr); + fcsr |= __excepts | (__excepts << _FCSR_CAUSE_SHIFT); + __ctc1(fcsr); + + return (0); +} + +__fenv_static inline int +fetestexcept(int __excepts) +{ + fexcept_t fcsr; + + __excepts &= FE_ALL_EXCEPT; + __cfc1(fcsr); + + return (fcsr & __excepts); +} + +__fenv_static inline int +fegetround(void) +{ + fexcept_t fcsr; + + __cfc1(fcsr); + + return (fcsr & _ROUND_MASK); +} + +__fenv_static inline int +fesetround(int __round) +{ + fexcept_t fcsr; + + if (__round & ~_ROUND_MASK) + return (-1); + + __cfc1(fcsr); + fcsr &= ~_ROUND_MASK; + fcsr |= __round; + __ctc1(fcsr); + + return (0); +} + +__fenv_static inline int +fegetenv(fenv_t *__envp) +{ + + __cfc1(*__envp); + + return (0); +} + +__fenv_static inline int +feholdexcept(fenv_t *__envp) +{ + fexcept_t fcsr; + + __cfc1(fcsr); + *__envp = fcsr; + fcsr &= ~(FE_ALL_EXCEPT | _ENABLE_MASK); + __ctc1(fcsr); + + return (0); +} + +__fenv_static inline int +fesetenv(const fenv_t *__envp) +{ + + __ctc1(*__envp); + + return (0); +} + +__fenv_static inline int +feupdateenv(const fenv_t *__envp) +{ + fexcept_t fcsr; + + __cfc1(fcsr); + fesetenv(__envp); + feraiseexcept(fcsr); + + return (0); +} +#endif /* !__mips_soft_float */ + +#if __BSD_VISIBLE + +/* We currently provide no external definitions of the functions below. */ + +#ifdef __mips_soft_float +int feenableexcept(int __mask); +int fedisableexcept(int __mask); +int fegetexcept(void); +#else +static inline int +feenableexcept(int __mask) +{ + fenv_t __old_fcsr, __new_fcsr; + + __cfc1(__old_fcsr); + __new_fcsr = __old_fcsr | (__mask & FE_ALL_EXCEPT) << _ENABLE_SHIFT; + __ctc1(__new_fcsr); + + return ((__old_fcsr >> _ENABLE_SHIFT) & FE_ALL_EXCEPT); +} + +static inline int +fedisableexcept(int __mask) +{ + fenv_t __old_fcsr, __new_fcsr; + + __cfc1(__old_fcsr); + __new_fcsr = __old_fcsr & ~((__mask & FE_ALL_EXCEPT) << _ENABLE_SHIFT); + __ctc1(__new_fcsr); + + return ((__old_fcsr >> _ENABLE_SHIFT) & FE_ALL_EXCEPT); +} + +static inline int +fegetexcept(void) +{ + fexcept_t fcsr; + + __cfc1(fcsr); + + return ((fcsr & _ENABLE_MASK) >> _ENABLE_SHIFT); +} + +#endif /* !__mips_soft_float */ + +#endif /* __BSD_VISIBLE */ + +__END_DECLS + +#endif /* !_FENV_H_ */ diff --git a/openlibm/include/openlibm_fenv_powerpc.h b/openlibm/include/openlibm_fenv_powerpc.h new file mode 100644 index 0000000..232ea83 --- /dev/null +++ b/openlibm/include/openlibm_fenv_powerpc.h @@ -0,0 +1,279 @@ +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + */ + +#ifndef _FENV_H_ +#define _FENV_H_ + +#include + +#ifndef __fenv_static +#define __fenv_static static +#endif + +typedef __uint32_t fenv_t; +typedef __uint32_t fexcept_t; + +/* Exception flags */ +#define FE_INEXACT 0x02000000 +#define FE_DIVBYZERO 0x04000000 +#define FE_UNDERFLOW 0x08000000 +#define FE_OVERFLOW 0x10000000 +#define FE_INVALID 0x20000000 /* all types of invalid FP ops */ + +/* + * The PowerPC architecture has extra invalid flags that indicate the + * specific type of invalid operation occurred. These flags may be + * tested, set, and cleared---but not masked---separately. All of + * these bits are cleared when FE_INVALID is cleared, but only + * FE_VXSOFT is set when FE_INVALID is explicitly set in software. + */ +#define FE_VXCVI 0x00000100 /* invalid integer convert */ +#define FE_VXSQRT 0x00000200 /* square root of a negative */ +#define FE_VXSOFT 0x00000400 /* software-requested exception */ +#define FE_VXVC 0x00080000 /* ordered comparison involving NaN */ +#define FE_VXIMZ 0x00100000 /* inf * 0 */ +#define FE_VXZDZ 0x00200000 /* 0 / 0 */ +#define FE_VXIDI 0x00400000 /* inf / inf */ +#define FE_VXISI 0x00800000 /* inf - inf */ +#define FE_VXSNAN 0x01000000 /* operation on a signalling NaN */ +#define FE_ALL_INVALID (FE_VXCVI | FE_VXSQRT | FE_VXSOFT | FE_VXVC | \ + FE_VXIMZ | FE_VXZDZ | FE_VXIDI | FE_VXISI | \ + FE_VXSNAN | FE_INVALID) +#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_INEXACT | \ + FE_ALL_INVALID | FE_OVERFLOW | FE_UNDERFLOW) + +/* Rounding modes */ +#define FE_TONEAREST 0x0000 +#define FE_TOWARDZERO 0x0001 +#define FE_UPWARD 0x0002 +#define FE_DOWNWARD 0x0003 +#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \ + FE_UPWARD | FE_TOWARDZERO) + +__BEGIN_DECLS + +/* Default floating-point environment */ +extern const fenv_t __fe_dfl_env; +#define FE_DFL_ENV (&__fe_dfl_env) + +/* We need to be able to map status flag positions to mask flag positions */ +#define _FPUSW_SHIFT 22 +#define _ENABLE_MASK ((FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \ + FE_OVERFLOW | FE_UNDERFLOW) >> _FPUSW_SHIFT) + +#ifndef _SOFT_FLOAT +#define __mffs(__env) __asm __volatile("mffs %0" : "=f" (*(__env))) +#define __mtfsf(__env) __asm __volatile("mtfsf 255,%0" : : "f" (__env)) +#else +#define __mffs(__env) +#define __mtfsf(__env) +#endif + +union __fpscr { + double __d; + struct { +#if defined(__BYTE_ORDER__) && (__BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__) + fenv_t __reg; + __uint32_t __junk; +#else + __uint32_t __junk; + fenv_t __reg; +#endif + } __bits; +}; + +__fenv_static inline int +feclearexcept(int __excepts) +{ + union __fpscr __r; + + if (__excepts & FE_INVALID) + __excepts |= FE_ALL_INVALID; + __mffs(&__r.__d); + __r.__bits.__reg &= ~__excepts; + __mtfsf(__r.__d); + return (0); +} + +__fenv_static inline int +fegetexceptflag(fexcept_t *__flagp, int __excepts) +{ + union __fpscr __r; + + __mffs(&__r.__d); + *__flagp = __r.__bits.__reg & __excepts; + return (0); +} + +__fenv_static inline int +fesetexceptflag(const fexcept_t *__flagp, int __excepts) +{ + union __fpscr __r; + + if (__excepts & FE_INVALID) + __excepts |= FE_ALL_EXCEPT; + __mffs(&__r.__d); + __r.__bits.__reg &= ~__excepts; + __r.__bits.__reg |= *__flagp & __excepts; + __mtfsf(__r.__d); + return (0); +} + +__fenv_static inline int +feraiseexcept(int __excepts) +{ + union __fpscr __r; + + if (__excepts & FE_INVALID) + __excepts |= FE_VXSOFT; + __mffs(&__r.__d); + __r.__bits.__reg |= __excepts; + __mtfsf(__r.__d); + return (0); +} + +__fenv_static inline int +fetestexcept(int __excepts) +{ + union __fpscr __r; + + __mffs(&__r.__d); + return (__r.__bits.__reg & __excepts); +} + +__fenv_static inline int +fegetround(void) +{ + union __fpscr __r; + + __mffs(&__r.__d); + return (__r.__bits.__reg & _ROUND_MASK); +} + +__fenv_static inline int +fesetround(int __round) +{ + union __fpscr __r; + + if (__round & ~_ROUND_MASK) + return (-1); + __mffs(&__r.__d); + __r.__bits.__reg &= ~_ROUND_MASK; + __r.__bits.__reg |= __round; + __mtfsf(__r.__d); + return (0); +} + +__fenv_static inline int +fegetenv(fenv_t *__envp) +{ + union __fpscr __r; + + __mffs(&__r.__d); + *__envp = __r.__bits.__reg; + return (0); +} + +__fenv_static inline int +feholdexcept(fenv_t *__envp) +{ + union __fpscr __r; + + __mffs(&__r.__d); + *__envp = __r.__d; + __r.__bits.__reg &= ~(FE_ALL_EXCEPT | _ENABLE_MASK); + __mtfsf(__r.__d); + return (0); +} + +__fenv_static inline int +fesetenv(const fenv_t *__envp) +{ + union __fpscr __r; + + __r.__bits.__reg = *__envp; + __mtfsf(__r.__d); + return (0); +} + +__fenv_static inline int +feupdateenv(const fenv_t *__envp) +{ + union __fpscr __r; + + __mffs(&__r.__d); + __r.__bits.__reg &= FE_ALL_EXCEPT; + __r.__bits.__reg |= *__envp; + __mtfsf(__r.__d); + return (0); +} + +#if __BSD_VISIBLE + +/* We currently provide no external definitions of the functions below. */ + +static inline int +feenableexcept(int __mask) +{ + union __fpscr __r; + fenv_t __oldmask; + + __mffs(&__r.__d); + __oldmask = __r.__bits.__reg; + __r.__bits.__reg |= (__mask & FE_ALL_EXCEPT) >> _FPUSW_SHIFT; + __mtfsf(__r.__d); + return ((__oldmask & _ENABLE_MASK) << _FPUSW_SHIFT); +} + +static inline int +fedisableexcept(int __mask) +{ + union __fpscr __r; + fenv_t __oldmask; + + __mffs(&__r.__d); + __oldmask = __r.__bits.__reg; + __r.__bits.__reg &= ~((__mask & FE_ALL_EXCEPT) >> _FPUSW_SHIFT); + __mtfsf(__r.__d); + return ((__oldmask & _ENABLE_MASK) << _FPUSW_SHIFT); +} + +static inline int +fegetexcept(void) +{ + union __fpscr __r; + + __mffs(&__r.__d); + return ((__r.__bits.__reg & _ENABLE_MASK) << _FPUSW_SHIFT); +} + +#endif /* __BSD_VISIBLE */ + +__END_DECLS + +#endif /* !_FENV_H_ */ diff --git a/openlibm/include/openlibm_fenv_riscv.h b/openlibm/include/openlibm_fenv_riscv.h new file mode 100644 index 0000000..e8ce78e --- /dev/null +++ b/openlibm/include/openlibm_fenv_riscv.h @@ -0,0 +1,261 @@ +/*- + * Copyright (c) 2004-2005 David Schultz + * Copyright (c) 2015-2016 Ruslan Bukin + * All rights reserved. + * + * Portions of this software were developed by SRI International and the + * University of Cambridge Computer Laboratory under DARPA/AFRL contract + * FA8750-10-C-0237 ("CTSRD"), as part of the DARPA CRASH research programme. + * + * Portions of this software were developed by the University of Cambridge + * Computer Laboratory as part of the CTSRD Project, with support from the + * UK Higher Education Innovation Fund (HEIF). + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: head/lib/msun/riscv/fenv.h 332792 2018-04-19 20:36:15Z brooks $ + */ + +#ifndef _FENV_H_ +#define _FENV_H_ + +#include +#include "cdefs-compat.h" + +#ifndef __fenv_static +#define __fenv_static static +#endif + +typedef uint64_t fenv_t; +typedef uint64_t fexcept_t; + +/* Exception flags */ +#define FE_INVALID 0x0010 +#define FE_DIVBYZERO 0x0008 +#define FE_OVERFLOW 0x0004 +#define FE_UNDERFLOW 0x0002 +#define FE_INEXACT 0x0001 +#define FE_ALL_EXCEPT (FE_DIVBYZERO | FE_INEXACT | \ + FE_INVALID | FE_OVERFLOW | FE_UNDERFLOW) + +/* + * RISC-V Rounding modes + */ +#define _ROUND_SHIFT 5 +#define FE_TONEAREST (0x00 << _ROUND_SHIFT) +#define FE_TOWARDZERO (0x01 << _ROUND_SHIFT) +#define FE_DOWNWARD (0x02 << _ROUND_SHIFT) +#define FE_UPWARD (0x03 << _ROUND_SHIFT) +#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \ + FE_UPWARD | FE_TOWARDZERO) + +__BEGIN_DECLS + +/* Default floating-point environment */ +extern const fenv_t __fe_dfl_env; +#define FE_DFL_ENV (&__fe_dfl_env) + +#if !defined(__riscv_float_abi_soft) && !defined(__riscv_float_abi_double) +#if defined(__riscv_float_abi_single) +#error single precision floating point ABI not supported +#else +#error compiler did not set soft/hard float macros +#endif +#endif + +#ifndef __riscv_float_abi_soft +#define __rfs(__fcsr) __asm __volatile("csrr %0, fcsr" : "=r" (__fcsr)) +#define __wfs(__fcsr) __asm __volatile("csrw fcsr, %0" :: "r" (__fcsr)) +#endif + +#ifdef __riscv_float_abi_soft +int feclearexcept(int __excepts); +int fegetexceptflag(fexcept_t *__flagp, int __excepts); +int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +int feraiseexcept(int __excepts); +int fetestexcept(int __excepts); +int fegetround(void); +int fesetround(int __round); +int fegetenv(fenv_t *__envp); +int feholdexcept(fenv_t *__envp); +int fesetenv(const fenv_t *__envp); +int feupdateenv(const fenv_t *__envp); +#else +__fenv_static inline int +feclearexcept(int __excepts) +{ + + __asm __volatile("csrc fflags, %0" :: "r"(__excepts)); + + return (0); +} + +__fenv_static inline int +fegetexceptflag(fexcept_t *__flagp, int __excepts) +{ + fexcept_t __fcsr; + + __rfs(__fcsr); + *__flagp = __fcsr & __excepts; + + return (0); +} + +__fenv_static inline int +fesetexceptflag(const fexcept_t *__flagp, int __excepts) +{ + fexcept_t __fcsr; + + __fcsr = *__flagp; + __asm __volatile("csrc fflags, %0" :: "r"(__excepts)); + __asm __volatile("csrs fflags, %0" :: "r"(__fcsr & __excepts)); + + return (0); +} + +__fenv_static inline int +feraiseexcept(int __excepts) +{ + + __asm __volatile("csrs fflags, %0" :: "r"(__excepts)); + + return (0); +} + +__fenv_static inline int +fetestexcept(int __excepts) +{ + fexcept_t __fcsr; + + __rfs(__fcsr); + + return (__fcsr & __excepts); +} + +__fenv_static inline int +fegetround(void) +{ + fexcept_t __fcsr; + + __rfs(__fcsr); + + return (__fcsr & _ROUND_MASK); +} + +__fenv_static inline int +fesetround(int __round) +{ + fexcept_t __fcsr; + + if (__round & ~_ROUND_MASK) + return (-1); + + __rfs(__fcsr); + __fcsr &= ~_ROUND_MASK; + __fcsr |= __round; + __wfs(__fcsr); + + return (0); +} + +__fenv_static inline int +fegetenv(fenv_t *__envp) +{ + + __rfs(*__envp); + + return (0); +} + +__fenv_static inline int +feholdexcept(fenv_t *__envp) +{ + + /* No exception traps. */ + + return (-1); +} + +__fenv_static inline int +fesetenv(const fenv_t *__envp) +{ + + __wfs(*__envp); + + return (0); +} + +__fenv_static inline int +feupdateenv(const fenv_t *__envp) +{ + fexcept_t __fcsr; + + __rfs(__fcsr); + __wfs(*__envp); + feraiseexcept(__fcsr & FE_ALL_EXCEPT); + + return (0); +} +#endif /* !__riscv_float_abi_soft */ + +#if __BSD_VISIBLE + +/* We currently provide no external definitions of the functions below. */ + +#ifdef __riscv_float_abi_soft +int feenableexcept(int __mask); +int fedisableexcept(int __mask); +int fegetexcept(void); +#else +static inline int +feenableexcept(int __mask) +{ + + /* No exception traps. */ + + return (-1); +} + +static inline int +fedisableexcept(int __mask) +{ + + /* No exception traps. */ + + return (0); +} + +static inline int +fegetexcept(void) +{ + + /* No exception traps. */ + + return (0); +} +#endif /* !__riscv_float_abi_soft */ + +#endif /* __BSD_VISIBLE */ + +__END_DECLS + +#endif /* !_FENV_H_ */ diff --git a/openlibm/include/openlibm_fenv_s390.h b/openlibm/include/openlibm_fenv_s390.h new file mode 100644 index 0000000..84ef080 --- /dev/null +++ b/openlibm/include/openlibm_fenv_s390.h @@ -0,0 +1,235 @@ +/*- + * Copyright (c) 2016 Dan Horák + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + */ + +#ifndef _FENV_H_ +#define _FENV_H_ + +#include + +#ifndef __fenv_static +#define __fenv_static static +#endif + +typedef __uint32_t fenv_t; +typedef __uint32_t fexcept_t; + +/* Exception flags */ +#define FE_INEXACT 0x080000 +#define FE_UNDERFLOW 0x100000 +#define FE_OVERFLOW 0x200000 +#define FE_DIVBYZERO 0x400000 +#define FE_INVALID 0x800000 /* all types of invalid FP ops */ + +#define FE_ALL_EXCEPT (FE_INVALID | FE_DIVBYZERO | FE_INEXACT | FE_OVERFLOW | FE_UNDERFLOW) + +/* Rounding modes */ +#define FE_TONEAREST 0x0000 +#define FE_TOWARDZERO 0x0001 +#define FE_UPWARD 0x0002 +#define FE_DOWNWARD 0x0003 +#define _ROUND_MASK (FE_TONEAREST | FE_DOWNWARD | \ + FE_UPWARD | FE_TOWARDZERO) + +__BEGIN_DECLS + +/* Default floating-point environment */ +extern const fenv_t __fe_dfl_env; +#define FE_DFL_ENV (&__fe_dfl_env) + +/* We need to be able to map status flag positions to mask flag positions */ +#define _FPC_EXC_MASK_SHIFT 8 +#define _ENABLE_MASK ((FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \ + FE_OVERFLOW | FE_UNDERFLOW) << _FPC_EXC_MASK_SHIFT) + +/* Macros for accessing the hardware control word. */ +#define _FPU_GETCW(cw) __asm__ __volatile__ ("efpc %0,0" : "=d" (cw)) +#define _FPU_SETCW(cw) __asm__ __volatile__ ("sfpc %0,0" : : "d" (cw)) + +__fenv_static inline int +feclearexcept(int __excepts) +{ + fexcept_t __r; + + if (__excepts & FE_INVALID) + __excepts |= FE_ALL_EXCEPT; + _FPU_GETCW(__r); + __r &= ~__excepts; + _FPU_SETCW(__r); + return (0); +} + +__fenv_static inline int +fegetexceptflag(fexcept_t *__flagp, int __excepts) +{ + fexcept_t __r; + + _FPU_GETCW(__r); + *__flagp = __r & __excepts; + return (0); +} + +__fenv_static inline int +fesetexceptflag(const fexcept_t *__flagp, int __excepts) +{ + fexcept_t __r; + + if (__excepts & FE_INVALID) + __excepts |= FE_ALL_EXCEPT; + _FPU_GETCW(__r); + __r &= ~__excepts; + __r |= *__flagp & __excepts; + _FPU_SETCW(__r); + return (0); +} + +__fenv_static inline int +feraiseexcept(int __excepts) +{ + fexcept_t __r; + + _FPU_GETCW(__r); + __r |= __excepts; + _FPU_SETCW(__r); + return (0); +} + +__fenv_static inline int +fetestexcept(int __excepts) +{ + fexcept_t __r; + + _FPU_GETCW(__r); + return (__r & __excepts); +} + +__fenv_static inline int +fegetround(void) +{ + fexcept_t __r; + + _FPU_GETCW(__r); + return (__r & _ROUND_MASK); +} + +__fenv_static inline int +fesetround(int __round) +{ + fexcept_t __r; + + if (__round & ~_ROUND_MASK) + return (-1); + + _FPU_GETCW(__r); + __r &= ~_ROUND_MASK; + __r |= __round; + _FPU_SETCW(__r); + return (0); +} + +__fenv_static inline int +fegetenv(fenv_t *__envp) +{ + _FPU_GETCW(*__envp); + return (0); +} + +__fenv_static inline int +feholdexcept(fenv_t *__envp) +{ + fexcept_t __r; + + _FPU_GETCW(__r); + *__envp = __r; + __r &= ~(FE_ALL_EXCEPT | _ENABLE_MASK); + _FPU_SETCW(__r); + return (0); +} + +__fenv_static inline int +fesetenv(const fenv_t *__envp) +{ + _FPU_SETCW(*__envp); + return (0); +} + +__fenv_static inline int +feupdateenv(const fenv_t *__envp) +{ + fexcept_t __r; + + _FPU_GETCW(__r); + __r &= FE_ALL_EXCEPT; + __r |= *__envp; + _FPU_SETCW(__r); + return (0); +} + +#if __BSD_VISIBLE + +/* We currently provide no external definitions of the functions below. */ + +static inline int +feenableexcept(int __mask) +{ + fenv_t __r; + fenv_t __oldmask; + + _FPU_GETCW(__r); + __oldmask = __r; + __r |= (__mask & FE_ALL_EXCEPT) << _FPC_EXC_MASK_SHIFT; + _FPU_SETCW(__r); + return ((__oldmask & _ENABLE_MASK) >> _FPC_EXC_MASK_SHIFT); +} + +static inline int +fedisableexcept(int __mask) +{ + fenv_t __r; + fenv_t __oldmask; + + _FPU_GETCW(__r); + __oldmask = __r; + __r &= ~((__mask & FE_ALL_EXCEPT) << _FPC_EXC_MASK_SHIFT); + _FPU_SETCW(__r); + return ((__oldmask & _ENABLE_MASK) >> _FPC_EXC_MASK_SHIFT); +} + +static inline int +fegetexcept(void) +{ + fexcept_t __r; + + _FPU_GETCW(__r); + return (__r & (_ENABLE_MASK >> _FPC_EXC_MASK_SHIFT)); +} + +#endif /* __BSD_VISIBLE */ + +__END_DECLS + +#endif /* !_FENV_H_ */ diff --git a/openlibm/include/openlibm_math.h b/openlibm/include/openlibm_math.h new file mode 100644 index 0000000..701ad70 --- /dev/null +++ b/openlibm/include/openlibm_math.h @@ -0,0 +1,493 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $FreeBSD: src/lib/msun/src/openlibm.h,v 1.82 2011/11/12 19:55:48 theraven Exp $ + */ + +#ifdef OPENLIBM_USE_HOST_MATH_H +#include +#else /* !OPENLIBM_USE_HOST_MATH_H */ + +#include + +#ifndef OPENLIBM_MATH_H +#define OPENLIBM_MATH_H + +#if (defined(_WIN32) || defined (_MSC_VER)) && !defined(__WIN32__) + #define __WIN32__ +#endif + +#if !defined(__arm__) && !defined(__wasm__) +#define OLM_LONG_DOUBLE +#endif + +#ifndef __pure2 +#define __pure2 +#endif + +/* + * ANSI/POSIX + */ +extern const union __infinity_un { + unsigned char __uc[8]; + double __ud; +} __infinity; + +extern const union __nan_un { + unsigned char __uc[sizeof(float)]; + float __uf; +} __nan; + +/* VBS +#if __GNUC_PREREQ__(3, 3) || (defined(__INTEL_COMPILER) && __INTEL_COMPILER >= 800) +#define __MATH_BUILTIN_CONSTANTS +#endif + +#if __GNUC_PREREQ__(3, 0) && !defined(__INTEL_COMPILER) +#define __MATH_BUILTIN_RELOPS +#endif +*/ + +//VBS begin +#define __MATH_BUILTIN_CONSTANTS +#define __MATH_BUILTIN_RELOPS +#ifndef __ISO_C_VISIBLE +#define __ISO_C_VISIBLE 1999 +#endif +//VBS end + +#ifdef __MATH_BUILTIN_CONSTANTS +#define HUGE_VAL __builtin_huge_val() +#else +#define HUGE_VAL (__infinity.__ud) +#endif + +#if __ISO_C_VISIBLE >= 1999 +#define FP_ILOGB0 (-INT_MAX) +#define FP_ILOGBNAN INT_MAX + +#ifdef __MATH_BUILTIN_CONSTANTS +#define HUGE_VALF __builtin_huge_valf() +#define HUGE_VALL __builtin_huge_vall() +#define INFINITY __builtin_inff() +#define NAN __builtin_nanf("") +#else +#define HUGE_VALF (float)HUGE_VAL +#define HUGE_VALL (long double)HUGE_VAL +#define INFINITY HUGE_VALF +#define NAN (__nan.__uf) +#endif /* __MATH_BUILTIN_CONSTANTS */ + +#define MATH_ERRNO 1 +#define MATH_ERREXCEPT 2 +#define math_errhandling MATH_ERREXCEPT + +#define FP_FAST_FMAF 1 +#ifdef __ia64__ +#define FP_FAST_FMA 1 +#define FP_FAST_FMAL 1 +#endif + +/* Symbolic constants to classify floating point numbers. */ +#define FP_INFINITE 0x01 +#define FP_NAN 0x02 +#define FP_NORMAL 0x04 +#define FP_SUBNORMAL 0x08 +#define FP_ZERO 0x10 +#define fpclassify(x) \ + ((sizeof (x) == sizeof (float)) ? __fpclassifyf(x) \ + : (sizeof (x) == sizeof (double)) ? __fpclassifyd(x) \ + : __fpclassifyl(x)) + +#define isfinite(x) \ + ((sizeof (x) == sizeof (float)) ? __isfinitef(x) \ + : (sizeof (x) == sizeof (double)) ? __isfinite(x) \ + : __isfinitel(x)) +#define isinf(x) \ + ((sizeof (x) == sizeof (float)) ? __isinff(x) \ + : (sizeof (x) == sizeof (double)) ? isinf(x) \ + : __isinfl(x)) +#define isnan(x) \ + ((sizeof (x) == sizeof (float)) ? __isnanf(x) \ + : (sizeof (x) == sizeof (double)) ? isnan(x) \ + : __isnanl(x)) +#define isnormal(x) \ + ((sizeof (x) == sizeof (float)) ? __isnormalf(x) \ + : (sizeof (x) == sizeof (double)) ? __isnormal(x) \ + : __isnormall(x)) + +#ifdef __MATH_BUILTIN_RELOPS +#define isgreater(x, y) __builtin_isgreater((x), (y)) +#define isgreaterequal(x, y) __builtin_isgreaterequal((x), (y)) +#define isless(x, y) __builtin_isless((x), (y)) +#define islessequal(x, y) __builtin_islessequal((x), (y)) +#define islessgreater(x, y) __builtin_islessgreater((x), (y)) +#define isunordered(x, y) __builtin_isunordered((x), (y)) +#else +#define isgreater(x, y) (!isunordered((x), (y)) && (x) > (y)) +#define isgreaterequal(x, y) (!isunordered((x), (y)) && (x) >= (y)) +#define isless(x, y) (!isunordered((x), (y)) && (x) < (y)) +#define islessequal(x, y) (!isunordered((x), (y)) && (x) <= (y)) +#define islessgreater(x, y) (!isunordered((x), (y)) && \ + ((x) > (y) || (y) > (x))) +#define isunordered(x, y) (isnan(x) || isnan(y)) +#endif /* __MATH_BUILTIN_RELOPS */ + +#define signbit(x) \ + ((sizeof (x) == sizeof (float)) ? __signbitf(x) \ + : (sizeof (x) == sizeof (double)) ? __signbit(x) \ + : __signbitl(x)) + +//VBS +//typedef __double_t double_t; +//typedef __float_t float_t; +#endif /* __ISO_C_VISIBLE >= 1999 */ + +/* + * XOPEN/SVID + */ +#if __BSD_VISIBLE || __XSI_VISIBLE +#define M_E 2.7182818284590452354 /* e */ +#define M_LOG2E 1.4426950408889634074 /* log 2e */ +#define M_LOG10E 0.43429448190325182765 /* log 10e */ +#define M_LN2 0.69314718055994530942 /* log e2 */ +#define M_LN10 2.30258509299404568402 /* log e10 */ +#define M_PI 3.14159265358979323846 /* pi */ +#define M_PI_2 1.57079632679489661923 /* pi/2 */ +#define M_PI_4 0.78539816339744830962 /* pi/4 */ +#define M_1_PI 0.31830988618379067154 /* 1/pi */ +#define M_2_PI 0.63661977236758134308 /* 2/pi */ +#define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ +#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ +#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ + +#define MAXFLOAT ((float)3.40282346638528860e+38) + +#ifndef OPENLIBM_ONLY_THREAD_SAFE +OLM_DLLEXPORT extern int signgam; +#endif +#endif /* __BSD_VISIBLE || __XSI_VISIBLE */ + +#if __BSD_VISIBLE +#if 0 +/* Old value from 4.4BSD-Lite openlibm.h; this is probably better. */ +#define HUGE HUGE_VAL +#else +#define HUGE MAXFLOAT +#endif +#endif /* __BSD_VISIBLE */ + +/* + * Most of these functions depend on the rounding mode and have the side + * effect of raising floating-point exceptions, so they are not declared + * as __pure2. In C99, FENV_ACCESS affects the purity of these functions. + */ + +#if defined(__cplusplus) +extern "C" { +#endif +/* Symbol present when OpenLibm is used. */ +int isopenlibm(void); + +/* + * ANSI/POSIX + */ +OLM_DLLEXPORT int __fpclassifyd(double) __pure2; +OLM_DLLEXPORT int __fpclassifyf(float) __pure2; +OLM_DLLEXPORT int __fpclassifyl(long double) __pure2; +OLM_DLLEXPORT int __isfinitef(float) __pure2; +OLM_DLLEXPORT int __isfinite(double) __pure2; +OLM_DLLEXPORT int __isfinitel(long double) __pure2; +OLM_DLLEXPORT int __isinff(float) __pure2; +OLM_DLLEXPORT int __isinfl(long double) __pure2; +OLM_DLLEXPORT int __isnanf(float) __pure2; +OLM_DLLEXPORT int __isnanl(long double) __pure2; +OLM_DLLEXPORT int __isnormalf(float) __pure2; +OLM_DLLEXPORT int __isnormal(double) __pure2; +OLM_DLLEXPORT int __isnormall(long double) __pure2; +OLM_DLLEXPORT int __signbit(double) __pure2; +OLM_DLLEXPORT int __signbitf(float) __pure2; +OLM_DLLEXPORT int __signbitl(long double) __pure2; + +OLM_DLLEXPORT double acos(double); +OLM_DLLEXPORT double asin(double); +OLM_DLLEXPORT double atan(double); +OLM_DLLEXPORT double atan2(double, double); +OLM_DLLEXPORT double cos(double); +OLM_DLLEXPORT double sin(double); +OLM_DLLEXPORT double tan(double); + +OLM_DLLEXPORT double cosh(double); +OLM_DLLEXPORT double sinh(double); +OLM_DLLEXPORT double tanh(double); + +OLM_DLLEXPORT double exp(double); +OLM_DLLEXPORT double frexp(double, int *); /* fundamentally !__pure2 */ +OLM_DLLEXPORT double ldexp(double, int); +OLM_DLLEXPORT double log(double); +OLM_DLLEXPORT double log10(double); +OLM_DLLEXPORT double modf(double, double *); /* fundamentally !__pure2 */ + +OLM_DLLEXPORT double pow(double, double); +OLM_DLLEXPORT double sqrt(double); + +OLM_DLLEXPORT double ceil(double); +OLM_DLLEXPORT double fabs(double) __pure2; +OLM_DLLEXPORT double floor(double); +OLM_DLLEXPORT double fmod(double, double); + +/* + * These functions are not in C90. + */ +#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE +OLM_DLLEXPORT double acosh(double); +OLM_DLLEXPORT double asinh(double); +OLM_DLLEXPORT double atanh(double); +OLM_DLLEXPORT double cbrt(double); +OLM_DLLEXPORT double erf(double); +OLM_DLLEXPORT double erfc(double); +OLM_DLLEXPORT double exp2(double); +OLM_DLLEXPORT double expm1(double); +OLM_DLLEXPORT double fma(double, double, double); +OLM_DLLEXPORT double hypot(double, double); +OLM_DLLEXPORT int ilogb(double) __pure2; +OLM_DLLEXPORT int (isinf)(double) __pure2; +OLM_DLLEXPORT int (isnan)(double) __pure2; +OLM_DLLEXPORT double lgamma(double); +OLM_DLLEXPORT long long llrint(double); +OLM_DLLEXPORT long long llround(double); +OLM_DLLEXPORT double log1p(double); +OLM_DLLEXPORT double log2(double); +OLM_DLLEXPORT double logb(double); +OLM_DLLEXPORT long lrint(double); +OLM_DLLEXPORT long lround(double); +OLM_DLLEXPORT double nan(const char *) __pure2; +OLM_DLLEXPORT double nextafter(double, double); +OLM_DLLEXPORT double remainder(double, double); +OLM_DLLEXPORT double remquo(double, double, int *); +OLM_DLLEXPORT double rint(double); +#endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */ + +#if __BSD_VISIBLE || __XSI_VISIBLE +OLM_DLLEXPORT double j0(double); +OLM_DLLEXPORT double j1(double); +OLM_DLLEXPORT double jn(int, double); +OLM_DLLEXPORT double y0(double); +OLM_DLLEXPORT double y1(double); +OLM_DLLEXPORT double yn(int, double); +#endif /* __BSD_VISIBLE || __XSI_VISIBLE */ + +#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 +OLM_DLLEXPORT double copysign(double, double) __pure2; +OLM_DLLEXPORT double fdim(double, double); +OLM_DLLEXPORT double fmax(double, double) __pure2; +OLM_DLLEXPORT double fmin(double, double) __pure2; +OLM_DLLEXPORT double nearbyint(double); +OLM_DLLEXPORT double round(double); +OLM_DLLEXPORT double scalbln(double, long); +OLM_DLLEXPORT double scalbn(double, int); +OLM_DLLEXPORT double tgamma(double); +OLM_DLLEXPORT double trunc(double); +#endif + +/* + * BSD math library entry points + */ +#if __BSD_VISIBLE +OLM_DLLEXPORT int isinff(float) __pure2; +OLM_DLLEXPORT int isnanf(float) __pure2; + +/* + * Reentrant version of lgamma; passes signgam back by reference as the + * second argument; user must allocate space for signgam. + */ +OLM_DLLEXPORT double lgamma_r(double, int *); + +/* + * Single sine/cosine function. + */ +OLM_DLLEXPORT void sincos(double, double *, double *); +#endif /* __BSD_VISIBLE */ + +/* float versions of ANSI/POSIX functions */ +#if __ISO_C_VISIBLE >= 1999 +OLM_DLLEXPORT float acosf(float); +OLM_DLLEXPORT float asinf(float); +OLM_DLLEXPORT float atanf(float); +OLM_DLLEXPORT float atan2f(float, float); +OLM_DLLEXPORT float cosf(float); +OLM_DLLEXPORT float sinf(float); +OLM_DLLEXPORT float tanf(float); + +OLM_DLLEXPORT float coshf(float); +OLM_DLLEXPORT float sinhf(float); +OLM_DLLEXPORT float tanhf(float); + +OLM_DLLEXPORT float exp2f(float); +OLM_DLLEXPORT float expf(float); +OLM_DLLEXPORT float expm1f(float); +OLM_DLLEXPORT float frexpf(float, int *); /* fundamentally !__pure2 */ +OLM_DLLEXPORT int ilogbf(float) __pure2; +OLM_DLLEXPORT float ldexpf(float, int); +OLM_DLLEXPORT float log10f(float); +OLM_DLLEXPORT float log1pf(float); +OLM_DLLEXPORT float log2f(float); +OLM_DLLEXPORT float logf(float); +OLM_DLLEXPORT float modff(float, float *); /* fundamentally !__pure2 */ + +OLM_DLLEXPORT float powf(float, float); +OLM_DLLEXPORT float sqrtf(float); + +OLM_DLLEXPORT float ceilf(float); +OLM_DLLEXPORT float fabsf(float) __pure2; +OLM_DLLEXPORT float floorf(float); +OLM_DLLEXPORT float fmodf(float, float); +OLM_DLLEXPORT float roundf(float); + +OLM_DLLEXPORT float erff(float); +OLM_DLLEXPORT float erfcf(float); +OLM_DLLEXPORT float hypotf(float, float); +OLM_DLLEXPORT float lgammaf(float); +OLM_DLLEXPORT float tgammaf(float); + +OLM_DLLEXPORT float acoshf(float); +OLM_DLLEXPORT float asinhf(float); +OLM_DLLEXPORT float atanhf(float); +OLM_DLLEXPORT float cbrtf(float); +OLM_DLLEXPORT float logbf(float); +OLM_DLLEXPORT float copysignf(float, float) __pure2; +OLM_DLLEXPORT long long llrintf(float); +OLM_DLLEXPORT long long llroundf(float); +OLM_DLLEXPORT long lrintf(float); +OLM_DLLEXPORT long lroundf(float); +OLM_DLLEXPORT float nanf(const char *) __pure2; +OLM_DLLEXPORT float nearbyintf(float); +OLM_DLLEXPORT float nextafterf(float, float); +OLM_DLLEXPORT float remainderf(float, float); +OLM_DLLEXPORT float remquof(float, float, int *); +OLM_DLLEXPORT float rintf(float); +OLM_DLLEXPORT float scalblnf(float, long); +OLM_DLLEXPORT float scalbnf(float, int); +OLM_DLLEXPORT float truncf(float); + +OLM_DLLEXPORT float fdimf(float, float); +OLM_DLLEXPORT float fmaf(float, float, float); +OLM_DLLEXPORT float fmaxf(float, float) __pure2; +OLM_DLLEXPORT float fminf(float, float) __pure2; +#endif + +/* + * float versions of BSD math library entry points + */ +#if __BSD_VISIBLE +OLM_DLLEXPORT float dremf(float, float); +OLM_DLLEXPORT float j0f(float); +OLM_DLLEXPORT float j1f(float); +OLM_DLLEXPORT float jnf(int, float); +OLM_DLLEXPORT float y0f(float); +OLM_DLLEXPORT float y1f(float); +OLM_DLLEXPORT float ynf(int, float); + +/* + * Float versions of reentrant version of lgamma; passes signgam back by + * reference as the second argument; user must allocate space for signgam. + */ +OLM_DLLEXPORT float lgammaf_r(float, int *); + +/* + * Single sine/cosine function. + */ +OLM_DLLEXPORT void sincosf(float, float *, float *); +#endif /* __BSD_VISIBLE */ + +/* + * long double versions of ISO/POSIX math functions + */ +#if __ISO_C_VISIBLE >= 1999 +OLM_DLLEXPORT long double acoshl(long double); +OLM_DLLEXPORT long double acosl(long double); +OLM_DLLEXPORT long double asinhl(long double); +OLM_DLLEXPORT long double asinl(long double); +OLM_DLLEXPORT long double atan2l(long double, long double); +OLM_DLLEXPORT long double atanhl(long double); +OLM_DLLEXPORT long double atanl(long double); +OLM_DLLEXPORT long double cbrtl(long double); +OLM_DLLEXPORT long double ceill(long double); +OLM_DLLEXPORT long double copysignl(long double, long double) __pure2; +OLM_DLLEXPORT long double coshl(long double); +OLM_DLLEXPORT long double cosl(long double); +OLM_DLLEXPORT long double erfcl(long double); +OLM_DLLEXPORT long double erfl(long double); +OLM_DLLEXPORT long double exp2l(long double); +OLM_DLLEXPORT long double expl(long double); +OLM_DLLEXPORT long double expm1l(long double); +OLM_DLLEXPORT long double fabsl(long double) __pure2; +OLM_DLLEXPORT long double fdiml(long double, long double); +OLM_DLLEXPORT long double floorl(long double); +OLM_DLLEXPORT long double fmal(long double, long double, long double); +OLM_DLLEXPORT long double fmaxl(long double, long double) __pure2; +OLM_DLLEXPORT long double fminl(long double, long double) __pure2; +OLM_DLLEXPORT long double fmodl(long double, long double); +OLM_DLLEXPORT long double frexpl(long double value, int *); /* fundamentally !__pure2 */ +OLM_DLLEXPORT long double hypotl(long double, long double); +OLM_DLLEXPORT int ilogbl(long double) __pure2; +OLM_DLLEXPORT long double ldexpl(long double, int); +OLM_DLLEXPORT long double lgammal(long double); +OLM_DLLEXPORT long long llrintl(long double); +OLM_DLLEXPORT long long llroundl(long double); +OLM_DLLEXPORT long double log10l(long double); +OLM_DLLEXPORT long double log1pl(long double); +OLM_DLLEXPORT long double log2l(long double); +OLM_DLLEXPORT long double logbl(long double); +OLM_DLLEXPORT long double logl(long double); +OLM_DLLEXPORT long lrintl(long double); +OLM_DLLEXPORT long lroundl(long double); +OLM_DLLEXPORT long double modfl(long double, long double *); /* fundamentally !__pure2 */ +OLM_DLLEXPORT long double nanl(const char *) __pure2; +OLM_DLLEXPORT long double nearbyintl(long double); +OLM_DLLEXPORT long double nextafterl(long double, long double); +OLM_DLLEXPORT double nexttoward(double, long double); +OLM_DLLEXPORT float nexttowardf(float, long double); +OLM_DLLEXPORT long double nexttowardl(long double, long double); +OLM_DLLEXPORT long double powl(long double, long double); +OLM_DLLEXPORT long double remainderl(long double, long double); +OLM_DLLEXPORT long double remquol(long double, long double, int *); +OLM_DLLEXPORT long double rintl(long double); +OLM_DLLEXPORT long double roundl(long double); +OLM_DLLEXPORT long double scalblnl(long double, long); +OLM_DLLEXPORT long double scalbnl(long double, int); +OLM_DLLEXPORT long double sinhl(long double); +OLM_DLLEXPORT long double sinl(long double); +OLM_DLLEXPORT long double sqrtl(long double); +OLM_DLLEXPORT long double tanhl(long double); +OLM_DLLEXPORT long double tanl(long double); +OLM_DLLEXPORT long double tgammal(long double); +OLM_DLLEXPORT long double truncl(long double); +#endif /* __ISO_C_VISIBLE >= 1999 */ + +/* Reentrant version of lgammal. */ +#if __BSD_VISIBLE +OLM_DLLEXPORT long double lgammal_r(long double, int *); + +/* + * Single sine/cosine function. + */ +OLM_DLLEXPORT void sincosl(long double, long double *, long double *); +#endif /* __BSD_VISIBLE */ + +#if defined(__cplusplus) +} +#endif +#endif /* !OPENLIBM_MATH_H */ + +#endif /* OPENLIBM_USE_HOST_MATH_H */ diff --git a/openlibm/ld128/Make.files b/openlibm/ld128/Make.files new file mode 100644 index 0000000..1198cfb --- /dev/null +++ b/openlibm/ld128/Make.files @@ -0,0 +1,13 @@ +$(CUR_SRCS) += invtrig.c \ + e_acoshl.c e_powl.c k_tanl.c s_exp2l.c \ + e_atanhl.c e_lgammal_r.c e_sinhl.c s_asinhl.c s_expm1l.c \ + e_coshl.c e_log10l.c e_tgammal.c \ + e_expl.c e_log2l.c k_cosl.c s_log1pl.c s_tanhl.c \ + e_logl.c k_sinl.c s_erfl.c + +# s_remquol.c e_fmodl.c s_truncl.c +# e_hypotl.c s_floorl.c s_nextafterl.c s_ceill.c s_modfl.c + +ifneq ($(OS), WINNT) +$(CUR_SRCS) += s_nanl.c +endif diff --git a/openlibm/ld128/e_acoshl.c b/openlibm/ld128/e_acoshl.c new file mode 100644 index 0000000..e7cfd03 --- /dev/null +++ b/openlibm/ld128/e_acoshl.c @@ -0,0 +1,58 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* acoshl(x) + * Method : + * Based on + * acoshl(x) = logl [ x + sqrtl(x*x-1) ] + * we have + * acoshl(x) := logl(x)+ln2, if x is large; else + * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else + * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acoshl(x) is NaN with signal if x<1. + * acoshl(NaN) is NaN without signal. + */ + +#include + +#include "math_private.h" + +static const long double +one = 1.0, +ln2 = 0.6931471805599453094172321214581766L; + +long double +acoshl(long double x) +{ + long double t; + u_int64_t lx; + int64_t hx; + GET_LDOUBLE_WORDS64(hx,lx,x); + if(hx<0x3fff000000000000LL) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */ + if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */ + return x+x; + } else + return logl(x)+ln2; /* acoshl(huge)=logl(2x) */ + } else if(((hx-0x3fff000000000000LL)|lx)==0) { + return 0.0L; /* acosh(1) = 0 */ + } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */ + t=x*x; + return logl(2.0L*x-one/(x+sqrtl(t-one))); + } else { /* 1=0.5 + * 1 2x x + * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x)) + * + * Special cases: + * atanhl(x) is NaN if |x| > 1 with signal; + * atanhl(NaN) is that NaN with no signal; + * atanhl(+-1) is +-INF with signal. + * + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0L, huge = 1e4900L; + +static const long double zero = 0.0L; + +long double +atanhl(long double x) +{ + long double t; + u_int32_t jx, ix; + ieee_quad_shape_type u; + + u.value = x; + jx = u.parts32.mswhi; + ix = jx & 0x7fffffff; + u.parts32.mswhi = ix; + if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */ + { + if (u.value == one) + return x/zero; + else + return (x-x)/(x-x); + } + if(ix<0x3fc60000 && (huge+x)>zero) return x; /* x < 2^-57 */ + + if(ix<0x3ffe0000) { /* x < 0.5 */ + t = u.value+u.value; + t = 0.5*log1pl(t+t*u.value/(one-u.value)); + } else + t = 0.5*log1pl((u.value+u.value)/(one-u.value)); + if(jx & 0x80000000) return -t; else return t; +} diff --git a/openlibm/ld128/e_coshl.c b/openlibm/ld128/e_coshl.c new file mode 100644 index 0000000..955c378 --- /dev/null +++ b/openlibm/ld128/e_coshl.c @@ -0,0 +1,105 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* coshl(x) + * Method : + * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (coshl(x) = coshl(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : coshl(x) := ------------------- + * 2 + * 22 <= x <= lnovft : coshl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : coshl(x) := huge*huge (overflow) + * + * Special cases: + * coshl(x) is |x| if x is +INF, -INF, or NaN. + * only coshl(0)=1 is exact for finite x. + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0, half = 0.5, huge = 1.0e4900L, +ovf_thresh = 1.1357216553474703894801348310092223067821E4L; + +long double +coshl(long double x) +{ + long double t, w; + int32_t ex; + ieee_quad_shape_type u; + + u.value = x; + ex = u.parts32.mswhi & 0x7fffffff; + + /* Absolute value of x. */ + u.parts32.mswhi = ex; + + /* x is INF or NaN */ + if (ex >= 0x7fff0000) + return x * x; + + /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ + if (ex < 0x3ffd62e4) /* 0.3465728759765625 */ + { + t = expm1l (u.value); + w = one + t; + if (ex < 0x3fb80000) /* |x| < 2^-116 */ + return w; /* cosh(tiny) = 1 */ + + return one + (t * t) / (w + w); + } + + /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ + if (ex < 0x40044000) + { + t = expl (u.value); + return half * t + half / t; + } + + /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ + if (ex <= 0x400c62e3) /* 11356.375 */ + return half * expl (u.value); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (u.value <= ovf_thresh) + { + w = expl (half * u.value); + t = half * w; + return t * w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge * huge; +} diff --git a/openlibm/ld128/e_expl.c b/openlibm/ld128/e_expl.c new file mode 100644 index 0000000..24c7b50 --- /dev/null +++ b/openlibm/ld128/e_expl.c @@ -0,0 +1,145 @@ +/* $OpenBSD: e_expl.c,v 1.3 2013/11/12 20:35:18 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* expl.c + * + * Exponential function, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, expl(); + * + * y = expl( x ); + * + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) raised to the x power. + * + * Range reduction is accomplished by separating the argument + * into an integer k and fraction f such that + * + * x k f + * e = 2 e. + * + * A Pade' form of degree 2/3 is used to approximate exp(f) - 1 + * in the basic range [-0.5 ln 2, 0.5 ln 2]. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE +-MAXLOG 100,000 2.6e-34 8.6e-35 + * + * + * Error amplification in the exponential function can be + * a serious matter. The error propagation involves + * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ), + * which shows that a 1 lsb error in representing X produces + * a relative error of X times 1 lsb in the function. + * While the routine gives an accurate result for arguments + * that are exactly represented by a long double precision + * computer number, the result contains amplified roundoff + * error for large arguments not exactly represented. + * + * + * ERROR MESSAGES: + * + * message condition value returned + * exp underflow x < MINLOG 0.0 + * exp overflow x > MAXLOG MAXNUM + * + */ + +/* Exponential function */ + +#include +#include + +#include "math_private.h" + +/* Pade' coefficients for exp(x) - 1 + Theoretical peak relative error = 2.2e-37, + relative peak error spread = 9.2e-38 + */ +static long double P[5] = { + 3.279723985560247033712687707263393506266E-10L, + 6.141506007208645008909088812338454698548E-7L, + 2.708775201978218837374512615596512792224E-4L, + 3.508710990737834361215404761139478627390E-2L, + 9.999999999999999999999999999999999998502E-1L +}; +static long double Q[6] = { + 2.980756652081995192255342779918052538681E-12L, + 1.771372078166251484503904874657985291164E-8L, + 1.504792651814944826817779302637284053660E-5L, + 3.611828913847589925056132680618007270344E-3L, + 2.368408864814233538909747618894558968880E-1L, + 2.000000000000000000000000000000000000150E0L +}; +/* C1 + C2 = ln 2 */ +static const long double C1 = -6.93145751953125E-1L; +static const long double C2 = -1.428606820309417232121458176568075500134E-6L; + +static const long double LOG2EL = 1.442695040888963407359924681001892137426646L; +static const long double MAXLOGL = 1.1356523406294143949491931077970764891253E4L; +static const long double MINLOGL = -1.143276959615573793352782661133116431383730e4L; +static const long double huge = 0x1p10000L; +#if 0 /* XXX Prevent gcc from erroneously constant folding this. */ +static const long double twom10000 = 0x1p-10000L; +#else +static volatile long double twom10000 = 0x1p-10000L; +#endif + +long double +expl(long double x) +{ +long double px, xx; +int n; + +if( x > MAXLOGL) + return (huge*huge); /* overflow */ + +if( x < MINLOGL ) + return (twom10000*twom10000); /* underflow */ + +/* Express e**x = e**g 2**n + * = e**g e**( n loge(2) ) + * = e**( g + n loge(2) ) + */ +px = floorl( LOG2EL * x + 0.5L ); /* floor() truncates toward -infinity. */ +n = px; +x += px * C1; +x += px * C2; +/* rational approximation for exponential + * of the fractional part: + * e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) ) + */ +xx = x * x; +px = x * __polevll( xx, P, 4 ); +xx = __polevll( xx, Q, 5 ); +x = px/( xx - px ); +x = 1.0L + x + x; + +x = ldexpl( x, n ); +return(x); +} diff --git a/openlibm/ld128/e_fmodl.c b/openlibm/ld128/e_fmodl.c new file mode 100644 index 0000000..698fa3a --- /dev/null +++ b/openlibm/ld128/e_fmodl.c @@ -0,0 +1,129 @@ +/* @(#)e_fmod.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * fmodl(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0, Zero[] = {0.0, -0.0,}; + +long double +fmodl(long double x, long double y) +{ + int64_t n,hx,hy,hz,ix,iy,sx,i; + u_int64_t lx,ly,lz; + + GET_LDOUBLE_WORDS64(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + sx = hx&0x8000000000000000ULL; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffffffffffffLL; /* |y| */ + + /* purge off exception values */ + if((hy|ly)==0||(hx>=0x7fff000000000000LL)|| /* y=0,or x not finite */ + ((hy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<=hy) { + if((hx>63]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(hx<0x0001000000000000LL) { /* subnormal x */ + if(hx==0) { + for (ix = -16431, i=lx; i>0; i<<=1) ix -=1; + } else { + for (ix = -16382, i=hx<<15; i>0; i<<=1) ix -=1; + } + } else ix = (hx>>48)-0x3fff; + + /* determine iy = ilogb(y) */ + if(hy<0x0001000000000000LL) { /* subnormal y */ + if(hy==0) { + for (iy = -16431, i=ly; i>0; i<<=1) iy -=1; + } else { + for (iy = -16382, i=hy<<15; i>0; i<<=1) iy -=1; + } + } else iy = (hy>>48)-0x3fff; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -16382) + hx = 0x0001000000000000LL|(0x0000ffffffffffffLL&hx); + else { /* subnormal x, shift x to normal */ + n = -16382-ix; + if(n<=63) { + hx = (hx<>(64-n)); + lx <<= n; + } else { + hx = lx<<(n-64); + lx = 0; + } + } + if(iy >= -16382) + hy = 0x0001000000000000LL|(0x0000ffffffffffffLL&hy); + else { /* subnormal y, shift y to normal */ + n = -16382-iy; + if(n<=63) { + hy = (hy<>(64-n)); + ly <<= n; + } else { + hy = ly<<(n-64); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx>63); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + hx = hz+hz+(lz>>63); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int64_t)sx>>63]; + while(hx<0x0001000000000000LL) { /* normalize x */ + hx = hx+hx+(lx>>63); lx = lx+lx; + iy -= 1; + } + if(iy>= -16382) { /* normalize output */ + hx = ((hx-0x0001000000000000LL)|((iy+16383)<<48)); + SET_LDOUBLE_WORDS64(x,hx|sx,lx); + } else { /* subnormal output */ + n = -16382 - iy; + if(n<=48) { + lx = (lx>>n)|((u_int64_t)hx<<(64-n)); + hx >>= n; + } else if (n<=63) { + lx = (hx<<(64-n))|(lx>>n); hx = sx; + } else { + lx = hx>>(n-64); hx = sx; + } + SET_LDOUBLE_WORDS64(x,hx|sx,lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/openlibm/ld128/e_hypotl.c b/openlibm/ld128/e_hypotl.c new file mode 100644 index 0000000..1cdf3d8 --- /dev/null +++ b/openlibm/ld128/e_hypotl.c @@ -0,0 +1,122 @@ +/* @(#)e_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* hypotl(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrtl(2)/2 ulp, than + * sqrtl(z) has error less than 1 ulp (exercise). + * + * So, compute sqrtl(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 64 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, + * yy1= y with lower 64 bits chopped, y2 = y-yy1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypotl(x,y) is INF if x or y is +INF or -INF; else + * hypotl(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypotl(x,y) returns sqrtl(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include + +#include "math_private.h" + +long double +hypotl(long double x, long double y) +{ + long double a,b,t1,t2,yy1,y2,w; + int64_t j,k,ha,hb; + + GET_LDOUBLE_MSW64(ha,x); + ha &= 0x7fffffffffffffffLL; + GET_LDOUBLE_MSW64(hb,y); + hb &= 0x7fffffffffffffffLL; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_LDOUBLE_MSW64(a,ha); /* a <- |a| */ + SET_LDOUBLE_MSW64(b,hb); /* b <- |b| */ + if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */ + k=0; + if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */ + if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */ + u_int64_t low; + w = a+b; /* for sNaN */ + GET_LDOUBLE_LSW64(low,a); + if(((ha&0xffffffffffffLL)|low)==0) w = a; + GET_LDOUBLE_LSW64(low,b); + if(((hb^0x7fff000000000000LL)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-9600 */ + ha -= 0x2580000000000000LL; + hb -= 0x2580000000000000LL; k += 9600; + SET_LDOUBLE_MSW64(a,ha); + SET_LDOUBLE_MSW64(b,hb); + } + if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */ + if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */ + u_int64_t low; + GET_LDOUBLE_LSW64(low,b); + if((hb|low)==0) return a; + t1=0; + SET_LDOUBLE_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */ + b *= t1; + a *= t1; + k -= 16382; + } else { /* scale a and b by 2^9600 */ + ha += 0x2580000000000000LL; /* a *= 2^9600 */ + hb += 0x2580000000000000LL; /* b *= 2^9600 */ + k -= 9600; + SET_LDOUBLE_MSW64(a,ha); + SET_LDOUBLE_MSW64(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_LDOUBLE_MSW64(t1,ha); + t2 = a-t1; + w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + yy1 = 0; + SET_LDOUBLE_MSW64(yy1,hb); + y2 = b - yy1; + t1 = 0; + SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL); + t2 = a - t1; + w = sqrtl(t1*yy1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int64_t high; + t1 = 1.0L; + GET_LDOUBLE_MSW64(high,t1); + SET_LDOUBLE_MSW64(t1,high+(k<<48)); + return t1*w; + } else return w; +} diff --git a/openlibm/ld128/e_lgammal_r.c b/openlibm/ld128/e_lgammal_r.c new file mode 100644 index 0000000..dd8ea5d --- /dev/null +++ b/openlibm/ld128/e_lgammal_r.c @@ -0,0 +1,1037 @@ +/* $OpenBSD: e_lgammal.c,v 1.3 2011/07/09 05:29:06 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* lgammal_r + * + * Natural logarithm of gamma function + * + * + * + * SYNOPSIS: + * + * long double x, y, lgammal_r(); + * int signgam; + * + * y = lgammal_r(x, &signgam); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of the absolute + * value of the gamma function of the argument. + * The sign (+1 or -1) of the gamma function is returned through signgamp. + * + * The positive domain is partitioned into numerous segments for approximation. + * For x > 10, + * log gamma(x) = (x - 0.5) log(x) - x + log sqrt(2 pi) + 1/x R(1/x^2) + * Near the minimum at x = x0 = 1.46... the approximation is + * log gamma(x0 + z) = log gamma(x0) + z^2 P(z)/Q(z) + * for small z. + * Elsewhere between 0 and 10, + * log gamma(n + z) = log gamma(n) + z P(z)/Q(z) + * for various selected n and small z. + * + * The cosecant reflection formula is employed for negative arguments. + * + * + * + * ACCURACY: + * + * + * arithmetic domain # trials peak rms + * Relative error: + * IEEE 10, 30 100000 3.9e-34 9.8e-35 + * IEEE 0, 10 100000 3.8e-34 5.3e-35 + * Absolute error: + * IEEE -10, 0 100000 8.0e-34 8.0e-35 + * IEEE -30, -10 100000 4.4e-34 1.0e-34 + * IEEE -100, 100 100000 1.0e-34 + * + * The absolute error criterion is the same as relative error + * when the function magnitude is greater than one but it is absolute + * when the magnitude is less than one. + * + */ + +#include + +#include "math_private.h" + +static const long double PIL = 3.1415926535897932384626433832795028841972E0L; +static const long double MAXLGM = 1.0485738685148938358098967157129705071571E4928L; +static const long double one = 1.0L; +static const long double huge = 1.0e4000L; + +/* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x P(1/x^2) + 1/x <= 0.0741 (x >= 13.495...) + Peak relative error 1.5e-36 */ +static const long double ls2pi = 9.1893853320467274178032973640561763986140E-1L; +#define NRASY 12 +static const long double RASY[NRASY + 1] = +{ + 8.333333333333333333333333333310437112111E-2L, + -2.777777777777777777777774789556228296902E-3L, + 7.936507936507936507795933938448586499183E-4L, + -5.952380952380952041799269756378148574045E-4L, + 8.417508417507928904209891117498524452523E-4L, + -1.917526917481263997778542329739806086290E-3L, + 6.410256381217852504446848671499409919280E-3L, + -2.955064066900961649768101034477363301626E-2L, + 1.796402955865634243663453415388336954675E-1L, + -1.391522089007758553455753477688592767741E0L, + 1.326130089598399157988112385013829305510E1L, + -1.420412699593782497803472576479997819149E2L, + 1.218058922427762808938869872528846787020E3L +}; + + +/* log gamma(x+13) = log gamma(13) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 12.5 <= x+13 <= 13.5 + Peak relative error 1.1e-36 */ +static const long double lgam13a = 1.9987213134765625E1L; +static const long double lgam13b = 1.3608962611495173623870550785125024484248E-6L; +#define NRN13 7 +static const long double RN13[NRN13 + 1] = +{ + 8.591478354823578150238226576156275285700E11L, + 2.347931159756482741018258864137297157668E11L, + 2.555408396679352028680662433943000804616E10L, + 1.408581709264464345480765758902967123937E9L, + 4.126759849752613822953004114044451046321E7L, + 6.133298899622688505854211579222889943778E5L, + 3.929248056293651597987893340755876578072E3L, + 6.850783280018706668924952057996075215223E0L +}; +#define NRD13 6 +static const long double RD13[NRD13 + 1] = +{ + 3.401225382297342302296607039352935541669E11L, + 8.756765276918037910363513243563234551784E10L, + 8.873913342866613213078554180987647243903E9L, + 4.483797255342763263361893016049310017973E8L, + 1.178186288833066430952276702931512870676E7L, + 1.519928623743264797939103740132278337476E5L, + 7.989298844938119228411117593338850892311E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+12) = log gamma(12) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 11.5 <= x+12 <= 12.5 + Peak relative error 4.1e-36 */ +static const long double lgam12a = 1.75023040771484375E1L; +static const long double lgam12b = 3.7687254483392876529072161996717039575982E-6L; +#define NRN12 7 +static const long double RN12[NRN12 + 1] = +{ + 4.709859662695606986110997348630997559137E11L, + 1.398713878079497115037857470168777995230E11L, + 1.654654931821564315970930093932954900867E10L, + 9.916279414876676861193649489207282144036E8L, + 3.159604070526036074112008954113411389879E7L, + 5.109099197547205212294747623977502492861E5L, + 3.563054878276102790183396740969279826988E3L, + 6.769610657004672719224614163196946862747E0L +}; +#define NRD12 6 +static const long double RD12[NRD12 + 1] = +{ + 1.928167007860968063912467318985802726613E11L, + 5.383198282277806237247492369072266389233E10L, + 5.915693215338294477444809323037871058363E9L, + 3.241438287570196713148310560147925781342E8L, + 9.236680081763754597872713592701048455890E6L, + 1.292246897881650919242713651166596478850E5L, + 7.366532445427159272584194816076600211171E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+11) = log gamma(11) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 10.5 <= x+11 <= 11.5 + Peak relative error 1.8e-35 */ +static const long double lgam11a = 1.5104400634765625E1L; +static const long double lgam11b = 1.1938309890295225709329251070371882250744E-5L; +#define NRN11 7 +static const long double RN11[NRN11 + 1] = +{ + 2.446960438029415837384622675816736622795E11L, + 7.955444974446413315803799763901729640350E10L, + 1.030555327949159293591618473447420338444E10L, + 6.765022131195302709153994345470493334946E8L, + 2.361892792609204855279723576041468347494E7L, + 4.186623629779479136428005806072176490125E5L, + 3.202506022088912768601325534149383594049E3L, + 6.681356101133728289358838690666225691363E0L +}; +#define NRD11 6 +static const long double RD11[NRD11 + 1] = +{ + 1.040483786179428590683912396379079477432E11L, + 3.172251138489229497223696648369823779729E10L, + 3.806961885984850433709295832245848084614E9L, + 2.278070344022934913730015420611609620171E8L, + 7.089478198662651683977290023829391596481E6L, + 1.083246385105903533237139380509590158658E5L, + 6.744420991491385145885727942219463243597E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+10) = log gamma(10) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 9.5 <= x+10 <= 10.5 + Peak relative error 5.4e-37 */ +static const long double lgam10a = 1.280181884765625E1L; +static const long double lgam10b = 8.6324252196112077178745667061642811492557E-6L; +#define NRN10 7 +static const long double RN10[NRN10 + 1] = +{ + -1.239059737177249934158597996648808363783E14L, + -4.725899566371458992365624673357356908719E13L, + -7.283906268647083312042059082837754850808E12L, + -5.802855515464011422171165179767478794637E11L, + -2.532349691157548788382820303182745897298E10L, + -5.884260178023777312587193693477072061820E8L, + -6.437774864512125749845840472131829114906E6L, + -2.350975266781548931856017239843273049384E4L +}; +#define NRD10 7 +static const long double RD10[NRD10 + 1] = +{ + -5.502645997581822567468347817182347679552E13L, + -1.970266640239849804162284805400136473801E13L, + -2.819677689615038489384974042561531409392E12L, + -2.056105863694742752589691183194061265094E11L, + -8.053670086493258693186307810815819662078E9L, + -1.632090155573373286153427982504851867131E8L, + -1.483575879240631280658077826889223634921E6L, + -4.002806669713232271615885826373550502510E3L + /* 1.0E0L */ +}; + + +/* log gamma(x+9) = log gamma(9) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 8.5 <= x+9 <= 9.5 + Peak relative error 3.6e-36 */ +static const long double lgam9a = 1.06045989990234375E1L; +static const long double lgam9b = 3.9037218127284172274007216547549861681400E-6L; +#define NRN9 7 +static const long double RN9[NRN9 + 1] = +{ + -4.936332264202687973364500998984608306189E13L, + -2.101372682623700967335206138517766274855E13L, + -3.615893404644823888655732817505129444195E12L, + -3.217104993800878891194322691860075472926E11L, + -1.568465330337375725685439173603032921399E10L, + -4.073317518162025744377629219101510217761E8L, + -4.983232096406156139324846656819246974500E6L, + -2.036280038903695980912289722995505277253E4L +}; +#define NRD9 7 +static const long double RD9[NRD9 + 1] = +{ + -2.306006080437656357167128541231915480393E13L, + -9.183606842453274924895648863832233799950E12L, + -1.461857965935942962087907301194381010380E12L, + -1.185728254682789754150068652663124298303E11L, + -5.166285094703468567389566085480783070037E9L, + -1.164573656694603024184768200787835094317E8L, + -1.177343939483908678474886454113163527909E6L, + -3.529391059783109732159524500029157638736E3L + /* 1.0E0L */ +}; + + +/* log gamma(x+8) = log gamma(8) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 7.5 <= x+8 <= 8.5 + Peak relative error 2.4e-37 */ +static const long double lgam8a = 8.525146484375E0L; +static const long double lgam8b = 1.4876690414300165531036347125050759667737E-5L; +#define NRN8 8 +static const long double RN8[NRN8 + 1] = +{ + 6.600775438203423546565361176829139703289E11L, + 3.406361267593790705240802723914281025800E11L, + 7.222460928505293914746983300555538432830E10L, + 8.102984106025088123058747466840656458342E9L, + 5.157620015986282905232150979772409345927E8L, + 1.851445288272645829028129389609068641517E7L, + 3.489261702223124354745894067468953756656E5L, + 2.892095396706665774434217489775617756014E3L, + 6.596977510622195827183948478627058738034E0L +}; +#define NRD8 7 +static const long double RD8[NRD8 + 1] = +{ + 3.274776546520735414638114828622673016920E11L, + 1.581811207929065544043963828487733970107E11L, + 3.108725655667825188135393076860104546416E10L, + 3.193055010502912617128480163681842165730E9L, + 1.830871482669835106357529710116211541839E8L, + 5.790862854275238129848491555068073485086E6L, + 9.305213264307921522842678835618803553589E4L, + 6.216974105861848386918949336819572333622E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+7) = log gamma(7) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 6.5 <= x+7 <= 7.5 + Peak relative error 3.2e-36 */ +static const long double lgam7a = 6.5792388916015625E0L; +static const long double lgam7b = 1.2320408538495060178292903945321122583007E-5L; +#define NRN7 8 +static const long double RN7[NRN7 + 1] = +{ + 2.065019306969459407636744543358209942213E11L, + 1.226919919023736909889724951708796532847E11L, + 2.996157990374348596472241776917953749106E10L, + 3.873001919306801037344727168434909521030E9L, + 2.841575255593761593270885753992732145094E8L, + 1.176342515359431913664715324652399565551E7L, + 2.558097039684188723597519300356028511547E5L, + 2.448525238332609439023786244782810774702E3L, + 6.460280377802030953041566617300902020435E0L +}; +#define NRD7 7 +static const long double RD7[NRD7 + 1] = +{ + 1.102646614598516998880874785339049304483E11L, + 6.099297512712715445879759589407189290040E10L, + 1.372898136289611312713283201112060238351E10L, + 1.615306270420293159907951633566635172343E9L, + 1.061114435798489135996614242842561967459E8L, + 3.845638971184305248268608902030718674691E6L, + 7.081730675423444975703917836972720495507E4L, + 5.423122582741398226693137276201344096370E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+6) = log gamma(6) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 5.5 <= x+6 <= 6.5 + Peak relative error 6.2e-37 */ +static const long double lgam6a = 4.7874908447265625E0L; +static const long double lgam6b = 8.9805548349424770093452324304839959231517E-7L; +#define NRN6 8 +static const long double RN6[NRN6 + 1] = +{ + -3.538412754670746879119162116819571823643E13L, + -2.613432593406849155765698121483394257148E13L, + -8.020670732770461579558867891923784753062E12L, + -1.322227822931250045347591780332435433420E12L, + -1.262809382777272476572558806855377129513E11L, + -7.015006277027660872284922325741197022467E9L, + -2.149320689089020841076532186783055727299E8L, + -3.167210585700002703820077565539658995316E6L, + -1.576834867378554185210279285358586385266E4L +}; +#define NRD6 8 +static const long double RD6[NRD6 + 1] = +{ + -2.073955870771283609792355579558899389085E13L, + -1.421592856111673959642750863283919318175E13L, + -4.012134994918353924219048850264207074949E12L, + -6.013361045800992316498238470888523722431E11L, + -5.145382510136622274784240527039643430628E10L, + -2.510575820013409711678540476918249524123E9L, + -6.564058379709759600836745035871373240904E7L, + -7.861511116647120540275354855221373571536E5L, + -2.821943442729620524365661338459579270561E3L + /* 1.0E0L */ +}; + + +/* log gamma(x+5) = log gamma(5) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 4.5 <= x+5 <= 5.5 + Peak relative error 3.4e-37 */ +static const long double lgam5a = 3.17803955078125E0L; +static const long double lgam5b = 1.4279566695619646941601297055408873990961E-5L; +#define NRN5 9 +static const long double RN5[NRN5 + 1] = +{ + 2.010952885441805899580403215533972172098E11L, + 1.916132681242540921354921906708215338584E11L, + 7.679102403710581712903937970163206882492E10L, + 1.680514903671382470108010973615268125169E10L, + 2.181011222911537259440775283277711588410E9L, + 1.705361119398837808244780667539728356096E8L, + 7.792391565652481864976147945997033946360E6L, + 1.910741381027985291688667214472560023819E5L, + 2.088138241893612679762260077783794329559E3L, + 6.330318119566998299106803922739066556550E0L +}; +#define NRD5 8 +static const long double RD5[NRD5 + 1] = +{ + 1.335189758138651840605141370223112376176E11L, + 1.174130445739492885895466097516530211283E11L, + 4.308006619274572338118732154886328519910E10L, + 8.547402888692578655814445003283720677468E9L, + 9.934628078575618309542580800421370730906E8L, + 6.847107420092173812998096295422311820672E7L, + 2.698552646016599923609773122139463150403E6L, + 5.526516251532464176412113632726150253215E4L, + 4.772343321713697385780533022595450486932E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+4) = log gamma(4) + x P(x)/Q(x) + -0.5 <= x <= 0.5 + 3.5 <= x+4 <= 4.5 + Peak relative error 6.7e-37 */ +static const long double lgam4a = 1.791748046875E0L; +static const long double lgam4b = 1.1422353055000812477358380702272722990692E-5L; +#define NRN4 9 +static const long double RN4[NRN4 + 1] = +{ + -1.026583408246155508572442242188887829208E13L, + -1.306476685384622809290193031208776258809E13L, + -7.051088602207062164232806511992978915508E12L, + -2.100849457735620004967624442027793656108E12L, + -3.767473790774546963588549871673843260569E11L, + -4.156387497364909963498394522336575984206E10L, + -2.764021460668011732047778992419118757746E9L, + -1.036617204107109779944986471142938641399E8L, + -1.895730886640349026257780896972598305443E6L, + -1.180509051468390914200720003907727988201E4L +}; +#define NRD4 9 +static const long double RD4[NRD4 + 1] = +{ + -8.172669122056002077809119378047536240889E12L, + -9.477592426087986751343695251801814226960E12L, + -4.629448850139318158743900253637212801682E12L, + -1.237965465892012573255370078308035272942E12L, + -1.971624313506929845158062177061297598956E11L, + -1.905434843346570533229942397763361493610E10L, + -1.089409357680461419743730978512856675984E9L, + -3.416703082301143192939774401370222822430E7L, + -4.981791914177103793218433195857635265295E5L, + -2.192507743896742751483055798411231453733E3L + /* 1.0E0L */ +}; + + +/* log gamma(x+3) = log gamma(3) + x P(x)/Q(x) + -0.25 <= x <= 0.5 + 2.75 <= x+3 <= 3.5 + Peak relative error 6.0e-37 */ +static const long double lgam3a = 6.93145751953125E-1L; +static const long double lgam3b = 1.4286068203094172321214581765680755001344E-6L; + +#define NRN3 9 +static const long double RN3[NRN3 + 1] = +{ + -4.813901815114776281494823863935820876670E11L, + -8.425592975288250400493910291066881992620E11L, + -6.228685507402467503655405482985516909157E11L, + -2.531972054436786351403749276956707260499E11L, + -6.170200796658926701311867484296426831687E10L, + -9.211477458528156048231908798456365081135E9L, + -8.251806236175037114064561038908691305583E8L, + -4.147886355917831049939930101151160447495E7L, + -1.010851868928346082547075956946476932162E6L, + -8.333374463411801009783402800801201603736E3L +}; +#define NRD3 9 +static const long double RD3[NRD3 + 1] = +{ + -5.216713843111675050627304523368029262450E11L, + -8.014292925418308759369583419234079164391E11L, + -5.180106858220030014546267824392678611990E11L, + -1.830406975497439003897734969120997840011E11L, + -3.845274631904879621945745960119924118925E10L, + -4.891033385370523863288908070309417710903E9L, + -3.670172254411328640353855768698287474282E8L, + -1.505316381525727713026364396635522516989E7L, + -2.856327162923716881454613540575964890347E5L, + -1.622140448015769906847567212766206894547E3L + /* 1.0E0L */ +}; + + +/* log gamma(x+2.5) = log gamma(2.5) + x P(x)/Q(x) + -0.125 <= x <= 0.25 + 2.375 <= x+2.5 <= 2.75 */ +static const long double lgam2r5a = 2.8466796875E-1L; +static const long double lgam2r5b = 1.4901722919159632494669682701924320137696E-5L; +#define NRN2r5 8 +static const long double RN2r5[NRN2r5 + 1] = +{ + -4.676454313888335499356699817678862233205E9L, + -9.361888347911187924389905984624216340639E9L, + -7.695353600835685037920815799526540237703E9L, + -3.364370100981509060441853085968900734521E9L, + -8.449902011848163568670361316804900559863E8L, + -1.225249050950801905108001246436783022179E8L, + -9.732972931077110161639900388121650470926E6L, + -3.695711763932153505623248207576425983573E5L, + -4.717341584067827676530426007495274711306E3L +}; +#define NRD2r5 8 +static const long double RD2r5[NRD2r5 + 1] = +{ + -6.650657966618993679456019224416926875619E9L, + -1.099511409330635807899718829033488771623E10L, + -7.482546968307837168164311101447116903148E9L, + -2.702967190056506495988922973755870557217E9L, + -5.570008176482922704972943389590409280950E8L, + -6.536934032192792470926310043166993233231E7L, + -4.101991193844953082400035444146067511725E6L, + -1.174082735875715802334430481065526664020E5L, + -9.932840389994157592102947657277692978511E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+2) = x P(x)/Q(x) + -0.125 <= x <= +0.375 + 1.875 <= x+2 <= 2.375 + Peak relative error 4.6e-36 */ +#define NRN2 9 +static const long double RN2[NRN2 + 1] = +{ + -3.716661929737318153526921358113793421524E9L, + -1.138816715030710406922819131397532331321E10L, + -1.421017419363526524544402598734013569950E10L, + -9.510432842542519665483662502132010331451E9L, + -3.747528562099410197957514973274474767329E9L, + -8.923565763363912474488712255317033616626E8L, + -1.261396653700237624185350402781338231697E8L, + -9.918402520255661797735331317081425749014E6L, + -3.753996255897143855113273724233104768831E5L, + -4.778761333044147141559311805999540765612E3L +}; +#define NRD2 9 +static const long double RD2[NRD2 + 1] = +{ + -8.790916836764308497770359421351673950111E9L, + -2.023108608053212516399197678553737477486E10L, + -1.958067901852022239294231785363504458367E10L, + -1.035515043621003101254252481625188704529E10L, + -3.253884432621336737640841276619272224476E9L, + -6.186383531162456814954947669274235815544E8L, + -6.932557847749518463038934953605969951466E7L, + -4.240731768287359608773351626528479703758E6L, + -1.197343995089189188078944689846348116630E5L, + -1.004622911670588064824904487064114090920E3L +/* 1.0E0 */ +}; + + +/* log gamma(x+1.75) = log gamma(1.75) + x P(x)/Q(x) + -0.125 <= x <= +0.125 + 1.625 <= x+1.75 <= 1.875 + Peak relative error 9.2e-37 */ +static const long double lgam1r75a = -8.441162109375E-2L; +static const long double lgam1r75b = 1.0500073264444042213965868602268256157604E-5L; +#define NRN1r75 8 +static const long double RN1r75[NRN1r75 + 1] = +{ + -5.221061693929833937710891646275798251513E7L, + -2.052466337474314812817883030472496436993E8L, + -2.952718275974940270675670705084125640069E8L, + -2.132294039648116684922965964126389017840E8L, + -8.554103077186505960591321962207519908489E7L, + -1.940250901348870867323943119132071960050E7L, + -2.379394147112756860769336400290402208435E6L, + -1.384060879999526222029386539622255797389E5L, + -2.698453601378319296159355612094598695530E3L +}; +#define NRD1r75 8 +static const long double RD1r75[NRD1r75 + 1] = +{ + -2.109754689501705828789976311354395393605E8L, + -5.036651829232895725959911504899241062286E8L, + -4.954234699418689764943486770327295098084E8L, + -2.589558042412676610775157783898195339410E8L, + -7.731476117252958268044969614034776883031E7L, + -1.316721702252481296030801191240867486965E7L, + -1.201296501404876774861190604303728810836E6L, + -5.007966406976106636109459072523610273928E4L, + -6.155817990560743422008969155276229018209E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+x0) = y0 + x^2 P(x)/Q(x) + -0.0867 <= x <= +0.1634 + 1.374932... <= x+x0 <= 1.625032... + Peak relative error 4.0e-36 */ +static const long double x0a = 1.4616241455078125L; +static const long double x0b = 7.9994605498412626595423257213002588621246E-6L; +static const long double y0a = -1.21490478515625E-1L; +static const long double y0b = 4.1879797753919044854428223084178486438269E-6L; +#define NRN1r5 8 +static const long double RN1r5[NRN1r5 + 1] = +{ + 6.827103657233705798067415468881313128066E5L, + 1.910041815932269464714909706705242148108E6L, + 2.194344176925978377083808566251427771951E6L, + 1.332921400100891472195055269688876427962E6L, + 4.589080973377307211815655093824787123508E5L, + 8.900334161263456942727083580232613796141E4L, + 9.053840838306019753209127312097612455236E3L, + 4.053367147553353374151852319743594873771E2L, + 5.040631576303952022968949605613514584950E0L +}; +#define NRD1r5 8 +static const long double RD1r5[NRD1r5 + 1] = +{ + 1.411036368843183477558773688484699813355E6L, + 4.378121767236251950226362443134306184849E6L, + 5.682322855631723455425929877581697918168E6L, + 3.999065731556977782435009349967042222375E6L, + 1.653651390456781293163585493620758410333E6L, + 4.067774359067489605179546964969435858311E5L, + 5.741463295366557346748361781768833633256E4L, + 4.226404539738182992856094681115746692030E3L, + 1.316980975410327975566999780608618774469E2L, + /* 1.0E0L */ +}; + + +/* log gamma(x+1.25) = log gamma(1.25) + x P(x)/Q(x) + -.125 <= x <= +.125 + 1.125 <= x+1.25 <= 1.375 + Peak relative error = 4.9e-36 */ +static const long double lgam1r25a = -9.82818603515625E-2L; +static const long double lgam1r25b = 1.0023929749338536146197303364159774377296E-5L; +#define NRN1r25 9 +static const long double RN1r25[NRN1r25 + 1] = +{ + -9.054787275312026472896002240379580536760E4L, + -8.685076892989927640126560802094680794471E4L, + 2.797898965448019916967849727279076547109E5L, + 6.175520827134342734546868356396008898299E5L, + 5.179626599589134831538516906517372619641E5L, + 2.253076616239043944538380039205558242161E5L, + 5.312653119599957228630544772499197307195E4L, + 6.434329437514083776052669599834938898255E3L, + 3.385414416983114598582554037612347549220E2L, + 4.907821957946273805080625052510832015792E0L +}; +#define NRD1r25 8 +static const long double RD1r25[NRD1r25 + 1] = +{ + 3.980939377333448005389084785896660309000E5L, + 1.429634893085231519692365775184490465542E6L, + 2.145438946455476062850151428438668234336E6L, + 1.743786661358280837020848127465970357893E6L, + 8.316364251289743923178092656080441655273E5L, + 2.355732939106812496699621491135458324294E5L, + 3.822267399625696880571810137601310855419E4L, + 3.228463206479133236028576845538387620856E3L, + 1.152133170470059555646301189220117965514E2L + /* 1.0E0L */ +}; + + +/* log gamma(x + 1) = x P(x)/Q(x) + 0.0 <= x <= +0.125 + 1.0 <= x+1 <= 1.125 + Peak relative error 1.1e-35 */ +#define NRN1 8 +static const long double RN1[NRN1 + 1] = +{ + -9.987560186094800756471055681088744738818E3L, + -2.506039379419574361949680225279376329742E4L, + -1.386770737662176516403363873617457652991E4L, + 1.439445846078103202928677244188837130744E4L, + 2.159612048879650471489449668295139990693E4L, + 1.047439813638144485276023138173676047079E4L, + 2.250316398054332592560412486630769139961E3L, + 1.958510425467720733041971651126443864041E2L, + 4.516830313569454663374271993200291219855E0L +}; +#define NRD1 7 +static const long double RD1[NRD1 + 1] = +{ + 1.730299573175751778863269333703788214547E4L, + 6.807080914851328611903744668028014678148E4L, + 1.090071629101496938655806063184092302439E5L, + 9.124354356415154289343303999616003884080E4L, + 4.262071638655772404431164427024003253954E4L, + 1.096981664067373953673982635805821283581E4L, + 1.431229503796575892151252708527595787588E3L, + 7.734110684303689320830401788262295992921E1L + /* 1.0E0 */ +}; + + +/* log gamma(x + 1) = x P(x)/Q(x) + -0.125 <= x <= 0 + 0.875 <= x+1 <= 1.0 + Peak relative error 7.0e-37 */ +#define NRNr9 8 +static const long double RNr9[NRNr9 + 1] = +{ + 4.441379198241760069548832023257571176884E5L, + 1.273072988367176540909122090089580368732E6L, + 9.732422305818501557502584486510048387724E5L, + -5.040539994443998275271644292272870348684E5L, + -1.208719055525609446357448132109723786736E6L, + -7.434275365370936547146540554419058907156E5L, + -2.075642969983377738209203358199008185741E5L, + -2.565534860781128618589288075109372218042E4L, + -1.032901669542994124131223797515913955938E3L, +}; +#define NRDr9 8 +static const long double RDr9[NRDr9 + 1] = +{ + -7.694488331323118759486182246005193998007E5L, + -3.301918855321234414232308938454112213751E6L, + -5.856830900232338906742924836032279404702E6L, + -5.540672519616151584486240871424021377540E6L, + -3.006530901041386626148342989181721176919E6L, + -9.350378280513062139466966374330795935163E5L, + -1.566179100031063346901755685375732739511E5L, + -1.205016539620260779274902967231510804992E4L, + -2.724583156305709733221564484006088794284E2L +/* 1.0E0 */ +}; + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +long double +lgammal_r(long double x, int *signgamp) +{ + long double p, q, w, z, nx; + int i, nn; + + *signgamp = 1; + + if (!isfinite (x)) + return x * x; + + if (x == 0.0L) + { + if (signbit (x)) + *signgamp = -1; + return one / fabsl (x); + } + + if (x < 0.0L) + { + q = -x; + p = floorl (q); + if (p == q) + return (one / (p - p)); + i = p; + if ((i & 1) == 0) + *signgamp = -1; + else + *signgamp = 1; + z = q - p; + if (z > 0.5L) + { + p += 1.0L; + z = p - q; + } + z = q * sinl (PIL * z); + if (z == 0.0L) + return (*signgamp * huge * huge); + w = lgammal (q); + z = logl (PIL / z) - w; + return (z); + } + + if (x < 13.5L) + { + p = 0.0L; + nx = floorl (x + 0.5L); + nn = nx; + switch (nn) + { + case 0: + /* log gamma (x + 1) = log(x) + log gamma(x) */ + if (x <= 0.125) + { + p = x * neval (x, RN1, NRN1) / deval (x, RD1, NRD1); + } + else if (x <= 0.375) + { + z = x - 0.25L; + p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); + p += lgam1r25b; + p += lgam1r25a; + } + else if (x <= 0.625) + { + z = x + (1.0L - x0a); + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + else if (x <= 0.875) + { + z = x - 0.75L; + p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); + p += lgam1r75b; + p += lgam1r75a; + } + else + { + z = x - 1.0L; + p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); + } + p = p - logl (x); + break; + + case 1: + if (x < 0.875L) + { + if (x <= 0.625) + { + z = x + (1.0L - x0a); + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + else if (x <= 0.875) + { + z = x - 0.75L; + p = z * neval (z, RN1r75, NRN1r75) + / deval (z, RD1r75, NRD1r75); + p += lgam1r75b; + p += lgam1r75a; + } + else + { + z = x - 1.0L; + p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); + } + p = p - logl (x); + } + else if (x < 1.0L) + { + z = x - 1.0L; + p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9); + } + else if (x == 1.0L) + p = 0.0L; + else if (x <= 1.125L) + { + z = x - 1.0L; + p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1); + } + else if (x <= 1.375) + { + z = x - 1.25L; + p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); + p += lgam1r25b; + p += lgam1r25a; + } + else + { + /* 1.375 <= x+x0 <= 1.625 */ + z = x - x0a; + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + break; + + case 2: + if (x < 1.625L) + { + z = x - x0a; + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + else if (x < 1.875L) + { + z = x - 1.75L; + p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); + p += lgam1r75b; + p += lgam1r75a; + } + else if (x == 2.0L) + p = 0.0L; + else if (x < 2.375L) + { + z = x - 2.0L; + p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); + } + else + { + z = x - 2.5L; + p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); + p += lgam2r5b; + p += lgam2r5a; + } + break; + + case 3: + if (x < 2.75) + { + z = x - 2.5L; + p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); + p += lgam2r5b; + p += lgam2r5a; + } + else + { + z = x - 3.0L; + p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3); + p += lgam3b; + p += lgam3a; + } + break; + + case 4: + z = x - 4.0L; + p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4); + p += lgam4b; + p += lgam4a; + break; + + case 5: + z = x - 5.0L; + p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5); + p += lgam5b; + p += lgam5a; + break; + + case 6: + z = x - 6.0L; + p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6); + p += lgam6b; + p += lgam6a; + break; + + case 7: + z = x - 7.0L; + p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7); + p += lgam7b; + p += lgam7a; + break; + + case 8: + z = x - 8.0L; + p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8); + p += lgam8b; + p += lgam8a; + break; + + case 9: + z = x - 9.0L; + p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9); + p += lgam9b; + p += lgam9a; + break; + + case 10: + z = x - 10.0L; + p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10); + p += lgam10b; + p += lgam10a; + break; + + case 11: + z = x - 11.0L; + p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11); + p += lgam11b; + p += lgam11a; + break; + + case 12: + z = x - 12.0L; + p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12); + p += lgam12b; + p += lgam12a; + break; + + case 13: + z = x - 13.0L; + p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13); + p += lgam13b; + p += lgam13a; + break; + } + return p; + } + + if (x > MAXLGM) + return (*signgamp * huge * huge); + + q = ls2pi - x; + q = (x - 0.5L) * logl (x) + q; + if (x > 1.0e18L) + return (q); + + p = 1.0L / (x * x); + q += neval (p, RASY, NRASY) / x; + return (q); +} diff --git a/openlibm/ld128/e_log10l.c b/openlibm/ld128/e_log10l.c new file mode 100644 index 0000000..9448101 --- /dev/null +++ b/openlibm/ld128/e_log10l.c @@ -0,0 +1,255 @@ +/* $OpenBSD: e_log10l.c,v 1.1 2011/07/06 00:02:42 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* log10l.c + * + * Common logarithm, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log10l(); + * + * y = log10l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 10 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 30000 2.3e-34 4.9e-35 + * IEEE exp(+-10000) 30000 1.0e-34 4.1e-35 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + */ + +#include + +#include "math_private.h" + +/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const long double P[13] = +{ + 1.313572404063446165910279910527789794488E4L, + 7.771154681358524243729929227226708890930E4L, + 2.014652742082537582487669938141683759923E5L, + 3.007007295140399532324943111654767187848E5L, + 2.854829159639697837788887080758954924001E5L, + 1.797628303815655343403735250238293741397E5L, + 7.594356839258970405033155585486712125861E4L, + 2.128857716871515081352991964243375186031E4L, + 3.824952356185897735160588078446136783779E3L, + 4.114517881637811823002128927449878962058E2L, + 2.321125933898420063925789532045674660756E1L, + 4.998469661968096229986658302195402690910E-1L, + 1.538612243596254322971797716843006400388E-6L +}; +static const long double Q[12] = +{ + 3.940717212190338497730839731583397586124E4L, + 2.626900195321832660448791748036714883242E5L, + 7.777690340007566932935753241556479363645E5L, + 1.347518538384329112529391120390701166528E6L, + 1.514882452993549494932585972882995548426E6L, + 1.158019977462989115839826904108208787040E6L, + 6.132189329546557743179177159925690841200E5L, + 2.248234257620569139969141618556349415120E5L, + 5.605842085972455027590989944010492125825E4L, + 9.147150349299596453976674231612674085381E3L, + 9.104928120962988414618126155557301584078E2L, + 4.839208193348159620282142911143429644326E1L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const long double R[6] = +{ + 1.418134209872192732479751274970992665513E5L, + -8.977257995689735303686582344659576526998E4L, + 2.048819892795278657810231591630928516206E4L, + -2.024301798136027039250415126250455056397E3L, + 8.057002716646055371965756206836056074715E1L, + -8.828896441624934385266096344596648080902E-1L +}; +static const long double S[6] = +{ + 1.701761051846631278975701529965589676574E6L, + -1.332535117259762928288745111081235577029E6L, + 4.001557694070773974936904547424676279307E5L, + -5.748542087379434595104154610899551484314E4L, + 3.998526750980007367835804959888064681098E3L, + -1.186359407982897997337150403816839480438E2L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double +/* log10(2) */ +L102A = 0.3125L, +L102B = -1.14700043360188047862611052755069732318101185E-2L, +/* log10(e) */ +L10EA = 0.5L, +L10EB = -6.570551809674817234887108108339491770560299E-2L, +/* sqrt(2)/2 */ +SQRTH = 7.071067811865475244008443621048490392848359E-1L; + + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +long double +log10l(long double x) +{ + long double z; + long double y; + int e; + int64_t hx, lx; + +/* Test for domain */ + GET_LDOUBLE_WORDS64 (hx, lx, x); + if (((hx & 0x7fffffffffffffffLL) | lx) == 0) + return (-1.0L / (x - x)); + if (hx < 0) + return (x - x) / (x - x); + if (hx >= 0x7fff000000000000LL) + return (x + x); + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ + x = frexpl (x, &e); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ + if ((e > 2) || (e < -2)) + { + if (x < SQRTH) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } + else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x * x; + y = x * (z * neval (z, R, 5) / deval (z, S, 5)); + goto done; + } + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + + if (x < SQRTH) + { + e -= 1; + x = 2.0 * x - 1.0L; /* 2x - 1 */ + } + else + { + x = x - 1.0L; + } + z = x * x; + y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); + y = y - 0.5 * z; + +done: + + /* Multiply log of fraction by log10(e) + * and base 2 exponent by log10(2). + */ + z = y * L10EB; + z += x * L10EB; + z += e * L102B; + z += y * L10EA; + z += x * L10EA; + z += e * L102A; + return (z); +} diff --git a/openlibm/ld128/e_log2l.c b/openlibm/ld128/e_log2l.c new file mode 100644 index 0000000..2ce4d94 --- /dev/null +++ b/openlibm/ld128/e_log2l.c @@ -0,0 +1,248 @@ +/* $OpenBSD: e_log2l.c,v 1.1 2011/07/06 00:02:42 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* log2l.c + * Base 2 logarithm, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log2l(); + * + * y = log2l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 2 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the (natural) + * logarithm of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 100,000 2.6e-34 4.9e-35 + * IEEE exp(+-10000) 100,000 9.6e-35 4.0e-35 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + */ + +#include + +#include "math_private.h" + +/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const long double P[13] = +{ + 1.313572404063446165910279910527789794488E4L, + 7.771154681358524243729929227226708890930E4L, + 2.014652742082537582487669938141683759923E5L, + 3.007007295140399532324943111654767187848E5L, + 2.854829159639697837788887080758954924001E5L, + 1.797628303815655343403735250238293741397E5L, + 7.594356839258970405033155585486712125861E4L, + 2.128857716871515081352991964243375186031E4L, + 3.824952356185897735160588078446136783779E3L, + 4.114517881637811823002128927449878962058E2L, + 2.321125933898420063925789532045674660756E1L, + 4.998469661968096229986658302195402690910E-1L, + 1.538612243596254322971797716843006400388E-6L +}; +static const long double Q[12] = +{ + 3.940717212190338497730839731583397586124E4L, + 2.626900195321832660448791748036714883242E5L, + 7.777690340007566932935753241556479363645E5L, + 1.347518538384329112529391120390701166528E6L, + 1.514882452993549494932585972882995548426E6L, + 1.158019977462989115839826904108208787040E6L, + 6.132189329546557743179177159925690841200E5L, + 2.248234257620569139969141618556349415120E5L, + 5.605842085972455027590989944010492125825E4L, + 9.147150349299596453976674231612674085381E3L, + 9.104928120962988414618126155557301584078E2L, + 4.839208193348159620282142911143429644326E1L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const long double R[6] = +{ + 1.418134209872192732479751274970992665513E5L, + -8.977257995689735303686582344659576526998E4L, + 2.048819892795278657810231591630928516206E4L, + -2.024301798136027039250415126250455056397E3L, + 8.057002716646055371965756206836056074715E1L, + -8.828896441624934385266096344596648080902E-1L +}; +static const long double S[6] = +{ + 1.701761051846631278975701529965589676574E6L, + -1.332535117259762928288745111081235577029E6L, + 4.001557694070773974936904547424676279307E5L, + -5.748542087379434595104154610899551484314E4L, + 3.998526750980007367835804959888064681098E3L, + -1.186359407982897997337150403816839480438E2L +/* 1.000000000000000000000000000000000000000E0L, */ +}; + +static const long double +/* log2(e) - 1 */ +LOG2EA = 4.4269504088896340735992468100189213742664595E-1L, +/* sqrt(2)/2 */ +SQRTH = 7.071067811865475244008443621048490392848359E-1L; + + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +long double +log2l(long double x) +{ + long double z; + long double y; + int e; + int64_t hx, lx; + +/* Test for domain */ + GET_LDOUBLE_WORDS64 (hx, lx, x); + if (((hx & 0x7fffffffffffffffLL) | lx) == 0) + return (-1.0L / (x - x)); + if (hx < 0) + return (x - x) / (x - x); + if (hx >= 0x7fff000000000000LL) + return (x + x); + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ + x = frexpl (x, &e); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ + if ((e > 2) || (e < -2)) + { + if (x < SQRTH) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } + else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x * x; + y = x * (z * neval (z, R, 5) / deval (z, S, 5)); + goto done; + } + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + + if (x < SQRTH) + { + e -= 1; + x = 2.0 * x - 1.0L; /* 2x - 1 */ + } + else + { + x = x - 1.0L; + } + z = x * x; + y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); + y = y - 0.5 * z; + +done: + +/* Multiply log of fraction by log2(e) + * and base 2 exponent by 1 + */ + z = y * LOG2EA; + z += x * LOG2EA; + z += y; + z += x; + z += e; + return (z); +} diff --git a/openlibm/ld128/e_logl.c b/openlibm/ld128/e_logl.c new file mode 100644 index 0000000..f6da91f --- /dev/null +++ b/openlibm/ld128/e_logl.c @@ -0,0 +1,283 @@ +/* $OpenBSD: e_logl.c,v 1.1 2011/07/06 00:02:42 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* logl.c + * + * Natural logarithm for 128-bit long double precision. + * + * + * + * SYNOPSIS: + * + * long double x, y, logl(); + * + * y = logl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. Use of a lookup table increases the speed of the routine. + * The program uses logarithms tabulated at intervals of 1/128 to + * cover the domain from approximately 0.7 to 1.4. + * + * On the interval [-1/128, +1/128] the logarithm of 1+x is approximated by + * log(1+x) = x - 0.5 x^2 + x^3 P(x) . + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.875, 1.125 100000 1.2e-34 4.1e-35 + * IEEE 0.125, 8 100000 1.2e-34 4.1e-35 + * + * + * WARNING: + * + * This program uses integer operations on bit fields of floating-point + * numbers. It does not work with data structures other than the + * structure assumed. + * + */ + +#include + +#include "math_private.h" + +/* log(1+x) = x - .5 x^2 + x^3 l(x) + -.0078125 <= x <= +.0078125 + peak relative error 1.2e-37 */ +static const long double +l3 = 3.333333333333333333333333333333336096926E-1L, +l4 = -2.499999999999999999999999999486853077002E-1L, +l5 = 1.999999999999999999999999998515277861905E-1L, +l6 = -1.666666666666666666666798448356171665678E-1L, +l7 = 1.428571428571428571428808945895490721564E-1L, +l8 = -1.249999999999999987884655626377588149000E-1L, +l9 = 1.111111111111111093947834982832456459186E-1L, +l10 = -1.000000000000532974938900317952530453248E-1L, +l11 = 9.090909090915566247008015301349979892689E-2L, +l12 = -8.333333211818065121250921925397567745734E-2L, +l13 = 7.692307559897661630807048686258659316091E-2L, +l14 = -7.144242754190814657241902218399056829264E-2L, +l15 = 6.668057591071739754844678883223432347481E-2L; + +/* Lookup table of ln(t) - (t-1) + t = 0.5 + (k+26)/128) + k = 0, ..., 91 */ +static const long double logtbl[92] = { +-5.5345593589352099112142921677820359632418E-2L, +-5.2108257402767124761784665198737642086148E-2L, +-4.8991686870576856279407775480686721935120E-2L, +-4.5993270766361228596215288742353061431071E-2L, +-4.3110481649613269682442058976885699556950E-2L, +-4.0340872319076331310838085093194799765520E-2L, +-3.7682072451780927439219005993827431503510E-2L, +-3.5131785416234343803903228503274262719586E-2L, +-3.2687785249045246292687241862699949178831E-2L, +-3.0347913785027239068190798397055267411813E-2L, +-2.8110077931525797884641940838507561326298E-2L, +-2.5972247078357715036426583294246819637618E-2L, +-2.3932450635346084858612873953407168217307E-2L, +-2.1988775689981395152022535153795155900240E-2L, +-2.0139364778244501615441044267387667496733E-2L, +-1.8382413762093794819267536615342902718324E-2L, +-1.6716169807550022358923589720001638093023E-2L, +-1.5138929457710992616226033183958974965355E-2L, +-1.3649036795397472900424896523305726435029E-2L, +-1.2244881690473465543308397998034325468152E-2L, +-1.0924898127200937840689817557742469105693E-2L, +-9.6875626072830301572839422532631079809328E-3L, +-8.5313926245226231463436209313499745894157E-3L, +-7.4549452072765973384933565912143044991706E-3L, +-6.4568155251217050991200599386801665681310E-3L, +-5.5356355563671005131126851708522185605193E-3L, +-4.6900728132525199028885749289712348829878E-3L, +-3.9188291218610470766469347968659624282519E-3L, +-3.2206394539524058873423550293617843896540E-3L, +-2.5942708080877805657374888909297113032132E-3L, +-2.0385211375711716729239156839929281289086E-3L, +-1.5522183228760777967376942769773768850872E-3L, +-1.1342191863606077520036253234446621373191E-3L, +-7.8340854719967065861624024730268350459991E-4L, +-4.9869831458030115699628274852562992756174E-4L, +-2.7902661731604211834685052867305795169688E-4L, +-1.2335696813916860754951146082826952093496E-4L, +-3.0677461025892873184042490943581654591817E-5L, +#define ZERO logtbl[38] + 0.0000000000000000000000000000000000000000E0L, +-3.0359557945051052537099938863236321874198E-5L, +-1.2081346403474584914595395755316412213151E-4L, +-2.7044071846562177120083903771008342059094E-4L, +-4.7834133324631162897179240322783590830326E-4L, +-7.4363569786340080624467487620270965403695E-4L, +-1.0654639687057968333207323853366578860679E-3L, +-1.4429854811877171341298062134712230604279E-3L, +-1.8753781835651574193938679595797367137975E-3L, +-2.3618380914922506054347222273705859653658E-3L, +-2.9015787624124743013946600163375853631299E-3L, +-3.4938307889254087318399313316921940859043E-3L, +-4.1378413103128673800485306215154712148146E-3L, +-4.8328735414488877044289435125365629849599E-3L, +-5.5782063183564351739381962360253116934243E-3L, +-6.3731336597098858051938306767880719015261E-3L, +-7.2169643436165454612058905294782949315193E-3L, +-8.1090214990427641365934846191367315083867E-3L, +-9.0486422112807274112838713105168375482480E-3L, +-1.0035177140880864314674126398350812606841E-2L, +-1.1067990155502102718064936259435676477423E-2L, +-1.2146457974158024928196575103115488672416E-2L, +-1.3269969823361415906628825374158424754308E-2L, +-1.4437927104692837124388550722759686270765E-2L, +-1.5649743073340777659901053944852735064621E-2L, +-1.6904842527181702880599758489058031645317E-2L, +-1.8202661505988007336096407340750378994209E-2L, +-1.9542647000370545390701192438691126552961E-2L, +-2.0924256670080119637427928803038530924742E-2L, +-2.2346958571309108496179613803760727786257E-2L, +-2.3810230892650362330447187267648486279460E-2L, +-2.5313561699385640380910474255652501521033E-2L, +-2.6856448685790244233704909690165496625399E-2L, +-2.8438398935154170008519274953860128449036E-2L, +-3.0058928687233090922411781058956589863039E-2L, +-3.1717563112854831855692484086486099896614E-2L, +-3.3413836095418743219397234253475252001090E-2L, +-3.5147290019036555862676702093393332533702E-2L, +-3.6917475563073933027920505457688955423688E-2L, +-3.8723951502862058660874073462456610731178E-2L, +-4.0566284516358241168330505467000838017425E-2L, +-4.2444048996543693813649967076598766917965E-2L, +-4.4356826869355401653098777649745233339196E-2L, +-4.6304207416957323121106944474331029996141E-2L, +-4.8285787106164123613318093945035804818364E-2L, +-5.0301169421838218987124461766244507342648E-2L, +-5.2349964705088137924875459464622098310997E-2L, +-5.4431789996103111613753440311680967840214E-2L, +-5.6546268881465384189752786409400404404794E-2L, +-5.8693031345788023909329239565012647817664E-2L, +-6.0871713627532018185577188079210189048340E-2L, +-6.3081958078862169742820420185833800925568E-2L, +-6.5323413029406789694910800219643791556918E-2L, +-6.7595732653791419081537811574227049288168E-2L +}; + +/* ln(2) = ln2a + ln2b with extended precision. */ +static const long double + ln2a = 6.93145751953125e-1L, + ln2b = 1.4286068203094172321214581765680755001344E-6L; + +long double +logl(long double x) +{ + long double z, y, w; + ieee_quad_shape_type u, t; + unsigned int m; + int k, e; + + u.value = x; + m = u.parts32.mswhi; + + /* Check for IEEE special cases. */ + k = m & 0x7fffffff; + /* log(0) = -infinity. */ + if ((k | u.parts32.mswlo | u.parts32.lswhi | u.parts32.lswlo) == 0) + { + return -0.5L / ZERO; + } + /* log ( x < 0 ) = NaN */ + if (m & 0x80000000) + { + return (x - x) / ZERO; + } + /* log (infinity or NaN) */ + if (k >= 0x7fff0000) + { + return x + x; + } + + /* Extract exponent and reduce domain to 0.703125 <= u < 1.40625 */ + e = (int) (m >> 16) - (int) 0x3ffe; + m &= 0xffff; + u.parts32.mswhi = m | 0x3ffe0000; + m |= 0x10000; + /* Find lookup table index k from high order bits of the significand. */ + if (m < 0x16800) + { + k = (m - 0xff00) >> 9; + /* t is the argument 0.5 + (k+26)/128 + of the nearest item to u in the lookup table. */ + t.parts32.mswhi = 0x3fff0000 + (k << 9); + t.parts32.mswlo = 0; + t.parts32.lswhi = 0; + t.parts32.lswlo = 0; + u.parts32.mswhi += 0x10000; + e -= 1; + k += 64; + } + else + { + k = (m - 0xfe00) >> 10; + t.parts32.mswhi = 0x3ffe0000 + (k << 10); + t.parts32.mswlo = 0; + t.parts32.lswhi = 0; + t.parts32.lswlo = 0; + } + /* On this interval the table is not used due to cancellation error. */ + if ((x <= 1.0078125L) && (x >= 0.9921875L)) + { + z = x - 1.0L; + k = 64; + t.value = 1.0L; + e = 0; + } + else + { + /* log(u) = log( t u/t ) = log(t) + log(u/t) + log(t) is tabulated in the lookup table. + Express log(u/t) = log(1+z), where z = u/t - 1 = (u-t)/t. + cf. Cody & Waite. */ + z = (u.value - t.value) / t.value; + } + /* Series expansion of log(1+z). */ + w = z * z; + y = ((((((((((((l15 * z + + l14) * z + + l13) * z + + l12) * z + + l11) * z + + l10) * z + + l9) * z + + l8) * z + + l7) * z + + l6) * z + + l5) * z + + l4) * z + + l3) * z * w; + y -= 0.5 * w; + y += e * ln2b; /* Base 2 exponent offset times ln(2). */ + y += z; + y += logtbl[k-26]; /* log(t) - (t-1) */ + y += (t.value - 1.0L); + y += e * ln2a; + return y; +} diff --git a/openlibm/ld128/e_powl.c b/openlibm/ld128/e_powl.c new file mode 100644 index 0000000..430b261 --- /dev/null +++ b/openlibm/ld128/e_powl.c @@ -0,0 +1,439 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* powl(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 113-53 = 60 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + */ + +#include + +#include "math_private.h" + +static const long double bp[] = { + 1.0L, + 1.5L, +}; + +/* log_2(1.5) */ +static const long double dp_h[] = { + 0.0, + 5.8496250072115607565592654282227158546448E-1L +}; + +/* Low part of log_2(1.5) */ +static const long double dp_l[] = { + 0.0, + 1.0579781240112554492329533686862998106046E-16L +}; + +static const long double zero = 0.0L, + one = 1.0L, + two = 2.0L, + two113 = 1.0384593717069655257060992658440192E34L, + huge = 1.0e3000L, + tiny = 1.0e-3000L; + +/* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2)) + z = (x-1)/(x+1) + 1 <= x <= 1.25 + Peak relative error 2.3e-37 */ +static const long double LN[] = +{ + -3.0779177200290054398792536829702930623200E1L, + 6.5135778082209159921251824580292116201640E1L, + -4.6312921812152436921591152809994014413540E1L, + 1.2510208195629420304615674658258363295208E1L, + -9.9266909031921425609179910128531667336670E-1L +}; +static const long double LD[] = +{ + -5.129862866715009066465422805058933131960E1L, + 1.452015077564081884387441590064272782044E2L, + -1.524043275549860505277434040464085593165E2L, + 7.236063513651544224319663428634139768808E1L, + -1.494198912340228235853027849917095580053E1L + /* 1.0E0 */ +}; + +/* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2))) + 0 <= x <= 0.5 + Peak relative error 5.7e-38 */ +static const long double PN[] = +{ + 5.081801691915377692446852383385968225675E8L, + 9.360895299872484512023336636427675327355E6L, + 4.213701282274196030811629773097579432957E4L, + 5.201006511142748908655720086041570288182E1L, + 9.088368420359444263703202925095675982530E-3L, +}; +static const long double PD[] = +{ + 3.049081015149226615468111430031590411682E9L, + 1.069833887183886839966085436512368982758E8L, + 8.259257717868875207333991924545445705394E5L, + 1.872583833284143212651746812884298360922E3L, + /* 1.0E0 */ +}; + +static const long double + /* ln 2 */ + lg2 = 6.9314718055994530941723212145817656807550E-1L, + lg2_h = 6.9314718055994528622676398299518041312695E-1L, + lg2_l = 2.3190468138462996154948554638754786504121E-17L, + ovt = 8.0085662595372944372e-0017L, + /* 2/(3*log(2)) */ + cp = 9.6179669392597560490661645400126142495110E-1L, + cp_h = 9.6179669392597555432899980587535537779331E-1L, + cp_l = 5.0577616648125906047157785230014751039424E-17L; + +long double +powl(long double x, long double y) +{ + long double z, ax, z_h, z_l, p_h, p_l; + long double yy1, t1, t2, r, s, t, u, v, w; + long double s2, s_h, s_l, t_h, t_l; + int32_t i, j, k, yisint, n; + u_int32_t ix, iy; + int32_t hx, hy; + ieee_quad_shape_type o, p, q; + + p.value = x; + hx = p.parts32.mswhi; + ix = hx & 0x7fffffff; + + q.value = y; + hy = q.parts32.mswhi; + iy = hy & 0x7fffffff; + + + /* y==zero: x**0 = 1 */ + if ((iy | q.parts32.mswlo | q.parts32.lswhi | q.parts32.lswlo) == 0) + return one; + + /* 1.0**y = 1; -1.0**+-Inf = 1 */ + if (x == one) + return one; + if (x == -1.0L && iy == 0x7fff0000 + && (q.parts32.mswlo | q.parts32.lswhi | q.parts32.lswlo) == 0) + return one; + + /* +-NaN return x+y */ + if ((ix > 0x7fff0000) + || ((ix == 0x7fff0000) + && ((p.parts32.mswlo | p.parts32.lswhi | p.parts32.lswlo) != 0)) + || (iy > 0x7fff0000) + || ((iy == 0x7fff0000) + && ((q.parts32.mswlo | q.parts32.lswhi | q.parts32.lswlo) != 0))) + return x + y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if (hx < 0) + { + if (iy >= 0x40700000) /* 2^113 */ + yisint = 2; /* even integer y */ + else if (iy >= 0x3fff0000) /* 1.0 */ + { + if (floorl (y) == y) + { + z = 0.5 * y; + if (floorl (z) == z) + yisint = 2; + else + yisint = 1; + } + } + } + + /* special value of y */ + if ((q.parts32.mswlo | q.parts32.lswhi | q.parts32.lswlo) == 0) + { + if (iy == 0x7fff0000) /* y is +-inf */ + { + if (((ix - 0x3fff0000) | p.parts32.mswlo | p.parts32.lswhi | + p.parts32.lswlo) == 0) + return y - y; /* +-1**inf is NaN */ + else if (ix >= 0x3fff0000) /* (|x|>1)**+-inf = inf,0 */ + return (hy >= 0) ? y : zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy < 0) ? -y : zero; + } + if (iy == 0x3fff0000) + { /* y is +-1 */ + if (hy < 0) + return one / x; + else + return x; + } + if (hy == 0x40000000) + return x * x; /* y is 2 */ + if (hy == 0x3ffe0000) + { /* y is 0.5 */ + if (hx >= 0) /* x >= +0 */ + return sqrtl (x); + } + } + + ax = fabsl (x); + /* special value of x */ + if ((p.parts32.mswlo | p.parts32.lswhi | p.parts32.lswlo) == 0) + { + if (ix == 0x7fff0000 || ix == 0 || ix == 0x3fff0000) + { + z = ax; /*x is +-0,+-inf,+-1 */ + if (hy < 0) + z = one / z; /* z = (1/|x|) */ + if (hx < 0) + { + if (((ix - 0x3fff0000) | yisint) == 0) + { + z = (z - z) / (z - z); /* (-1)**non-int is NaN */ + } + else if (yisint == 1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + /* (x<0)**(non-int) is NaN */ + if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0) + return (x - x) / (x - x); + + /* |y| is huge. + 2^-16495 = 1/2 of smallest representable value. + If (1 - 1/131072)^y underflows, y > 1.4986e9 */ + if (iy > 0x401d654b) + { + /* if (1 - 2^-113)^y underflows, y > 1.1873e38 */ + if (iy > 0x407d654b) + { + if (ix <= 0x3ffeffff) + return (hy < 0) ? huge * huge : tiny * tiny; + if (ix >= 0x3fff0000) + return (hy > 0) ? huge * huge : tiny * tiny; + } + /* over/underflow if x is not close to one */ + if (ix < 0x3ffeffff) + return (hy < 0) ? huge * huge : tiny * tiny; + if (ix > 0x3fff0000) + return (hy > 0) ? huge * huge : tiny * tiny; + } + + n = 0; + /* take care subnormal number */ + if (ix < 0x00010000) + { + ax *= two113; + n -= 113; + o.value = ax; + ix = o.parts32.mswhi; + } + n += ((ix) >> 16) - 0x3fff; + j = ix & 0x0000ffff; + /* determine interval */ + ix = j | 0x3fff0000; /* normalize ix */ + if (j <= 0x3988) + k = 0; /* |x|> 31) - 1) | (yisint - 1)) == 0) + s = -one; /* (-ve)**(odd int) */ + + /* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */ + yy1 = y; + o.value = yy1; + o.parts32.lswlo = 0; + o.parts32.lswhi &= 0xf8000000; + yy1 = o.value; + p_l = (y - yy1) * t1 + y * t2; + p_h = yy1 * t1; + z = p_l + p_h; + o.value = z; + j = o.parts32.mswhi; + if (j >= 0x400d0000) /* z >= 16384 */ + { + /* if z > 16384 */ + if (((j - 0x400d0000) | o.parts32.mswlo | o.parts32.lswhi | + o.parts32.lswlo) != 0) + return s * huge * huge; /* overflow */ + else + { + if (p_l + ovt > z - p_h) + return s * huge * huge; /* overflow */ + } + } + else if ((j & 0x7fffffff) >= 0x400d01b9) /* z <= -16495 */ + { + /* z < -16495 */ + if (((j - 0xc00d01bc) | o.parts32.mswlo | o.parts32.lswhi | + o.parts32.lswlo) + != 0) + return s * tiny * tiny; /* underflow */ + else + { + if (p_l <= z - p_h) + return s * tiny * tiny; /* underflow */ + } + } + /* compute 2**(p_h+p_l) */ + i = j & 0x7fffffff; + k = (i >> 16) - 0x3fff; + n = 0; + if (i > 0x3ffe0000) + { /* if |z| > 0.5, set n = [z+0.5] */ + n = floorl (z + 0.5L); + t = n; + p_h -= t; + } + t = p_l + p_h; + o.value = t; + o.parts32.lswlo = 0; + o.parts32.lswhi &= 0xf8000000; + t = o.value; + u = t * lg2_h; + v = (p_l - (t - p_h)) * lg2 + t * lg2_l; + z = u + v; + w = v - (z - u); + /* exp(z) */ + t = z * z; + u = PN[0] + t * (PN[1] + t * (PN[2] + t * (PN[3] + t * PN[4]))); + v = PD[0] + t * (PD[1] + t * (PD[2] + t * (PD[3] + t))); + t1 = z - t * u / v; + r = (z * t1) / (t1 - two) - (w + z * w); + z = one - (r - z); + o.value = z; + j = o.parts32.mswhi; + j += (n << 16); + if ((j >> 16) <= 0) + z = scalbnl (z, n); /* subnormal output */ + else + { + o.parts32.mswhi = j; + z = o.value; + } + return s * z; +} diff --git a/openlibm/ld128/e_rem_pio2l.h b/openlibm/ld128/e_rem_pio2l.h new file mode 100644 index 0000000..5224245 --- /dev/null +++ b/openlibm/ld128/e_rem_pio2l.h @@ -0,0 +1,144 @@ +/* From: @(#)e_rem_pio2.c 1.4 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld128/e_rem_pio2l.h,v 1.2 2011/05/30 19:41:28 kargl Exp $"); + +/* ld128 version of __ieee754_rem_pio2l(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include +#include + +#include "math_private.h" +#include "fpmath.h" + +#define BIAS (LDBL_MAX_EXP - 1) + +/* + * XXX need to verify that nonzero integer multiples of pi/2 within the + * range get no closer to a long double than 2**-140, or that + * ilogb(x) + ilogb(min_delta) < 45 - -140. + */ +/* + * invpio2: 113 bits of 2/pi + * pio2_1: first 68 bits of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 68 bits of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 68 bits of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const double +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +two24 = 1.67772160000000000000e+07; /* 0x41700000, 0x00000000 */ + +static const long double +invpio2 = 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eafa3ea6a.0p-113 */ +pio2_1 = 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000000000.0p-112 */ +pio2_1t = 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a4093822299f3.0p-181 */ +pio2_2 = 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000000000.0p-181 */ +pio2_2t = 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d89cd91.0p-254 */ +pio2_3 = 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000000000.0p-254 */ +pio2_3t = -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */ + +//VBS +//static inline __always_inline int +//__ieee754_rem_pio2l(long double x, long double *y) + +static inline int +__ieee754_rem_pio2l(long double x, long double *y) +{ + union IEEEl2bits u,u1; + long double z,w,t,r,fn; + double tx[5],ty[3]; + int64_t n; + int e0,ex,i,j,nx; + int16_t expsign; + + u.e = x; + expsign = u.xbits.expsign; + ex = expsign & 0x7fff; + if (ex < BIAS + 45 || ex == BIAS + 45 && + u.bits.manh < 0x921fb54442d1LL) { + /* |x| ~< 2^45*(pi/2), medium size */ + /* Use a specialized rint() to get fn. Assume round-to-nearest. */ + fn = x*invpio2+0x1.8p112; + fn = fn-0x1.8p112; +#ifdef HAVE_EFFICIENT_I64RINT + n = i64rint(fn); +#else + n = fn; +#endif + r = x-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 180 bit */ + { + union IEEEl2bits u2; + int ex1; + j = ex; + y[0] = r-w; + u2.e = y[0]; + ex1 = u2.xbits.expsign & 0x7fff; + i = j-ex1; + if(i>51) { /* 2nd iteration needed, good to 248 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + u2.e = y[0]; + ex1 = u2.xbits.expsign & 0x7fff; + i = j-ex1; + if(i>119) { /* 3rd iteration need, 316 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + return n; + } + /* + * all other (large) arguments + */ + if(ex==0x7fff) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + u1.e = x; + e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */ + u1.xbits.expsign = ex - e0; + z = u1.e; + for(i=0;i<4;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[4] = z; + nx = 5; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,ty,e0,nx,3); + t = (long double)ty[2] + ty[1]; + r = t + ty[0]; + w = ty[0] - (r - t); + if(expsign<0) {y[0] = -r; y[1] = -w; return -n;} + y[0] = r; y[1] = w; return n; +} diff --git a/openlibm/ld128/e_sinhl.c b/openlibm/ld128/e_sinhl.c new file mode 100644 index 0000000..3bfdb5d --- /dev/null +++ b/openlibm/ld128/e_sinhl.c @@ -0,0 +1,104 @@ +/* @(#)e_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* sinhl(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x) + * 2 + * + * 25 <= x <= lnovft : sinhl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : sinhl(x) := x*shuge (overflow) + * + * Special cases: + * sinhl(x) is |x| if x is +INF, -INF, or NaN. + * only sinhl(0)=0 is exact for finite x. + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0, shuge = 1.0e4931L, +ovf_thresh = 1.1357216553474703894801348310092223067821E4L; + +long double +sinhl(long double x) +{ + long double t, w, h; + u_int32_t jx, ix; + ieee_quad_shape_type u; + + /* Words of |x|. */ + u.value = x; + jx = u.parts32.mswhi; + ix = jx & 0x7fffffff; + + /* x is INF or NaN */ + if (ix >= 0x7fff0000) + return x + x; + + h = 0.5; + if (jx & 0x80000000) + h = -h; + + /* Absolute value of x. */ + u.parts32.mswhi = ix; + + /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix <= 0x40044000) + { + if (ix < 0x3fc60000) /* |x| < 2^-57 */ + if (shuge + x > one) + return x; /* sinh(tiny) = tiny with inexact */ + t = expm1l (u.value); + if (ix < 0x3fff0000) + return h * (2.0 * t - t * t / (t + one)); + return h * (t + t / (t + one)); + } + + /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix <= 0x400c62e3) /* 11356.375 */ + return h * expl (u.value); + + /* |x| in [log(maxdouble), overflowthreshold] + Overflow threshold is log(2 * maxdouble). */ + if (u.value <= ovf_thresh) + { + w = expl (0.5 * u.value); + t = h * w; + return t * w; + } + + /* |x| > overflowthreshold, sinhl(x) overflow */ + return x * shuge; +} diff --git a/openlibm/ld128/e_tgammal.c b/openlibm/ld128/e_tgammal.c new file mode 100644 index 0000000..6c78c24 --- /dev/null +++ b/openlibm/ld128/e_tgammal.c @@ -0,0 +1,39 @@ +/* $OpenBSD: e_tgammal.c,v 1.1 2011/07/06 00:02:42 martynas Exp $ */ + +/* + * Copyright (c) 2011 Martynas Venckus + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#include + +#include "math_private.h" + +long double +tgammal(long double x) +{ + int64_t i0,i1; + + GET_LDOUBLE_WORDS64(i0,i1,x); + if (((i0&0x7fffffffffffffffLL)|i1) == 0) + return (1.0/x); + + if (i0<0 && (u_int64_t)i0<0xffff000000000000ULL && rintl(x)==x) + return (x-x)/(x-x); + + if (i0==0xffff000000000000ULL && i1==0) + return (x-x); + + return expl(lgammal(x)); +} diff --git a/openlibm/ld128/invtrig.c b/openlibm/ld128/invtrig.c new file mode 100644 index 0000000..5a869c2 --- /dev/null +++ b/openlibm/ld128/invtrig.c @@ -0,0 +1,100 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld128/invtrig.c,v 1.1 2008/07/31 22:41:26 das Exp $"); + +#include "ld128/invtrig.h" + +/* + * asinl() and acosl() + */ +const long double +pS0 = 1.66666666666666666666666666666700314e-01L, +pS1 = -7.32816946414566252574527475428622708e-01L, +pS2 = 1.34215708714992334609030036562143589e+00L, +pS3 = -1.32483151677116409805070261790752040e+00L, +pS4 = 7.61206183613632558824485341162121989e-01L, +pS5 = -2.56165783329023486777386833928147375e-01L, +pS6 = 4.80718586374448793411019434585413855e-02L, +pS7 = -4.42523267167024279410230886239774718e-03L, +pS8 = 1.44551535183911458253205638280410064e-04L, +pS9 = -2.10558957916600254061591040482706179e-07L, +qS1 = -4.84690167848739751544716485245697428e+00L, +qS2 = 9.96619113536172610135016921140206980e+00L, +qS3 = -1.13177895428973036660836798461641458e+01L, +qS4 = 7.74004374389488266169304117714658761e+00L, +qS5 = -3.25871986053534084709023539900339905e+00L, +qS6 = 8.27830318881232209752469022352928864e-01L, +qS7 = -1.18768052702942805423330715206348004e-01L, +qS8 = 8.32600764660522313269101537926539470e-03L, +qS9 = -1.99407384882605586705979504567947007e-04L; + +/* + * atanl() + */ +const long double atanhi[] = { + 4.63647609000806116214256231461214397e-01L, + 7.85398163397448309615660845819875699e-01L, + 9.82793723247329067985710611014666038e-01L, + 1.57079632679489661923132169163975140e+00L, +}; + +const long double atanlo[] = { + 4.89509642257333492668618435220297706e-36L, + 2.16795253253094525619926100651083806e-35L, + -2.31288434538183565909319952098066272e-35L, + 4.33590506506189051239852201302167613e-35L, +}; + +const long double aT[] = { + 3.33333333333333333333333333333333125e-01L, + -1.99999999999999999999999999999180430e-01L, + 1.42857142857142857142857142125269827e-01L, + -1.11111111111111111111110834490810169e-01L, + 9.09090909090909090908522355708623681e-02L, + -7.69230769230769230696553844935357021e-02L, + 6.66666666666666660390096773046256096e-02L, + -5.88235294117646671706582985209643694e-02L, + 5.26315789473666478515847092020327506e-02L, + -4.76190476189855517021024424991436144e-02L, + 4.34782608678695085948531993458097026e-02L, + -3.99999999632663469330634215991142368e-02L, + 3.70370363987423702891250829918659723e-02L, + -3.44827496515048090726669907612335954e-02L, + 3.22579620681420149871973710852268528e-02L, + -3.03020767654269261041647570626778067e-02L, + 2.85641979882534783223403715930946138e-02L, + -2.69824879726738568189929461383741323e-02L, + 2.54194698498808542954187110873675769e-02L, + -2.35083879708189059926183138130183215e-02L, + 2.04832358998165364349957325067131428e-02L, + -1.54489555488544397858507248612362957e-02L, + 8.64492360989278761493037861575248038e-03L, + -2.58521121597609872727919154569765469e-03L, +}; + +const long double pi_lo = 8.67181013012378102479704402604335225e-35L; diff --git a/openlibm/ld128/invtrig.h b/openlibm/ld128/invtrig.h new file mode 100644 index 0000000..c85a615 --- /dev/null +++ b/openlibm/ld128/invtrig.h @@ -0,0 +1,113 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/ld128/invtrig.h,v 1.1 2008/07/31 22:41:26 das Exp $ + */ + +#include + +#include "fpmath.h" + +#define BIAS (LDBL_MAX_EXP - 1) +#define MANH_SIZE (LDBL_MANH_SIZE + 1) + +/* Approximation thresholds. */ +#define ASIN_LINEAR (BIAS - 56) /* 2**-56 */ +#define ACOS_CONST (BIAS - 113) /* 2**-113 */ +#define ATAN_CONST (BIAS + 113) /* 2**113 */ +#define ATAN_LINEAR (BIAS - 56) /* 2**-56 */ + +/* 0.95 */ +#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT) + +/* Constants shared by the long double inverse trig functions. */ +#define pS0 _ItL_pS0 +#define pS1 _ItL_pS1 +#define pS2 _ItL_pS2 +#define pS3 _ItL_pS3 +#define pS4 _ItL_pS4 +#define pS5 _ItL_pS5 +#define pS6 _ItL_pS6 +#define pS7 _ItL_pS7 +#define pS8 _ItL_pS8 +#define pS9 _ItL_pS9 +#define qS1 _ItL_qS1 +#define qS2 _ItL_qS2 +#define qS3 _ItL_qS3 +#define qS4 _ItL_qS4 +#define qS5 _ItL_qS5 +#define qS6 _ItL_qS6 +#define qS7 _ItL_qS7 +#define qS8 _ItL_qS8 +#define qS9 _ItL_qS9 +#define atanhi _ItL_atanhi +#define atanlo _ItL_atanlo +#define aT _ItL_aT +#define pi_lo _ItL_pi_lo + +#define pio2_hi atanhi[3] +#define pio2_lo atanlo[3] +#define pio4_hi atanhi[1] + +/* Constants shared by the long double inverse trig functions. */ +extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9; +extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9; +extern const long double atanhi[], atanlo[], aT[]; +extern const long double pi_lo; + +static inline long double +P(long double x) +{ + + return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ + (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \ + pS9)))))))))); +} + +static inline long double +Q(long double x) +{ + + return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \ + (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9))))))))); +} + +static inline long double +T_even(long double x) +{ + + return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ + (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \ + (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22]))))))))))); +} + +static inline long double +T_odd(long double x) +{ + + return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \ + (aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \ + (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23]))))))))))); +} diff --git a/openlibm/ld128/k_cosl.c b/openlibm/ld128/k_cosl.c new file mode 100644 index 0000000..37666dc --- /dev/null +++ b/openlibm/ld128/k_cosl.c @@ -0,0 +1,61 @@ +/* From: @(#)k_cos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld128/k_cosl.c,v 1.1 2008/02/17 07:32:31 das Exp $"); + +/* + * ld128 version of k_cos.c. See ../src/k_cos.c for most comments. + */ + +#include "math_private.h" + +/* + * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]: + * |cos(x) - c(x))| < 2**-122.0 + * + * 113-bit precision requires more care than 64-bit precision, since + * simple methods give a minimax polynomial with coefficient for x^2 + * that is 1 ulp below 0.5, but we want it to be precisely 0.5. See + * ../ld80/k_cosl.c for more details. + */ +static const double +one = 1.0; + +static const long double +C1 = 0.04166666666666666666666666666666658424671L, +C2 = -0.001388888888888888888888888888863490893732L, +C3 = 0.00002480158730158730158730158600795304914210L, +C4 = -0.2755731922398589065255474947078934284324e-6L, +C5 = 0.2087675698786809897659225313136400793948e-8L, +C6 = -0.1147074559772972315817149986812031204775e-10L, +C7 = 0.4779477332386808976875457937252120293400e-13L; + +static const double +C8 = -0.1561920696721507929516718307820958119868e-15, +C9 = 0.4110317413744594971475941557607804508039e-18, +C10 = -0.8896592467191938803288521958313920156409e-21, +C11 = 0.1601061435794535138244346256065192782581e-23; + +long double +__kernel_cosl(long double x, long double y) +{ + long double hz,z,r,w; + + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ + z*(C8+z*(C9+z*(C10+z*C11)))))))))); + hz = 0.5*z; + w = one-hz; + return w + (((one-w)-hz) + (z*r-x*y)); +} diff --git a/openlibm/ld128/k_sinl.c b/openlibm/ld128/k_sinl.c new file mode 100644 index 0000000..1079159 --- /dev/null +++ b/openlibm/ld128/k_sinl.c @@ -0,0 +1,59 @@ +/* From: @(#)k_sin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld128/k_sinl.c,v 1.1 2008/02/17 07:32:31 das Exp $"); + +/* + * ld128 version of k_sin.c. See ../src/k_sin.c for most comments. + */ + +#include "math_private.h" + +static const double +half = 0.5; + +/* + * Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37] + * |sin(x)/x - s(x)| < 2**-122.1 + * + * See ../ld80/k_cosl.c for more details about the polynomial. + */ +static const long double +S1 = -0.16666666666666666666666666666666666606732416116558L, +S2 = 0.0083333333333333333333333333333331135404851288270047L, +S3 = -0.00019841269841269841269841269839935785325638310428717L, +S4 = 0.27557319223985890652557316053039946268333231205686e-5L, +S5 = -0.25052108385441718775048214826384312253862930064745e-7L, +S6 = 0.16059043836821614596571832194524392581082444805729e-9L, +S7 = -0.76471637318198151807063387954939213287488216303768e-12L, +S8 = 0.28114572543451292625024967174638477283187397621303e-14L; + +static const double +S9 = -0.82206352458348947812512122163446202498005154296863e-17, +S10 = 0.19572940011906109418080609928334380560135358385256e-19, +S11 = -0.38680813379701966970673724299207480965452616911420e-22, +S12 = 0.64038150078671872796678569586315881020659912139412e-25; + +long double +__kernel_sinl(long double x, long double y, int iy) +{ + long double z,r,v; + + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+ + z*(S9+z*(S10+z*(S11+z*S12))))))))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/openlibm/ld128/k_tanl.c b/openlibm/ld128/k_tanl.c new file mode 100644 index 0000000..7255076 --- /dev/null +++ b/openlibm/ld128/k_tanl.c @@ -0,0 +1,120 @@ +/* From: @(#)k_tan.c 1.5 04/04/22 SMI */ + +/* + * ==================================================== + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld128/k_tanl.c,v 1.1 2008/02/17 07:32:31 das Exp $"); + +/* + * ld128 version of k_tan.c. See ../src/k_tan.c for most comments. + */ + +#include + +#include "math_private.h" + +/* + * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37] + * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37) + * + * See ../ld80/k_cosl.c for more details about the polynomial. + */ +static const long double +T3 = 0x1.5555555555555555555555555553p-2L, +T5 = 0x1.1111111111111111111111111eb5p-3L, +T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L, +T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L, +T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L, +T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L, +T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L, +T17 = 0x1.355824803674477dfcf726649efep-11L, +T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L, +T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L, +T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L, +T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L, +T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L, +T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L, +T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L, +T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L, +T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L, +T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L, +pio4 = 0x1.921fb54442d18469898cc51701b8p-1L, +pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L; + +static const double +T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */ +T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */ +T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */ +T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */ +T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */ +T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */ +T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */ +T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */ +T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */ +T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */ + +long double +__kernel_tanl(long double x, long double y, int iy) { + long double z, r, v, w, s; + long double osign; + int i; + + iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ + osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ + if (fabsl(x) >= 0.67434) { + if (x < 0) { + x = -x; + y = -y; + } + z = pio4 - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + i = 1; + } else + i = 0; + z = x * x; + w = z * z; + r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + + w * (T25 + w * (T29 + w * (T33 + + w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 + + w * T57)))))))))))); + v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + + w * (T27 + w * (T31 + w * (T35 + + w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * T55)))))))))))); + s = z * x; + r = y + z * (s * (r + v) + y); + r += T3 * s; + w = x + r; + if (i == 1) { + v = (long double) iy; + return osign * + (v - 2.0 * (x - (w * w / (w + v) - r))); + } + if (iy == 1) + return w; + else { + /* + * if allow error up to 2 ulp, simply return + * -1.0 / (x+r) here + */ + /* compute -1.0 / (x+r) accurately */ + long double a, t; + z = w; + z = z + 0x1p32 - 0x1p32; + v = r - (z - x); /* z+v = r+x */ + t = a = -1.0 / w; /* a = -1.0/w */ + t = t + 0x1p32 - 0x1p32; + s = 1.0 + t * z; + return t + a * (s + t * v); + } +} diff --git a/openlibm/ld128/s_asinhl.c b/openlibm/ld128/s_asinhl.c new file mode 100644 index 0000000..29791e8 --- /dev/null +++ b/openlibm/ld128/s_asinhl.c @@ -0,0 +1,69 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* asinhl(x) + * Method : + * Based on + * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] + * we have + * asinhl(x) := x if 1+x*x=1, + * := signl(x)*(logl(x)+ln2)) for large |x|, else + * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else + * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) + */ + +#include + +#include "math_private.h" + +static const long double + one = 1.0L, + ln2 = 6.931471805599453094172321214581765681e-1L, + huge = 1.0e+4900L; + +long double +asinhl(long double x) +{ + long double t, w; + int32_t ix, sign; + ieee_quad_shape_type u; + + u.value = x; + sign = u.parts32.mswhi; + ix = sign & 0x7fffffff; + if (ix == 0x7fff0000) + return x + x; /* x is inf or NaN */ + if (ix < 0x3fc70000) + { /* |x| < 2^ -56 */ + if (huge + x > one) + return x; /* return x inexact except 0 */ + } + u.parts32.mswhi = ix; + if (ix > 0x40350000) + { /* |x| > 2 ^ 54 */ + w = logl (u.value) + ln2; + } + else if (ix >0x40000000) + { /* 2^ 54 > |x| > 2.0 */ + t = u.value; + w = logl (2.0 * t + one / (sqrtl (x * x + one) + t)); + } + else + { /* 2.0 > |x| > 2 ^ -56 */ + t = x * x; + w = log1pl (u.value + t / (one + sqrtl (one + t))); + } + if (sign & 0x80000000) + return -w; + else + return w; +} diff --git a/openlibm/ld128/s_ceill.c b/openlibm/ld128/s_ceill.c new file mode 100644 index 0000000..719e7fc --- /dev/null +++ b/openlibm/ld128/s_ceill.c @@ -0,0 +1,69 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * ceill(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include + +#include "math_private.h" + +static const long double huge = 1.0e4930L; + +long double +ceill(long double x) +{ + int64_t i0,i1,jj0; + u_int64_t i,j; + GET_LDOUBLE_WORDS64(i0,i1,x); + jj0 = ((i0>>48)&0x7fff)-0x3fff; + if(jj0<48) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x8000000000000000ULL;i1=0;} + else if((i0|i1)!=0) { i0=0x3fff000000000000ULL;i1=0;} + } + } else { + i = (0x0000ffffffffffffULL)>>jj0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x0001000000000000LL)>>jj0; + i0 &= (~i); i1=0; + } + } + } else if (jj0>111) { + if(jj0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = -1ULL>>(jj0-48); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) { + if(jj0==48) i0+=1; + else { + j = i1+(1LL<<(112-jj0)); + if(j + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. erf(x) = x + x*R(x^2) for |x| in [0, 7/8] + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. + * + * 1a. erf(x) = 1 - erfc(x), for |x| > 1.0 + * erfc(x) = 1 - erf(x) if |x| < 1/4 + * + * 2. For |x| in [7/8, 1], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(s + c) = sign(x) * (c + P1(s)/Q1(s)) + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * + * 3. For x in [1/4, 5/4], + * erfc(s + const) = erfc(const) + s P1(s)/Q1(s) + * for const = 1/4, 3/8, ..., 9/8 + * and 0 <= s <= 1/8 . + * + * 4. For x in [5/4, 107], + * erfc(x) = (1/x)*exp(-x*x-0.5625 + R(z)) + * z=1/x^2 + * The interval is partitioned into several segments + * of width 1/8 in 1/x. + * + * Note1: + * To compute exp(-x*x-0.5625+R/S), let s be a single + * precision number and s := x; then + * -x*x = -s*s + (s-x)*(s+x) + * exp(-x*x-0.5626+R/S) = + * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); + * Note2: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) + * x*sqrt(pi) + * + * 5. For inf > x >= 107 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + +#include + +#include "math_private.h" + +/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +neval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ + +static long double +deval (long double x, const long double *p, int n) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + + +static const long double +tiny = 1e-4931L, + one = 1.0L, + two = 2.0L, + /* 2/sqrt(pi) - 1 */ + efx = 1.2837916709551257389615890312154517168810E-1L, + /* 8 * (2/sqrt(pi) - 1) */ + efx8 = 1.0270333367641005911692712249723613735048E0L; + + +/* erf(x) = x + x R(x^2) + 0 <= x <= 7/8 + Peak relative error 1.8e-35 */ +#define NTN1 8 +static const long double TN1[NTN1 + 1] = +{ + -3.858252324254637124543172907442106422373E10L, + 9.580319248590464682316366876952214879858E10L, + 1.302170519734879977595901236693040544854E10L, + 2.922956950426397417800321486727032845006E9L, + 1.764317520783319397868923218385468729799E8L, + 1.573436014601118630105796794840834145120E7L, + 4.028077380105721388745632295157816229289E5L, + 1.644056806467289066852135096352853491530E4L, + 3.390868480059991640235675479463287886081E1L +}; +#define NTD1 8 +static const long double TD1[NTD1 + 1] = +{ + -3.005357030696532927149885530689529032152E11L, + -1.342602283126282827411658673839982164042E11L, + -2.777153893355340961288511024443668743399E10L, + -3.483826391033531996955620074072768276974E9L, + -2.906321047071299585682722511260895227921E8L, + -1.653347985722154162439387878512427542691E7L, + -6.245520581562848778466500301865173123136E5L, + -1.402124304177498828590239373389110545142E4L, + -1.209368072473510674493129989468348633579E2L +/* 1.0E0 */ +}; + + +/* erf(z+1) = erf_const + P(z)/Q(z) + -.125 <= z <= 0 + Peak relative error 7.3e-36 */ +static const long double erf_const = 0.845062911510467529296875L; +#define NTN2 8 +static const long double TN2[NTN2 + 1] = +{ + -4.088889697077485301010486931817357000235E1L, + 7.157046430681808553842307502826960051036E3L, + -2.191561912574409865550015485451373731780E3L, + 2.180174916555316874988981177654057337219E3L, + 2.848578658049670668231333682379720943455E2L, + 1.630362490952512836762810462174798925274E2L, + 6.317712353961866974143739396865293596895E0L, + 2.450441034183492434655586496522857578066E1L, + 5.127662277706787664956025545897050896203E-1L +}; +#define NTD2 8 +static const long double TD2[NTD2 + 1] = +{ + 1.731026445926834008273768924015161048885E4L, + 1.209682239007990370796112604286048173750E4L, + 1.160950290217993641320602282462976163857E4L, + 5.394294645127126577825507169061355698157E3L, + 2.791239340533632669442158497532521776093E3L, + 8.989365571337319032943005387378993827684E2L, + 2.974016493766349409725385710897298069677E2L, + 6.148192754590376378740261072533527271947E1L, + 1.178502892490738445655468927408440847480E1L + /* 1.0E0 */ +}; + + +/* erfc(x + 0.25) = erfc(0.25) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.4e-35 */ +#define NRNr13 8 +static const long double RNr13[NRNr13 + 1] = +{ + -2.353707097641280550282633036456457014829E3L, + 3.871159656228743599994116143079870279866E2L, + -3.888105134258266192210485617504098426679E2L, + -2.129998539120061668038806696199343094971E1L, + -8.125462263594034672468446317145384108734E1L, + 8.151549093983505810118308635926270319660E0L, + -5.033362032729207310462422357772568553670E0L, + -4.253956621135136090295893547735851168471E-2L, + -8.098602878463854789780108161581050357814E-2L +}; +#define NRDr13 7 +static const long double RDr13[NRDr13 + 1] = +{ + 2.220448796306693503549505450626652881752E3L, + 1.899133258779578688791041599040951431383E2L, + 1.061906712284961110196427571557149268454E3L, + 7.497086072306967965180978101974566760042E1L, + 2.146796115662672795876463568170441327274E2L, + 1.120156008362573736664338015952284925592E1L, + 2.211014952075052616409845051695042741074E1L, + 6.469655675326150785692908453094054988938E-1L + /* 1.0E0 */ +}; +/* erfc(0.25) = C13a + C13b to extra precision. */ +static const long double C13a = 0.723663330078125L; +static const long double C13b = 1.0279753638067014931732235184287934646022E-5L; + + +/* erfc(x + 0.375) = erfc(0.375) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.2e-35 */ +#define NRNr14 8 +static const long double RNr14[NRNr14 + 1] = +{ + -2.446164016404426277577283038988918202456E3L, + 6.718753324496563913392217011618096698140E2L, + -4.581631138049836157425391886957389240794E2L, + -2.382844088987092233033215402335026078208E1L, + -7.119237852400600507927038680970936336458E1L, + 1.313609646108420136332418282286454287146E1L, + -6.188608702082264389155862490056401365834E0L, + -2.787116601106678287277373011101132659279E-2L, + -2.230395570574153963203348263549700967918E-2L +}; +#define NRDr14 7 +static const long double RDr14[NRDr14 + 1] = +{ + 2.495187439241869732696223349840963702875E3L, + 2.503549449872925580011284635695738412162E2L, + 1.159033560988895481698051531263861842461E3L, + 9.493751466542304491261487998684383688622E1L, + 2.276214929562354328261422263078480321204E2L, + 1.367697521219069280358984081407807931847E1L, + 2.276988395995528495055594829206582732682E1L, + 7.647745753648996559837591812375456641163E-1L + /* 1.0E0 */ +}; +/* erfc(0.375) = C14a + C14b to extra precision. */ +static const long double C14a = 0.5958709716796875L; +static const long double C14b = 1.2118885490201676174914080878232469565953E-5L; + +/* erfc(x + 0.5) = erfc(0.5) + x R(x) + 0 <= x < 0.125 + Peak relative error 4.7e-36 */ +#define NRNr15 8 +static const long double RNr15[NRNr15 + 1] = +{ + -2.624212418011181487924855581955853461925E3L, + 8.473828904647825181073831556439301342756E2L, + -5.286207458628380765099405359607331669027E2L, + -3.895781234155315729088407259045269652318E1L, + -6.200857908065163618041240848728398496256E1L, + 1.469324610346924001393137895116129204737E1L, + -6.961356525370658572800674953305625578903E0L, + 5.145724386641163809595512876629030548495E-3L, + 1.990253655948179713415957791776180406812E-2L +}; +#define NRDr15 7 +static const long double RDr15[NRDr15 + 1] = +{ + 2.986190760847974943034021764693341524962E3L, + 5.288262758961073066335410218650047725985E2L, + 1.363649178071006978355113026427856008978E3L, + 1.921707975649915894241864988942255320833E2L, + 2.588651100651029023069013885900085533226E2L, + 2.628752920321455606558942309396855629459E1L, + 2.455649035885114308978333741080991380610E1L, + 1.378826653595128464383127836412100939126E0L + /* 1.0E0 */ +}; +/* erfc(0.5) = C15a + C15b to extra precision. */ +static const long double C15a = 0.4794921875L; +static const long double C15b = 7.9346869534623172533461080354712635484242E-6L; + +/* erfc(x + 0.625) = erfc(0.625) + x R(x) + 0 <= x < 0.125 + Peak relative error 5.1e-36 */ +#define NRNr16 8 +static const long double RNr16[NRNr16 + 1] = +{ + -2.347887943200680563784690094002722906820E3L, + 8.008590660692105004780722726421020136482E2L, + -5.257363310384119728760181252132311447963E2L, + -4.471737717857801230450290232600243795637E1L, + -4.849540386452573306708795324759300320304E1L, + 1.140885264677134679275986782978655952843E1L, + -6.731591085460269447926746876983786152300E0L, + 1.370831653033047440345050025876085121231E-1L, + 2.022958279982138755020825717073966576670E-2L, +}; +#define NRDr16 7 +static const long double RDr16[NRDr16 + 1] = +{ + 3.075166170024837215399323264868308087281E3L, + 8.730468942160798031608053127270430036627E2L, + 1.458472799166340479742581949088453244767E3L, + 3.230423687568019709453130785873540386217E2L, + 2.804009872719893612081109617983169474655E2L, + 4.465334221323222943418085830026979293091E1L, + 2.612723259683205928103787842214809134746E1L, + 2.341526751185244109722204018543276124997E0L, + /* 1.0E0 */ +}; +/* erfc(0.625) = C16a + C16b to extra precision. */ +static const long double C16a = 0.3767547607421875L; +static const long double C16b = 4.3570693945275513594941232097252997287766E-6L; + +/* erfc(x + 0.75) = erfc(0.75) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.7e-35 */ +#define NRNr17 8 +static const long double RNr17[NRNr17 + 1] = +{ + -1.767068734220277728233364375724380366826E3L, + 6.693746645665242832426891888805363898707E2L, + -4.746224241837275958126060307406616817753E2L, + -2.274160637728782675145666064841883803196E1L, + -3.541232266140939050094370552538987982637E1L, + 6.988950514747052676394491563585179503865E0L, + -5.807687216836540830881352383529281215100E0L, + 3.631915988567346438830283503729569443642E-1L, + -1.488945487149634820537348176770282391202E-2L +}; +#define NRDr17 7 +static const long double RDr17[NRDr17 + 1] = +{ + 2.748457523498150741964464942246913394647E3L, + 1.020213390713477686776037331757871252652E3L, + 1.388857635935432621972601695296561952738E3L, + 3.903363681143817750895999579637315491087E2L, + 2.784568344378139499217928969529219886578E2L, + 5.555800830216764702779238020065345401144E1L, + 2.646215470959050279430447295801291168941E1L, + 2.984905282103517497081766758550112011265E0L, + /* 1.0E0 */ +}; +/* erfc(0.75) = C17a + C17b to extra precision. */ +static const long double C17a = 0.2888336181640625L; +static const long double C17b = 1.0748182422368401062165408589222625794046E-5L; + + +/* erfc(x + 0.875) = erfc(0.875) + x R(x) + 0 <= x < 0.125 + Peak relative error 2.2e-35 */ +#define NRNr18 8 +static const long double RNr18[NRNr18 + 1] = +{ + -1.342044899087593397419622771847219619588E3L, + 6.127221294229172997509252330961641850598E2L, + -4.519821356522291185621206350470820610727E2L, + 1.223275177825128732497510264197915160235E1L, + -2.730789571382971355625020710543532867692E1L, + 4.045181204921538886880171727755445395862E0L, + -4.925146477876592723401384464691452700539E0L, + 5.933878036611279244654299924101068088582E-1L, + -5.557645435858916025452563379795159124753E-2L +}; +#define NRDr18 7 +static const long double RDr18[NRDr18 + 1] = +{ + 2.557518000661700588758505116291983092951E3L, + 1.070171433382888994954602511991940418588E3L, + 1.344842834423493081054489613250688918709E3L, + 4.161144478449381901208660598266288188426E2L, + 2.763670252219855198052378138756906980422E2L, + 5.998153487868943708236273854747564557632E1L, + 2.657695108438628847733050476209037025318E1L, + 3.252140524394421868923289114410336976512E0L, + /* 1.0E0 */ +}; +/* erfc(0.875) = C18a + C18b to extra precision. */ +static const long double C18a = 0.215911865234375L; +static const long double C18b = 1.3073705765341685464282101150637224028267E-5L; + +/* erfc(x + 1.0) = erfc(1.0) + x R(x) + 0 <= x < 0.125 + Peak relative error 1.6e-35 */ +#define NRNr19 8 +static const long double RNr19[NRNr19 + 1] = +{ + -1.139180936454157193495882956565663294826E3L, + 6.134903129086899737514712477207945973616E2L, + -4.628909024715329562325555164720732868263E2L, + 4.165702387210732352564932347500364010833E1L, + -2.286979913515229747204101330405771801610E1L, + 1.870695256449872743066783202326943667722E0L, + -4.177486601273105752879868187237000032364E0L, + 7.533980372789646140112424811291782526263E-1L, + -8.629945436917752003058064731308767664446E-2L +}; +#define NRDr19 7 +static const long double RDr19[NRDr19 + 1] = +{ + 2.744303447981132701432716278363418643778E3L, + 1.266396359526187065222528050591302171471E3L, + 1.466739461422073351497972255511919814273E3L, + 4.868710570759693955597496520298058147162E2L, + 2.993694301559756046478189634131722579643E2L, + 6.868976819510254139741559102693828237440E1L, + 2.801505816247677193480190483913753613630E1L, + 3.604439909194350263552750347742663954481E0L, + /* 1.0E0 */ +}; +/* erfc(1.0) = C19a + C19b to extra precision. */ +static const long double C19a = 0.15728759765625L; +static const long double C19b = 1.1609394035130658779364917390740703933002E-5L; + +/* erfc(x + 1.125) = erfc(1.125) + x R(x) + 0 <= x < 0.125 + Peak relative error 3.6e-36 */ +#define NRNr20 8 +static const long double RNr20[NRNr20 + 1] = +{ + -9.652706916457973956366721379612508047640E2L, + 5.577066396050932776683469951773643880634E2L, + -4.406335508848496713572223098693575485978E2L, + 5.202893466490242733570232680736966655434E1L, + -1.931311847665757913322495948705563937159E1L, + -9.364318268748287664267341457164918090611E-2L, + -3.306390351286352764891355375882586201069E0L, + 7.573806045289044647727613003096916516475E-1L, + -9.611744011489092894027478899545635991213E-2L +}; +#define NRDr20 7 +static const long double RDr20[NRDr20 + 1] = +{ + 3.032829629520142564106649167182428189014E3L, + 1.659648470721967719961167083684972196891E3L, + 1.703545128657284619402511356932569292535E3L, + 6.393465677731598872500200253155257708763E2L, + 3.489131397281030947405287112726059221934E2L, + 8.848641738570783406484348434387611713070E1L, + 3.132269062552392974833215844236160958502E1L, + 4.430131663290563523933419966185230513168E0L + /* 1.0E0 */ +}; +/* erfc(1.125) = C20a + C20b to extra precision. */ +static const long double C20a = 0.111602783203125L; +static const long double C20b = 8.9850951672359304215530728365232161564636E-6L; + +/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2)) + 7/8 <= 1/x < 1 + Peak relative error 1.4e-35 */ +#define NRNr8 9 +static const long double RNr8[NRNr8 + 1] = +{ + 3.587451489255356250759834295199296936784E1L, + 5.406249749087340431871378009874875889602E2L, + 2.931301290625250886238822286506381194157E3L, + 7.359254185241795584113047248898753470923E3L, + 9.201031849810636104112101947312492532314E3L, + 5.749697096193191467751650366613289284777E3L, + 1.710415234419860825710780802678697889231E3L, + 2.150753982543378580859546706243022719599E2L, + 8.740953582272147335100537849981160931197E0L, + 4.876422978828717219629814794707963640913E-2L +}; +#define NRDr8 8 +static const long double RDr8[NRDr8 + 1] = +{ + 6.358593134096908350929496535931630140282E1L, + 9.900253816552450073757174323424051765523E2L, + 5.642928777856801020545245437089490805186E3L, + 1.524195375199570868195152698617273739609E4L, + 2.113829644500006749947332935305800887345E4L, + 1.526438562626465706267943737310282977138E4L, + 5.561370922149241457131421914140039411782E3L, + 9.394035530179705051609070428036834496942E2L, + 6.147019596150394577984175188032707343615E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2)) + 0.75 <= 1/x <= 0.875 + Peak relative error 2.0e-36 */ +#define NRNr7 9 +static const long double RNr7[NRNr7 + 1] = +{ + 1.686222193385987690785945787708644476545E1L, + 1.178224543567604215602418571310612066594E3L, + 1.764550584290149466653899886088166091093E4L, + 1.073758321890334822002849369898232811561E5L, + 3.132840749205943137619839114451290324371E5L, + 4.607864939974100224615527007793867585915E5L, + 3.389781820105852303125270837910972384510E5L, + 1.174042187110565202875011358512564753399E5L, + 1.660013606011167144046604892622504338313E4L, + 6.700393957480661937695573729183733234400E2L +}; +#define NRDr7 9 +static const long double RDr7[NRDr7 + 1] = +{ +-1.709305024718358874701575813642933561169E3L, +-3.280033887481333199580464617020514788369E4L, +-2.345284228022521885093072363418750835214E5L, +-8.086758123097763971926711729242327554917E5L, +-1.456900414510108718402423999575992450138E6L, +-1.391654264881255068392389037292702041855E6L, +-6.842360801869939983674527468509852583855E5L, +-1.597430214446573566179675395199807533371E5L, +-1.488876130609876681421645314851760773480E4L, +-3.511762950935060301403599443436465645703E2L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 5/8 <= 1/x < 3/4 + Peak relative error 1.9e-35 */ +#define NRNr6 9 +static const long double RNr6[NRNr6 + 1] = +{ + 1.642076876176834390623842732352935761108E0L, + 1.207150003611117689000664385596211076662E2L, + 2.119260779316389904742873816462800103939E3L, + 1.562942227734663441801452930916044224174E4L, + 5.656779189549710079988084081145693580479E4L, + 1.052166241021481691922831746350942786299E5L, + 9.949798524786000595621602790068349165758E4L, + 4.491790734080265043407035220188849562856E4L, + 8.377074098301530326270432059434791287601E3L, + 4.506934806567986810091824791963991057083E2L +}; +#define NRDr6 9 +static const long double RDr6[NRDr6 + 1] = +{ +-1.664557643928263091879301304019826629067E2L, +-3.800035902507656624590531122291160668452E3L, +-3.277028191591734928360050685359277076056E4L, +-1.381359471502885446400589109566587443987E5L, +-3.082204287382581873532528989283748656546E5L, +-3.691071488256738343008271448234631037095E5L, +-2.300482443038349815750714219117566715043E5L, +-6.873955300927636236692803579555752171530E4L, +-8.262158817978334142081581542749986845399E3L, +-2.517122254384430859629423488157361983661E2L + /* 1.00 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/2 <= 1/x < 5/8 + Peak relative error 4.6e-36 */ +#define NRNr5 10 +static const long double RNr5[NRNr5 + 1] = +{ +-3.332258927455285458355550878136506961608E-3L, +-2.697100758900280402659586595884478660721E-1L, +-6.083328551139621521416618424949137195536E0L, +-6.119863528983308012970821226810162441263E1L, +-3.176535282475593173248810678636522589861E2L, +-8.933395175080560925809992467187963260693E2L, +-1.360019508488475978060917477620199499560E3L, +-1.075075579828188621541398761300910213280E3L, +-4.017346561586014822824459436695197089916E2L, +-5.857581368145266249509589726077645791341E1L, +-2.077715925587834606379119585995758954399E0L +}; +#define NRDr5 9 +static const long double RDr5[NRDr5 + 1] = +{ + 3.377879570417399341550710467744693125385E-1L, + 1.021963322742390735430008860602594456187E1L, + 1.200847646592942095192766255154827011939E2L, + 7.118915528142927104078182863387116942836E2L, + 2.318159380062066469386544552429625026238E3L, + 4.238729853534009221025582008928765281620E3L, + 4.279114907284825886266493994833515580782E3L, + 2.257277186663261531053293222591851737504E3L, + 5.570475501285054293371908382916063822957E2L, + 5.142189243856288981145786492585432443560E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 3/8 <= 1/x < 1/2 + Peak relative error 2.0e-36 */ +#define NRNr4 10 +static const long double RNr4[NRNr4 + 1] = +{ + 3.258530712024527835089319075288494524465E-3L, + 2.987056016877277929720231688689431056567E-1L, + 8.738729089340199750734409156830371528862E0L, + 1.207211160148647782396337792426311125923E2L, + 8.997558632489032902250523945248208224445E2L, + 3.798025197699757225978410230530640879762E3L, + 9.113203668683080975637043118209210146846E3L, + 1.203285891339933238608683715194034900149E4L, + 8.100647057919140328536743641735339740855E3L, + 2.383888249907144945837976899822927411769E3L, + 2.127493573166454249221983582495245662319E2L +}; +#define NRDr4 10 +static const long double RDr4[NRDr4 + 1] = +{ +-3.303141981514540274165450687270180479586E-1L, +-1.353768629363605300707949368917687066724E1L, +-2.206127630303621521950193783894598987033E2L, +-1.861800338758066696514480386180875607204E3L, +-8.889048775872605708249140016201753255599E3L, +-2.465888106627948210478692168261494857089E4L, +-3.934642211710774494879042116768390014289E4L, +-3.455077258242252974937480623730228841003E4L, +-1.524083977439690284820586063729912653196E4L, +-2.810541887397984804237552337349093953857E3L, +-1.343929553541159933824901621702567066156E2L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/4 <= 1/x < 3/8 + Peak relative error 8.4e-37 */ +#define NRNr3 11 +static const long double RNr3[NRNr3 + 1] = +{ +-1.952401126551202208698629992497306292987E-6L, +-2.130881743066372952515162564941682716125E-4L, +-8.376493958090190943737529486107282224387E-3L, +-1.650592646560987700661598877522831234791E-1L, +-1.839290818933317338111364667708678163199E0L, +-1.216278715570882422410442318517814388470E1L, +-4.818759344462360427612133632533779091386E1L, +-1.120994661297476876804405329172164436784E2L, +-1.452850765662319264191141091859300126931E2L, +-9.485207851128957108648038238656777241333E1L, +-2.563663855025796641216191848818620020073E1L, +-1.787995944187565676837847610706317833247E0L +}; +#define NRDr3 10 +static const long double RDr3[NRDr3 + 1] = +{ + 1.979130686770349481460559711878399476903E-4L, + 1.156941716128488266238105813374635099057E-2L, + 2.752657634309886336431266395637285974292E-1L, + 3.482245457248318787349778336603569327521E0L, + 2.569347069372696358578399521203959253162E1L, + 1.142279000180457419740314694631879921561E2L, + 3.056503977190564294341422623108332700840E2L, + 4.780844020923794821656358157128719184422E2L, + 4.105972727212554277496256802312730410518E2L, + 1.724072188063746970865027817017067646246E2L, + 2.815939183464818198705278118326590370435E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/8 <= 1/x < 1/4 + Peak relative error 1.5e-36 */ +#define NRNr2 11 +static const long double RNr2[NRNr2 + 1] = +{ +-2.638914383420287212401687401284326363787E-8L, +-3.479198370260633977258201271399116766619E-6L, +-1.783985295335697686382487087502222519983E-4L, +-4.777876933122576014266349277217559356276E-3L, +-7.450634738987325004070761301045014986520E-2L, +-7.068318854874733315971973707247467326619E-1L, +-4.113919921935944795764071670806867038732E0L, +-1.440447573226906222417767283691888875082E1L, +-2.883484031530718428417168042141288943905E1L, +-2.990886974328476387277797361464279931446E1L, +-1.325283914915104866248279787536128997331E1L, +-1.572436106228070195510230310658206154374E0L +}; +#define NRDr2 10 +static const long double RDr2[NRDr2 + 1] = +{ + 2.675042728136731923554119302571867799673E-6L, + 2.170997868451812708585443282998329996268E-4L, + 7.249969752687540289422684951196241427445E-3L, + 1.302040375859768674620410563307838448508E-1L, + 1.380202483082910888897654537144485285549E0L, + 8.926594113174165352623847870299170069350E0L, + 3.521089584782616472372909095331572607185E1L, + 8.233547427533181375185259050330809105570E1L, + 1.072971579885803033079469639073292840135E2L, + 6.943803113337964469736022094105143158033E1L, + 1.775695341031607738233608307835017282662E1L + /* 1.0E0 */ +}; + +/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2)) + 1/128 <= 1/x < 1/8 + Peak relative error 2.2e-36 */ +#define NRNr1 9 +static const long double RNr1[NRNr1 + 1] = +{ +-4.250780883202361946697751475473042685782E-8L, +-5.375777053288612282487696975623206383019E-6L, +-2.573645949220896816208565944117382460452E-4L, +-6.199032928113542080263152610799113086319E-3L, +-8.262721198693404060380104048479916247786E-2L, +-6.242615227257324746371284637695778043982E-1L, +-2.609874739199595400225113299437099626386E0L, +-5.581967563336676737146358534602770006970E0L, +-5.124398923356022609707490956634280573882E0L, +-1.290865243944292370661544030414667556649E0L +}; +#define NRDr1 8 +static const long double RDr1[NRDr1 + 1] = +{ + 4.308976661749509034845251315983612976224E-6L, + 3.265390126432780184125233455960049294580E-4L, + 9.811328839187040701901866531796570418691E-3L, + 1.511222515036021033410078631914783519649E-1L, + 1.289264341917429958858379585970225092274E0L, + 6.147640356182230769548007536914983522270E0L, + 1.573966871337739784518246317003956180750E1L, + 1.955534123435095067199574045529218238263E1L, + 9.472613121363135472247929109615785855865E0L + /* 1.0E0 */ +}; + + +long double +erfl(long double x) +{ + long double a, y, z; + int32_t i, ix, sign; + ieee_quad_shape_type u; + + u.value = x; + sign = u.parts32.mswhi; + ix = sign & 0x7fffffff; + + if (ix >= 0x7fff0000) + { /* erf(nan)=nan */ + i = ((sign & 0xffff0000) >> 31) << 1; + return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + } + + if (ix >= 0x3fff0000) /* |x| >= 1.0 */ + { + y = erfcl (x); + return (one - y); + /* return (one - erfcl (x)); */ + } + u.parts32.mswhi = ix; + a = u.value; + z = x * x; + if (ix < 0x3ffec000) /* a < 0.875 */ + { + if (ix < 0x3fc60000) /* |x|<2**-57 */ + { + if (ix < 0x00080000) + return 0.125 * (8.0 * x + efx8 * x); /*avoid underflow */ + return x + efx * x; + } + y = a + a * neval (z, TN1, NTN1) / deval (z, TD1, NTD1); + } + else + { + a = a - one; + y = erf_const + neval (a, TN2, NTN2) / deval (a, TD2, NTD2); + } + + if (sign & 0x80000000) /* x < 0 */ + y = -y; + return( y ); +} + +long double +erfcl(long double x) +{ + long double y, z, p, r; + int32_t i, ix, sign; + ieee_quad_shape_type u; + + u.value = x; + sign = u.parts32.mswhi; + ix = sign & 0x7fffffff; + u.parts32.mswhi = ix; + + if (ix >= 0x7fff0000) + { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (long double) (((u_int32_t) sign >> 31) << 1) + one / x; + } + + if (ix < 0x3ffd0000) /* |x| <1/4 */ + { + if (ix < 0x3f8d0000) /* |x|<2**-114 */ + return one - x; + return one - erfl (x); + } + if (ix < 0x3fff4000) /* 1.25 */ + { + x = u.value; + i = 8.0 * x; + switch (i) + { + case 2: + z = x - 0.25L; + y = C13b + z * neval (z, RNr13, NRNr13) / deval (z, RDr13, NRDr13); + y += C13a; + break; + case 3: + z = x - 0.375L; + y = C14b + z * neval (z, RNr14, NRNr14) / deval (z, RDr14, NRDr14); + y += C14a; + break; + case 4: + z = x - 0.5L; + y = C15b + z * neval (z, RNr15, NRNr15) / deval (z, RDr15, NRDr15); + y += C15a; + break; + case 5: + z = x - 0.625L; + y = C16b + z * neval (z, RNr16, NRNr16) / deval (z, RDr16, NRDr16); + y += C16a; + break; + case 6: + z = x - 0.75L; + y = C17b + z * neval (z, RNr17, NRNr17) / deval (z, RDr17, NRDr17); + y += C17a; + break; + case 7: + z = x - 0.875L; + y = C18b + z * neval (z, RNr18, NRNr18) / deval (z, RDr18, NRDr18); + y += C18a; + break; + case 8: + z = x - 1.0L; + y = C19b + z * neval (z, RNr19, NRNr19) / deval (z, RDr19, NRDr19); + y += C19a; + break; + case 9: + z = x - 1.125L; + y = C20b + z * neval (z, RNr20, NRNr20) / deval (z, RDr20, NRDr20); + y += C20a; + break; + } + if (sign & 0x80000000) + y = 2.0L - y; + return y; + } + /* 1.25 < |x| < 107 */ + if (ix < 0x4005ac00) + { + /* x < -9 */ + if ((ix >= 0x40022000) && (sign & 0x80000000)) + return two - tiny; + + x = fabsl (x); + z = one / (x * x); + i = 8.0 / x; + switch (i) + { + default: + case 0: + p = neval (z, RNr1, NRNr1) / deval (z, RDr1, NRDr1); + break; + case 1: + p = neval (z, RNr2, NRNr2) / deval (z, RDr2, NRDr2); + break; + case 2: + p = neval (z, RNr3, NRNr3) / deval (z, RDr3, NRDr3); + break; + case 3: + p = neval (z, RNr4, NRNr4) / deval (z, RDr4, NRDr4); + break; + case 4: + p = neval (z, RNr5, NRNr5) / deval (z, RDr5, NRDr5); + break; + case 5: + p = neval (z, RNr6, NRNr6) / deval (z, RDr6, NRDr6); + break; + case 6: + p = neval (z, RNr7, NRNr7) / deval (z, RDr7, NRDr7); + break; + case 7: + p = neval (z, RNr8, NRNr8) / deval (z, RDr8, NRDr8); + break; + } + u.value = x; + u.parts32.lswlo = 0; + u.parts32.lswhi &= 0xfe000000; + z = u.value; + r = expl (-z * z - 0.5625) * + expl ((z - x) * (z + x) + p); + if ((sign & 0x80000000) == 0) + return r / x; + else + return two - r / x; + } + else + { + if ((sign & 0x80000000) == 0) + return tiny * tiny; + else + return two - tiny; + } +} diff --git a/openlibm/ld128/s_exp2l.c b/openlibm/ld128/s_exp2l.c new file mode 100644 index 0000000..c5f997f --- /dev/null +++ b/openlibm/ld128/s_exp2l.c @@ -0,0 +1,431 @@ +/*- + * Copyright (c) 2005-2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld128/s_exp2l.c,v 1.3 2008/02/13 10:44:44 bde Exp $"); + +#include +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#define TBLBITS 7 +#define TBLSIZE (1 << TBLBITS) + +#define BIAS (LDBL_MAX_EXP - 1) +#define EXPMASK (BIAS + LDBL_MAX_EXP) + +#if 0 /* XXX Prevent gcc from erroneously constant folding this. */ +static const long double twom10000 = 0x1p-10000L; +#else +static volatile long double twom10000 = 0x1p-10000L; +#endif + +static const long double + huge = 0x1p10000L, + P1 = 0x1.62e42fefa39ef35793c7673007e6p-1L, + P2 = 0x1.ebfbdff82c58ea86f16b06ec9736p-3L, + P3 = 0x1.c6b08d704a0bf8b33a762bad3459p-5L, + P4 = 0x1.3b2ab6fba4e7729ccbbe0b4f3fc2p-7L, + P5 = 0x1.5d87fe78a67311071dee13fd11d9p-10L, + P6 = 0x1.430912f86c7876f4b663b23c5fe5p-13L; + +static const double + P7 = 0x1.ffcbfc588b041p-17, + P8 = 0x1.62c0223a5c7c7p-20, + P9 = 0x1.b52541ff59713p-24, + P10 = 0x1.e4cf56a391e22p-28, + redux = 0x1.8p112 / TBLSIZE; + +static const long double tbl[TBLSIZE] = { + 0x1.6a09e667f3bcc908b2fb1366dfeap-1L, + 0x1.6c012750bdabeed76a99800f4edep-1L, + 0x1.6dfb23c651a2ef220e2cbe1bc0d4p-1L, + 0x1.6ff7df9519483cf87e1b4f3e1e98p-1L, + 0x1.71f75e8ec5f73dd2370f2ef0b148p-1L, + 0x1.73f9a48a58173bd5c9a4e68ab074p-1L, + 0x1.75feb564267c8bf6e9aa33a489a8p-1L, + 0x1.780694fde5d3f619ae02808592a4p-1L, + 0x1.7a11473eb0186d7d51023f6ccb1ap-1L, + 0x1.7c1ed0130c1327c49334459378dep-1L, + 0x1.7e2f336cf4e62105d02ba1579756p-1L, + 0x1.80427543e1a11b60de67649a3842p-1L, + 0x1.82589994cce128acf88afab34928p-1L, + 0x1.8471a4623c7acce52f6b97c6444cp-1L, + 0x1.868d99b4492ec80e41d90ac2556ap-1L, + 0x1.88ac7d98a669966530bcdf2d4cc0p-1L, + 0x1.8ace5422aa0db5ba7c55a192c648p-1L, + 0x1.8cf3216b5448bef2aa1cd161c57ap-1L, + 0x1.8f1ae991577362b982745c72eddap-1L, + 0x1.9145b0b91ffc588a61b469f6b6a0p-1L, + 0x1.93737b0cdc5e4f4501c3f2540ae8p-1L, + 0x1.95a44cbc8520ee9b483695a0e7fep-1L, + 0x1.97d829fde4e4f8b9e920f91e8eb6p-1L, + 0x1.9a0f170ca07b9ba3109b8c467844p-1L, + 0x1.9c49182a3f0901c7c46b071f28dep-1L, + 0x1.9e86319e323231824ca78e64c462p-1L, + 0x1.a0c667b5de564b29ada8b8cabbacp-1L, + 0x1.a309bec4a2d3358c171f770db1f4p-1L, + 0x1.a5503b23e255c8b424491caf88ccp-1L, + 0x1.a799e1330b3586f2dfb2b158f31ep-1L, + 0x1.a9e6b5579fdbf43eb243bdff53a2p-1L, + 0x1.ac36bbfd3f379c0db966a3126988p-1L, + 0x1.ae89f995ad3ad5e8734d17731c80p-1L, + 0x1.b0e07298db66590842acdfc6fb4ep-1L, + 0x1.b33a2b84f15faf6bfd0e7bd941b0p-1L, + 0x1.b59728de559398e3881111648738p-1L, + 0x1.b7f76f2fb5e46eaa7b081ab53ff6p-1L, + 0x1.ba5b030a10649840cb3c6af5b74cp-1L, + 0x1.bcc1e904bc1d2247ba0f45b3d06cp-1L, + 0x1.bf2c25bd71e088408d7025190cd0p-1L, + 0x1.c199bdd85529c2220cb12a0916bap-1L, + 0x1.c40ab5fffd07a6d14df820f17deap-1L, + 0x1.c67f12e57d14b4a2137fd20f2a26p-1L, + 0x1.c8f6d9406e7b511acbc48805c3f6p-1L, + 0x1.cb720dcef90691503cbd1e949d0ap-1L, + 0x1.cdf0b555dc3f9c44f8958fac4f12p-1L, + 0x1.d072d4a07897b8d0f22f21a13792p-1L, + 0x1.d2f87080d89f18ade123989ea50ep-1L, + 0x1.d5818dcfba48725da05aeb66dff8p-1L, + 0x1.d80e316c98397bb84f9d048807a0p-1L, + 0x1.da9e603db3285708c01a5b6d480cp-1L, + 0x1.dd321f301b4604b695de3c0630c0p-1L, + 0x1.dfc97337b9b5eb968cac39ed284cp-1L, + 0x1.e264614f5a128a12761fa17adc74p-1L, + 0x1.e502ee78b3ff6273d130153992d0p-1L, + 0x1.e7a51fbc74c834b548b2832378a4p-1L, + 0x1.ea4afa2a490d9858f73a18f5dab4p-1L, + 0x1.ecf482d8e67f08db0312fb949d50p-1L, + 0x1.efa1bee615a27771fd21a92dabb6p-1L, + 0x1.f252b376bba974e8696fc3638f24p-1L, + 0x1.f50765b6e4540674f84b762861a6p-1L, + 0x1.f7bfdad9cbe138913b4bfe72bd78p-1L, + 0x1.fa7c1819e90d82e90a7e74b26360p-1L, + 0x1.fd3c22b8f71f10975ba4b32bd006p-1L, + 0x1.0000000000000000000000000000p+0L, + 0x1.0163da9fb33356d84a66ae336e98p+0L, + 0x1.02c9a3e778060ee6f7caca4f7a18p+0L, + 0x1.04315e86e7f84bd738f9a20da442p+0L, + 0x1.059b0d31585743ae7c548eb68c6ap+0L, + 0x1.0706b29ddf6ddc6dc403a9d87b1ep+0L, + 0x1.0874518759bc808c35f25d942856p+0L, + 0x1.09e3ecac6f3834521e060c584d5cp+0L, + 0x1.0b5586cf9890f6298b92b7184200p+0L, + 0x1.0cc922b7247f7407b705b893dbdep+0L, + 0x1.0e3ec32d3d1a2020742e4f8af794p+0L, + 0x1.0fb66affed31af232091dd8a169ep+0L, + 0x1.11301d0125b50a4ebbf1aed9321cp+0L, + 0x1.12abdc06c31cbfb92bad324d6f84p+0L, + 0x1.1429aaea92ddfb34101943b2588ep+0L, + 0x1.15a98c8a58e512480d573dd562aep+0L, + 0x1.172b83c7d517adcdf7c8c50eb162p+0L, + 0x1.18af9388c8de9bbbf70b9a3c269cp+0L, + 0x1.1a35beb6fcb753cb698f692d2038p+0L, + 0x1.1bbe084045cd39ab1e72b442810ep+0L, + 0x1.1d4873168b9aa7805b8028990be8p+0L, + 0x1.1ed5022fcd91cb8819ff61121fbep+0L, + 0x1.2063b88628cd63b8eeb0295093f6p+0L, + 0x1.21f49917ddc962552fd29294bc20p+0L, + 0x1.2387a6e75623866c1fadb1c159c0p+0L, + 0x1.251ce4fb2a63f3582ab7de9e9562p+0L, + 0x1.26b4565e27cdd257a673281d3068p+0L, + 0x1.284dfe1f5638096cf15cf03c9fa0p+0L, + 0x1.29e9df51fdee12c25d15f5a25022p+0L, + 0x1.2b87fd0dad98ffddea46538fca24p+0L, + 0x1.2d285a6e4030b40091d536d0733ep+0L, + 0x1.2ecafa93e2f5611ca0f45d5239a4p+0L, + 0x1.306fe0a31b7152de8d5a463063bep+0L, + 0x1.32170fc4cd8313539cf1c3009330p+0L, + 0x1.33c08b26416ff4c9c8610d96680ep+0L, + 0x1.356c55f929ff0c94623476373be4p+0L, + 0x1.371a7373aa9caa7145502f45452ap+0L, + 0x1.38cae6d05d86585a9cb0d9bed530p+0L, + 0x1.3a7db34e59ff6ea1bc9299e0a1fep+0L, + 0x1.3c32dc313a8e484001f228b58cf0p+0L, + 0x1.3dea64c12342235b41223e13d7eep+0L, + 0x1.3fa4504ac801ba0bf701aa417b9cp+0L, + 0x1.4160a21f72e29f84325b8f3dbacap+0L, + 0x1.431f5d950a896dc704439410b628p+0L, + 0x1.44e086061892d03136f409df0724p+0L, + 0x1.46a41ed1d005772512f459229f0ap+0L, + 0x1.486a2b5c13cd013c1a3b69062f26p+0L, + 0x1.4a32af0d7d3de672d8bcf46f99b4p+0L, + 0x1.4bfdad5362a271d4397afec42e36p+0L, + 0x1.4dcb299fddd0d63b36ef1a9e19dep+0L, + 0x1.4f9b2769d2ca6ad33d8b69aa0b8cp+0L, + 0x1.516daa2cf6641c112f52c84d6066p+0L, + 0x1.5342b569d4f81df0a83c49d86bf4p+0L, + 0x1.551a4ca5d920ec52ec620243540cp+0L, + 0x1.56f4736b527da66ecb004764e61ep+0L, + 0x1.58d12d497c7fd252bc2b7343d554p+0L, + 0x1.5ab07dd48542958c93015191e9a8p+0L, + 0x1.5c9268a5946b701c4b1b81697ed4p+0L, + 0x1.5e76f15ad21486e9be4c20399d12p+0L, + 0x1.605e1b976dc08b076f592a487066p+0L, + 0x1.6247eb03a5584b1f0fa06fd2d9eap+0L, + 0x1.6434634ccc31fc76f8714c4ee122p+0L, + 0x1.66238825522249127d9e29b92ea2p+0L, + 0x1.68155d44ca973081c57227b9f69ep+0L, +}; + +static const float eps[TBLSIZE] = { + -0x1.5c50p-101, + -0x1.5d00p-106, + 0x1.8e90p-102, + -0x1.5340p-103, + 0x1.1bd0p-102, + -0x1.4600p-105, + -0x1.7a40p-104, + 0x1.d590p-102, + -0x1.d590p-101, + 0x1.b100p-103, + -0x1.0d80p-105, + 0x1.6b00p-103, + -0x1.9f00p-105, + 0x1.c400p-103, + 0x1.e120p-103, + -0x1.c100p-104, + -0x1.9d20p-103, + 0x1.a800p-108, + 0x1.4c00p-106, + -0x1.9500p-106, + 0x1.6900p-105, + -0x1.29d0p-100, + 0x1.4c60p-103, + 0x1.13a0p-102, + -0x1.5b60p-103, + -0x1.1c40p-103, + 0x1.db80p-102, + 0x1.91a0p-102, + 0x1.dc00p-105, + 0x1.44c0p-104, + 0x1.9710p-102, + 0x1.8760p-103, + -0x1.a720p-103, + 0x1.ed20p-103, + -0x1.49c0p-102, + -0x1.e000p-111, + 0x1.86a0p-103, + 0x1.2b40p-103, + -0x1.b400p-108, + 0x1.1280p-99, + -0x1.02d8p-102, + -0x1.e3d0p-103, + -0x1.b080p-105, + -0x1.f100p-107, + -0x1.16c0p-105, + -0x1.1190p-103, + -0x1.a7d2p-100, + 0x1.3450p-103, + -0x1.67c0p-105, + 0x1.4b80p-104, + -0x1.c4e0p-103, + 0x1.6000p-108, + -0x1.3f60p-105, + 0x1.93f0p-104, + 0x1.5fe0p-105, + 0x1.6f80p-107, + -0x1.7600p-106, + 0x1.21e0p-106, + -0x1.3a40p-106, + -0x1.40c0p-104, + -0x1.9860p-105, + -0x1.5d40p-108, + -0x1.1d70p-106, + 0x1.2760p-105, + 0x0.0000p+0, + 0x1.21e2p-104, + -0x1.9520p-108, + -0x1.5720p-106, + -0x1.4810p-106, + -0x1.be00p-109, + 0x1.0080p-105, + -0x1.5780p-108, + -0x1.d460p-105, + -0x1.6140p-105, + 0x1.4630p-104, + 0x1.ad50p-103, + 0x1.82e0p-105, + 0x1.1d3cp-101, + 0x1.6100p-107, + 0x1.ec30p-104, + 0x1.f200p-108, + 0x1.0b40p-103, + 0x1.3660p-102, + 0x1.d9d0p-103, + -0x1.02d0p-102, + 0x1.b070p-103, + 0x1.b9c0p-104, + -0x1.01c0p-103, + -0x1.dfe0p-103, + 0x1.1b60p-104, + -0x1.ae94p-101, + -0x1.3340p-104, + 0x1.b3d8p-102, + -0x1.6e40p-105, + -0x1.3670p-103, + 0x1.c140p-104, + 0x1.1840p-101, + 0x1.1ab0p-102, + -0x1.a400p-104, + 0x1.1f00p-104, + -0x1.7180p-103, + 0x1.4ce0p-102, + 0x1.9200p-107, + -0x1.54c0p-103, + 0x1.1b80p-105, + -0x1.1828p-101, + 0x1.5720p-102, + -0x1.a060p-100, + 0x1.9160p-102, + 0x1.a280p-104, + 0x1.3400p-107, + 0x1.2b20p-102, + 0x1.7800p-108, + 0x1.cfd0p-101, + 0x1.2ef0p-102, + -0x1.2760p-99, + 0x1.b380p-104, + 0x1.0048p-101, + -0x1.60b0p-102, + 0x1.a1ccp-100, + -0x1.a640p-104, + -0x1.08a0p-101, + 0x1.7e60p-102, + 0x1.22c0p-103, + -0x1.7200p-106, + 0x1.f0f0p-102, + 0x1.eb4ep-99, + 0x1.c6e0p-103, +}; + +/* + * exp2l(x): compute the base 2 exponential of x + * + * Accuracy: Peak error < 0.502 ulp. + * + * Method: (accurate tables) + * + * Reduce x: + * x = 2**k + y, for integer k and |y| <= 1/2. + * Thus we have exp2(x) = 2**k * exp2(y). + * + * Reduce y: + * y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE. + * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]), + * with |z - eps[i]| <= 2**-8 + 2**-98 for the table used. + * + * We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via + * a degree-10 minimax polynomial with maximum error under 2**-120. + * The values in exp2t[] and eps[] are chosen such that + * exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such + * that exp2t[i] is accurate to 2**-122. + * + * Note that the range of i is +-TBLSIZE/2, so we actually index the tables + * by i0 = i + TBLSIZE/2. + * + * This method is due to Gal, with many details due to Gal and Bachelis: + * + * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library + * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). + */ +OLM_DLLEXPORT long double +exp2l(long double x) +{ + union IEEEl2bits u, v; + long double r, t, twopk, twopkp10000, z; + uint32_t hx, ix, i0; + int k; + + u.e = x; + + /* Filter out exceptional cases. */ + hx = u.xbits.expsign; + ix = hx & EXPMASK; + if (ix >= BIAS + 14) { /* |x| >= 16384 */ + if (ix == BIAS + LDBL_MAX_EXP) { + if (u.xbits.manh != 0 + || u.xbits.manl != 0 + || (hx & 0x8000) == 0) + return (x + x); /* x is NaN or +Inf */ + else + return (0.0); /* x is -Inf */ + } + if (x >= 16384) + return (huge * huge); /* overflow */ + if (x <= -16495) + return (twom10000 * twom10000); /* underflow */ + } else if (ix <= BIAS - 115) { /* |x| < 0x1p-115 */ + return (1.0 + x); + } + + /* + * Reduce x, computing z, i0, and k. The low bits of x + redux + * contain the 16-bit integer part of the exponent (k) followed by + * TBLBITS fractional bits (i0). We use bit tricks to extract these + * as integers, then set z to the remainder. + * + * Example: Suppose x is 0xabc.123456p0 and TBLBITS is 8. + * Then the low-order word of x + redux is 0x000abc12, + * We split this into k = 0xabc and i0 = 0x12 (adjusted to + * index into the table), then we compute z = 0x0.003456p0. + * + * XXX If the exponent is negative, the computation of k depends on + * '>>' doing sign extension. + */ + u.e = x + redux; + i0 = (u.bits.manl & 0xffffffff) + TBLSIZE / 2; + k = (int)i0 >> TBLBITS; + i0 = i0 & (TBLSIZE - 1); + u.e -= redux; + z = x - u.e; + v.xbits.manh = 0; + v.xbits.manl = 0; + if (k >= LDBL_MIN_EXP) { + v.xbits.expsign = LDBL_MAX_EXP - 1 + k; + twopk = v.e; + } else { + v.xbits.expsign = LDBL_MAX_EXP - 1 + k + 10000; + twopkp10000 = v.e; + } + + /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ + t = tbl[i0]; /* exp2t[i0] */ + z -= eps[i0]; /* eps[i0] */ + r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * (P5 + z * (P6 + + z * (P7 + z * (P8 + z * (P9 + z * P10))))))))); + + /* Scale by 2**k. */ + if(k >= LDBL_MIN_EXP) { + if (k == LDBL_MAX_EXP) + return (r * 2.0 * 0x1p16383L); + return (r * twopk); + } else { + return (r * twopkp10000 * twom10000); + } +} diff --git a/openlibm/ld128/s_expm1l.c b/openlibm/ld128/s_expm1l.c new file mode 100644 index 0000000..1c22696 --- /dev/null +++ b/openlibm/ld128/s_expm1l.c @@ -0,0 +1,162 @@ +/* $OpenBSD: s_expm1l.c,v 1.1 2011/07/06 00:02:42 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* expm1l.c + * + * Exponential function, minus 1 + * 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, expm1l(); + * + * y = expm1l( x ); + * + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) raised to the x power, minus one. + * + * Range reduction is accomplished by separating the argument + * into an integer k and fraction f such that + * + * x k f + * e = 2 e. + * + * An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1 + * in the basic range [-0.5 ln 2, 0.5 ln 2]. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -79,+MAXLOG 100,000 1.7e-34 4.5e-35 + * + */ + +#include +#include + +#include "math_private.h" + +/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x) + -.5 ln 2 < x < .5 ln 2 + Theoretical peak relative error = 8.1e-36 */ + +static const long double + P0 = 2.943520915569954073888921213330863757240E8L, + P1 = -5.722847283900608941516165725053359168840E7L, + P2 = 8.944630806357575461578107295909719817253E6L, + P3 = -7.212432713558031519943281748462837065308E5L, + P4 = 4.578962475841642634225390068461943438441E4L, + P5 = -1.716772506388927649032068540558788106762E3L, + P6 = 4.401308817383362136048032038528753151144E1L, + P7 = -4.888737542888633647784737721812546636240E-1L, + Q0 = 1.766112549341972444333352727998584753865E9L, + Q1 = -7.848989743695296475743081255027098295771E8L, + Q2 = 1.615869009634292424463780387327037251069E8L, + Q3 = -2.019684072836541751428967854947019415698E7L, + Q4 = 1.682912729190313538934190635536631941751E6L, + Q5 = -9.615511549171441430850103489315371768998E4L, + Q6 = 3.697714952261803935521187272204485251835E3L, + Q7 = -8.802340681794263968892934703309274564037E1L, + /* Q8 = 1.000000000000000000000000000000000000000E0 */ +/* C1 + C2 = ln 2 */ + + C1 = 6.93145751953125E-1L, + C2 = 1.428606820309417232121458176568075500134E-6L, +/* ln (2^16384 * (1 - 2^-113)) */ + maxlog = 1.1356523406294143949491931077970764891253E4L, +/* ln 2^-114 */ + minarg = -7.9018778583833765273564461846232128760607E1L, big = 1e4932L; + + +long double +expm1l(long double x) +{ + long double px, qx, xx; + int32_t ix, sign; + ieee_quad_shape_type u; + int k; + + /* Detect infinity and NaN. */ + u.value = x; + ix = u.parts32.mswhi; + sign = ix & 0x80000000; + ix &= 0x7fffffff; + if (ix >= 0x7fff0000) + { + /* Infinity. */ + if (((ix & 0xffff) | u.parts32.mswlo | u.parts32.lswhi | + u.parts32.lswlo) == 0) + { + if (sign) + return -1.0L; + else + return x; + } + /* NaN. No invalid exception. */ + return x; + } + + /* expm1(+- 0) = +- 0. */ + if ((ix == 0) && (u.parts32.mswlo | u.parts32.lswhi | u.parts32.lswlo) == 0) + return x; + + /* Overflow. */ + if (x > maxlog) + return (big * big); + + /* Minimum value. */ + if (x < minarg) + return (4.0/big - 1.0L); + + /* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */ + xx = C1 + C2; /* ln 2. */ + px = floorl (0.5 + x / xx); + k = px; + /* remainder times ln 2 */ + x -= px * C1; + x -= px * C2; + + /* Approximate exp(remainder ln 2). */ + px = (((((((P7 * x + + P6) * x + + P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x; + + qx = (((((((x + + Q7) * x + + Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0; + + xx = x * x; + qx = x + (0.5 * xx + xx * px / qx); + + /* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2). + + We have qx = exp(remainder ln 2) - 1, so + exp(x) - 1 = 2^k (qx + 1) - 1 + = 2^k qx + 2^k - 1. */ + + px = ldexpl (1.0L, k); + x = px * qx + (px - 1.0); + return x; +} diff --git a/openlibm/ld128/s_floorl.c b/openlibm/ld128/s_floorl.c new file mode 100644 index 0000000..f00dcfa --- /dev/null +++ b/openlibm/ld128/s_floorl.c @@ -0,0 +1,71 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * floorl(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include + +#include "math_private.h" + +static const long double huge = 1.0e4930L; + +long double +floorl(long double x) +{ + int64_t i0,i1,jj0; + u_int64_t i,j; + GET_LDOUBLE_WORDS64(i0,i1,x); + jj0 = ((i0>>48)&0x7fff)-0x3fff; + if(jj0<48) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) { + if(i0>=0) + return 0.0L; + else if(((i0&0x7fffffffffffffffLL)|i1)!=0) + return -1.0L; + } + } else { + i = (0x0000ffffffffffffULL)>>jj0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x0001000000000000LL)>>jj0; + i0 &= (~i); i1=0; + } + } + } else if (jj0>111) { + if(jj0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = -1ULL>>(jj0-48); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) { + if(jj0==48) i0+=1; + else { + j = i1+(1LL<<(112-jj0)); + if(j + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* log1pl.c + * + * Relative error logarithm + * Natural logarithm of 1+x, 128-bit long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log1pl(); + * + * y = log1pl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of 1+x. + * + * The argument 1+x is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(w-1)/(w+1), + * + * log(w) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -1, 8 100000 1.9e-34 4.3e-35 + */ + +#include + +#include "math_private.h" + +/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) + * 1/sqrt(2) <= 1+x < sqrt(2) + * Theoretical peak relative error = 5.3e-37, + * relative peak error spread = 2.3e-14 + */ +static const long double + P12 = 1.538612243596254322971797716843006400388E-6L, + P11 = 4.998469661968096229986658302195402690910E-1L, + P10 = 2.321125933898420063925789532045674660756E1L, + P9 = 4.114517881637811823002128927449878962058E2L, + P8 = 3.824952356185897735160588078446136783779E3L, + P7 = 2.128857716871515081352991964243375186031E4L, + P6 = 7.594356839258970405033155585486712125861E4L, + P5 = 1.797628303815655343403735250238293741397E5L, + P4 = 2.854829159639697837788887080758954924001E5L, + P3 = 3.007007295140399532324943111654767187848E5L, + P2 = 2.014652742082537582487669938141683759923E5L, + P1 = 7.771154681358524243729929227226708890930E4L, + P0 = 1.313572404063446165910279910527789794488E4L, + /* Q12 = 1.000000000000000000000000000000000000000E0L, */ + Q11 = 4.839208193348159620282142911143429644326E1L, + Q10 = 9.104928120962988414618126155557301584078E2L, + Q9 = 9.147150349299596453976674231612674085381E3L, + Q8 = 5.605842085972455027590989944010492125825E4L, + Q7 = 2.248234257620569139969141618556349415120E5L, + Q6 = 6.132189329546557743179177159925690841200E5L, + Q5 = 1.158019977462989115839826904108208787040E6L, + Q4 = 1.514882452993549494932585972882995548426E6L, + Q3 = 1.347518538384329112529391120390701166528E6L, + Q2 = 7.777690340007566932935753241556479363645E5L, + Q1 = 2.626900195321832660448791748036714883242E5L, + Q0 = 3.940717212190338497730839731583397586124E4L; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 1.1e-35, + * relative peak error spread 1.1e-9 + */ +static const long double + R5 = -8.828896441624934385266096344596648080902E-1L, + R4 = 8.057002716646055371965756206836056074715E1L, + R3 = -2.024301798136027039250415126250455056397E3L, + R2 = 2.048819892795278657810231591630928516206E4L, + R1 = -8.977257995689735303686582344659576526998E4L, + R0 = 1.418134209872192732479751274970992665513E5L, + /* S6 = 1.000000000000000000000000000000000000000E0L, */ + S5 = -1.186359407982897997337150403816839480438E2L, + S4 = 3.998526750980007367835804959888064681098E3L, + S3 = -5.748542087379434595104154610899551484314E4L, + S2 = 4.001557694070773974936904547424676279307E5L, + S1 = -1.332535117259762928288745111081235577029E6L, + S0 = 1.701761051846631278975701529965589676574E6L; + +/* C1 + C2 = ln 2 */ +static const long double C1 = 6.93145751953125E-1L; +static const long double C2 = 1.428606820309417232121458176568075500134E-6L; + +static const long double sqrth = 0.7071067811865475244008443621048490392848L; +/* ln (2^16384 * (1 - 2^-113)) */ +static const long double zero = 0.0L; + +long double +log1pl(long double xm1) +{ + long double x, y, z, r, s; + ieee_quad_shape_type u; + int32_t hx; + int e; + + /* Test for NaN or infinity input. */ + u.value = xm1; + hx = u.parts32.mswhi; + if (hx >= 0x7fff0000) + return xm1; + + /* log1p(+- 0) = +- 0. */ + if (((hx & 0x7fffffff) == 0) + && (u.parts32.mswlo | u.parts32.lswhi | u.parts32.lswlo) == 0) + return xm1; + + x = xm1 + 1.0L; + + /* log1p(-1) = -inf */ + if (x <= 0.0L) + { + if (x == 0.0L) + return (-1.0L / (x - x)); + else + return (zero / (x - x)); + } + + /* Separate mantissa from exponent. */ + + /* Use frexp used so that denormal numbers will be handled properly. */ + x = frexpl (x, &e); + + /* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2), + where z = 2(x-1)/x+1). */ + if ((e > 2) || (e < -2)) + { + if (x < sqrth) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } + else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } + x = z / y; + z = x * x; + r = ((((R5 * z + + R4) * z + + R3) * z + + R2) * z + + R1) * z + + R0; + s = (((((z + + S5) * z + + S4) * z + + S3) * z + + S2) * z + + S1) * z + + S0; + z = x * (z * r / s); + z = z + e * C2; + z = z + x; + z = z + e * C1; + return (z); + } + + + /* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */ + + if (x < sqrth) + { + e -= 1; + if (e != 0) + x = 2.0L * x - 1.0L; /* 2x - 1 */ + else + x = xm1; + } + else + { + if (e != 0) + x = x - 1.0L; + else + x = xm1; + } + z = x * x; + r = (((((((((((P12 * x + + P11) * x + + P10) * x + + P9) * x + + P8) * x + + P7) * x + + P6) * x + + P5) * x + + P4) * x + + P3) * x + + P2) * x + + P1) * x + + P0; + s = (((((((((((x + + Q11) * x + + Q10) * x + + Q9) * x + + Q8) * x + + Q7) * x + + Q6) * x + + Q5) * x + + Q4) * x + + Q3) * x + + Q2) * x + + Q1) * x + + Q0; + y = x * (z * r / s); + y = y + e * C2; + z = y - 0.5L * z; + z = z + x; + z = z + e * C1; + return (z); +} diff --git a/openlibm/ld128/s_modfl.c b/openlibm/ld128/s_modfl.c new file mode 100644 index 0000000..bd18cba --- /dev/null +++ b/openlibm/ld128/s_modfl.c @@ -0,0 +1,73 @@ +/* @(#)s_modf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * modfl(long double x, long double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0; + +long double +modfl(long double x, long double *iptr) +{ + int64_t i0,i1,jj0; + u_int64_t i; + GET_LDOUBLE_WORDS64(i0,i1,x); + jj0 = ((i0>>48)&0x7fff)-0x3fff; /* exponent of x */ + if(jj0<48) { /* integer part in high x */ + if(jj0<0) { /* |x|<1 */ + /* *iptr = +-0 */ + SET_LDOUBLE_WORDS64(*iptr,i0&0x8000000000000000ULL,0); + return x; + } else { + i = (0x0000ffffffffffffLL)>>jj0; + if(((i0&i)|i1)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0); + return x; + } else { + SET_LDOUBLE_WORDS64(*iptr,i0&(~i),0); + return x - *iptr; + } + } + } else if (jj0>111) { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (jj0 == 0x4000 && ((i0 & 0x0000ffffffffffffLL) | i1)) + return x*one; + /* return +-0 */ + SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0); + return x; + } else { /* fraction part in low x */ + i = -1ULL>>(jj0-48); + if((i1&i)==0) { /* x is integral */ + *iptr = x; + /* return +-0 */ + SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0); + return x; + } else { + SET_LDOUBLE_WORDS64(*iptr,i0,i1&(~i)); + return x - *iptr; + } + } +} diff --git a/openlibm/ld128/s_nanl.c b/openlibm/ld128/s_nanl.c new file mode 100644 index 0000000..4dcdb4e --- /dev/null +++ b/openlibm/ld128/s_nanl.c @@ -0,0 +1,46 @@ +/*- + * Copyright (c) 2007 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/ld128/s_nanl.c,v 1.3 2008/03/02 20:16:55 das Exp $ + */ + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT long double +nanl(const char *s) +{ + union { + union IEEEl2bits ieee; + uint32_t bits[4]; + } u; + + __scan_nan(u.bits, 4, s); + u.ieee.bits.exp = 0x7fff; + u.ieee.bits.manh |= 1ULL << 47; /* make it a quiet NaN */ + return (u.ieee.e); +} diff --git a/openlibm/ld128/s_nextafterl.c b/openlibm/ld128/s_nextafterl.c new file mode 100644 index 0000000..af667a0 --- /dev/null +++ b/openlibm/ld128/s_nextafterl.c @@ -0,0 +1,72 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* IEEE functions + * nextafterl(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include + +#include "math_private.h" + +long double +nextafterl(long double x, long double y) +{ + int64_t hx,hy,ix,iy; + u_int64_t lx,ly; + + GET_LDOUBLE_WORDS64(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + ix = hx&0x7fffffffffffffffLL; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if(((ix>=0x7fff000000000000LL)&&((ix-0x7fff000000000000LL)|lx)!=0) || /* x is nan */ + ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) /* y is nan */ + return x+y; + if(x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + volatile long double u; + SET_LDOUBLE_WORDS64(x,hy&0x8000000000000000ULL,1);/* return +-minsubnormal */ + u = x; + u = u * u; /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ + if(lx==0) hx--; + lx--; + } else { /* x < y, x += ulp */ + lx++; + if(lx==0) hx++; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */ + if(lx==0) hx--; + lx--; + } else { /* x > y, x += ulp */ + lx++; + if(lx==0) hx++; + } + } + hy = hx&0x7fff000000000000LL; + if(hy==0x7fff000000000000LL) return x+x;/* overflow */ + if(hy==0) { + volatile long double u = x*x; /* underflow */ + } + SET_LDOUBLE_WORDS64(x,hx,lx); + return x; +} + +__strong_alias(nexttowardl, nextafterl); diff --git a/openlibm/ld128/s_nexttoward.c b/openlibm/ld128/s_nexttoward.c new file mode 100644 index 0000000..a9ff797 --- /dev/null +++ b/openlibm/ld128/s_nexttoward.c @@ -0,0 +1,85 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* IEEE functions + * nexttoward(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include +#include + +#include "math_private.h" + +double +nexttoward(double x, long double y) +{ + int32_t hx,ix; + int64_t hy,iy; + u_int32_t lx; + u_int64_t ly; + + EXTRACT_WORDS(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) + /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + volatile double u; + INSERT_WORDS(x,(u_int32_t)((hy>>32)&0x80000000),1);/* return +-minsub */ + u = x; + u = u * u; /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if (hy<0||(ix>>20)>(iy>>48)-0x3c00 + || ((ix>>20)==(iy>>48)-0x3c00 + && (((((int64_t)hx)<<28)|(lx>>4))>(hy&0x0000ffffffffffffLL) + || (((((int64_t)hx)<<28)|(lx>>4))==(hy&0x0000ffffffffffffLL) + && (lx&0xf)>(ly>>60))))) { /* x > y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if (hy>=0||(ix>>20)>(iy>>48)-0x3c00 + || ((ix>>20)==(iy>>48)-0x3c00 + && (((((int64_t)hx)<<28)|(lx>>4))>(hy&0x0000ffffffffffffLL) + || (((((int64_t)hx)<<28)|(lx>>4))==(hy&0x0000ffffffffffffLL) + && (lx&0xf)>(ly>>60))))) { /* x < y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) { + x = x+x; /* overflow */ + return x; + } + if(hy<0x00100000) { + volatile double u = x*x; /* underflow */ + } + INSERT_WORDS(x,hx,lx); + return x; +} diff --git a/openlibm/ld128/s_nexttowardf.c b/openlibm/ld128/s_nexttowardf.c new file mode 100644 index 0000000..61387ac --- /dev/null +++ b/openlibm/ld128/s_nexttowardf.c @@ -0,0 +1,65 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include + +#include "math_private.h" + +float +nexttowardf(float x, long double y) +{ + int32_t hx,ix; + int64_t hy,iy; + u_int64_t ly; + + GET_FLOAT_WORD(hx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffffffffffffLL; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) + /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + volatile float u; + SET_FLOAT_WORD(x,(u_int32_t)((hy>>32)&0x80000000)|1);/* return +-minsub*/ + u = x; + u = u * u; /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(hy<0||(ix>>23)>(iy>>48)-0x3f80 + || ((ix>>23)==(iy>>48)-0x3f80 + && (ix&0x7fffff)>((hy>>25)&0x7fffff))) {/* x > y, x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||(ix>>23)>(iy>>48)-0x3f80 + || ((ix>>23)==(iy>>48)-0x3f80 + && (ix&0x7fffff)>((hy>>25)&0x7fffff))) {/* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) return x+x; /* overflow */ + if(hy<0x00800000) { + volatile float u = x*x; /* underflow */ + } + SET_FLOAT_WORD(x,hx); + return x; +} diff --git a/openlibm/ld128/s_remquol.c b/openlibm/ld128/s_remquol.c new file mode 100644 index 0000000..f56ce4f --- /dev/null +++ b/openlibm/ld128/s_remquol.c @@ -0,0 +1,168 @@ +/* @(#)e_fmod.c 1.3 95/01/18 */ +/*- + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#include + +#include +#include +#include + +#include "math_private.h" + +#define BIAS (LDBL_MAX_EXP - 1) + +/* + * These macros add and remove an explicit integer bit in front of the + * fractional mantissa, if the architecture doesn't have such a bit by + * default already. + */ +#ifdef LDBL_IMPLICIT_NBIT +#define LDBL_NBIT 0 +#define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) +#define HFRAC_BITS (EXT_FRACHBITS + EXT_FRACHMBITS) +#else +#define LDBL_NBIT 0x80000000 +#define SET_NBIT(hx) (hx) +#define HFRAC_BITS (EXT_FRACHBITS + EXT_FRACHMBITS - 1) +#endif + +#define MANL_SHIFT (EXT_FRACLMBITS + EXT_FRACLBITS - 1) + +static const long double Zero[] = {0.0L, -0.0L}; + +/* + * Return the IEEE remainder and set *quo to the last n bits of the + * quotient, rounded to the nearest integer. We choose n=31 because + * we wind up computing all the integer bits of the quotient anyway as + * a side-effect of computing the remainder by the shift and subtract + * method. In practice, this is far more bits than are needed to use + * remquo in reduction algorithms. + * + * Assumptions: + * - The low part of the mantissa fits in a manl_t exactly. + * - The high part of the mantissa fits in an int64_t with enough room + * for an explicit integer bit in front of the fractional bits. + */ +long double +remquol(long double x, long double y, int *quo) +{ + int64_t hx,hz,hy,_hx; + uint64_t lx,ly,lz; + uint64_t sx,sxy; + int ix,iy,n,q; + + GET_LDOUBLE_WORDS64(hx,lx,x); + GET_LDOUBLE_WORDS64(hy,ly,y); + sx = (hx>>48)&0x8000; + sxy = sx ^ ((hy>>48)&0x8000); + hx &= 0x7fffffffffffffffLL; /* |x| */ + hy &= 0x7fffffffffffffffLL; /* |y| */ + SET_LDOUBLE_WORDS64(x,hx,lx); + SET_LDOUBLE_WORDS64(y,hy,ly); + + /* purge off exception values */ + if((hy|ly)==0 || /* y=0 */ + ((hx>>48) == BIAS + LDBL_MAX_EXP) || /* or x not finite */ + ((hy>>48) == BIAS + LDBL_MAX_EXP && + (((hy&0x0000ffffffffffffLL)&~LDBL_NBIT)|ly)!=0)) /* or y is NaN */ + return (x*y)/(x*y); + if((hx>>48)<=(hy>>48)) { + if(((hx>>48)<(hy>>48)) || + ((hx&0x0000ffffffffffffLL)<=(hy&0x0000ffffffffffffLL) && + ((hx&0x0000ffffffffffffLL)<(hy&0x0000ffffffffffffLL) || + lx>48) == 0) { /* subnormal x */ + x *= 0x1.0p512; + GET_LDOUBLE_WORDS64(hx,lx,x); + ix = (hx>>48) - (BIAS + 512); + } else { + ix = (hx>>48) - BIAS; + } + + /* determine iy = ilogb(y) */ + if((hy>>48) == 0) { /* subnormal y */ + y *= 0x1.0p512; + GET_LDOUBLE_WORDS64(hy,ly,y); + iy = (hy>>48) - (BIAS + 512); + } else { + iy = (hy>>48) - BIAS; + } + + /* set up {hx,lx}, {hy,ly} and align y to x */ + _hx = SET_NBIT(hx) & 0x0000ffffffffffffLL; + hy = SET_NBIT(hy); + + /* fix point fmod */ + n = ix - iy; + q = 0; + + while(n--) { + hz=_hx-hy;lz=lx-ly; if(lx>MANL_SHIFT); lx = lx+lx;} + else {_hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;} + q <<= 1; + } + hz=_hx-hy;lz=lx-ly; if(lx=0) {_hx=hz;lx=lz;q++;} + + /* convert back to floating value and restore the sign */ + if((_hx|lx)==0) { /* return sign(x)*0 */ + *quo = (sxy ? -q : q); + return Zero[sx!=0]; + } + while(_hx<(1ULL<>MANL_SHIFT); lx = lx+lx; + iy -= 1; + } + hx = (hx&0xffff000000000000LL) | (_hx&0x0000ffffffffffffLL); + if (iy < LDBL_MIN_EXP) { + hx = (hx&0x0000ffffffffffffLL) | (uint64_t)(iy + BIAS + 512)<<48; + SET_LDOUBLE_WORDS64(x,hx,lx); + x *= 0x1p-512; + GET_LDOUBLE_WORDS64(hx,lx,x); + } else { + hx = (hx&0x0000ffffffffffffLL) | (uint64_t)(iy + BIAS)<<48; + } + hx &= 0x7fffffffffffffffLL; + SET_LDOUBLE_WORDS64(x,hx,lx); +fixup: + y = fabsl(y); + if (y < LDBL_MIN * 2) { + if (x+x>y || (x+x==y && (q & 1))) { + q++; + x-=y; + } + } else if (x>0.5*y || (x==0.5*y && (q & 1))) { + q++; + x-=y; + } + + GET_LDOUBLE_MSW64(hx,x); + hx ^= sx; + SET_LDOUBLE_MSW64(x,hx); + + q &= 0x7fffffff; + *quo = (sxy ? -q : q); + return x; +} diff --git a/openlibm/ld128/s_tanhl.c b/openlibm/ld128/s_tanhl.c new file mode 100644 index 0000000..f8e6291 --- /dev/null +++ b/openlibm/ld128/s_tanhl.c @@ -0,0 +1,105 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* tanhl(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanhl(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). + * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x) + * -t + * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) + * t + 2 + * 2 + * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) + * t + 2 + * 40.0 < x <= INF : tanhl(x) := 1. + * + * Special cases: + * tanhl(NaN) is NaN; + * only tanhl(0)=0 is exact for finite argument. + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0, two = 2.0, tiny = 1.0e-4900L; + +long double +tanhl(long double x) +{ + long double t, z; + u_int32_t jx, ix; + ieee_quad_shape_type u; + + /* Words of |x|. */ + u.value = x; + jx = u.parts32.mswhi; + ix = jx & 0x7fffffff; + /* x is INF or NaN */ + if (ix >= 0x7fff0000) + { + /* for NaN it's not important which branch: tanhl(NaN) = NaN */ + if (jx & 0x80000000) + return one / x - one; /* tanhl(-inf)= -1; */ + else + return one / x + one; /* tanhl(+inf)=+1 */ + } + + /* |x| < 40 */ + if (ix < 0x40044000) + { + if (u.value == 0) + return x; /* x == +- 0 */ + if (ix < 0x3fc60000) /* |x| < 2^-57 */ + return x * (one + tiny); /* tanh(small) = small */ + u.parts32.mswhi = ix; /* Absolute value of x. */ + if (ix >= 0x3fff0000) + { /* |x| >= 1 */ + t = expm1l (two * u.value); + z = one - two / (t + two); + } + else + { + t = expm1l (-two * u.value); + z = -t / (t + two); + } + /* |x| > 40, return +-1 */ + } + else + { + z = one - tiny; /* raised inexact flag */ + } + return (jx & 0x80000000) ? -z : z; +} diff --git a/openlibm/ld128/s_truncl.c b/openlibm/ld128/s_truncl.c new file mode 100644 index 0000000..a0d8bd5 --- /dev/null +++ b/openlibm/ld128/s_truncl.c @@ -0,0 +1,72 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * From: @(#)s_floor.c 5.1 93/09/24 + */ + +/* + * truncl(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to truncl(x). + */ + +#include +#include + +#include +#include +#include + +#include "math_private.h" + +#ifdef LDBL_IMPLICIT_NBIT +#define MANH_SIZE (EXT_FRACHBITS + EXT_FRACHMBITS + 1) +#else +#define MANH_SIZE (EXT_FRACHBITS + EXT_FRACHMBITS) +#endif + +static const long double huge = 1.0e300; +static const float zero[] = { 0.0, -0.0 }; + +long double +truncl(long double x) +{ + int e; + int64_t ix0, ix1; + + GET_LDOUBLE_WORDS64(ix0,ix1,x); + e = ((ix0>>48)&0x7fff) - LDBL_MAX_EXP + 1; + + if (e < MANH_SIZE - 1) { + if (e < 0) { /* raise inexact if x != 0 */ + if (huge + x > 0.0) + return (zero[((ix0>>48)&0x8000)!=0]); + } else { + uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1); + if (((ix0 & m) | ix1) == 0) + return (x); /* x is integral */ + if (huge + x > 0.0) { /* raise inexact flag */ + ix0 &= ~m; + ix1 = 0; + } + } + } else if (e < LDBL_MANT_DIG - 1) { + uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1); + if ((ix1 & m) == 0) + return (x); /* x is integral */ + if (huge + x > 0.0) /* raise inexact flag */ + ix1 &= ~m; + } + SET_LDOUBLE_WORDS64(x,ix0,ix1); + return (x); +} diff --git a/openlibm/ld80/Make.files b/openlibm/ld80/Make.files new file mode 100644 index 0000000..1198cfb --- /dev/null +++ b/openlibm/ld80/Make.files @@ -0,0 +1,13 @@ +$(CUR_SRCS) += invtrig.c \ + e_acoshl.c e_powl.c k_tanl.c s_exp2l.c \ + e_atanhl.c e_lgammal_r.c e_sinhl.c s_asinhl.c s_expm1l.c \ + e_coshl.c e_log10l.c e_tgammal.c \ + e_expl.c e_log2l.c k_cosl.c s_log1pl.c s_tanhl.c \ + e_logl.c k_sinl.c s_erfl.c + +# s_remquol.c e_fmodl.c s_truncl.c +# e_hypotl.c s_floorl.c s_nextafterl.c s_ceill.c s_modfl.c + +ifneq ($(OS), WINNT) +$(CUR_SRCS) += s_nanl.c +endif diff --git a/openlibm/ld80/e_acoshl.c b/openlibm/ld80/e_acoshl.c new file mode 100644 index 0000000..35758bb --- /dev/null +++ b/openlibm/ld80/e_acoshl.c @@ -0,0 +1,57 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* acoshl(x) + * Method : + * Based on + * acoshl(x) = logl [ x + sqrtl(x*x-1) ] + * we have + * acoshl(x) := logl(x)+ln2, if x is large; else + * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else + * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acoshl(x) is NaN with signal if x<1. + * acoshl(NaN) is NaN without signal. + */ + +#include + +#include "math_private.h" + +static const long double +one = 1.0, +ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ + +long double +acoshl(long double x) +{ + long double t; + u_int32_t se,i0,i1; + GET_LDOUBLE_WORDS(se,i0,i1,x); + if(se<0x3fff || se & 0x8000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(se >=0x401d) { /* x > 2**30 */ + if(se >=0x7fff) { /* x is inf of NaN */ + return x+x; + } else + return logl(x)+ln2; /* acoshl(huge)=logl(2x) */ + } else if(((se-0x3fff)|i0|i1)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (se > 0x4000) { /* 2**28 > x > 2 */ + t=x*x; + return logl(2.0*x-one/(x+sqrtl(t-one))); + } else { /* 1=0.5 + * 1 2x x + * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x)) + * + * Special cases: + * atanhl(x) is NaN if |x| > 1 with signal; + * atanhl(NaN) is that NaN with no signal; + * atanhl(+-1) is +-INF with signal. + * + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0, huge = 1e4900L; + +static const long double zero = 0.0; + +long double +atanhl(long double x) +{ + long double t; + int32_t ix; + u_int32_t se,i0,i1; + GET_LDOUBLE_WORDS(se,i0,i1,x); + ix = se&0x7fff; + if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31))>0x3fff) + /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3fff) + return x/zero; + if(ix<0x3fe3&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_LDOUBLE_EXP(x,ix); + if(ix<0x3ffe) { /* x < 0.5 */ + t = x+x; + t = 0.5*log1pl(t+t*x/(one-x)); + } else + t = 0.5*log1pl((x+x)/(one-x)); + if(se<=0x7fff) return t; else return -t; +} diff --git a/openlibm/ld80/e_coshl.c b/openlibm/ld80/e_coshl.c new file mode 100644 index 0000000..a0fb9b5 --- /dev/null +++ b/openlibm/ld80/e_coshl.c @@ -0,0 +1,83 @@ +/* @(#)e_cosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* coshl(x) + * Method : + * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (coshl(x) = coshl(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : coshl(x) := ------------------- + * 2 + * 22 <= x <= lnovft : coshl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : coshl(x) := huge*huge (overflow) + * + * Special cases: + * coshl(x) is |x| if x is +INF, -INF, or NaN. + * only coshl(0)=1 is exact for finite x. + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0, half=0.5, huge = 1.0e4900L; + +long double +coshl(long double x) +{ + long double t,w; + int32_t ex; + u_int32_t mx,lx; + + /* High word of |x|. */ + GET_LDOUBLE_WORDS(ex,mx,lx,x); + ex &= 0x7fff; + + /* x is INF or NaN */ + if(ex==0x7fff) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ + if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { + t = expm1l(fabsl(x)); + w = one+t; + if (ex<0x3fbc) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { + t = expl(fabsl(x)); + return half*t+half/t; + } + + /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ + if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) + return half*expl(fabsl(x)); + + /* |x| in [log(maxdouble), log(2*maxdouble)) */ + if (ex == 0x400c && (mx < 0xb174ddc0u + || (mx == 0xb174ddc0u && lx < 0x31aec0ebu))) + { + w = expl(half*fabsl(x)); + t = half*w; + return t*w; + } + + /* |x| >= log(2*maxdouble), cosh(x) overflow */ + return huge*huge; +} diff --git a/openlibm/ld80/e_expl.c b/openlibm/ld80/e_expl.c new file mode 100644 index 0000000..db0d1ca --- /dev/null +++ b/openlibm/ld80/e_expl.c @@ -0,0 +1,131 @@ +/* $OpenBSD: e_expl.c,v 1.3 2013/11/12 20:35:19 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* expl.c + * + * Exponential function, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, expl(); + * + * y = expl( x ); + * + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) raised to the x power. + * + * Range reduction is accomplished by separating the argument + * into an integer k and fraction f such that + * + * x k f + * e = 2 e. + * + * A Pade' form of degree 2/3 is used to approximate exp(f) - 1 + * in the basic range [-0.5 ln 2, 0.5 ln 2]. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE +-10000 50000 1.12e-19 2.81e-20 + * + * + * Error amplification in the exponential function can be + * a serious matter. The error propagation involves + * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ), + * which shows that a 1 lsb error in representing X produces + * a relative error of X times 1 lsb in the function. + * While the routine gives an accurate result for arguments + * that are exactly represented by a long double precision + * computer number, the result contains amplified roundoff + * error for large arguments not exactly represented. + * + * + * ERROR MESSAGES: + * + * message condition value returned + * exp underflow x < MINLOG 0.0 + * exp overflow x > MAXLOG MAXNUM + * + */ + +/* Exponential function */ + +#include + +#include "math_private.h" + +static long double P[3] = { + 1.2617719307481059087798E-4L, + 3.0299440770744196129956E-2L, + 9.9999999999999999991025E-1L, +}; +static long double Q[4] = { + 3.0019850513866445504159E-6L, + 2.5244834034968410419224E-3L, + 2.2726554820815502876593E-1L, + 2.0000000000000000000897E0L, +}; +static const long double C1 = 6.9314575195312500000000E-1L; +static const long double C2 = 1.4286068203094172321215E-6L; +static const long double MAXLOGL = 1.1356523406294143949492E4L; +static const long double MINLOGL = -1.13994985314888605586758E4L; +static const long double LOG2EL = 1.4426950408889634073599E0L; + +long double +expl(long double x) +{ +long double px, xx; +int n; + +if( isnan(x) ) + return(x); +if( x > MAXLOGL) + return( INFINITY ); + +if( x < MINLOGL ) + return(0.0L); + +/* Express e**x = e**g 2**n + * = e**g e**( n loge(2) ) + * = e**( g + n loge(2) ) + */ +px = floorl( LOG2EL * x + 0.5L ); /* floor() truncates toward -infinity. */ +n = px; +x -= px * C1; +x -= px * C2; + + +/* rational approximation for exponential + * of the fractional part: + * e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) ) + */ +xx = x * x; +px = x * __polevll( xx, P, 2 ); +x = px/( __polevll( xx, Q, 3 ) - px ); +x = 1.0L + ldexpl( x, 1 ); + +x = ldexpl( x, n ); +return(x); +} diff --git a/openlibm/ld80/e_fmodl.c b/openlibm/ld80/e_fmodl.c new file mode 100644 index 0000000..ec792e3 --- /dev/null +++ b/openlibm/ld80/e_fmodl.c @@ -0,0 +1,142 @@ +/* @(#)e_fmod.c 1.3 95/01/18 */ +/*- + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +//#include + +#include +#include +#include + +#include "math_private.h" + +#define BIAS (LDBL_MAX_EXP - 1) + +/* + * These macros add and remove an explicit integer bit in front of the + * fractional mantissa, if the architecture doesn't have such a bit by + * default already. + */ +#ifdef LDBL_IMPLICIT_NBIT +#define LDBL_NBIT 0 +#define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) +#define HFRAC_BITS EXT_FRACHBITS +#else +#define LDBL_NBIT 0x80000000 +#define SET_NBIT(hx) (hx) +#define HFRAC_BITS (EXT_FRACHBITS - 1) +#endif + +#define MANL_SHIFT (EXT_FRACLBITS - 1) + +static const long double one = 1.0, Zero[] = {0.0, -0.0,}; + +/* + * fmodl(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + * + * Assumptions: + * - The low part of the mantissa fits in a manl_t exactly. + * - The high part of the mantissa fits in an int64_t with enough room + * for an explicit integer bit in front of the fractional bits. + */ +long double +fmodl(long double x, long double y) +{ + union { + long double e; + struct ieee_ext bits; + } ux, uy; + int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ + uint32_t hy; + uint32_t lx,ly,lz; + int ix,iy,n,sx; + + ux.e = x; + uy.e = y; + sx = ux.bits.ext_sign; + + /* purge off exception values */ + if((uy.bits.ext_exp|uy.bits.ext_frach|uy.bits.ext_fracl)==0 || /* y=0 */ + (ux.bits.ext_exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ + (uy.bits.ext_exp == BIAS + LDBL_MAX_EXP && + ((uy.bits.ext_frach&~LDBL_NBIT)|uy.bits.ext_fracl)!=0)) /* or y is NaN */ + return (x*y)/(x*y); + if(ux.bits.ext_exp<=uy.bits.ext_exp) { + if((ux.bits.ext_exp>MANL_SHIFT); lx = lx+lx;} + else { + if ((hz|lz)==0) /* return sign(x)*0 */ + return Zero[sx]; + hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[sx]; + while(hx<(1ULL<>MANL_SHIFT); lx = lx+lx; + iy -= 1; + } + ux.bits.ext_frach = hx; /* The mantissa is truncated here if needed. */ + ux.bits.ext_fracl = lx; + if (iy < LDBL_MIN_EXP) { + ux.bits.ext_exp = iy + (BIAS + 512); + ux.e *= 0x1p-512; + } else { + ux.bits.ext_exp = iy + BIAS; + } + x = ux.e * one; /* create necessary signal */ + return x; /* exact output */ +} diff --git a/openlibm/ld80/e_hypotl.c b/openlibm/ld80/e_hypotl.c new file mode 100644 index 0000000..e6faa22 --- /dev/null +++ b/openlibm/ld80/e_hypotl.c @@ -0,0 +1,122 @@ +/* @(#)e_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* hypotl(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * yy1= y with lower 32 bits chopped, y2 = y-yy1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include + +#include "math_private.h" + +long double +hypotl(long double x, long double y) +{ + long double a,b,t1,t2,yy1,y2,w; + u_int32_t j,k,ea,eb; + + GET_LDOUBLE_EXP(ea,x); + ea &= 0x7fff; + GET_LDOUBLE_EXP(eb,y); + eb &= 0x7fff; + if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;} + SET_LDOUBLE_EXP(a,ea); /* a <- |a| */ + SET_LDOUBLE_EXP(b,eb); /* b <- |b| */ + if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */ + k=0; + if(ea > 0x5f3f) { /* a>2**8000 */ + if(ea == 0x7fff) { /* Inf or NaN */ + u_int32_t es,high,low; + w = a+b; /* for sNaN */ + GET_LDOUBLE_WORDS(es,high,low,a); + if(((high&0x7fffffff)|low)==0) w = a; + GET_LDOUBLE_WORDS(es,high,low,b); + if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-9600 */ + ea -= 0x2580; eb -= 0x2580; k += 9600; + SET_LDOUBLE_EXP(a,ea); + SET_LDOUBLE_EXP(b,eb); + } + if(eb < 0x20bf) { /* b < 2**-8000 */ + if(eb == 0) { /* subnormal b or 0 */ + u_int32_t es,high,low; + GET_LDOUBLE_WORDS(es,high,low,b); + if((high|low)==0) return a; + SET_LDOUBLE_WORDS(t1, 0x7ffd, 0, 0); /* t1=2^16382 */ + b *= t1; + a *= t1; + k -= 16382; + } else { /* scale a and b by 2^9600 */ + ea += 0x2580; /* a *= 2^9600 */ + eb += 0x2580; /* b *= 2^9600 */ + k -= 9600; + SET_LDOUBLE_EXP(a,ea); + SET_LDOUBLE_EXP(b,eb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + u_int32_t high; + GET_LDOUBLE_MSW(high,a); + SET_LDOUBLE_WORDS(t1,ea,high,0); + t2 = a-t1; + w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + u_int32_t high; + GET_LDOUBLE_MSW(high,b); + a = a+a; + SET_LDOUBLE_WORDS(yy1,eb,high,0); + y2 = b - yy1; + GET_LDOUBLE_MSW(high,a); + SET_LDOUBLE_WORDS(t1,ea+1,high,0); + t2 = a - t1; + w = sqrtl(t1*yy1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int32_t es; + t1 = 1.0; + GET_LDOUBLE_EXP(es,t1); + SET_LDOUBLE_EXP(t1,es+k); + return t1*w; + } else return w; +} diff --git a/openlibm/ld80/e_lgammal_r.c b/openlibm/ld80/e_lgammal_r.c new file mode 100644 index 0000000..0af5420 --- /dev/null +++ b/openlibm/ld80/e_lgammal_r.c @@ -0,0 +1,425 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* lgammal_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include + +#include "math_private.h" + +static const long double + half = 0.5L, + one = 1.0L, + pi = 3.14159265358979323846264L, + two63 = 9.223372036854775808e18L, + + /* lgam(1+x) = 0.5 x + x a(x)/b(x) + -0.268402099609375 <= x <= 0 + peak relative error 6.6e-22 */ + a0 = -6.343246574721079391729402781192128239938E2L, + a1 = 1.856560238672465796768677717168371401378E3L, + a2 = 2.404733102163746263689288466865843408429E3L, + a3 = 8.804188795790383497379532868917517596322E2L, + a4 = 1.135361354097447729740103745999661157426E2L, + a5 = 3.766956539107615557608581581190400021285E0L, + + b0 = 8.214973713960928795704317259806842490498E3L, + b1 = 1.026343508841367384879065363925870888012E4L, + b2 = 4.553337477045763320522762343132210919277E3L, + b3 = 8.506975785032585797446253359230031874803E2L, + b4 = 6.042447899703295436820744186992189445813E1L, + /* b5 = 1.000000000000000000000000000000000000000E0 */ + + + tc = 1.4616321449683623412626595423257213284682E0L, + tf = -1.2148629053584961146050602565082954242826E-1,/* double precision */ +/* tt = (tail of tf), i.e. tf + tt has extended precision. */ + tt = 3.3649914684731379602768989080467587736363E-18L, + /* lgam ( 1.4616321449683623412626595423257213284682E0 ) = +-1.2148629053584960809551455717769158215135617312999903886372437313313530E-1 */ + + /* lgam (x + tc) = tf + tt + x g(x)/h(x) + - 0.230003726999612341262659542325721328468 <= x + <= 0.2699962730003876587373404576742786715318 + peak relative error 2.1e-21 */ + g0 = 3.645529916721223331888305293534095553827E-18L, + g1 = 5.126654642791082497002594216163574795690E3L, + g2 = 8.828603575854624811911631336122070070327E3L, + g3 = 5.464186426932117031234820886525701595203E3L, + g4 = 1.455427403530884193180776558102868592293E3L, + g5 = 1.541735456969245924860307497029155838446E2L, + g6 = 4.335498275274822298341872707453445815118E0L, + + h0 = 1.059584930106085509696730443974495979641E4L, + h1 = 2.147921653490043010629481226937850618860E4L, + h2 = 1.643014770044524804175197151958100656728E4L, + h3 = 5.869021995186925517228323497501767586078E3L, + h4 = 9.764244777714344488787381271643502742293E2L, + h5 = 6.442485441570592541741092969581997002349E1L, + /* h6 = 1.000000000000000000000000000000000000000E0 */ + + + /* lgam (x+1) = -0.5 x + x u(x)/v(x) + -0.100006103515625 <= x <= 0.231639862060546875 + peak relative error 1.3e-21 */ + u0 = -8.886217500092090678492242071879342025627E1L, + u1 = 6.840109978129177639438792958320783599310E2L, + u2 = 2.042626104514127267855588786511809932433E3L, + u3 = 1.911723903442667422201651063009856064275E3L, + u4 = 7.447065275665887457628865263491667767695E2L, + u5 = 1.132256494121790736268471016493103952637E2L, + u6 = 4.484398885516614191003094714505960972894E0L, + + v0 = 1.150830924194461522996462401210374632929E3L, + v1 = 3.399692260848747447377972081399737098610E3L, + v2 = 3.786631705644460255229513563657226008015E3L, + v3 = 1.966450123004478374557778781564114347876E3L, + v4 = 4.741359068914069299837355438370682773122E2L, + v5 = 4.508989649747184050907206782117647852364E1L, + /* v6 = 1.000000000000000000000000000000000000000E0 */ + + + /* lgam (x+2) = .5 x + x s(x)/r(x) + 0 <= x <= 1 + peak relative error 7.2e-22 */ + s0 = 1.454726263410661942989109455292824853344E6L, + s1 = -3.901428390086348447890408306153378922752E6L, + s2 = -6.573568698209374121847873064292963089438E6L, + s3 = -3.319055881485044417245964508099095984643E6L, + s4 = -7.094891568758439227560184618114707107977E5L, + s5 = -6.263426646464505837422314539808112478303E4L, + s6 = -1.684926520999477529949915657519454051529E3L, + + r0 = -1.883978160734303518163008696712983134698E7L, + r1 = -2.815206082812062064902202753264922306830E7L, + r2 = -1.600245495251915899081846093343626358398E7L, + r3 = -4.310526301881305003489257052083370058799E6L, + r4 = -5.563807682263923279438235987186184968542E5L, + r5 = -3.027734654434169996032905158145259713083E4L, + r6 = -4.501995652861105629217250715790764371267E2L, + /* r6 = 1.000000000000000000000000000000000000000E0 */ + + +/* lgam(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x w(1/x^2) + x >= 8 + Peak relative error 1.51e-21 + w0 = LS2PI - 0.5 */ + w0 = 4.189385332046727417803e-1L, + w1 = 8.333333333333331447505E-2L, + w2 = -2.777777777750349603440E-3L, + w3 = 7.936507795855070755671E-4L, + w4 = -5.952345851765688514613E-4L, + w5 = 8.412723297322498080632E-4L, + w6 = -1.880801938119376907179E-3L, + w7 = 4.885026142432270781165E-3L; + +static const long double zero = 0.0L; + +static long double +sin_pi(long double x) +{ + long double y, z; + int n, ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + ix = (ix << 16) | (i0 >> 16); + if (ix < 0x3ffd8000) /* 0.25 */ + return sinl (pi * x); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floorl (y); + if (z != y) + { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - floorl(y)); /* y = |x| mod 2.0 */ + n = (int) (y*4.0); + } + else + { + if (ix >= 0x403f8000) /* 2^64 */ + { + y = zero; n = 0; /* y must be even */ + } + else + { + if (ix < 0x403e8000) /* 2^63 */ + z = y + two63; /* exact */ + GET_LDOUBLE_WORDS (se, i0, i1, z); + n = i1 & 1; + y = n; + n <<= 2; + } + } + + switch (n) + { + case 0: + y = sinl (pi * y); + break; + case 1: + case 2: + y = cosl (pi * (half - y)); + break; + case 3: + case 4: + y = sinl (pi * (one - y)); + break; + case 5: + case 6: + y = -cosl (pi * (y - 1.5)); + break; + default: + y = sinl (pi * (y - 2.0)); + break; + } + return -y; +} + + +long double +lgammal_r(long double x, int *signgamp) +{ + long double t, y, z, nadj, p, p1, p2, q, r, w; + int i, ix; + u_int32_t se, i0, i1; + + *signgamp = 1; + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + + if ((ix | i0 | i1) == 0) + { + if (se & 0x8000) + *signgamp = -1; + return one / fabsl (x); + } + + ix = (ix << 16) | (i0 >> 16); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + if (ix >= 0x7fff0000) + return x * x; + + if (ix < 0x3fc08000) /* 2^-63 */ + { /* |x|<2**-63, return -log(|x|) */ + if (se & 0x8000) + { + *signgamp = -1; + return -logl (-x); + } + else + return -logl (x); + } + if (se & 0x8000) + { + t = sin_pi (x); + if (t == zero) + return one / fabsl (t); /* -integer */ + nadj = logl (pi / fabsl (t * x)); + if (t < zero) + *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if ((((ix - 0x3fff8000) | i0 | i1) == 0) + || (((ix - 0x40008000) | i0 | i1) == 0)) + r = 0; + else if (ix < 0x40008000) /* 2.0 */ + { + /* x < 2.0 */ + if (ix <= 0x3ffee666) /* 8.99993896484375e-1 */ + { + /* lgamma(x) = lgamma(x+1) - log(x) */ + r = -logl (x); + if (ix >= 0x3ffebb4a) /* 7.31597900390625e-1 */ + { + y = x - one; + i = 0; + } + else if (ix >= 0x3ffced33)/* 2.31639862060546875e-1 */ + { + y = x - (tc - one); + i = 1; + } + else + { + /* x < 0.23 */ + y = x; + i = 2; + } + } + else + { + r = zero; + if (ix >= 0x3fffdda6) /* 1.73162841796875 */ + { + /* [1.7316,2] */ + y = x - 2.0; + i = 0; + } + else if (ix >= 0x3fff9da6)/* 1.23162841796875 */ + { + /* [1.23,1.73] */ + y = x - tc; + i = 1; + } + else + { + /* [0.9, 1.23] */ + y = x - one; + i = 2; + } + } + switch (i) + { + case 0: + p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5)))); + p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y)))); + r += half * y + y * p1/p2; + break; + case 1: + p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6))))); + p2 = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y))))); + p = tt + y * p1/p2; + r += (tf + p); + break; + case 2: + p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6)))))); + p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y))))); + r += (-half * y + p1 / p2); + } + } + else if (ix < 0x40028000) /* 8.0 */ + { + /* x < 8.0 */ + i = (int) x; + t = zero; + y = x - (double) i; + p = y * + (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6)))))); + q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y)))))); + r = half * y + p / q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch (i) + { + case 7: + z *= (y + 6.0); /* FALLTHRU */ + case 6: + z *= (y + 5.0); /* FALLTHRU */ + case 5: + z *= (y + 4.0); /* FALLTHRU */ + case 4: + z *= (y + 3.0); /* FALLTHRU */ + case 3: + z *= (y + 2.0); /* FALLTHRU */ + r += logl (z); + break; + } + } + else if (ix < 0x40418000) /* 2^66 */ + { + /* 8.0 <= x < 2**66 */ + t = logl (x); + z = one / x; + y = z * z; + w = w0 + z * (w1 + + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7)))))); + r = (x - half) * (t - one) + w; + } + else + /* 2**66 <= x <= inf */ + r = x * (logl (x) - one); + if (se & 0x8000) + r = nadj - r; + return r; +} diff --git a/openlibm/ld80/e_log10l.c b/openlibm/ld80/e_log10l.c new file mode 100644 index 0000000..bb6cd7d --- /dev/null +++ b/openlibm/ld80/e_log10l.c @@ -0,0 +1,205 @@ +/* $OpenBSD: e_log10l.c,v 1.2 2013/11/12 20:35:19 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* log10l.c + * + * Common logarithm, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log10l(); + * + * y = log10l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 10 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z**3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 30000 9.0e-20 2.6e-20 + * IEEE exp(+-10000) 30000 6.0e-20 2.3e-20 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + * ERROR MESSAGES: + * + * log singularity: x = 0; returns MINLOG + * log domain: x < 0; returns MINLOG + */ + +#include + +#include "math_private.h" + +/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 6.2e-22 + */ +static long double P[] = { + 4.9962495940332550844739E-1L, + 1.0767376367209449010438E1L, + 7.7671073698359539859595E1L, + 2.5620629828144409632571E2L, + 4.2401812743503691187826E2L, + 3.4258224542413922935104E2L, + 1.0747524399916215149070E2L, +}; +static long double Q[] = { +/* 1.0000000000000000000000E0,*/ + 2.3479774160285863271658E1L, + 1.9444210022760132894510E2L, + 7.7952888181207260646090E2L, + 1.6911722418503949084863E3L, + 2.0307734695595183428202E3L, + 1.2695660352705325274404E3L, + 3.2242573199748645407652E2L, +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 6.16e-22 + */ + +static long double R[4] = { + 1.9757429581415468984296E-3L, +-7.1990767473014147232598E-1L, + 1.0777257190312272158094E1L, +-3.5717684488096787370998E1L, +}; +static long double S[4] = { +/* 1.00000000000000000000E0L,*/ +-2.6201045551331104417768E1L, + 1.9361891836232102174846E2L, +-4.2861221385716144629696E2L, +}; +/* log10(2) */ +#define L102A 0.3125L +#define L102B -1.1470004336018804786261e-2L +/* log10(e) */ +#define L10EA 0.5L +#define L10EB -6.5705518096748172348871e-2L + +#define SQRTH 0.70710678118654752440L + +long double +log10l(long double x) +{ +long double y; +volatile long double z; +int e; + +if( isnan(x) ) + return(x); +/* Test for domain */ +if( x <= 0.0L ) + { + if( x == 0.0L ) + return (-1.0L / (x - x)); + else + return (x - x) / (x - x); + } +if( x == INFINITY ) + return(INFINITY); +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ +x = frexpl( x, &e ); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ +if( (e > 2) || (e < -2) ) +{ +if( x < SQRTH ) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } +else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } +x = z / y; +z = x*x; +y = x * ( z * __polevll( z, R, 3 ) / __p1evll( z, S, 3 ) ); +goto done; +} + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + +if( x < SQRTH ) + { + e -= 1; + x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */ + } +else + { + x = x - 1.0L; + } +z = x*x; +y = x * ( z * __polevll( x, P, 6 ) / __p1evll( x, Q, 7 ) ); +y = y - ldexpl( z, -1 ); /* -0.5x^2 + ... */ + +done: + +/* Multiply log of fraction by log10(e) + * and base 2 exponent by log10(2). + * + * ***CAUTION*** + * + * This sequence of operations is critical and it may + * be horribly defeated by some compiler optimizers. + */ +z = y * (L10EB); +z += x * (L10EB); +z += e * (L102B); +z += y * (L10EA); +z += x * (L10EA); +z += e * (L102A); + +return( z ); +} diff --git a/openlibm/ld80/e_log2l.c b/openlibm/ld80/e_log2l.c new file mode 100644 index 0000000..6ff6fe9 --- /dev/null +++ b/openlibm/ld80/e_log2l.c @@ -0,0 +1,199 @@ +/* $OpenBSD: e_log2l.c,v 1.2 2013/11/12 20:35:19 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* log2l.c + * + * Base 2 logarithm, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log2l(); + * + * y = log2l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 2 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the (natural) + * logarithm of the fraction is approximated by + * + * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z**3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 30000 9.8e-20 2.7e-20 + * IEEE exp(+-10000) 70000 5.4e-20 2.3e-20 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + * ERROR MESSAGES: + * + * log singularity: x = 0; returns -INFINITY + * log domain: x < 0; returns NAN + */ + +#include + +#include "math_private.h" + +/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 6.2e-22 + */ +static long double P[] = { + 4.9962495940332550844739E-1L, + 1.0767376367209449010438E1L, + 7.7671073698359539859595E1L, + 2.5620629828144409632571E2L, + 4.2401812743503691187826E2L, + 3.4258224542413922935104E2L, + 1.0747524399916215149070E2L, +}; +static long double Q[] = { +/* 1.0000000000000000000000E0,*/ + 2.3479774160285863271658E1L, + 1.9444210022760132894510E2L, + 7.7952888181207260646090E2L, + 1.6911722418503949084863E3L, + 2.0307734695595183428202E3L, + 1.2695660352705325274404E3L, + 3.2242573199748645407652E2L, +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 6.16e-22 + */ +static long double R[4] = { + 1.9757429581415468984296E-3L, +-7.1990767473014147232598E-1L, + 1.0777257190312272158094E1L, +-3.5717684488096787370998E1L, +}; +static long double S[4] = { +/* 1.00000000000000000000E0L,*/ +-2.6201045551331104417768E1L, + 1.9361891836232102174846E2L, +-4.2861221385716144629696E2L, +}; +/* log2(e) - 1 */ +#define LOG2EA 4.4269504088896340735992e-1L + +#define SQRTH 0.70710678118654752440L + +long double +log2l(long double x) +{ +volatile long double z; +long double y; +int e; + +if( isnan(x) ) + return(x); +if( x == INFINITY ) + return(x); +/* Test for domain */ +if( x <= 0.0L ) + { + if( x == 0.0L ) + return( -INFINITY ); + else + return( NAN ); + } + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ +x = frexpl( x, &e ); + + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ +if( (e > 2) || (e < -2) ) +{ +if( x < SQRTH ) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } +else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } +x = z / y; +z = x*x; +y = x * ( z * __polevll( z, R, 3 ) / __p1evll( z, S, 3 ) ); +goto done; +} + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + +if( x < SQRTH ) + { + e -= 1; + x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */ + } +else + { + x = x - 1.0L; + } +z = x*x; +y = x * ( z * __polevll( x, P, 6 ) / __p1evll( x, Q, 7 ) ); +y = y - ldexpl( z, -1 ); /* -0.5x^2 + ... */ + +done: + +/* Multiply log of fraction by log2(e) + * and base 2 exponent by 1 + * + * ***CAUTION*** + * + * This sequence of operations is critical and it may + * be horribly defeated by some compiler optimizers. + */ +z = y * LOG2EA; +z += x * LOG2EA; +z += y; +z += x; +z += e; +return( z ); +} diff --git a/openlibm/ld80/e_logl.c b/openlibm/ld80/e_logl.c new file mode 100644 index 0000000..4722014 --- /dev/null +++ b/openlibm/ld80/e_logl.c @@ -0,0 +1,190 @@ +/* $OpenBSD: e_logl.c,v 1.3 2013/11/12 20:35:19 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* logl.c + * + * Natural logarithm, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, logl(); + * + * y = logl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z**3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE 0.5, 2.0 150000 8.71e-20 2.75e-20 + * IEEE exp(+-10000) 100000 5.39e-20 2.34e-20 + * + * In the tests over the interval exp(+-10000), the logarithms + * of the random arguments were uniformly distributed over + * [-10000, +10000]. + * + * ERROR MESSAGES: + * + * log singularity: x = 0; returns -INFINITY + * log domain: x < 0; returns NAN + */ + +#include + +#include "math_private.h" + +/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 2.32e-20 + */ +static long double P[] = { + 4.5270000862445199635215E-5L, + 4.9854102823193375972212E-1L, + 6.5787325942061044846969E0L, + 2.9911919328553073277375E1L, + 6.0949667980987787057556E1L, + 5.7112963590585538103336E1L, + 2.0039553499201281259648E1L, +}; +static long double Q[] = { +/* 1.0000000000000000000000E0,*/ + 1.5062909083469192043167E1L, + 8.3047565967967209469434E1L, + 2.2176239823732856465394E2L, + 3.0909872225312059774938E2L, + 2.1642788614495947685003E2L, + 6.0118660497603843919306E1L, +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 6.16e-22 + */ + +static long double R[4] = { + 1.9757429581415468984296E-3L, +-7.1990767473014147232598E-1L, + 1.0777257190312272158094E1L, +-3.5717684488096787370998E1L, +}; +static long double S[4] = { +/* 1.00000000000000000000E0L,*/ +-2.6201045551331104417768E1L, + 1.9361891836232102174846E2L, +-4.2861221385716144629696E2L, +}; +static const long double C1 = 6.9314575195312500000000E-1L; +static const long double C2 = 1.4286068203094172321215E-6L; + +#define SQRTH 0.70710678118654752440L + +long double +logl(long double x) +{ +long double y, z; +int e; + +if( isnan(x) ) + return(x); +if( x == INFINITY ) + return(x); +/* Test for domain */ +if( x <= 0.0L ) + { + if( x == 0.0L ) + return( -INFINITY ); + else + return( NAN ); + } + +/* separate mantissa from exponent */ + +/* Note, frexp is used so that denormal numbers + * will be handled properly. + */ +x = frexpl( x, &e ); + +/* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ +if( (e > 2) || (e < -2) ) +{ +if( x < SQRTH ) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } +else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } +x = z / y; +z = x*x; +z = x * ( z * __polevll( z, R, 3 ) / __p1evll( z, S, 3 ) ); +z = z + e * C2; +z = z + x; +z = z + e * C1; +return( z ); +} + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + +if( x < SQRTH ) + { + e -= 1; + x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */ + } +else + { + x = x - 1.0L; + } +z = x*x; +y = x * ( z * __polevll( x, P, 6 ) / __p1evll( x, Q, 6 ) ); +y = y + e * C2; +z = y - ldexpl( z, -1 ); /* y - 0.5 * z */ +/* Note, the sum of above terms does not exceed x/4, + * so it contributes at most about 1/4 lsb to the error. + */ +z = z + x; +z = z + e * C1; /* This sum has an error of 1/2 lsb. */ +return( z ); +} diff --git a/openlibm/ld80/e_powl.c b/openlibm/ld80/e_powl.c new file mode 100644 index 0000000..dcb2b45 --- /dev/null +++ b/openlibm/ld80/e_powl.c @@ -0,0 +1,615 @@ +/* $OpenBSD: e_powl.c,v 1.5 2013/11/12 20:35:19 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* powl.c + * + * Power function, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, z, powl(); + * + * z = powl( x, y ); + * + * + * + * DESCRIPTION: + * + * Computes x raised to the yth power. Analytically, + * + * x**y = exp( y log(x) ). + * + * Following Cody and Waite, this program uses a lookup table + * of 2**-i/32 and pseudo extended precision arithmetic to + * obtain several extra bits of accuracy in both the logarithm + * and the exponential. + * + * + * + * ACCURACY: + * + * The relative error of pow(x,y) can be estimated + * by y dl ln(2), where dl is the absolute error of + * the internally computed base 2 logarithm. At the ends + * of the approximation interval the logarithm equal 1/32 + * and its relative error is about 1 lsb = 1.1e-19. Hence + * the predicted relative error in the result is 2.3e-21 y . + * + * Relative error: + * arithmetic domain # trials peak rms + * + * IEEE +-1000 40000 2.8e-18 3.7e-19 + * .001 < x < 1000, with log(x) uniformly distributed. + * -1000 < y < 1000, y uniformly distributed. + * + * IEEE 0,8700 60000 6.5e-18 1.0e-18 + * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed. + * + * + * ERROR MESSAGES: + * + * message condition value returned + * pow overflow x**y > MAXNUM INFINITY + * pow underflow x**y < 1/MAXNUM 0.0 + * pow domain x<0 and y noninteger 0.0 + * + */ + +#include +#include + +#include "math_private.h" + +/* Table size */ +#define NXT 32 +/* log2(Table size) */ +#define LNXT 5 + +/* log(1+x) = x - .5x^2 + x^3 * P(z)/Q(z) + * on the domain 2^(-1/32) - 1 <= x <= 2^(1/32) - 1 + */ +static long double P[] = { + 8.3319510773868690346226E-4L, + 4.9000050881978028599627E-1L, + 1.7500123722550302671919E0L, + 1.4000100839971580279335E0L, +}; +static long double Q[] = { +/* 1.0000000000000000000000E0L,*/ + 5.2500282295834889175431E0L, + 8.4000598057587009834666E0L, + 4.2000302519914740834728E0L, +}; +/* A[i] = 2^(-i/32), rounded to IEEE long double precision. + * If i is even, A[i] + B[i/2] gives additional accuracy. + */ +static long double A[33] = { + 1.0000000000000000000000E0L, + 9.7857206208770013448287E-1L, + 9.5760328069857364691013E-1L, + 9.3708381705514995065011E-1L, + 9.1700404320467123175367E-1L, + 8.9735453750155359320742E-1L, + 8.7812608018664974155474E-1L, + 8.5930964906123895780165E-1L, + 8.4089641525371454301892E-1L, + 8.2287773907698242225554E-1L, + 8.0524516597462715409607E-1L, + 7.8799042255394324325455E-1L, + 7.7110541270397041179298E-1L, + 7.5458221379671136985669E-1L, + 7.3841307296974965571198E-1L, + 7.2259040348852331001267E-1L, + 7.0710678118654752438189E-1L, + 6.9195494098191597746178E-1L, + 6.7712777346844636413344E-1L, + 6.6261832157987064729696E-1L, + 6.4841977732550483296079E-1L, + 6.3452547859586661129850E-1L, + 6.2092890603674202431705E-1L, + 6.0762367999023443907803E-1L, + 5.9460355750136053334378E-1L, + 5.8186242938878875689693E-1L, + 5.6939431737834582684856E-1L, + 5.5719337129794626814472E-1L, + 5.4525386633262882960438E-1L, + 5.3357020033841180906486E-1L, + 5.2213689121370692017331E-1L, + 5.1094857432705833910408E-1L, + 5.0000000000000000000000E-1L, +}; +static long double B[17] = { + 0.0000000000000000000000E0L, + 2.6176170809902549338711E-20L, +-1.0126791927256478897086E-20L, + 1.3438228172316276937655E-21L, + 1.2207982955417546912101E-20L, +-6.3084814358060867200133E-21L, + 1.3164426894366316434230E-20L, +-1.8527916071632873716786E-20L, + 1.8950325588932570796551E-20L, + 1.5564775779538780478155E-20L, + 6.0859793637556860974380E-21L, +-2.0208749253662532228949E-20L, + 1.4966292219224761844552E-20L, + 3.3540909728056476875639E-21L, +-8.6987564101742849540743E-22L, +-1.2327176863327626135542E-20L, + 0.0000000000000000000000E0L, +}; + +/* 2^x = 1 + x P(x), + * on the interval -1/32 <= x <= 0 + */ +static long double R[] = { + 1.5089970579127659901157E-5L, + 1.5402715328927013076125E-4L, + 1.3333556028915671091390E-3L, + 9.6181291046036762031786E-3L, + 5.5504108664798463044015E-2L, + 2.4022650695910062854352E-1L, + 6.9314718055994530931447E-1L, +}; + +#define douba(k) A[k] +#define doubb(k) B[k] +#define MEXP (NXT*16384.0L) +/* The following if denormal numbers are supported, else -MEXP: */ +#define MNEXP (-NXT*(16384.0L+64.0L)) +/* log2(e) - 1 */ +#define LOG2EA 0.44269504088896340735992L + +#define F W +#define Fa Wa +#define Fb Wb +#define G W +#define Ga Wa +#define Gb u +#define H W +#define Ha Wb +#define Hb Wb + +static const long double MAXLOGL = 1.1356523406294143949492E4L; +static const long double MINLOGL = -1.13994985314888605586758E4L; +static const long double LOGE2L = 6.9314718055994530941723E-1L; +static volatile long double z; +static long double w, W, Wa, Wb, ya, yb, u; +static const long double huge = 0x1p10000L; +#if 0 /* XXX Prevent gcc from erroneously constant folding this. */ +static const long double twom10000 = 0x1p-10000L; +#else +static volatile long double twom10000 = 0x1p-10000L; +#endif + +static long double reducl( long double ); +static long double powil ( long double, int ); + +long double +powl(long double x, long double y) +{ +/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */ +int i, nflg, iyflg, yoddint; +long e; + +if( y == 0.0L ) + return( 1.0L ); + +if( x == 1.0L ) + return( 1.0L ); + +if( isnan(x) ) + return( x ); +if( isnan(y) ) + return( y ); + +if( y == 1.0L ) + return( x ); + +if( !isfinite(y) && x == -1.0L ) + return( 1.0L ); + +if( y >= LDBL_MAX ) + { + if( x > 1.0L ) + return( INFINITY ); + if( x > 0.0L && x < 1.0L ) + return( 0.0L ); + if( x < -1.0L ) + return( INFINITY ); + if( x > -1.0L && x < 0.0L ) + return( 0.0L ); + } +if( y <= -LDBL_MAX ) + { + if( x > 1.0L ) + return( 0.0L ); + if( x > 0.0L && x < 1.0L ) + return( INFINITY ); + if( x < -1.0L ) + return( 0.0L ); + if( x > -1.0L && x < 0.0L ) + return( INFINITY ); + } +if( x >= LDBL_MAX ) + { + if( y > 0.0L ) + return( INFINITY ); + return( 0.0L ); + } + +w = floorl(y); +/* Set iyflg to 1 if y is an integer. */ +iyflg = 0; +if( w == y ) + iyflg = 1; + +/* Test for odd integer y. */ +yoddint = 0; +if( iyflg ) + { + ya = fabsl(y); + ya = floorl(0.5L * ya); + yb = 0.5L * fabsl(w); + if( ya != yb ) + yoddint = 1; + } + +if( x <= -LDBL_MAX ) + { + if( y > 0.0L ) + { + if( yoddint ) + return( -INFINITY ); + return( INFINITY ); + } + if( y < 0.0L ) + { + if( yoddint ) + return( -0.0L ); + return( 0.0 ); + } + } + + +nflg = 0; /* flag = 1 if x<0 raised to integer power */ +if( x <= 0.0L ) + { + if( x == 0.0L ) + { + if( y < 0.0 ) + { + if( signbit(x) && yoddint ) + return( -INFINITY ); + return( INFINITY ); + } + if( y > 0.0 ) + { + if( signbit(x) && yoddint ) + return( -0.0L ); + return( 0.0 ); + } + if( y == 0.0L ) + return( 1.0L ); /* 0**0 */ + else + return( 0.0L ); /* 0**y */ + } + else + { + if( iyflg == 0 ) + return (x - x) / (x - x); /* (x<0)**(non-int) is NaN */ + nflg = 1; + } + } + +/* Integer power of an integer. */ + +if( iyflg ) + { + i = w; + w = floorl(x); + if( (w == x) && (fabsl(y) < 32768.0) ) + { + w = powil( x, (int) y ); + return( w ); + } + } + + +if( nflg ) + x = fabsl(x); + +/* separate significand from exponent */ +x = frexpl( x, &i ); +e = i; + +/* find significand in antilog table A[] */ +i = 1; +if( x <= douba(17) ) + i = 17; +if( x <= douba(i+8) ) + i += 8; +if( x <= douba(i+4) ) + i += 4; +if( x <= douba(i+2) ) + i += 2; +if( x >= douba(1) ) + i = -1; +i += 1; + + +/* Find (x - A[i])/A[i] + * in order to compute log(x/A[i]): + * + * log(x) = log( a x/a ) = log(a) + log(x/a) + * + * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a + */ +x -= douba(i); +x -= doubb(i/2); +x /= douba(i); + + +/* rational approximation for log(1+v): + * + * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v) + */ +z = x*x; +w = x * ( z * __polevll( x, P, 3 ) / __p1evll( x, Q, 3 ) ); +w = w - ldexpl( z, -1 ); /* w - 0.5 * z */ + +/* Convert to base 2 logarithm: + * multiply by log2(e) = 1 + LOG2EA + */ +z = LOG2EA * w; +z += w; +z += LOG2EA * x; +z += x; + +/* Compute exponent term of the base 2 logarithm. */ +w = -i; +w = ldexpl( w, -LNXT ); /* divide by NXT */ +w += e; +/* Now base 2 log of x is w + z. */ + +/* Multiply base 2 log by y, in extended precision. */ + +/* separate y into large part ya + * and small part yb less than 1/NXT + */ +ya = reducl(y); +yb = y - ya; + +/* (w+z)(ya+yb) + * = w*ya + w*yb + z*y + */ +F = z * y + w * yb; +Fa = reducl(F); +Fb = F - Fa; + +G = Fa + w * ya; +Ga = reducl(G); +Gb = G - Ga; + +H = Fb + Gb; +Ha = reducl(H); +w = ldexpl( Ga+Ha, LNXT ); + +/* Test the power of 2 for overflow */ +if( w > MEXP ) + return (huge * huge); /* overflow */ + +if( w < MNEXP ) + return (twom10000 * twom10000); /* underflow */ + +e = w; +Hb = H - Ha; + +if( Hb > 0.0L ) + { + e += 1; + Hb -= (1.0L/NXT); /*0.0625L;*/ + } + +/* Now the product y * log2(x) = Hb + e/NXT. + * + * Compute base 2 exponential of Hb, + * where -0.0625 <= Hb <= 0. + */ +z = Hb * __polevll( Hb, R, 6 ); /* z = 2**Hb - 1 */ + +/* Express e/NXT as an integer plus a negative number of (1/NXT)ths. + * Find lookup table entry for the fractional power of 2. + */ +if( e < 0 ) + i = 0; +else + i = 1; +i = e/NXT + i; +e = NXT*i - e; +w = douba( e ); +z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */ +z = z + w; +z = ldexpl( z, i ); /* multiply by integer power of 2 */ + +if( nflg ) + { +/* For negative x, + * find out if the integer exponent + * is odd or even. + */ + w = ldexpl( y, -1 ); + w = floorl(w); + w = ldexpl( w, 1 ); + if( w != y ) + z = -z; /* odd exponent */ + } + +return( z ); +} + + +/* Find a multiple of 1/NXT that is within 1/NXT of x. */ +static long double +reducl(long double x) +{ +long double t; + +t = ldexpl( x, LNXT ); +t = floorl( t ); +t = ldexpl( t, -LNXT ); +return(t); +} + +/* powil.c + * + * Real raised to integer power, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, powil(); + * int n; + * + * y = powil( x, n ); + * + * + * + * DESCRIPTION: + * + * Returns argument x raised to the nth power. + * The routine efficiently decomposes n as a sum of powers of + * two. The desired power is a product of two-to-the-kth + * powers of x. Thus to compute the 32767 power of x requires + * 28 multiplications instead of 32767 multiplications. + * + * + * + * ACCURACY: + * + * + * Relative error: + * arithmetic x domain n domain # trials peak rms + * IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18 + * IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18 + * IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17 + * + * Returns MAXNUM on overflow, zero on underflow. + * + */ + +static long double +powil(long double x, int nn) +{ +long double ww, y; +long double s; +int n, e, sign, asign, lx; + +if( x == 0.0L ) + { + if( nn == 0 ) + return( 1.0L ); + else if( nn < 0 ) + return( LDBL_MAX ); + else + return( 0.0L ); + } + +if( nn == 0 ) + return( 1.0L ); + + +if( x < 0.0L ) + { + asign = -1; + x = -x; + } +else + asign = 0; + + +if( nn < 0 ) + { + sign = -1; + n = -nn; + } +else + { + sign = 1; + n = nn; + } + +/* Overflow detection */ + +/* Calculate approximate logarithm of answer */ +s = x; +s = frexpl( s, &lx ); +e = (lx - 1)*n; +if( (e == 0) || (e > 64) || (e < -64) ) + { + s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L); + s = (2.9142135623730950L * s - 0.5L + lx) * nn * LOGE2L; + } +else + { + s = LOGE2L * e; + } + +if( s > MAXLOGL ) + return (huge * huge); /* overflow */ + +if( s < MINLOGL ) + return (twom10000 * twom10000); /* underflow */ +/* Handle tiny denormal answer, but with less accuracy + * since roundoff error in 1.0/x will be amplified. + * The precise demarcation should be the gradual underflow threshold. + */ +if( s < (-MAXLOGL+2.0L) ) + { + x = 1.0L/x; + sign = -sign; + } + +/* First bit of the power */ +if( n & 1 ) + y = x; + +else + { + y = 1.0L; + asign = 0; + } + +ww = x; +n >>= 1; +while( n ) + { + ww = ww * ww; /* arg to the 2-to-the-kth power */ + if( n & 1 ) /* if that bit is set, then include in product */ + y *= ww; + n >>= 1; + } + +if( asign ) + y = -y; /* odd power of negative number */ +if( sign < 0 ) + y = 1.0L/y; +return(y); +} diff --git a/openlibm/ld80/e_rem_pio2l.h b/openlibm/ld80/e_rem_pio2l.h new file mode 100644 index 0000000..c44ad48 --- /dev/null +++ b/openlibm/ld80/e_rem_pio2l.h @@ -0,0 +1,152 @@ +/* From: @(#)e_rem_pio2.c 1.4 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld80/e_rem_pio2l.h,v 1.3 2011/06/18 13:56:33 benl Exp $"); + +/* ld80 version of __ieee754_rem_pio2l(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include +#include + +#include "math_private.h" + +#define BIAS (LDBL_MAX_EXP - 1) + +/* + * invpio2: 64 bits of 2/pi + * pio2_1: first 39 bits of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 39 bits of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 39 bits of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const double +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */ +pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */ +pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */ + +#if defined(__amd64__) || defined(__i386__) +/* Long double constants are slow on these arches, and broken on i386. */ +static const volatile double +invpio2hi = 6.3661977236758138e-01, /* 0x145f306dc9c883.0p-53 */ +invpio2lo = -3.9356538861223811e-17, /* -0x16b00000000000.0p-107 */ +pio2_1thi = -1.0746346554971943e-12, /* -0x12e7b9676733af.0p-92 */ +pio2_1tlo = 8.8451028997905949e-29, /* 0x1c080000000000.0p-146 */ +pio2_2thi = 6.3683171635109499e-25, /* 0x18a2e03707344a.0p-133 */ +pio2_2tlo = 2.3183081793789774e-41, /* 0x10280000000000.0p-187 */ +pio2_3thi = -2.7529965190440717e-37, /* -0x176b7ed8fbbacc.0p-174 */ +pio2_3tlo = -4.2006647512740502e-54; /* -0x19c00000000000.0p-230 */ +#define invpio2 ((long double)invpio2hi + invpio2lo) +#define pio2_1t ((long double)pio2_1thi + pio2_1tlo) +#define pio2_2t ((long double)pio2_2thi + pio2_2tlo) +#define pio2_3t ((long double)pio2_3thi + pio2_3tlo) +#else +static const long double +invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */ +pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */ +pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */ +pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */ +#endif + +//VBS +//static inline __always_inline int +//__ieee754_rem_pio2l(long double x, long double *y) + +static inline int +__ieee754_rem_pio2l(long double x, long double *y) +{ + union IEEEl2bits u,u1; + long double z,w,t,r,fn; + double tx[3],ty[2]; + int e0,ex,i,j,nx,n; + int16_t expsign; + + u.e = x; + expsign = u.xbits.expsign; + ex = expsign & 0x7fff; + if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) { + /* |x| ~< 2^25*(pi/2), medium size */ + /* Use a specialized rint() to get fn. Assume round-to-nearest. */ + fn = x*invpio2+0x1.8p63; + fn = fn-0x1.8p63; +#ifdef HAVE_EFFICIENT_IRINT + n = irint(fn); +#else + n = fn; +#endif + r = x-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 102 bit */ + { + union IEEEl2bits u2; + int ex1; + j = ex; + y[0] = r-w; + u2.e = y[0]; + ex1 = u2.xbits.expsign & 0x7fff; + i = j-ex1; + if(i>22) { /* 2nd iteration needed, good to 141 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + u2.e = y[0]; + ex1 = u2.xbits.expsign & 0x7fff; + i = j-ex1; + if(i>61) { /* 3rd iteration need, 180 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + return n; + } + /* + * all other (large) arguments + */ + if(ex==0x7fff) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + u1.e = x; + e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */ + u1.xbits.expsign = ex - e0; + z = u1.e; + for(i=0;i<2;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,ty,e0,nx,2); + r = (long double)ty[0] + ty[1]; + w = ty[1] - (r - ty[0]); + if(expsign<0) {y[0] = -r; y[1] = -w; return -n;} + y[0] = r; y[1] = w; return n; +} diff --git a/openlibm/ld80/e_sinhl.c b/openlibm/ld80/e_sinhl.c new file mode 100644 index 0000000..cb45204 --- /dev/null +++ b/openlibm/ld80/e_sinhl.c @@ -0,0 +1,76 @@ +/* @(#)e_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* sinhl(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x) + * 2 + * + * 25 <= x <= lnovft : sinhl(x) := expl(x)/2 + * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2) + * ln2ovft < x : sinhl(x) := x*shuge (overflow) + * + * Special cases: + * sinhl(x) is |x| if x is +INF, -INF, or NaN. + * only sinhl(0)=0 is exact for finite x. + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0, shuge = 1.0e4931L; + +long double +sinhl(long double x) +{ + long double t,w,h; + u_int32_t jx,ix,i0,i1; + + /* Words of |x|. */ + GET_LDOUBLE_WORDS(jx,i0,i1,x); + ix = jx&0x7fff; + + /* x is INF or NaN */ + if(ix==0x7fff) return x+x; + + h = 0.5; + if (jx & 0x8000) h = -h; + /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */ + if (ix<0x3fdf) /* |x|<2**-32 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1l(fabsl(x)); + if(ix<0x3fff) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7)) + return h*expl(fabsl(x)); + + /* |x| in [log(maxdouble), overflowthreshold] */ + if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 + || (i0 == 0xb174ddc0 + && i1 <= 0x31aec0ea)))) { + w = expl(0.5*fabsl(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthreshold, sinhl(x) overflow */ + return x*shuge; +} diff --git a/openlibm/ld80/e_tgammal.c b/openlibm/ld80/e_tgammal.c new file mode 100644 index 0000000..036061c --- /dev/null +++ b/openlibm/ld80/e_tgammal.c @@ -0,0 +1,313 @@ +/* $OpenBSD: e_tgammal.c,v 1.4 2013/11/12 20:35:19 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* tgammal.c + * + * Gamma function + * + * + * + * SYNOPSIS: + * + * long double x, y, tgammal(); + * + * y = tgammal( x ); + * + * + * + * DESCRIPTION: + * + * Returns gamma function of the argument. The result is correctly + * signed. This variable is also filled in by the logarithmic gamma + * function lgamma(). + * + * Arguments |x| <= 13 are reduced by recurrence and the function + * approximated by a rational function of degree 7/8 in the + * interval (2,3). Large arguments are handled by Stirling's + * formula. Large negative arguments are made positive using + * a reflection formula. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -40,+40 10000 3.6e-19 7.9e-20 + * IEEE -1755,+1755 10000 4.8e-18 6.5e-19 + * + * Accuracy for large arguments is dominated by error in powl(). + * + */ + +#include +#include + +#include "math_private.h" + +/* +tgamma(x+2) = tgamma(x+2) P(x)/Q(x) +0 <= x <= 1 +Relative error +n=7, d=8 +Peak error = 1.83e-20 +Relative error spread = 8.4e-23 +*/ + +static long double P[8] = { + 4.212760487471622013093E-5L, + 4.542931960608009155600E-4L, + 4.092666828394035500949E-3L, + 2.385363243461108252554E-2L, + 1.113062816019361559013E-1L, + 3.629515436640239168939E-1L, + 8.378004301573126728826E-1L, + 1.000000000000000000009E0L, +}; +static long double Q[9] = { +-1.397148517476170440917E-5L, + 2.346584059160635244282E-4L, +-1.237799246653152231188E-3L, +-7.955933682494738320586E-4L, + 2.773706565840072979165E-2L, +-4.633887671244534213831E-2L, +-2.243510905670329164562E-1L, + 4.150160950588455434583E-1L, + 9.999999999999999999908E-1L, +}; + +/* +static long double P[] = { +-3.01525602666895735709e0L, +-3.25157411956062339893e1L, +-2.92929976820724030353e2L, +-1.70730828800510297666e3L, +-7.96667499622741999770e3L, +-2.59780216007146401957e4L, +-5.99650230220855581642e4L, +-7.15743521530849602425e4L +}; +static long double Q[] = { + 1.00000000000000000000e0L, +-1.67955233807178858919e1L, + 8.85946791747759881659e1L, + 5.69440799097468430177e1L, +-1.98526250512761318471e3L, + 3.31667508019495079814e3L, + 1.60577839621734713377e4L, +-2.97045081369399940529e4L, +-7.15743521530849602412e4L +}; +*/ +#define MAXGAML 1755.455L +/*static const long double LOGPI = 1.14472988584940017414L;*/ + +/* Stirling's formula for the gamma function +tgamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x)) +z(x) = x +13 <= x <= 1024 +Relative error +n=8, d=0 +Peak error = 9.44e-21 +Relative error spread = 8.8e-4 +*/ + +static long double STIR[9] = { + 7.147391378143610789273E-4L, +-2.363848809501759061727E-5L, +-5.950237554056330156018E-4L, + 6.989332260623193171870E-5L, + 7.840334842744753003862E-4L, +-2.294719747873185405699E-4L, +-2.681327161876304418288E-3L, + 3.472222222230075327854E-3L, + 8.333333333333331800504E-2L, +}; + +#define MAXSTIR 1024.0L +static const long double SQTPI = 2.50662827463100050242E0L; + +/* 1/tgamma(x) = z P(z) + * z(x) = 1/x + * 0 < x < 0.03125 + * Peak relative error 4.2e-23 + */ + +static long double S[9] = { +-1.193945051381510095614E-3L, + 7.220599478036909672331E-3L, +-9.622023360406271645744E-3L, +-4.219773360705915470089E-2L, + 1.665386113720805206758E-1L, +-4.200263503403344054473E-2L, +-6.558780715202540684668E-1L, + 5.772156649015328608253E-1L, + 1.000000000000000000000E0L, +}; + +/* 1/tgamma(-x) = z P(z) + * z(x) = 1/x + * 0 < x < 0.03125 + * Peak relative error 5.16e-23 + * Relative error spread = 2.5e-24 + */ + +static long double SN[9] = { + 1.133374167243894382010E-3L, + 7.220837261893170325704E-3L, + 9.621911155035976733706E-3L, +-4.219773343731191721664E-2L, +-1.665386113944413519335E-1L, +-4.200263503402112910504E-2L, + 6.558780715202536547116E-1L, + 5.772156649015328608727E-1L, +-1.000000000000000000000E0L, +}; + +static const long double PIL = 3.1415926535897932384626L; + +static long double stirf ( long double ); + +/* Gamma function computed by Stirling's formula. + */ +static long double stirf(long double x) +{ +long double y, w, v; + +w = 1.0L/x; +/* For large x, use rational coefficients from the analytical expansion. */ +if( x > 1024.0L ) + w = (((((6.97281375836585777429E-5L * w + + 7.84039221720066627474E-4L) * w + - 2.29472093621399176955E-4L) * w + - 2.68132716049382716049E-3L) * w + + 3.47222222222222222222E-3L) * w + + 8.33333333333333333333E-2L) * w + + 1.0L; +else + w = 1.0L + w * __polevll( w, STIR, 8 ); +y = expl(x); +if( x > MAXSTIR ) + { /* Avoid overflow in pow() */ + v = powl( x, 0.5L * x - 0.25L ); + y = v * (v / y); + } +else + { + y = powl( x, x - 0.5L ) / y; + } +y = SQTPI * y * w; +return( y ); +} + +long double +tgammal(long double x) +{ +long double p, q, z; +int i; + +if( isnan(x) ) + return(NAN); +if(x == INFINITY) + return(INFINITY); +if(x == -INFINITY) + return(x - x); +if( x == 0.0L ) + return( 1.0L / x ); +q = fabsl(x); + +if( q > 13.0L ) + { + int sign = 1; + if( q > MAXGAML ) + goto goverf; + if( x < 0.0L ) + { + p = floorl(q); + if( p == q ) + return (x - x) / (x - x); + i = p; + if( (i & 1) == 0 ) + sign = -1; + z = q - p; + if( z > 0.5L ) + { + p += 1.0L; + z = q - p; + } + z = q * sinl( PIL * z ); + z = fabsl(z) * stirf(q); + if( z <= PIL/LDBL_MAX ) + { +goverf: + return( sign * INFINITY); + } + z = PIL/z; + } + else + { + z = stirf(x); + } + return( sign * z ); + } + +z = 1.0L; +while( x >= 3.0L ) + { + x -= 1.0L; + z *= x; + } + +while( x < -0.03125L ) + { + z /= x; + x += 1.0L; + } + +if( x <= 0.03125L ) + goto small; + +while( x < 2.0L ) + { + z /= x; + x += 1.0L; + } + +if( x == 2.0L ) + return(z); + +x -= 2.0L; +p = __polevll( x, P, 7 ); +q = __polevll( x, Q, 8 ); +z = z * p / q; +return z; + +small: +if( x == 0.0L ) + return (x - x) / (x - x); +else + { + if( x < 0.0L ) + { + x = -x; + q = z / (x * __polevll( x, SN, 8 )); + } + else + q = z / (x * __polevll( x, S, 8 )); + } +return q; +} diff --git a/openlibm/ld80/invtrig.c b/openlibm/ld80/invtrig.c new file mode 100644 index 0000000..15692ad --- /dev/null +++ b/openlibm/ld80/invtrig.c @@ -0,0 +1,82 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld80/invtrig.c,v 1.1 2008/07/31 22:41:26 das Exp $"); + +#include "ld80/invtrig.h" + +/* + * asinl() and acosl() + */ +const long double +pS0 = 1.66666666666666666631e-01L, +pS1 = -4.16313987993683104320e-01L, +pS2 = 3.69068046323246813704e-01L, +pS3 = -1.36213932016738603108e-01L, +pS4 = 1.78324189708471965733e-02L, +pS5 = -2.19216428382605211588e-04L, +pS6 = -7.10526623669075243183e-06L, +qS1 = -2.94788392796209867269e+00L, +qS2 = 3.27309890266528636716e+00L, +qS3 = -1.68285799854822427013e+00L, +qS4 = 3.90699412641738801874e-01L, +qS5 = -3.14365703596053263322e-02L; + +/* + * atanl() + */ +const long double atanhi[] = { + 4.63647609000806116202e-01L, + 7.85398163397448309628e-01L, + 9.82793723247329067960e-01L, + 1.57079632679489661926e+00L, +}; + +const long double atanlo[] = { + 1.18469937025062860669e-20L, + -1.25413940316708300586e-20L, + 2.55232234165405176172e-20L, + -2.50827880633416601173e-20L, +}; + +const long double aT[] = { + 3.33333333333333333017e-01L, + -1.99999999999999632011e-01L, + 1.42857142857046531280e-01L, + -1.11111111100562372733e-01L, + 9.09090902935647302252e-02L, + -7.69230552476207730353e-02L, + 6.66661718042406260546e-02L, + -5.88158892835030888692e-02L, + 5.25499891539726639379e-02L, + -4.70119845393155721494e-02L, + 4.03539201366454414072e-02L, + -2.91303858419364158725e-02L, + 1.24822046299269234080e-02L, +}; + +const long double pi_lo = -5.01655761266833202345e-20L; diff --git a/openlibm/ld80/invtrig.h b/openlibm/ld80/invtrig.h new file mode 100644 index 0000000..3d543e9 --- /dev/null +++ b/openlibm/ld80/invtrig.h @@ -0,0 +1,114 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/ld80/invtrig.h,v 1.2 2008/08/02 03:56:22 das Exp $ + */ + +#include + +#include + +#define BIAS (LDBL_MAX_EXP - 1) +#define MANH_SIZE LDBL_MANH_SIZE + +/* Approximation thresholds. */ +#define ASIN_LINEAR (BIAS - 32) /* 2**-32 */ +#define ACOS_CONST (BIAS - 65) /* 2**-65 */ +#define ATAN_CONST (BIAS + 65) /* 2**65 */ +#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */ + +/* 0.95 */ +#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT) + +/* Constants shared by the long double inverse trig functions. */ +#define pS0 _ItL_pS0 +#define pS1 _ItL_pS1 +#define pS2 _ItL_pS2 +#define pS3 _ItL_pS3 +#define pS4 _ItL_pS4 +#define pS5 _ItL_pS5 +#define pS6 _ItL_pS6 +#define qS1 _ItL_qS1 +#define qS2 _ItL_qS2 +#define qS3 _ItL_qS3 +#define qS4 _ItL_qS4 +#define qS5 _ItL_qS5 +#define atanhi _ItL_atanhi +#define atanlo _ItL_atanlo +#define aT _ItL_aT +#define pi_lo _ItL_pi_lo + +#define pio2_hi atanhi[3] +#define pio2_lo atanlo[3] +#define pio4_hi atanhi[1] + +#ifdef STRUCT_DECLS +typedef struct longdouble { + uint64_t mant; + uint16_t expsign; +} LONGDOUBLE; +#else +typedef long double LONGDOUBLE; +#endif + +extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6; +extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5; +extern const LONGDOUBLE atanhi[], atanlo[], aT[]; +extern const LONGDOUBLE pi_lo; + +#ifndef STRUCT_DECLS + +static inline long double +P(long double x) +{ + + return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ + (pS4 + x * (pS5 + x * pS6))))))); +} + +static inline long double +Q(long double x) +{ + + return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5))))); +} + +static inline long double +T_even(long double x) +{ + + return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ + (aT[8] + x * (aT[10] + x * aT[12])))))); +} + +static inline long double +T_odd(long double x) +{ + + return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \ + (aT[9] + x * aT[11]))))); +} + +#endif diff --git a/openlibm/ld80/k_cosl.c b/openlibm/ld80/k_cosl.c new file mode 100644 index 0000000..403da9d --- /dev/null +++ b/openlibm/ld80/k_cosl.c @@ -0,0 +1,78 @@ +/* From: @(#)k_cos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld80/k_cosl.c,v 1.1 2008/02/17 07:32:14 das Exp $"); + +/* + * ld80 version of k_cos.c. See ../src/k_cos.c for most comments. + */ + +#include "math_private.h" + +/* + * Domain [-0.7854, 0.7854], range ~[-2.43e-23, 2.425e-23]: + * |cos(x) - c(x)| < 2**-75.1 + * + * The coefficients of c(x) were generated by a pari-gp script using + * a Remez algorithm that searches for the best higher coefficients + * after rounding leading coefficients to a specified precision. + * + * Simpler methods like Chebyshev or basic Remez barely suffice for + * cos() in 64-bit precision, because we want the coefficient of x^2 + * to be precisely -0.5 so that multiplying by it is exact, and plain + * rounding of the coefficients of a good polynomial approximation only + * gives this up to about 64-bit precision. Plain rounding also gives + * a mediocre approximation for the coefficient of x^4, but a rounding + * error of 0.5 ulps for this coefficient would only contribute ~0.01 + * ulps to the final error, so this is unimportant. Rounding errors in + * higher coefficients are even less important. + * + * In fact, coefficients above the x^4 one only need to have 53-bit + * precision, and this is more efficient. We get this optimization + * almost for free from the complications needed to search for the best + * higher coefficients. + */ +static const double +one = 1.0; + +#if defined(__amd64__) || defined(__i386__) +/* Long double constants are slow on these arches, and broken on i386. */ +static const volatile double +C1hi = 0.041666666666666664, /* 0x15555555555555.0p-57 */ +C1lo = 2.2598839032744733e-18; /* 0x14d80000000000.0p-111 */ +#define C1 ((long double)C1hi + C1lo) +#else +static const long double +C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */ +#endif + +static const double +C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */ +C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */ +C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */ +C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */ +C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */ +C7 = 4.7383039476436467e-14; /* 0x1aac9d9af5c43e.0p-97 */ + +long double +__kernel_cosl(long double x, long double y) +{ + long double hz,z,r,w; + + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7)))))); + hz = 0.5*z; + w = one-hz; + return w + (((one-w)-hz) + (z*r-x*y)); +} diff --git a/openlibm/ld80/k_sinl.c b/openlibm/ld80/k_sinl.c new file mode 100644 index 0000000..792baf6 --- /dev/null +++ b/openlibm/ld80/k_sinl.c @@ -0,0 +1,62 @@ +/* From: @(#)k_sin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld80/k_sinl.c,v 1.1 2008/02/17 07:32:14 das Exp $"); + +/* + * ld80 version of k_sin.c. See ../src/k_sin.c for most comments. + */ + +#include "math_private.h" + +static const double +half = 0.5; + +/* + * Domain [-0.7854, 0.7854], range ~[-1.89e-22, 1.915e-22] + * |sin(x)/x - s(x)| < 2**-72.1 + * + * See ../ld80/k_cosl.c for more details about the polynomial. + */ +#if defined(__amd64__) || defined(__i386__) +/* Long double constants are slow on these arches, and broken on i386. */ +static const volatile double +S1hi = -0.16666666666666666, /* -0x15555555555555.0p-55 */ +S1lo = -9.2563760475949941e-18; /* -0x15580000000000.0p-109 */ +#define S1 ((long double)S1hi + S1lo) +#else +static const long double +S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */ +#endif + +static const double +S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */ +S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */ +S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */ +S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */ +S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */ +S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */ +S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */ + +long double +__kernel_sinl(long double x, long double y, int iy) +{ + long double z,r,v; + + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8))))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/openlibm/ld80/k_tanl.c b/openlibm/ld80/k_tanl.c new file mode 100644 index 0000000..691c952 --- /dev/null +++ b/openlibm/ld80/k_tanl.c @@ -0,0 +1,125 @@ +/* From: @(#)k_tan.c 1.5 04/04/22 SMI */ + +/* + * ==================================================== + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld80/k_tanl.c,v 1.3 2008/02/18 15:39:52 bde Exp $"); + +/* + * ld80 version of k_tan.c. See ../src/k_tan.c for most comments. + */ + +#include + +#include "math_private.h" + +/* + * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22] + * |tan(x)/x - t(x)| < 2**-71.9 + * + * See k_cosl.c for more details about the polynomial. + */ +#if defined(__amd64__) || defined(__i386__) +/* Long double constants are slow on these arches, and broken on i386. */ +static const volatile double +T3hi = 0.33333333333333331, /* 0x15555555555555.0p-54 */ +T3lo = 1.8350121769317163e-17, /* 0x15280000000000.0p-108 */ +T5hi = 0.13333333333333336, /* 0x11111111111112.0p-55 */ +T5lo = 1.3051083651294260e-17, /* 0x1e180000000000.0p-109 */ +T7hi = 0.053968253968250494, /* 0x1ba1ba1ba1b827.0p-57 */ +T7lo = 3.1509625637859973e-18, /* 0x1d100000000000.0p-111 */ +pio4_hi = 0.78539816339744828, /* 0x1921fb54442d18.0p-53 */ +pio4_lo = 3.0628711372715500e-17, /* 0x11a80000000000.0p-107 */ +pio4lo_hi = -1.2541394031670831e-20, /* -0x1d9cceba3f91f2.0p-119 */ +pio4lo_lo = 6.1493048227390915e-37; /* 0x1a280000000000.0p-173 */ +#define T3 ((long double)T3hi + T3lo) +#define T5 ((long double)T5hi + T5lo) +#define T7 ((long double)T7hi + T7lo) +#define pio4 ((long double)pio4_hi + pio4_lo) +#define pio4lo ((long double)pio4lo_hi + pio4lo_lo) +#else +static const long double +T3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */ +T5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */ +T7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */ +pio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */ +pio4lo = -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */ +#endif + +static const double +T9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */ +T11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */ +T13 = 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */ +T15 = 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */ +T17 = 0.00059003538700862256, /* 0x13559358685b83.0p-63 */ +T19 = 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */ +T21 = 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */ +T23 = 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */ +T25 = 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */ +T27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */ +T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */ +T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */ +T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */ + +long double +__kernel_tanl(long double x, long double y, int iy) { + long double z, r, v, w, s; + long double osign; + int i; + + iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ + osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ + if (fabsl(x) >= 0.67434) { + if (x < 0) { + x = -x; + y = -y; + } + z = pio4 - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + i = 1; + } else + i = 0; + z = x * x; + w = z * z; + r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + + w * (T25 + w * (T29 + w * T33)))))); + v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + + w * (T27 + w * T31)))))); + s = z * x; + r = y + z * (s * (r + v) + y); + r += T3 * s; + w = x + r; + if (i == 1) { + v = (long double) iy; + return osign * + (v - 2.0 * (x - (w * w / (w + v) - r))); + } + if (iy == 1) + return w; + else { + /* + * if allow error up to 2 ulp, simply return + * -1.0 / (x+r) here + */ + /* compute -1.0 / (x+r) accurately */ + long double a, t; + z = w; + z = z + 0x1p32 - 0x1p32; + v = r - (z - x); /* z+v = r+x */ + t = a = -1.0 / w; /* a = -1.0/w */ + t = t + 0x1p32 - 0x1p32; + s = 1.0 + t * z; + return t + a * (s + t * v); + } +} diff --git a/openlibm/ld80/s_asinhl.c b/openlibm/ld80/s_asinhl.c new file mode 100644 index 0000000..0453a9c --- /dev/null +++ b/openlibm/ld80/s_asinhl.c @@ -0,0 +1,54 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* asinhl(x) + * Method : + * Based on + * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] + * we have + * asinhl(x) := x if 1+x*x=1, + * := signl(x)*(logl(x)+ln2)) for large |x|, else + * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else + * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) + */ + +#include + +#include "math_private.h" + +static const long double +one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */ +ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ +huge= 1.000000000000000000e+4900L; + +long double +asinhl(long double x) +{ + long double t,w; + int32_t hx,ix; + GET_LDOUBLE_EXP(hx,x); + ix = hx&0x7fff; + if(ix==0x7fff) return x+x; /* x is inf or NaN */ + if(ix< 0x3fde) { /* |x|<2**-34 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x4020) { /* |x| > 2**34 */ + w = logl(fabsl(x))+ln2; + } else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */ + t = fabsl(x); + w = logl(2.0*t+one/(sqrtl(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1pl(fabsl(x)+t/(one+sqrtl(one+t))); + } + if(hx&0x8000) return -w; else return w; +} diff --git a/openlibm/ld80/s_ceill.c b/openlibm/ld80/s_ceill.c new file mode 100644 index 0000000..9a3e805 --- /dev/null +++ b/openlibm/ld80/s_ceill.c @@ -0,0 +1,78 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * ceill(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include + +#include "math_private.h" + +static const long double huge = 1.0e4930L; + +long double +ceill(long double x) +{ + int32_t i1,jj0; + u_int32_t i,j,se,i0,sx; + GET_LDOUBLE_WORDS(se,i0,i1,x); + sx = (se>>15)&1; + jj0 = (se&0x7fff)-0x3fff; + if(jj0<31) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(sx) {se=0x8000;i0=0;i1=0;} + else if((i0|i1)!=0) { se=0x3fff;i0=0;i1=0;} + } + } else { + i = (0x7fffffff)>>jj0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(sx==0) { + if (jj0>0 && (i0+(0x80000000>>jj0))>i0) + i0+=0x80000000>>jj0; + else + { + i = 0x7fffffff; + ++se; + } + } + i0 &= (~i); i1=0; + } + } + } else if (jj0>62) { + if(jj0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(jj0-31); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(sx==0) { + if(jj0==31) i0+=1; + else { + j = i1 + (1<<(63-jj0)); + if(j + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1(z)/S1(z)) + * z=1/x^2 + * erf(x) = 1 - erfc(x) + * + * 4. For x in [1/0.35,107] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2(z)/S2(z)) + * if -6.666 x >= 107 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + + +#include + +#include "math_private.h" + +static const long double +tiny = 1e-4931L, + half = 0.5L, + one = 1.0L, + two = 2.0L, + /* c = (float)0.84506291151 */ + erx = 0.845062911510467529296875L, +/* + * Coefficients for approximation to erf on [0,0.84375] + */ + /* 2/sqrt(pi) - 1 */ + efx = 1.2837916709551257389615890312154517168810E-1L, + /* 8 * (2/sqrt(pi) - 1) */ + efx8 = 1.0270333367641005911692712249723613735048E0L, + + pp[6] = { + 1.122751350964552113068262337278335028553E6L, + -2.808533301997696164408397079650699163276E6L, + -3.314325479115357458197119660818768924100E5L, + -6.848684465326256109712135497895525446398E4L, + -2.657817695110739185591505062971929859314E3L, + -1.655310302737837556654146291646499062882E2L, + }, + + qq[6] = { + 8.745588372054466262548908189000448124232E6L, + 3.746038264792471129367533128637019611485E6L, + 7.066358783162407559861156173539693900031E5L, + 7.448928604824620999413120955705448117056E4L, + 4.511583986730994111992253980546131408924E3L, + 1.368902937933296323345610240009071254014E2L, + /* 1.000000000000000000000000000000000000000E0 */ + }, + +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +/* erf(x+1) = 0.845062911510467529296875 + pa(x)/qa(x) + -0.15625 <= x <= +.25 + Peak relative error 8.5e-22 */ + + pa[8] = { + -1.076952146179812072156734957705102256059E0L, + 1.884814957770385593365179835059971587220E2L, + -5.339153975012804282890066622962070115606E1L, + 4.435910679869176625928504532109635632618E1L, + 1.683219516032328828278557309642929135179E1L, + -2.360236618396952560064259585299045804293E0L, + 1.852230047861891953244413872297940938041E0L, + 9.394994446747752308256773044667843200719E-2L, + }, + + qa[7] = { + 4.559263722294508998149925774781887811255E2L, + 3.289248982200800575749795055149780689738E2L, + 2.846070965875643009598627918383314457912E2L, + 1.398715859064535039433275722017479994465E2L, + 6.060190733759793706299079050985358190726E1L, + 2.078695677795422351040502569964299664233E1L, + 4.641271134150895940966798357442234498546E0L, + /* 1.000000000000000000000000000000000000000E0 */ + }, + +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + ra(x^2)/sa(x^2)) + 1/2.85711669921875 < 1/x < 1/1.25 + Peak relative error 3.1e-21 */ + + ra[] = { + 1.363566591833846324191000679620738857234E-1L, + 1.018203167219873573808450274314658434507E1L, + 1.862359362334248675526472871224778045594E2L, + 1.411622588180721285284945138667933330348E3L, + 5.088538459741511988784440103218342840478E3L, + 8.928251553922176506858267311750789273656E3L, + 7.264436000148052545243018622742770549982E3L, + 2.387492459664548651671894725748959751119E3L, + 2.220916652813908085449221282808458466556E2L, + }, + + sa[] = { + -1.382234625202480685182526402169222331847E1L, + -3.315638835627950255832519203687435946482E2L, + -2.949124863912936259747237164260785326692E3L, + -1.246622099070875940506391433635999693661E4L, + -2.673079795851665428695842853070996219632E4L, + -2.880269786660559337358397106518918220991E4L, + -1.450600228493968044773354186390390823713E4L, + -2.874539731125893533960680525192064277816E3L, + -1.402241261419067750237395034116942296027E2L, + /* 1.000000000000000000000000000000000000000E0 */ + }, +/* + * Coefficients for approximation to erfc in [1/.35,107] + */ +/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + rb(x^2)/sb(x^2)) + 1/6.6666259765625 < 1/x < 1/2.85711669921875 + Peak relative error 4.2e-22 */ + rb[] = { + -4.869587348270494309550558460786501252369E-5L, + -4.030199390527997378549161722412466959403E-3L, + -9.434425866377037610206443566288917589122E-2L, + -9.319032754357658601200655161585539404155E-1L, + -4.273788174307459947350256581445442062291E0L, + -8.842289940696150508373541814064198259278E0L, + -7.069215249419887403187988144752613025255E0L, + -1.401228723639514787920274427443330704764E0L, + }, + + sb[] = { + 4.936254964107175160157544545879293019085E-3L, + 1.583457624037795744377163924895349412015E-1L, + 1.850647991850328356622940552450636420484E0L, + 9.927611557279019463768050710008450625415E0L, + 2.531667257649436709617165336779212114570E1L, + 2.869752886406743386458304052862814690045E1L, + 1.182059497870819562441683560749192539345E1L, + /* 1.000000000000000000000000000000000000000E0 */ + }, +/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + rc(x^2)/sc(x^2)) + 1/107 <= 1/x <= 1/6.6666259765625 + Peak relative error 1.1e-21 */ + rc[] = { + -8.299617545269701963973537248996670806850E-5L, + -6.243845685115818513578933902532056244108E-3L, + -1.141667210620380223113693474478394397230E-1L, + -7.521343797212024245375240432734425789409E-1L, + -1.765321928311155824664963633786967602934E0L, + -1.029403473103215800456761180695263439188E0L, + }, + + sc[] = { + 8.413244363014929493035952542677768808601E-3L, + 2.065114333816877479753334599639158060979E-1L, + 1.639064941530797583766364412782135680148E0L, + 4.936788463787115555582319302981666347450E0L, + 5.005177727208955487404729933261347679090E0L, + /* 1.000000000000000000000000000000000000000E0 */ + }; + +long double +erfl(long double x) +{ + long double R, S, P, Q, s, y, z, r; + int32_t ix, i; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + + if (ix >= 0x7fff) + { /* erf(nan)=nan */ + i = ((se & 0xffff) >> 15) << 1; + return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + } + + ix = (ix << 16) | (i0 >> 16); + if (ix < 0x3ffed800) /* |x|<0.84375 */ + { + if (ix < 0x3fde8000) /* |x|<2**-33 */ + { + if (ix < 0x00080000) + return 0.125 * (8.0 * x + efx8 * x); /*avoid underflow */ + return x + efx * x; + } + z = x * x; + r = pp[0] + z * (pp[1] + + z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5])))); + s = qq[0] + z * (qq[1] + + z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z))))); + y = r / s; + return x + x * y; + } + if (ix < 0x3fffa000) /* 1.25 */ + { /* 0.84375 <= |x| < 1.25 */ + s = fabsl (x) - one; + P = pa[0] + s * (pa[1] + s * (pa[2] + + s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7])))))); + Q = qa[0] + s * (qa[1] + s * (qa[2] + + s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s)))))); + if ((se & 0x8000) == 0) + return erx + P / Q; + else + return -erx - P / Q; + } + if (ix >= 0x4001d555) /* 6.6666259765625 */ + { /* inf>|x|>=6.666 */ + if ((se & 0x8000) == 0) + return one - tiny; + else + return tiny - one; + } + x = fabsl (x); + s = one / (x * x); + if (ix < 0x4000b6db) /* 2.85711669921875 */ + { + R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] + + s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8]))))))); + S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] + + s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s)))))))); + } + else + { /* |x| >= 1/0.35 */ + R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] + + s * (rb[5] + s * (rb[6] + s * rb[7])))))); + S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] + + s * (sb[5] + s * (sb[6] + s)))))); + } + z = x; + GET_LDOUBLE_WORDS (i, i0, i1, z); + i1 = 0; + SET_LDOUBLE_WORDS (z, i, i0, i1); + r = + expl (-z * z - 0.5625) * expl ((z - x) * (z + x) + R / S); + if ((se & 0x8000) == 0) + return one - r / x; + else + return r / x - one; +} + +long double +erfcl(long double x) +{ + int32_t hx, ix; + long double R, S, P, Q, s, y, z, r; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + if (ix >= 0x7fff) + { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (long double) (((se & 0xffff) >> 15) << 1) + one / x; + } + + ix = (ix << 16) | (i0 >> 16); + if (ix < 0x3ffed800) /* |x|<0.84375 */ + { + if (ix < 0x3fbe0000) /* |x|<2**-65 */ + return one - x; + z = x * x; + r = pp[0] + z * (pp[1] + + z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5])))); + s = qq[0] + z * (qq[1] + + z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z))))); + y = r / s; + if (ix < 0x3ffd8000) /* x<1/4 */ + { + return one - (x + x * y); + } + else + { + r = x * y; + r += (x - half); + return half - r; + } + } + if (ix < 0x3fffa000) /* 1.25 */ + { /* 0.84375 <= |x| < 1.25 */ + s = fabsl (x) - one; + P = pa[0] + s * (pa[1] + s * (pa[2] + + s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7])))))); + Q = qa[0] + s * (qa[1] + s * (qa[2] + + s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s)))))); + if ((se & 0x8000) == 0) + { + z = one - erx; + return z - P / Q; + } + else + { + z = erx + P / Q; + return one + z; + } + } + if (ix < 0x4005d600) /* 107 */ + { /* |x|<107 */ + x = fabsl (x); + s = one / (x * x); + if (ix < 0x4000b6db) /* 2.85711669921875 */ + { /* |x| < 1/.35 ~ 2.857143 */ + R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] + + s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8]))))))); + S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] + + s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s)))))))); + } + else if (ix < 0x4001d555) /* 6.6666259765625 */ + { /* 6.666 > |x| >= 1/.35 ~ 2.857143 */ + R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] + + s * (rb[5] + s * (rb[6] + s * rb[7])))))); + S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] + + s * (sb[5] + s * (sb[6] + s)))))); + } + else + { /* |x| >= 6.666 */ + if (se & 0x8000) + return two - tiny; /* x < -6.666 */ + + R = rc[0] + s * (rc[1] + s * (rc[2] + s * (rc[3] + + s * (rc[4] + s * rc[5])))); + S = sc[0] + s * (sc[1] + s * (sc[2] + s * (sc[3] + + s * (sc[4] + s)))); + } + z = x; + GET_LDOUBLE_WORDS (hx, i0, i1, z); + i1 = 0; + i0 &= 0xffffff00; + SET_LDOUBLE_WORDS (z, hx, i0, i1); + r = expl (-z * z - 0.5625) * + expl ((z - x) * (z + x) + R / S); + if ((se & 0x8000) == 0) + return r / x; + else + return two - r / x; + } + else + { + if ((se & 0x8000) == 0) + return tiny * tiny; + else + return two - tiny; + } +} diff --git a/openlibm/ld80/s_exp2l.c b/openlibm/ld80/s_exp2l.c new file mode 100644 index 0000000..0cf5259 --- /dev/null +++ b/openlibm/ld80/s_exp2l.c @@ -0,0 +1,295 @@ +/*- + * Copyright (c) 2005-2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/ld80/s_exp2l.c,v 1.3 2008/02/13 10:44:44 bde Exp $"); + +#include +#include + +#include "bsd_cdefs.h" +#include "amd64/bsd_ieeefp.h" + +#include + +#include "math_private.h" + +#define TBLBITS 7 +#define TBLSIZE (1 << TBLBITS) + +#define BIAS (LDBL_MAX_EXP - 1) +#define EXPMASK (BIAS + LDBL_MAX_EXP) + +static const long double huge = 0x1p10000L; +#if 0 /* XXX Prevent gcc from erroneously constant folding this. */ +static const long double twom10000 = 0x1p-10000L; +#else +static volatile long double twom10000 = 0x1p-10000L; +#endif + +static const double + redux = 0x1.8p63 / TBLSIZE, + P1 = 0x1.62e42fefa39efp-1, + P2 = 0x1.ebfbdff82c58fp-3, + P3 = 0x1.c6b08d7049fap-5, + P4 = 0x1.3b2ab6fba4da5p-7, + P5 = 0x1.5d8804780a736p-10, + P6 = 0x1.430918835e33dp-13; + +static const double tbl[TBLSIZE * 2] = { + 0x1.6a09e667f3bcdp-1, -0x1.bdd3413b2648p-55, + 0x1.6c012750bdabfp-1, -0x1.2895667ff0cp-57, + 0x1.6dfb23c651a2fp-1, -0x1.bbe3a683c88p-58, + 0x1.6ff7df9519484p-1, -0x1.83c0f25860fp-56, + 0x1.71f75e8ec5f74p-1, -0x1.16e4786887bp-56, + 0x1.73f9a48a58174p-1, -0x1.0a8d96c65d5p-55, + 0x1.75feb564267c9p-1, -0x1.0245957316ep-55, + 0x1.780694fde5d3fp-1, 0x1.866b80a0216p-55, + 0x1.7a11473eb0187p-1, -0x1.41577ee0499p-56, + 0x1.7c1ed0130c132p-1, 0x1.f124cd1164ep-55, + 0x1.7e2f336cf4e62p-1, 0x1.05d02ba157ap-57, + 0x1.80427543e1a12p-1, -0x1.27c86626d97p-55, + 0x1.82589994cce13p-1, -0x1.d4c1dd41533p-55, + 0x1.8471a4623c7adp-1, -0x1.8d684a341cep-56, + 0x1.868d99b4492edp-1, -0x1.fc6f89bd4f68p-55, + 0x1.88ac7d98a6699p-1, 0x1.994c2f37cb5p-55, + 0x1.8ace5422aa0dbp-1, 0x1.6e9f156864bp-55, + 0x1.8cf3216b5448cp-1, -0x1.0d55e32e9e4p-57, + 0x1.8f1ae99157736p-1, 0x1.5cc13a2e397p-56, + 0x1.9145b0b91ffc6p-1, -0x1.dd6792e5825p-55, + 0x1.93737b0cdc5e5p-1, -0x1.75fc781b58p-58, + 0x1.95a44cbc8520fp-1, -0x1.64b7c96a5fp-57, + 0x1.97d829fde4e5p-1, -0x1.d185b7c1b86p-55, + 0x1.9a0f170ca07bap-1, -0x1.173bd91cee6p-55, + 0x1.9c49182a3f09p-1, 0x1.c7c46b071f2p-57, + 0x1.9e86319e32323p-1, 0x1.824ca78e64cp-57, + 0x1.a0c667b5de565p-1, -0x1.359495d1cd5p-55, + 0x1.a309bec4a2d33p-1, 0x1.6305c7ddc368p-55, + 0x1.a5503b23e255dp-1, -0x1.d2f6edb8d42p-55, + 0x1.a799e1330b358p-1, 0x1.bcb7ecac564p-55, + 0x1.a9e6b5579fdbfp-1, 0x1.0fac90ef7fdp-55, + 0x1.ac36bbfd3f37ap-1, -0x1.f9234cae76dp-56, + 0x1.ae89f995ad3adp-1, 0x1.7a1cd345dcc8p-55, + 0x1.b0e07298db666p-1, -0x1.bdef54c80e4p-55, + 0x1.b33a2b84f15fbp-1, -0x1.2805e3084d8p-58, + 0x1.b59728de5593ap-1, -0x1.c71dfbbba6ep-55, + 0x1.b7f76f2fb5e47p-1, -0x1.5584f7e54acp-57, + 0x1.ba5b030a1064ap-1, -0x1.efcd30e5429p-55, + 0x1.bcc1e904bc1d2p-1, 0x1.23dd07a2d9fp-56, + 0x1.bf2c25bd71e09p-1, -0x1.efdca3f6b9c8p-55, + 0x1.c199bdd85529cp-1, 0x1.11065895049p-56, + 0x1.c40ab5fffd07ap-1, 0x1.b4537e083c6p-55, + 0x1.c67f12e57d14bp-1, 0x1.2884dff483c8p-55, + 0x1.c8f6d9406e7b5p-1, 0x1.1acbc48805cp-57, + 0x1.cb720dcef9069p-1, 0x1.503cbd1e94ap-57, + 0x1.cdf0b555dc3fap-1, -0x1.dd83b53829dp-56, + 0x1.d072d4a07897cp-1, -0x1.cbc3743797a8p-55, + 0x1.d2f87080d89f2p-1, -0x1.d487b719d858p-55, + 0x1.d5818dcfba487p-1, 0x1.2ed02d75b37p-56, + 0x1.d80e316c98398p-1, -0x1.11ec18bedep-55, + 0x1.da9e603db3285p-1, 0x1.c2300696db5p-55, + 0x1.dd321f301b46p-1, 0x1.2da5778f019p-55, + 0x1.dfc97337b9b5fp-1, -0x1.1a5cd4f184b8p-55, + 0x1.e264614f5a129p-1, -0x1.7b627817a148p-55, + 0x1.e502ee78b3ff6p-1, 0x1.39e8980a9cdp-56, + 0x1.e7a51fbc74c83p-1, 0x1.2d522ca0c8ep-55, + 0x1.ea4afa2a490dap-1, -0x1.e9c23179c288p-55, + 0x1.ecf482d8e67f1p-1, -0x1.c93f3b411ad8p-55, + 0x1.efa1bee615a27p-1, 0x1.dc7f486a4b68p-55, + 0x1.f252b376bba97p-1, 0x1.3a1a5bf0d8e8p-55, + 0x1.f50765b6e454p-1, 0x1.9d3e12dd8a18p-55, + 0x1.f7bfdad9cbe14p-1, -0x1.dbb12d00635p-55, + 0x1.fa7c1819e90d8p-1, 0x1.74853f3a593p-56, + 0x1.fd3c22b8f71f1p-1, 0x1.2eb74966578p-58, + 0x1p+0, 0x0p+0, + 0x1.0163da9fb3335p+0, 0x1.b61299ab8cd8p-54, + 0x1.02c9a3e778061p+0, -0x1.19083535b08p-56, + 0x1.04315e86e7f85p+0, -0x1.0a31c1977c98p-54, + 0x1.059b0d3158574p+0, 0x1.d73e2a475b4p-55, + 0x1.0706b29ddf6dep+0, -0x1.c91dfe2b13cp-55, + 0x1.0874518759bc8p+0, 0x1.186be4bb284p-57, + 0x1.09e3ecac6f383p+0, 0x1.14878183161p-54, + 0x1.0b5586cf9890fp+0, 0x1.8a62e4adc61p-54, + 0x1.0cc922b7247f7p+0, 0x1.01edc16e24f8p-54, + 0x1.0e3ec32d3d1a2p+0, 0x1.03a1727c58p-59, + 0x1.0fb66affed31bp+0, -0x1.b9bedc44ebcp-57, + 0x1.11301d0125b51p+0, -0x1.6c51039449bp-54, + 0x1.12abdc06c31ccp+0, -0x1.1b514b36ca8p-58, + 0x1.1429aaea92dep+0, -0x1.32fbf9af1368p-54, + 0x1.15a98c8a58e51p+0, 0x1.2406ab9eeabp-55, + 0x1.172b83c7d517bp+0, -0x1.19041b9d78ap-55, + 0x1.18af9388c8deap+0, -0x1.11023d1970f8p-54, + 0x1.1a35beb6fcb75p+0, 0x1.e5b4c7b4969p-55, + 0x1.1bbe084045cd4p+0, -0x1.95386352ef6p-54, + 0x1.1d4873168b9aap+0, 0x1.e016e00a264p-54, + 0x1.1ed5022fcd91dp+0, -0x1.1df98027bb78p-54, + 0x1.2063b88628cd6p+0, 0x1.dc775814a85p-55, + 0x1.21f49917ddc96p+0, 0x1.2a97e9494a6p-55, + 0x1.2387a6e756238p+0, 0x1.9b07eb6c7058p-54, + 0x1.251ce4fb2a63fp+0, 0x1.ac155bef4f5p-55, + 0x1.26b4565e27cddp+0, 0x1.2bd339940eap-55, + 0x1.284dfe1f56381p+0, -0x1.a4c3a8c3f0d8p-54, + 0x1.29e9df51fdee1p+0, 0x1.612e8afad12p-55, + 0x1.2b87fd0dad99p+0, -0x1.10adcd6382p-59, + 0x1.2d285a6e4030bp+0, 0x1.0024754db42p-54, + 0x1.2ecafa93e2f56p+0, 0x1.1ca0f45d524p-56, + 0x1.306fe0a31b715p+0, 0x1.6f46ad23183p-55, + 0x1.32170fc4cd831p+0, 0x1.a9ce78e1804p-55, + 0x1.33c08b26416ffp+0, 0x1.327218436598p-54, + 0x1.356c55f929ff1p+0, -0x1.b5cee5c4e46p-55, + 0x1.371a7373aa9cbp+0, -0x1.63aeabf42ebp-54, + 0x1.38cae6d05d866p+0, -0x1.e958d3c99048p-54, + 0x1.3a7db34e59ff7p+0, -0x1.5e436d661f6p-56, + 0x1.3c32dc313a8e5p+0, -0x1.efff8375d2ap-54, + 0x1.3dea64c123422p+0, 0x1.ada0911f09fp-55, + 0x1.3fa4504ac801cp+0, -0x1.7d023f956fap-54, + 0x1.4160a21f72e2ap+0, -0x1.ef3691c309p-58, + 0x1.431f5d950a897p+0, -0x1.1c7dde35f7ap-55, + 0x1.44e086061892dp+0, 0x1.89b7a04ef8p-59, + 0x1.46a41ed1d0057p+0, 0x1.c944bd1648a8p-54, + 0x1.486a2b5c13cdp+0, 0x1.3c1a3b69062p-56, + 0x1.4a32af0d7d3dep+0, 0x1.9cb62f3d1be8p-54, + 0x1.4bfdad5362a27p+0, 0x1.d4397afec42p-56, + 0x1.4dcb299fddd0dp+0, 0x1.8ecdbbc6a78p-54, + 0x1.4f9b2769d2ca7p+0, -0x1.4b309d25958p-54, + 0x1.516daa2cf6642p+0, -0x1.f768569bd94p-55, + 0x1.5342b569d4f82p+0, -0x1.07abe1db13dp-55, + 0x1.551a4ca5d920fp+0, -0x1.d689cefede6p-55, + 0x1.56f4736b527dap+0, 0x1.9bb2c011d938p-54, + 0x1.58d12d497c7fdp+0, 0x1.295e15b9a1ep-55, + 0x1.5ab07dd485429p+0, 0x1.6324c0546478p-54, + 0x1.5c9268a5946b7p+0, 0x1.c4b1b81698p-60, + 0x1.5e76f15ad2148p+0, 0x1.ba6f93080e68p-54, + 0x1.605e1b976dc09p+0, -0x1.3e2429b56de8p-54, + 0x1.6247eb03a5585p+0, -0x1.383c17e40b48p-54, + 0x1.6434634ccc32p+0, -0x1.c483c759d89p-55, + 0x1.6623882552225p+0, -0x1.bb60987591cp-54, + 0x1.68155d44ca973p+0, 0x1.038ae44f74p-57, +}; + +/* + * exp2l(x): compute the base 2 exponential of x + * + * Accuracy: Peak error < 0.511 ulp. + * + * Method: (equally-spaced tables) + * + * Reduce x: + * x = 2**k + y, for integer k and |y| <= 1/2. + * Thus we have exp2l(x) = 2**k * exp2(y). + * + * Reduce y: + * y = i/TBLSIZE + z for integer i near y * TBLSIZE. + * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z), + * with |z| <= 2**-(TBLBITS+1). + * + * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a + * degree-6 minimax polynomial with maximum error under 2**-69. + * The table entries each have 104 bits of accuracy, encoded as + * a pair of double precision values. + */ +OLM_DLLEXPORT long double +exp2l(long double x) +{ + union IEEEl2bits u, v; + long double r, twopk, twopkp10000, z; + uint32_t hx, ix, i0; + int k; + + /* Filter out exceptional cases. */ + u.e = x; + hx = u.xbits.expsign; + ix = hx & EXPMASK; + if (ix >= BIAS + 14) { /* |x| >= 16384 or x is NaN */ + if (ix == BIAS + LDBL_MAX_EXP) { + if (u.xbits.man != 1ULL << 63 || (hx & 0x8000) == 0) + return (x + x); /* x is +Inf or NaN */ + else + return (0.0); /* x is -Inf */ + } + if (x >= 16384) + return (huge * huge); /* overflow */ + if (x <= -16446) + return (twom10000 * twom10000); /* underflow */ + } else if (ix <= BIAS - 66) { /* |x| < 0x1p-66 */ + return (1.0 + x); + } + +#ifdef __i386__ + /* + * The default precision on i386 is 53 bits, so long doubles are + * broken. Call exp2() to get an accurate (double precision) result. + */ + if (__fpgetprec() != FP_PE) + return (exp2(x)); +#endif + + + /* + * Reduce x, computing z, i0, and k. The low bits of x + redux + * contain the 16-bit integer part of the exponent (k) followed by + * TBLBITS fractional bits (i0). We use bit tricks to extract these + * as integers, then set z to the remainder. + * + * Example: Suppose x is 0xabc.123456p0 and TBLBITS is 8. + * Then the low-order word of x + redux is 0x000abc12, + * We split this into k = 0xabc and i0 = 0x12 (adjusted to + * index into the table), then we compute z = 0x0.003456p0. + * + * XXX If the exponent is negative, the computation of k depends on + * '>>' doing sign extension. + */ + u.e = x + redux; + i0 = u.bits.manl + TBLSIZE / 2; + k = (int)i0 >> TBLBITS; + i0 = (i0 & (TBLSIZE - 1)) << 1; + u.e -= redux; + z = x - u.e; + v.xbits.man = 1ULL << 63; + if (k >= LDBL_MIN_EXP) { + v.xbits.expsign = LDBL_MAX_EXP - 1 + k; + twopk = v.e; + } else { + v.xbits.expsign = LDBL_MAX_EXP - 1 + k + 10000; + twopkp10000 = v.e; + } + + /* Compute r = exp2l(y) = exp2lt[i0] * p(z). */ + long double t_hi = tbl[i0]; + long double t_lo = tbl[i0 + 1]; + /* XXX This gives > 1 ulp errors outside of FE_TONEAREST mode */ + r = t_lo + (t_hi + t_lo) * z * (P1 + z * (P2 + z * (P3 + z * (P4 + + z * (P5 + z * P6))))) + t_hi; + + /* Scale by 2**k. */ + if (k >= LDBL_MIN_EXP) { + if (k == LDBL_MAX_EXP) + return (r * 2.0 * 0x1p16383L); + return (r * twopk); + } else { + return (r * twopkp10000 * twom10000); + } +} diff --git a/openlibm/ld80/s_expm1l.c b/openlibm/ld80/s_expm1l.c new file mode 100644 index 0000000..6ad23fa --- /dev/null +++ b/openlibm/ld80/s_expm1l.c @@ -0,0 +1,138 @@ +/* $OpenBSD: s_expm1l.c,v 1.2 2011/07/20 21:02:51 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* expm1l.c + * + * Exponential function, minus 1 + * Long double precision + * + * + * SYNOPSIS: + * + * long double x, y, expm1l(); + * + * y = expm1l( x ); + * + * + * + * DESCRIPTION: + * + * Returns e (2.71828...) raised to the x power, minus 1. + * + * Range reduction is accomplished by separating the argument + * into an integer k and fraction f such that + * + * x k f + * e = 2 e. + * + * An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1 + * in the basic range [-0.5 ln 2, 0.5 ln 2]. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -45,+MAXLOG 200,000 1.2e-19 2.5e-20 + * + * ERROR MESSAGES: + * + * message condition value returned + * expm1l overflow x > MAXLOG MAXNUM + * + */ + +#include + +static const long double MAXLOGL = 1.1356523406294143949492E4L; + +/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x) + -.5 ln 2 < x < .5 ln 2 + Theoretical peak relative error = 3.4e-22 */ + +static const long double + P0 = -1.586135578666346600772998894928250240826E4L, + P1 = 2.642771505685952966904660652518429479531E3L, + P2 = -3.423199068835684263987132888286791620673E2L, + P3 = 1.800826371455042224581246202420972737840E1L, + P4 = -5.238523121205561042771939008061958820811E-1L, + + Q0 = -9.516813471998079611319047060563358064497E4L, + Q1 = 3.964866271411091674556850458227710004570E4L, + Q2 = -7.207678383830091850230366618190187434796E3L, + Q3 = 7.206038318724600171970199625081491823079E2L, + Q4 = -4.002027679107076077238836622982900945173E1L, + /* Q5 = 1.000000000000000000000000000000000000000E0 */ + +/* C1 + C2 = ln 2 */ +C1 = 6.93145751953125E-1L, +C2 = 1.428606820309417232121458176568075500134E-6L, +/* ln 2^-65 */ +minarg = -4.5054566736396445112120088E1L; +static const long double huge = 0x1p10000L; + +long double +expm1l(long double x) +{ +long double px, qx, xx; +int k; + +/* Overflow. */ +if (x > MAXLOGL) + return (huge*huge); /* overflow */ + +if (x == 0.0) + return x; + +/* Minimum value. */ +if (x < minarg) + return -1.0L; + +xx = C1 + C2; + +/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */ +px = floorl (0.5 + x / xx); +k = px; +/* remainder times ln 2 */ +x -= px * C1; +x -= px * C2; + +/* Approximate exp(remainder ln 2). */ +px = (((( P4 * x + + P3) * x + + P2) * x + + P1) * x + + P0) * x; + +qx = (((( x + + Q4) * x + + Q3) * x + + Q2) * x + + Q1) * x + + Q0; + +xx = x * x; +qx = x + (0.5 * xx + xx * px / qx); + +/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2). + We have qx = exp(remainder ln 2) - 1, so + exp(x) - 1 = 2^k (qx + 1) - 1 = 2^k qx + 2^k - 1. */ +px = ldexpl(1.0L, k); +x = px * qx + (px - 1.0); +return x; +} diff --git a/openlibm/ld80/s_floorl.c b/openlibm/ld80/s_floorl.c new file mode 100644 index 0000000..7d42bd6 --- /dev/null +++ b/openlibm/ld80/s_floorl.c @@ -0,0 +1,80 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * floorl(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include + +#include "math_private.h" + +static const long double huge = 1.0e4930L; + +long double +floorl(long double x) +{ + int32_t i1,jj0; + u_int32_t i,j,se,i0,sx; + GET_LDOUBLE_WORDS(se,i0,i1,x); + sx = (se>>15)&1; + jj0 = (se&0x7fff)-0x3fff; + if(jj0<31) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) { + if(sx==0) + return 0.0L; + else if(((se&0x7fff)|i0|i1)!=0) + return -1.0L; + } + } else { + i = (0x7fffffff)>>jj0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(sx) { + if (jj0>0 && (i0+(0x80000000>>jj0))>i0) + i0 += (0x80000000)>>jj0; + else + { + i = 0x7fffffff; + ++se; + } + } + i0 &= (~i); i1=0; + } + } + } else if (jj0>62) { + if(jj0==0x4000) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(jj0-31); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(sx) { + if(jj0==31) i0+=1; + else { + j = i1+(1<<(63-jj0)); + if(j + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* log1pl.c + * + * Relative error logarithm + * Natural logarithm of 1+x, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log1pl(); + * + * y = log1pl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base e (2.718...) logarithm of 1+x. + * + * The argument 1+x is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the logarithm + * of the fraction is approximated by + * + * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). + * + * Otherwise, setting z = 2(x-1)/x+1), + * + * log(x) = z + z^3 P(z)/Q(z). + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -1.0, 9.0 100000 8.2e-20 2.5e-20 + * + * ERROR MESSAGES: + * + * log singularity: x-1 = 0; returns -INFINITY + * log domain: x-1 < 0; returns NAN + */ + +#include + +#include "math_private.h" + +/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 2.32e-20 + */ + +static long double P[] = { + 4.5270000862445199635215E-5L, + 4.9854102823193375972212E-1L, + 6.5787325942061044846969E0L, + 2.9911919328553073277375E1L, + 6.0949667980987787057556E1L, + 5.7112963590585538103336E1L, + 2.0039553499201281259648E1L, +}; +static long double Q[] = { +/* 1.0000000000000000000000E0,*/ + 1.5062909083469192043167E1L, + 8.3047565967967209469434E1L, + 2.2176239823732856465394E2L, + 3.0909872225312059774938E2L, + 2.1642788614495947685003E2L, + 6.0118660497603843919306E1L, +}; + +/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), + * where z = 2(x-1)/(x+1) + * 1/sqrt(2) <= x < sqrt(2) + * Theoretical peak relative error = 6.16e-22 + */ + +static long double R[4] = { + 1.9757429581415468984296E-3L, +-7.1990767473014147232598E-1L, + 1.0777257190312272158094E1L, +-3.5717684488096787370998E1L, +}; +static long double S[4] = { +/* 1.00000000000000000000E0L,*/ +-2.6201045551331104417768E1L, + 1.9361891836232102174846E2L, +-4.2861221385716144629696E2L, +}; +static const long double C1 = 6.9314575195312500000000E-1L; +static const long double C2 = 1.4286068203094172321215E-6L; + +#define SQRTH 0.70710678118654752440L + +long double +log1pl(long double xm1) +{ +long double x, y, z; +int e; + +if( isnan(xm1) ) + return(xm1); +if( xm1 == INFINITY ) + return(xm1); +if(xm1 == 0.0) + return(xm1); + +x = xm1 + 1.0L; + +/* Test for domain errors. */ +if( x <= 0.0L ) + { + if( x == 0.0L ) + return( -INFINITY ); + else + return( NAN ); + } + +/* Separate mantissa from exponent. + Use frexp so that denormal numbers will be handled properly. */ +x = frexpl( x, &e ); + +/* logarithm using log(x) = z + z^3 P(z)/Q(z), + where z = 2(x-1)/x+1) */ +if( (e > 2) || (e < -2) ) +{ +if( x < SQRTH ) + { /* 2( 2x-1 )/( 2x+1 ) */ + e -= 1; + z = x - 0.5L; + y = 0.5L * z + 0.5L; + } +else + { /* 2 (x-1)/(x+1) */ + z = x - 0.5L; + z -= 0.5L; + y = 0.5L * x + 0.5L; + } +x = z / y; +z = x*x; +z = x * ( z * __polevll( z, R, 3 ) / __p1evll( z, S, 3 ) ); +z = z + e * C2; +z = z + x; +z = z + e * C1; +return( z ); +} + + +/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ + +if( x < SQRTH ) + { + e -= 1; + if (e != 0) + x = 2.0 * x - 1.0L; + else + x = xm1; + } +else + { + if (e != 0) + x = x - 1.0L; + else + x = xm1; + } +z = x*x; +y = x * ( z * __polevll( x, P, 6 ) / __p1evll( x, Q, 6 ) ); +y = y + e * C2; +z = y - 0.5 * z; +z = z + x; +z = z + e * C1; +return( z ); +} diff --git a/openlibm/ld80/s_modfl.c b/openlibm/ld80/s_modfl.c new file mode 100644 index 0000000..f9884af --- /dev/null +++ b/openlibm/ld80/s_modfl.c @@ -0,0 +1,69 @@ +/* @(#)s_modf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * modfl(long double x, long double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include + +#include "math_private.h" + +static const long double one = 1.0; + +long double +modfl(long double x, long double *iptr) +{ + int32_t i0,i1,jj0; + u_int32_t i,se; + GET_LDOUBLE_WORDS(se,i0,i1,x); + jj0 = (se&0x7fff)-0x3fff; /* exponent of x */ + if(jj0<32) { /* integer part in high x */ + if(jj0<0) { /* |x|<1 */ + SET_LDOUBLE_WORDS(*iptr,se&0x8000,0,0); /* *iptr = +-0 */ + return x; + } else { + i = (0x7fffffff)>>jj0; + if(((i0&i)|i1)==0) { /* x is integral */ + *iptr = x; + SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */ + return x; + } else { + SET_LDOUBLE_WORDS(*iptr,se,i0&(~i),0); + return x - *iptr; + } + } + } else if (jj0>63) { /* no fraction part */ + *iptr = x*one; + /* We must handle NaNs separately. */ + if (jj0 == 0x4000 && ((i0 & 0x7fffffff) | i1)) + return x*one; + SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */ + return x; + } else { /* fraction part in low x */ + i = ((u_int32_t)(0x7fffffff))>>(jj0-32); + if((i1&i)==0) { /* x is integral */ + *iptr = x; + SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */ + return x; + } else { + SET_LDOUBLE_WORDS(*iptr,se,i0,i1&(~i)); + return x - *iptr; + } + } +} diff --git a/openlibm/ld80/s_nanl.c b/openlibm/ld80/s_nanl.c new file mode 100644 index 0000000..ca77048 --- /dev/null +++ b/openlibm/ld80/s_nanl.c @@ -0,0 +1,45 @@ +/*- + * Copyright (c) 2007 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/ld80/s_nanl.c,v 1.2 2007/12/18 23:46:31 das Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double +nanl(const char *s) +{ + union { + union IEEEl2bits ieee; + uint32_t bits[3]; + } u; + + __scan_nan(u.bits, 3, s); + u.ieee.bits.exp = 0x7fff; + u.ieee.bits.manh |= 0xc0000000; /* make it a quiet NaN */ + return (u.ieee.e); +} diff --git a/openlibm/ld80/s_nextafterl.c b/openlibm/ld80/s_nextafterl.c new file mode 100644 index 0000000..1e0764b --- /dev/null +++ b/openlibm/ld80/s_nextafterl.c @@ -0,0 +1,90 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* IEEE functions + * nextafterl(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include + +#include "math_private.h" + +long double +nextafterl(long double x, long double y) +{ + int32_t hx,hy,ix,iy; + u_int32_t lx,ly,esx,esy; + + GET_LDOUBLE_WORDS(esx,hx,lx,x); + GET_LDOUBLE_WORDS(esy,hy,ly,y); + ix = esx&0x7fff; /* |x| */ + iy = esy&0x7fff; /* |y| */ + + if (((ix==0x7fff)&&((hx&0x7fffffff|lx)!=0)) || /* x is nan */ + ((iy==0x7fff)&&((hy&0x7fffffff|ly)!=0))) /* y is nan */ + return x+y; + if(x==y) return y; /* x=y, return y */ + if((ix|hx|lx)==0) { /* x == 0 */ + volatile long double u; + SET_LDOUBLE_WORDS(x,esy&0x8000,0,1);/* return +-minsubnormal */ + u = x; + u = u * u; /* raise underflow flag */ + return x; + } + if(esx<0x8000) { /* x > 0 */ + if(ix>iy||((ix==iy) && (hx>hy||((hx==hy)&&(lx>ly))))) { + /* x > y, x -= ulp */ + if(lx==0) { + if ((hx&0x7fffffff)==0) esx -= 1; + hx = (hx - 1) | (hx & 0x80000000); + } + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) { + hx = (hx + 1) | (hx & 0x80000000); + if ((hx&0x7fffffff)==0) esx += 1; + } + } + } else { /* x < 0 */ + if(esy>=0||(ix>iy||((ix==iy)&&(hx>hy||((hx==hy)&&(lx>ly)))))){ + /* x < y, x -= ulp */ + if(lx==0) { + if ((hx&0x7fffffff)==0) esx -= 1; + hx = (hx - 1) | (hx & 0x80000000); + } + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) { + hx = (hx + 1) | (hx & 0x80000000); + if ((hx&0x7fffffff)==0) esx += 1; + } + } + } + esy = esx&0x7fff; + if(esy==0x7fff) return x+x; /* overflow */ + if(esy==0) { + volatile long double u = x*x; /* underflow */ + if(u==x) { + SET_LDOUBLE_WORDS(x,esx,hx,lx); + return x; + } + } + SET_LDOUBLE_WORDS(x,esx,hx,lx); + return x; +} + +//__strong_alias(nexttowardl, nextafterl); diff --git a/openlibm/ld80/s_nexttoward.c b/openlibm/ld80/s_nexttoward.c new file mode 100644 index 0000000..b017668 --- /dev/null +++ b/openlibm/ld80/s_nexttoward.c @@ -0,0 +1,86 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* IEEE functions + * nexttoward(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include +#include + +#include "math_private.h" + +double +nexttoward(double x, long double y) +{ + int32_t hx,ix,iy; + u_int32_t lx,hy,ly,esy; + + EXTRACT_WORDS(hx,lx,x); + GET_LDOUBLE_WORDS(esy,hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = esy&0x7fff; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7fff)&&(hy|ly)!=0)) /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + volatile double u; + INSERT_WORDS(x,(esy&0x8000)<<16,1); /* return +-minsub */ + u = x; + u = u * u; /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if (esy>=0x8000||((ix>>20)&0x7ff)>iy-0x3c00 + || (((ix>>20)&0x7ff)==iy-0x3c00 + && (((hx<<11)|(lx>>21))>(hy&0x7fffffff) + || (((hx<<11)|(lx>>21))==(hy&0x7fffffff) + && (lx<<11)>ly)))) { /* x > y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if (esy<0x8000||((ix>>20)&0x7ff)>iy-0x3c00 + || (((ix>>20)&0x7ff)==iy-0x3c00 + && (((hx<<11)|(lx>>21))>(hy&0x7fffffff) + || (((hx<<11)|(lx>>21))==(hy&0x7fffffff) + && (lx<<11)>ly)))) {/* x < y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) { + x = x+x; /* overflow */ + return x; + } + if(hy<0x00100000) { + volatile double u = x*x; /* underflow */ + if(u==x) { + INSERT_WORDS(x,hx,lx); + return x; + } + } + INSERT_WORDS(x,hx,lx); + return x; +} diff --git a/openlibm/ld80/s_nexttowardf.c b/openlibm/ld80/s_nexttowardf.c new file mode 100644 index 0000000..f2ac10d --- /dev/null +++ b/openlibm/ld80/s_nexttowardf.c @@ -0,0 +1,67 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#include + +#include "math_private.h" + +float +nexttowardf(float x, long double y) +{ + int32_t hx,ix,iy; + u_int32_t hy,ly,esy; + + GET_FLOAT_WORD(hx,x); + GET_LDOUBLE_WORDS(esy,hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = esy&0x7fff; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>=0x7fff&&((hy|ly)!=0))) /* y is nan */ + return x+y; + if((long double) x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + volatile float u; + SET_FLOAT_WORD(x,((esy&0x8000)<<16)|1);/* return +-minsub*/ + u = x; + u = u * u; /* raise underflow flag */ + return x; + } + if(hx>=0) { /* x > 0 */ + if(esy>=0x8000||((ix>>23)&0xff)>iy-0x3f80 + || (((ix>>23)&0xff)==iy-0x3f80 + && ((ix&0x7fffff)<<8)>(hy&0x7fffffff))) {/* x > y, x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(esy<0x8000||((ix>>23)&0xff)>iy-0x3f80 + || (((ix>>23)&0xff)==iy-0x3f80 + && ((ix&0x7fffff)<<8)>(hy&0x7fffffff))) {/* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) { + x = x+x; /* overflow */ + return x; + } + if(hy<0x00800000) { + volatile float u = x*x; /* underflow */ + } + SET_FLOAT_WORD(x,hx); + return x; +} diff --git a/openlibm/ld80/s_remquol.c b/openlibm/ld80/s_remquol.c new file mode 100644 index 0000000..f649dca --- /dev/null +++ b/openlibm/ld80/s_remquol.c @@ -0,0 +1,166 @@ +/* @(#)e_fmod.c 1.3 95/01/18 */ +/*- + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#include + +#include +#include +#include + +#include "math_private.h" + +#define BIAS (LDBL_MAX_EXP - 1) + +/* + * These macros add and remove an explicit integer bit in front of the + * fractional mantissa, if the architecture doesn't have such a bit by + * default already. + */ +#ifdef LDBL_IMPLICIT_NBIT +#define LDBL_NBIT 0 +#define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) +#define HFRAC_BITS EXT_FRACHBITS +#else +#define LDBL_NBIT 0x80000000 +#define SET_NBIT(hx) (hx) +#define HFRAC_BITS (EXT_FRACHBITS - 1) +#endif + +#define MANL_SHIFT (EXT_FRACLBITS - 1) + +static const long double Zero[] = {0.0L, -0.0L}; + +/* + * Return the IEEE remainder and set *quo to the last n bits of the + * quotient, rounded to the nearest integer. We choose n=31 because + * we wind up computing all the integer bits of the quotient anyway as + * a side-effect of computing the remainder by the shift and subtract + * method. In practice, this is far more bits than are needed to use + * remquo in reduction algorithms. + * + * Assumptions: + * - The low part of the mantissa fits in a manl_t exactly. + * - The high part of the mantissa fits in an int64_t with enough room + * for an explicit integer bit in front of the fractional bits. + */ +long double +remquol(long double x, long double y, int *quo) +{ + int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ + uint32_t hy; + uint32_t lx,ly,lz; + uint32_t esx, esy; + int ix,iy,n,q,sx,sxy; + + GET_LDOUBLE_WORDS(esx,hx,lx,x); + GET_LDOUBLE_WORDS(esy,hy,ly,y); + sx = esx & 0x8000; + sxy = sx ^ (esy & 0x8000); + esx &= 0x7fff; /* |x| */ + esy &= 0x7fff; /* |y| */ + SET_LDOUBLE_EXP(x,esx); + SET_LDOUBLE_EXP(y,esy); + + /* purge off exception values */ + if((esy|hy|ly)==0 || /* y=0 */ + (esx == BIAS + LDBL_MAX_EXP) || /* or x not finite */ + (esy == BIAS + LDBL_MAX_EXP && + ((hy&~LDBL_NBIT)|ly)!=0)) /* or y is NaN */ + return (x*y)/(x*y); + if(esx<=esy) { + if((esx>MANL_SHIFT); lx = lx+lx;} + else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;} + q <<= 1; + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;q++;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) { /* return sign(x)*0 */ + *quo = (sxy ? -q : q); + return Zero[sx!=0]; + } + while(hx<(1ULL<>MANL_SHIFT); lx = lx+lx; + iy -= 1; + } + if (iy < LDBL_MIN_EXP) { + esx = (iy + BIAS + 512) & 0x7fff; + SET_LDOUBLE_WORDS(x,esx,hx,lx); + x *= 0x1p-512; + GET_LDOUBLE_WORDS(esx,hx,lx,x); + } else { + esx = (iy + BIAS) & 0x7fff; + } + SET_LDOUBLE_WORDS(x,esx,hx,lx); +fixup: + y = fabsl(y); + if (y < LDBL_MIN * 2) { + if (x+x>y || (x+x==y && (q & 1))) { + q++; + x-=y; + } + } else if (x>0.5*y || (x==0.5*y && (q & 1))) { + q++; + x-=y; + } + + GET_LDOUBLE_EXP(esx,x); + esx ^= sx; + SET_LDOUBLE_EXP(x,esx); + + q &= 0x7fffffff; + *quo = (sxy ? -q : q); + return x; +} diff --git a/openlibm/ld80/s_tanhl.c b/openlibm/ld80/s_tanhl.c new file mode 100644 index 0000000..1a46583 --- /dev/null +++ b/openlibm/ld80/s_tanhl.c @@ -0,0 +1,79 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* tanhl(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanhl(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). + * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) + * t + 2 + * 2 + * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) + * t + 2 + * 23.0 < x <= INF : tanhl(x) := 1. + * + * Special cases: + * tanhl(NaN) is NaN; + * only tanhl(0)=0 is exact for finite argument. + */ + +#include + +#include "math_private.h" + +static const long double one=1.0, two=2.0, tiny = 1.0e-4900L; + +long double +tanhl(long double x) +{ + long double t,z; + int32_t se; + u_int32_t jj0,jj1,ix; + + /* High word of |x|. */ + GET_LDOUBLE_WORDS(se,jj0,jj1,x); + ix = se&0x7fff; + + /* x is INF or NaN */ + if(ix==0x7fff) { + /* for NaN it's not important which branch: tanhl(NaN) = NaN */ + if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */ + else return one/x+one; /* tanhl(+inf)=+1 */ + } + + /* |x| < 23 */ + if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {/* |x|<23 */ + if ((ix|jj0|jj1) == 0) + return x; /* x == +- 0 */ + if (ix<0x3fc8) /* |x|<2**-55 */ + return x*(one+tiny); /* tanh(small) = small */ + if (ix>=0x3fff) { /* |x|>=1 */ + t = expm1l(two*fabsl(x)); + z = one - two/(t+two); + } else { + t = expm1l(-two*fabsl(x)); + z= -t/(t+two); + } + /* |x| > 23, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (se&0x8000)? -z: z; +} diff --git a/openlibm/ld80/s_truncl.c b/openlibm/ld80/s_truncl.c new file mode 100644 index 0000000..8a261d8 --- /dev/null +++ b/openlibm/ld80/s_truncl.c @@ -0,0 +1,72 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * From: @(#)s_floor.c 5.1 93/09/24 + */ + +/* + * truncl(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to truncl(x). + */ + +#include +//#include + +#include +#include +#include + +#include "math_private.h" + +#ifdef LDBL_IMPLICIT_NBIT +#define MANH_SIZE (EXT_FRACHBITS + 1) +#else +#define MANH_SIZE EXT_FRACHBITS +#endif + +static const long double huge = 1.0e300; +static const float zero[] = { 0.0, -0.0 }; + +long double +truncl(long double x) +{ + int e, es; + uint32_t ix0, ix1; + + GET_LDOUBLE_WORDS(es,ix0,ix1,x); + e = (es&0x7fff) - LDBL_MAX_EXP + 1; + + if (e < MANH_SIZE - 1) { + if (e < 0) { /* raise inexact if x != 0 */ + if (huge + x > 0.0) + return (zero[(es&0x8000)!=0]); + } else { + uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1); + if (((ix0 & m) | ix1) == 0) + return (x); /* x is integral */ + if (huge + x > 0.0) { /* raise inexact flag */ + ix0 &= ~m; + ix1 = 0; + } + } + } else if (e < LDBL_MANT_DIG - 1) { + uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1); + if ((ix1 & m) == 0) + return (x); /* x is integral */ + if (huge + x > 0.0) /* raise inexact flag */ + ix1 &= ~m; + } + SET_LDOUBLE_WORDS(x,es,ix0,ix1); + return (x); +} diff --git a/openlibm/loongarch64/Make.files b/openlibm/loongarch64/Make.files new file mode 100644 index 0000000..483a7cc --- /dev/null +++ b/openlibm/loongarch64/Make.files @@ -0,0 +1 @@ +$(CUR_SRCS) = fenv.c diff --git a/openlibm/loongarch64/fenv.c b/openlibm/loongarch64/fenv.c new file mode 100644 index 0000000..9c95f2a --- /dev/null +++ b/openlibm/loongarch64/fenv.c @@ -0,0 +1,27 @@ +#define __fenv_static +#include + +#ifdef __GNUC_GNU_INLINE__ +#error "This file must be compiled with C99 'inline' semantics" +#endif + +/* + * Hopefully the system ID byte is immutable, so it's valid to use + * this as a default environment. + */ +const fenv_t __fe_dfl_env = 0; + +extern inline int feclearexcept(int __excepts); +extern inline int fegetexceptflag(fexcept_t *__flagp, int __excepts); +extern inline int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +extern inline int feraiseexcept(int __excepts); +extern inline int fetestexcept(int __excepts); +extern inline int fegetround(void); +extern inline int fesetround(int __round); +extern inline int fegetenv(fenv_t *__envp); +extern inline int feholdexcept(fenv_t *__envp); +extern inline int fesetenv(const fenv_t *__envp); +extern inline int feupdateenv(const fenv_t *__envp); +extern inline int feenableexcept(int __mask); +extern inline int fedisableexcept(int __mask); +extern inline int fegetexcept(void); \ No newline at end of file diff --git a/openlibm/mips/Make.files b/openlibm/mips/Make.files new file mode 100644 index 0000000..483a7cc --- /dev/null +++ b/openlibm/mips/Make.files @@ -0,0 +1 @@ +$(CUR_SRCS) = fenv.c diff --git a/openlibm/mips/fenv-softfloat.h b/openlibm/mips/fenv-softfloat.h new file mode 100644 index 0000000..0511335 --- /dev/null +++ b/openlibm/mips/fenv-softfloat.h @@ -0,0 +1,184 @@ +/*- + * Copyright (c) 2004-2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + */ + +#ifndef _FENV_H_ +#error "This file is meant to be included only by ." +#endif + +/* + * This file implements the functionality of on platforms that + * lack an FPU and use softfloat in libc for floating point. To use it, + * you must write an that provides the following: + * + * - a typedef for fenv_t, which may be an integer or struct type + * - a typedef for fexcept_t (XXX This file assumes fexcept_t is a + * simple integer type containing the exception mask.) + * - definitions of FE_* constants for the five exceptions and four + * rounding modes in IEEE 754, as described in fenv(3) + * - a definition, and the corresponding external symbol, for FE_DFL_ENV + * - a macro __set_env(env, flags, mask, rnd), which sets the given fenv_t + * from the exception flags, mask, and rounding mode + * - macros __env_flags(env), __env_mask(env), and __env_round(env), which + * extract fields from an fenv_t + * - a definition of __fenv_static + * + * If the architecture supports an optional FPU, it's recommended that you + * define fenv_t and fexcept_t to match the hardware ABI. Otherwise, it + * doesn't matter how you define them. + */ + +extern int __softfloat_float_exception_flags; +extern int __softfloat_float_exception_mask; +extern int __softfloat_float_rounding_mode; +void __softfloat_float_raise(int); + +__fenv_static inline int +feclearexcept(int __excepts) +{ + + __softfloat_float_exception_flags &= ~__excepts; + return (0); +} + +__fenv_static inline int +fegetexceptflag(fexcept_t *__flagp, int __excepts) +{ + + *__flagp = __softfloat_float_exception_flags & __excepts; + return (0); +} + +__fenv_static inline int +fesetexceptflag(const fexcept_t *__flagp, int __excepts) +{ + + __softfloat_float_exception_flags &= ~__excepts; + __softfloat_float_exception_flags |= *__flagp & __excepts; + return (0); +} + +__fenv_static inline int +feraiseexcept(int __excepts) +{ + + __softfloat_float_raise(__excepts); + return (0); +} + +__fenv_static inline int +fetestexcept(int __excepts) +{ + + return (__softfloat_float_exception_flags & __excepts); +} + +__fenv_static inline int +fegetround(void) +{ + + return (__softfloat_float_rounding_mode); +} + +__fenv_static inline int +fesetround(int __round) +{ + + __softfloat_float_rounding_mode = __round; + return (0); +} + +__fenv_static inline int +fegetenv(fenv_t *__envp) +{ + + __set_env(*__envp, __softfloat_float_exception_flags, + __softfloat_float_exception_mask, __softfloat_float_rounding_mode); + return (0); +} + +__fenv_static inline int +feholdexcept(fenv_t *__envp) +{ + fenv_t __env; + + fegetenv(__envp); + __softfloat_float_exception_flags = 0; + __softfloat_float_exception_mask = 0; + return (0); +} + +__fenv_static inline int +fesetenv(const fenv_t *__envp) +{ + + __softfloat_float_exception_flags = __env_flags(*__envp); + __softfloat_float_exception_mask = __env_mask(*__envp); + __softfloat_float_rounding_mode = __env_round(*__envp); + return (0); +} + +__fenv_static inline int +feupdateenv(const fenv_t *__envp) +{ + int __oflags = __softfloat_float_exception_flags; + + fesetenv(__envp); + feraiseexcept(__oflags); + return (0); +} + +#if __BSD_VISIBLE + +/* We currently provide no external definitions of the functions below. */ + +__fenv_static inline int +feenableexcept(int __mask) +{ + int __omask = __softfloat_float_exception_mask; + + __softfloat_float_exception_mask |= __mask; + return (__omask); +} + +__fenv_static inline int +fedisableexcept(int __mask) +{ + int __omask = __softfloat_float_exception_mask; + + __softfloat_float_exception_mask &= ~__mask; + return (__omask); +} + +__fenv_static inline int +fegetexcept(void) +{ + + return (__softfloat_float_exception_mask); +} + +#endif /* __BSD_VISIBLE */ \ No newline at end of file diff --git a/openlibm/mips/fenv.c b/openlibm/mips/fenv.c new file mode 100644 index 0000000..4a7ed80 --- /dev/null +++ b/openlibm/mips/fenv.c @@ -0,0 +1,67 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + */ + +#define __fenv_static +#include "openlibm_fenv.h" + +#ifdef __GNUC_GNU_INLINE__ +#error "This file must be compiled with C99 'inline' semantics" +#endif + +/* + * Hopefully the system ID byte is immutable, so it's valid to use + * this as a default environment. + */ +const fenv_t __fe_dfl_env = 0; + +#ifdef __mips_soft_float +#define __set_env(env, flags, mask, rnd) env = ((flags) \ + | (mask)<<_FPUSW_SHIFT \ + | (rnd) << 24) +#define __env_flags(env) ((env) & FE_ALL_EXCEPT) +#define __env_mask(env) (((env) >> _FPUSW_SHIFT) \ + & FE_ALL_EXCEPT) +#define __env_round(env) (((env) >> 24) & _ROUND_MASK) +#include "fenv-softfloat.h" +#endif + +extern inline int feclearexcept(int __excepts); +extern inline int fegetexceptflag(fexcept_t *__flagp, int __excepts); +extern inline int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +extern inline int feraiseexcept(int __excepts); +extern inline int fetestexcept(int __excepts); +extern inline int fegetround(void); +extern inline int fesetround(int __round); +extern inline int fegetenv(fenv_t *__envp); +extern inline int feholdexcept(fenv_t *__envp); +extern inline int fesetenv(const fenv_t *__envp); +extern inline int feupdateenv(const fenv_t *__envp); +extern inline int feenableexcept(int __mask); +extern inline int fedisableexcept(int __mask); +extern inline int fegetexcept(void); + diff --git a/openlibm/openlibm.pc.in b/openlibm/openlibm.pc.in new file mode 100644 index 0000000..bfad876 --- /dev/null +++ b/openlibm/openlibm.pc.in @@ -0,0 +1,6 @@ +Name: openlibm +Version: ${version} +URL: https://github.com/JuliaMath/openlibm +Description: High quality system independent, open source libm. +Cflags: -I${includedir} +Libs: -L${libdir} -lopenlibm diff --git a/openlibm/powerpc/Make.files b/openlibm/powerpc/Make.files new file mode 100644 index 0000000..483a7cc --- /dev/null +++ b/openlibm/powerpc/Make.files @@ -0,0 +1 @@ +$(CUR_SRCS) = fenv.c diff --git a/openlibm/powerpc/fenv.c b/openlibm/powerpc/fenv.c new file mode 100644 index 0000000..bf7d0cb --- /dev/null +++ b/openlibm/powerpc/fenv.c @@ -0,0 +1,47 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + */ + +#include + +#ifdef __GNUC_GNU_INLINE__ +#error "This file must be compiled with C99 'inline' semantics" +#endif + +const fenv_t __fe_dfl_env = 0x00000000; + +extern inline int feclearexcept(int __excepts); +extern inline int fegetexceptflag(fexcept_t *__flagp, int __excepts); +extern inline int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +extern inline int feraiseexcept(int __excepts); +extern inline int fetestexcept(int __excepts); +extern inline int fegetround(void); +extern inline int fesetround(int __round); +extern inline int fegetenv(fenv_t *__envp); +extern inline int feholdexcept(fenv_t *__envp); +extern inline int fesetenv(const fenv_t *__envp); +extern inline int feupdateenv(const fenv_t *__envp); diff --git a/openlibm/riscv64/Make.files b/openlibm/riscv64/Make.files new file mode 100644 index 0000000..483a7cc --- /dev/null +++ b/openlibm/riscv64/Make.files @@ -0,0 +1 @@ +$(CUR_SRCS) = fenv.c diff --git a/openlibm/riscv64/fenv.c b/openlibm/riscv64/fenv.c new file mode 100644 index 0000000..467bffe --- /dev/null +++ b/openlibm/riscv64/fenv.c @@ -0,0 +1,63 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: head/lib/msun/riscv/fenv.c 332792 2018-04-19 20:36:15Z brooks $ + */ + +#define __fenv_static +#include + +#ifdef __GNUC_GNU_INLINE__ +#error "This file must be compiled with C99 'inline' semantics" +#endif + +/* + * Hopefully the system ID byte is immutable, so it's valid to use + * this as a default environment. + */ +const fenv_t __fe_dfl_env = 0; + +#ifdef __riscv_float_abi_soft +#define __set_env(env, flags, mask, rnd) env = ((flags) | (rnd) << 5) +#define __env_flags(env) ((env) & FE_ALL_EXCEPT) +#define __env_mask(env) (0) /* No exception traps. */ +#define __env_round(env) (((env) >> 5) & _ROUND_MASK) +#include "fenv-softfloat.h" +#endif + +extern inline int feclearexcept(int __excepts); +extern inline int fegetexceptflag(fexcept_t *__flagp, int __excepts); +extern inline int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +extern inline int feraiseexcept(int __excepts); +extern inline int fetestexcept(int __excepts); +extern inline int fegetround(void); +extern inline int fesetround(int __round); +extern inline int fegetenv(fenv_t *__envp); +extern inline int feholdexcept(fenv_t *__envp); +extern inline int fesetenv(const fenv_t *__envp); +extern inline int feupdateenv(const fenv_t *__envp); +extern inline int feenableexcept(int __mask); +extern inline int fedisableexcept(int __mask); +extern inline int fegetexcept(void); diff --git a/openlibm/s390/Make.files b/openlibm/s390/Make.files new file mode 100644 index 0000000..483a7cc --- /dev/null +++ b/openlibm/s390/Make.files @@ -0,0 +1 @@ +$(CUR_SRCS) = fenv.c diff --git a/openlibm/s390/fenv.c b/openlibm/s390/fenv.c new file mode 100644 index 0000000..2bcce76 --- /dev/null +++ b/openlibm/s390/fenv.c @@ -0,0 +1,50 @@ +/*- + * Copyright (c) 2016 Dan Horák + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + * + * cloned from ppc/fenv.c + */ + +#define __fenv_static +#include + +#ifdef __GNUC_GNU_INLINE__ +#error "This file must be compiled with C99 'inline' semantics" +#endif + +const fenv_t __fe_dfl_env = 0x00000000; + +extern inline int feclearexcept(int __excepts); +extern inline int fegetexceptflag(fexcept_t *__flagp, int __excepts); +extern inline int fesetexceptflag(const fexcept_t *__flagp, int __excepts); +extern inline int feraiseexcept(int __excepts); +extern inline int fetestexcept(int __excepts); +extern inline int fegetround(void); +extern inline int fesetround(int __round); +extern inline int fegetenv(fenv_t *__envp); +extern inline int feholdexcept(fenv_t *__envp); +extern inline int fesetenv(const fenv_t *__envp); +extern inline int feupdateenv(const fenv_t *__envp); diff --git a/openlibm/src/Make.files b/openlibm/src/Make.files new file mode 100644 index 0000000..5170403 --- /dev/null +++ b/openlibm/src/Make.files @@ -0,0 +1,78 @@ +$(CUR_SRCS) = common.c \ + e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \ + e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c e_exp.c \ + e_expf.c e_fmod.c e_fmodf.c \ + e_hypot.c e_hypotf.c e_j0.c e_j0f.c e_j1.c e_j1f.c \ + e_jn.c e_jnf.c e_lgamma.c e_lgamma_r.c e_lgammaf.c e_lgammaf_r.c \ + e_log.c e_log10.c e_log10f.c e_log2.c e_log2f.c e_logf.c \ + e_pow.c e_powf.c e_remainder.c e_remainderf.c \ + e_rem_pio2.c e_rem_pio2f.c \ + e_sinh.c e_sinhf.c e_sqrt.c e_sqrtf.c \ + k_cos.c k_exp.c k_expf.c k_rem_pio2.c k_sin.c k_tan.c \ + k_cosf.c k_sinf.c k_tanf.c \ + s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_carg.c s_cargf.c \ + s_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.c \ + s_copysign.c s_copysignf.c s_cos.c s_cosf.c \ + s_csqrt.c s_csqrtf.c s_erf.c s_erff.c \ + s_exp2.c s_exp2f.c s_expm1.c s_expm1f.c s_fabs.c s_fabsf.c s_fdim.c \ + s_floor.c s_floorf.c \ + s_fmax.c s_fmaxf.c s_fmin.c \ + s_fminf.c s_fpclassify.c \ + s_frexp.c s_frexpf.c s_ilogb.c s_ilogbf.c \ + s_isinf.c s_isfinite.c s_isnormal.c s_isnan.c \ + s_log1p.c s_log1pf.c s_logb.c s_logbf.c \ + s_modf.c s_modff.c \ + s_nextafter.c s_nextafterf.c \ + s_nexttowardf.c s_remquo.c s_remquof.c \ + s_rint.c s_rintf.c s_round.c s_roundf.c \ + s_scalbln.c s_scalbn.c s_scalbnf.c s_signbit.c \ + s_signgam.c s_sin.c s_sincos.c \ + s_sinf.c s_sincosf.c s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c \ + s_trunc.c s_truncf.c s_cpow.c s_cpowf.c \ + w_cabs.c w_cabsf.c + +ifneq ($(ARCH), wasm32) + +$(CUR_SRCS) += \ + s_fma.c s_fmaf.c s_lrint.c s_lrintf.c s_lround.c s_lroundf.c \ + s_llrint.c s_llrintf.c s_llround.c s_llroundf.c s_nearbyint.c + +ifneq ($(OS), WINNT) +$(CUR_SRCS) += s_nan.c +endif + +endif + +# Add in long double functions for x86, x64 and aarch64 +ifeq ($(LONG_DOUBLE_NOT_DOUBLE),1) +# C99 long double functions +$(CUR_SRCS) += s_copysignl.c s_fabsl.c s_llrintl.c s_lrintl.c s_modfl.c + +# If long double != double use these; otherwise, we alias the double versions. +$(CUR_SRCS) += e_acosl.c e_asinl.c e_atan2l.c e_fmodl.c \ + s_fmaxl.c s_fminl.c s_ilogbl.c \ + e_hypotl.c e_lgammal.c e_remainderl.c e_sqrtl.c \ + s_atanl.c s_ceill.c s_cosl.c s_cprojl.c \ + s_csqrtl.c s_floorl.c s_fmal.c \ + s_frexpl.c s_logbl.c s_nexttoward.c \ + s_remquol.c s_roundl.c s_lroundl.c s_llroundl.c \ + s_cpowl.c s_cargl.c \ + s_sinl.c s_sincosl.c s_tanl.c s_truncl.c w_cabsl.c \ + s_nextafterl.c s_rintl.c s_scalbnl.c polevll.c \ + s_casinl.c s_ctanl.c \ + s_cimagl.c s_conjl.c s_creall.c s_cacoshl.c s_catanhl.c s_casinhl.c \ + s_catanl.c s_csinl.c s_cacosl.c s_cexpl.c s_csinhl.c s_ccoshl.c \ + s_clogl.c s_ctanhl.c s_ccosl.c s_cbrtl.c +endif + +# C99 complex functions +$(CUR_SRCS) += s_ccosh.c s_ccoshf.c s_cexp.c s_cexpf.c \ + s_cimag.c s_cimagf.c \ + s_conj.c s_conjf.c \ + s_cproj.c s_cprojf.c s_creal.c s_crealf.c \ + s_csinh.c s_csinhf.c s_ctanh.c s_ctanhf.c \ + s_cacos.c s_cacosf.c \ + s_cacosh.c s_cacoshf.c \ + s_casin.c s_casinf.c s_casinh.c s_casinhf.c \ + s_catan.c s_catanf.c s_catanh.c s_catanhf.c \ + s_clog.c s_clogf.c diff --git a/openlibm/src/aarch64_fpmath.h b/openlibm/src/aarch64_fpmath.h new file mode 100644 index 0000000..e1fdc63 --- /dev/null +++ b/openlibm/src/aarch64_fpmath.h @@ -0,0 +1,60 @@ +/*- + * Copyright (c) 2002, 2003 David Schultz + * Copyright (2) 2014 The FreeBSD Foundation + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: head/lib/libc/aarch64/_fpmath.h 281197 2015-04-07 09:52:14Z andrew $ + */ + +#include + +union IEEEl2bits { + long double e; + struct { + uint64_t manl :64; + uint64_t manh :48; + unsigned int exp :15; + unsigned int sign :1; + } bits; + /* TODO andrew: Check the packing here */ + struct { + uint64_t manl :64; + uint64_t manh :48; + unsigned int expsign :16; + } xbits; +}; + +#define LDBL_NBIT 0 +#define LDBL_IMPLICIT_NBIT +#define mask_nbit_l(u) ((void)0) + +#define LDBL_MANH_SIZE 48 +#define LDBL_MANL_SIZE 64 + +#define LDBL_TO_ARRAY32(u, a) do { \ + (a)[0] = (uint32_t)(u).bits.manl; \ + (a)[1] = (uint32_t)((u).bits.manl >> 32); \ + (a)[2] = (uint32_t)(u).bits.manh; \ + (a)[3] = (uint32_t)((u).bits.manh >> 32); \ +} while(0) diff --git a/openlibm/src/amd64_fpmath.h b/openlibm/src/amd64_fpmath.h new file mode 100644 index 0000000..41b01c3 --- /dev/null +++ b/openlibm/src/amd64_fpmath.h @@ -0,0 +1,55 @@ +/*- + * Copyright (c) 2002, 2003 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/libc/amd64/_fpmath.h,v 1.7 2008/01/17 16:39:06 bde Exp $ + */ + +union IEEEl2bits { + long double e; + struct { + unsigned int manl :32; + unsigned int manh :32; + unsigned int exp :15; + unsigned int sign :1; + unsigned int junkl :16; + unsigned int junkh :32; + } bits; + struct { + unsigned long man :64; + unsigned int expsign :16; + unsigned long junk :48; + } xbits; +}; + +#define LDBL_NBIT 0x80000000 +#define mask_nbit_l(u) ((u).bits.manh &= ~LDBL_NBIT) + +#define LDBL_MANH_SIZE 32 +#define LDBL_MANL_SIZE 32 + +#define LDBL_TO_ARRAY32(u, a) do { \ + (a)[0] = (uint32_t)(u).bits.manl; \ + (a)[1] = (uint32_t)(u).bits.manh; \ +} while (0) diff --git a/openlibm/src/bsd_cdefs.h b/openlibm/src/bsd_cdefs.h new file mode 100644 index 0000000..5799193 --- /dev/null +++ b/openlibm/src/bsd_cdefs.h @@ -0,0 +1,102 @@ +/*- + * Copyright (c) 1991, 1993 + * The Regents of the University of California. All rights reserved. + * + * This code is derived from software contributed to Berkeley by + * Berkeley Software Design, Inc. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * @(#)cdefs.h 8.8 (Berkeley) 1/9/95 + * $FreeBSD: src/sys/sys/cdefs.h,v 1.114 2011/02/18 21:44:53 nwhitehorn Exp $ + */ + +/* Do not redefine macros if the system provides them in sys/cdefs.h. + * The two macros correspond to different platforms. */ +#ifndef _BSD_CDEFS_H_ +#define _BSD_CDEFS_H_ + +/* + * This code has been put in place to help reduce the addition of + * compiler specific defines in FreeBSD code. It helps to aid in + * having a compiler-agnostic source tree. + */ + +#if defined(__GNUC__) || defined(__INTEL_COMPILER) + +#if __GNUC__ >= 3 || defined(__INTEL_COMPILER) +#define __GNUCLIKE_ASM 3 +#else +#define __GNUCLIKE_ASM 2 +#endif + +#define __CC_SUPPORTS___INLINE__ 1 + +#endif /* __GNUC__ || __INTEL_COMPILER */ + +#if defined(__STDC__) || defined(__cplusplus) + +#define __volatile volatile +#if defined(__cplusplus) +#define __inline inline /* convert to C++ keyword */ +#else +#if !defined(__CC_SUPPORTS___INLINE) +#define __inline /* delete GCC keyword */ +#endif /* ! __CC_SUPPORTS___INLINE */ +#endif /* !__cplusplus */ + +#else /* !(__STDC__ || __cplusplus) */ + +#if !defined(__CC_SUPPORTS___INLINE) +#define __inline +#define __volatile +#endif /* !__CC_SUPPORTS___INLINE */ +#endif /* !(__STDC__ || __cplusplus) */ + +/* + * Macro to test if we're using a specific version of gcc or later. + */ +#ifndef __GNUC_PREREQ__ +#if defined(__GNUC__) && !defined(__INTEL_COMPILER) +#define __GNUC_PREREQ__(ma, mi) \ + (__GNUC__ > (ma) || __GNUC__ == (ma) && __GNUC_MINOR__ >= (mi)) +#else +#define __GNUC_PREREQ__(ma, mi) 0 +#endif +#endif /* __GNUC_PREREQ__ */ + +/* + * Compiler-dependent macro to help declare pure (no side effects) functions. + * It is null except for versions of gcc that are known to support the features + * properly (old versions of gcc-2 supported the dead and pure features + * in a different (wrong) way), and for icc. If we do not provide an implementation + * for a given compiler, let the compile fail if it is told to use + * a feature that we cannot live without. + */ +#if !defined(__pure2) && (__GNUC_PREREQ__(2, 7) || defined(__INTEL_COMPILER)) +#define __pure2 __attribute__((__const__)) +#endif + +#endif /* !_BSD_CDEFS_H_ */ diff --git a/openlibm/src/cdefs-compat.h b/openlibm/src/cdefs-compat.h new file mode 100644 index 0000000..834c547 --- /dev/null +++ b/openlibm/src/cdefs-compat.h @@ -0,0 +1,105 @@ +#ifndef _CDEFS_COMPAT_H_ +#define _CDEFS_COMPAT_H_ + +#if !defined(__BEGIN_DECLS) +#if defined(__cplusplus) +#define __BEGIN_DECLS extern "C" { +#define __END_DECLS } +#else +#define __BEGIN_DECLS +#define __END_DECLS +#endif +#endif /* !defined(__BEGIN_DECLS) */ + +#ifdef __GNUC__ +#if defined(__strong_alias) && defined(__NetBSD__) +#define openlibm_strong_reference(sym,alias) __strong_alias(alias,sym) +#elif defined(__strong_reference) +#define openlibm_strong_reference(sym,alias) __strong_reference(sym,alias) +#else +#ifdef __APPLE__ +#define openlibm_strong_reference(sym,aliassym) openlibm_weak_reference(sym,aliassym) +#else +#define openlibm_strong_reference(sym,aliassym) \ + OLM_DLLEXPORT extern __typeof (aliassym) aliassym __attribute__ ((__alias__ (#sym))); +#endif /* __APPLE__ */ +#endif /* __strong_reference */ + +#ifdef __wasm__ +#define openlibm_weak_reference(sym,alias) openlibm_strong_reference(sym,alias) +#elif defined(__weak_alias) && defined(__NetBSD__) +#define openlibm_weak_reference(sym,alias) __weak_alias(alias,sym) +#elif defined(__weak_reference) +#define openlibm_weak_reference(sym,alias) __weak_reference(sym,alias) +#else +#ifdef __ELF__ +#ifdef __STDC__ +#define openlibm_weak_reference(sym,alias) \ + __asm__(".weak " #alias); \ + __asm__(".equ " #alias ", " #sym) +#ifdef __warn_references +#define openlibm_warn_references(sym,msg) __warn_references(sym,msg) +#else +#define openlibm_warn_references(sym,msg) \ + __asm__(".section .gnu.warning." #sym); \ + __asm__(".asciz \"" msg "\""); \ + __asm__(".previous") +#endif /* __warn_references */ +#else +#define openlibm_weak_reference(sym,alias) \ + __asm__(".weak alias"); \ + __asm__(".equ alias, sym") +#ifdef __warn_references +#define openlibm_warn_references(sym,msg) __warn_references(sym,msg) +#else +#define openlibm_warn_references(sym,msg) \ + __asm__(".section .gnu.warning.sym"); \ + __asm__(".asciz \"msg\""); \ + __asm__(".previous") +#endif /* __warn_references */ +#endif /* __STDC__ */ +#elif defined(__clang__) /* CLANG */ +#if defined(_WIN32) && defined(_X86_) +#define openlibm_asm_symbol_prefix "_" +#else +#define openlibm_asm_symbol_prefix "" +#endif +#ifdef __STDC__ +#define openlibm_weak_reference(sym,alias) \ + __asm__(".weak_reference " openlibm_asm_symbol_prefix #alias); \ + __asm__(".set " openlibm_asm_symbol_prefix #alias ", " openlibm_asm_symbol_prefix #sym) +#else +#define openlibm_weak_reference(sym,alias) \ + __asm__(".weak_reference openlibm_asm_symbol_prefix/**/alias");\ + __asm__(".set openlibm_asm_symbol_prefix/**/alias, openlibm_asm_symbol_prefix/**/sym") +#endif +#else /* !__ELF__ */ +#ifdef __STDC__ +#define openlibm_weak_reference(sym,alias) \ + __asm__(".stabs \"_" #alias "\",11,0,0,0"); \ + __asm__(".stabs \"_" #sym "\",1,0,0,0") +#ifdef __warn_references +#define openlibm_warn_references(sym,msg) __warn_references(sym,msg) +#else +#define openlibm_warn_references(sym,msg) \ + __asm__(".stabs \"" msg "\",30,0,0,0"); \ + __asm__(".stabs \"_" #sym "\",1,0,0,0") +#endif /* __warn_references */ +#else +#define openlibm_weak_reference(sym,alias) \ + __asm__(".stabs \"_/**/alias\",11,0,0,0"); \ + __asm__(".stabs \"_/**/sym\",1,0,0,0") +#ifdef __warn_references +#define openlibm_warn_references(sym,msg) __warn_references(sym,msg) +#else +#define openlibm_warn_references(sym,msg) \ + __asm__(".stabs msg,30,0,0,0"); \ + __asm__(".stabs \"_/**/sym\",1,0,0,0") +#endif /* __warn_references */ +#endif /* __STDC__ */ +#endif /* __ELF__ */ +#endif /* __weak_reference */ +#endif /* __GNUC__ */ + + +#endif /* _CDEFS_COMPAT_H_ */ diff --git a/openlibm/src/common.c b/openlibm/src/common.c new file mode 100644 index 0000000..b02d697 --- /dev/null +++ b/openlibm/src/common.c @@ -0,0 +1,7 @@ +#include + +#include "math_private.h" + +OLM_DLLEXPORT int isopenlibm(void) { + return 1; +} diff --git a/openlibm/src/e_acos.c b/openlibm/src/e_acos.c new file mode 100644 index 0000000..7295ad6 --- /dev/null +++ b/openlibm/src/e_acos.c @@ -0,0 +1,111 @@ + +/* @(#)e_acos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_acos.c,v 1.13 2008/07/31 22:41:26 das Exp $"); + +/* __ieee754_acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 + * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) + * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) + * = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term + * for f so that f+c ~ sqrt(z). + * For x<-0.5 + * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) + * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: sqrt + */ + +#include +#include + +#include "math_private.h" + +static const double +one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ +static volatile double +pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ +static const double +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +OLM_DLLEXPORT double +__ieee754_acos(double x) +{ + double z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3ff00000) { /* |x| >= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3fe00000) { /* |x| < 0.5 */ + if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = sqrt(z); + r = p/q; + w = r*s-pio2_lo; + return pi - 2.0*(s+w); + } else { /* x > 0.5 */ + z = (one-x)*0.5; + s = sqrt(z); + df = s; + SET_LOW_WORD(df,0); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return 2.0*(df+w); + } +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(acos, acosl); +#endif diff --git a/openlibm/src/e_acosf.c b/openlibm/src/e_acosf.c new file mode 100644 index 0000000..2beab5c --- /dev/null +++ b/openlibm/src/e_acosf.c @@ -0,0 +1,78 @@ +/* e_acosf.c -- float version of e_acos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_acosf.c,v 1.11 2008/08/03 17:39:54 das Exp $"); + +#include + +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pio2_hi = 1.5707962513e+00; /* 0x3fc90fda */ +static volatile float +pio2_lo = 7.5497894159e-08; /* 0x33a22168 */ +static const float +pS0 = 1.6666586697e-01, +pS1 = -4.2743422091e-02, +pS2 = -8.6563630030e-03, +qS1 = -7.0662963390e-01; + +OLM_DLLEXPORT float +__ieee754_acosf(float x) +{ + float z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3f800000) { /* |x| >= 1 */ + if(ix==0x3f800000) { /* |x| == 1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3f000000) { /* |x| < 0.5 */ + if(ix<=0x32800000) return pio2_hi+pio2_lo;/*if|x|<2**-26*/ + z = x*x; + p = z*(pS0+z*(pS1+z*pS2)); + q = one+z*qS1; + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*(float)0.5; + p = z*(pS0+z*(pS1+z*pS2)); + q = one+z*qS1; + s = sqrtf(z); + r = p/q; + w = r*s-pio2_lo; + return pi - (float)2.0*(s+w); + } else { /* x > 0.5 */ + int32_t idf; + z = (one-x)*(float)0.5; + s = sqrtf(z); + df = s; + GET_FLOAT_WORD(idf,df); + SET_FLOAT_WORD(df,idf&0xfffff000); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*pS2)); + q = one+z*qS1; + r = p/q; + w = r*s+c; + return (float)2.0*(df+w); + } +} diff --git a/openlibm/src/e_acosh.c b/openlibm/src/e_acosh.c new file mode 100644 index 0000000..1e783a6 --- /dev/null +++ b/openlibm/src/e_acosh.c @@ -0,0 +1,68 @@ + +/* @(#)e_acosh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_acosh.c,v 1.9 2008/02/22 02:30:34 das Exp $"); + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include +#include + +#include "math_private.h" + +static const double +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +OLM_DLLEXPORT double +__ieee754_acosh(double x) +{ + double t; + int32_t hx; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + if(hx<0x3ff00000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x41b00000) { /* x > 2**28 */ + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); + } else { /* 1 + +#include "math_private.h" + +static const float +one = 1.0, +ln2 = 6.9314718246e-01; /* 0x3f317218 */ + +OLM_DLLEXPORT float +__ieee754_acoshf(float x) +{ + float t; + int32_t hx; + GET_FLOAT_WORD(hx,x); + if(hx<0x3f800000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4d800000) { /* x > 2**28 */ + if(hx >=0x7f800000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */ + } else if (hx==0x3f800000) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one))); + } else { /* 1. + */ + +#include +#include + +#include "invtrig.h" +#include "math_private.h" + +static const long double +one= 1.00000000000000000000e+00; + +#ifdef __i386__ +/* XXX Work around the fact that gcc truncates long double constants on i386 */ +static volatile double +pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ +pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ +#define pi ((long double)pi1 + pi2) +#else +static const long double +pi = 3.14159265358979323846264338327950280e+00L; +#endif + +OLM_DLLEXPORT long double +acosl(long double x) +{ + union IEEEl2bits u; + long double z,p,q,r,w,s,c,df; + int16_t expsign, expt; + u.e = x; + expsign = u.xbits.expsign; + expt = expsign & 0x7fff; + if(expt >= BIAS) { /* |x| >= 1 */ + if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) { + if (expsign>0) return 0.0; /* acos(1) = 0 */ + else return pi+2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(expt 0.5 */ + z = (one-x)*0.5; + s = sqrtl(z); + u.e = s; + u.bits.manl = 0; + df = u.e; + c = (z-df*df)/(s+df); + p = P(z); + q = Q(z); + r = p/q; + w = r*s+c; + return 2.0*(df+w); + } +} diff --git a/openlibm/src/e_asin.c b/openlibm/src/e_asin.c new file mode 100644 index 0000000..e287bf1 --- /dev/null +++ b/openlibm/src/e_asin.c @@ -0,0 +1,117 @@ + +/* @(#)e_asin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_asin.c,v 1.15 2011/02/10 07:37:50 das Exp $"); + +/* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * where + * R(x^2) is a rational approximation of (asin(x)-x)/x^3 + * and its remez error is bounded by + * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) + * + * For x in [0.5,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + +#include +#include + +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +huge = 1.000e+300, +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ + /* coefficient for R(x^2) */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +OLM_DLLEXPORT double +__ieee754_asin(double x) +{ + double t=0.0,w,p,q,c,r,s; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>= 0x3ff00000) { /* |x|>= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3fe00000) { /* |x|<0.5 */ + if(ix<0x3e500000) { /* if |x| < 2**-26 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabs(x); + t = w*0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = sqrt(t); + if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + w = s; + SET_LOW_WORD(w,0); + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(asin, asinl); +#endif diff --git a/openlibm/src/e_asinf.c b/openlibm/src/e_asinf.c new file mode 100644 index 0000000..1c1ab2c --- /dev/null +++ b/openlibm/src/e_asinf.c @@ -0,0 +1,66 @@ +/* e_asinf.c -- float version of e_asin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_asinf.c,v 1.13 2008/08/08 00:21:27 das Exp $"); + +#include + +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +huge = 1.000e+30, + /* coefficient for R(x^2) */ +pS0 = 1.6666586697e-01, +pS1 = -4.2743422091e-02, +pS2 = -8.6563630030e-03, +qS1 = -7.0662963390e-01; + +static const double +pio2 = 1.570796326794896558e+00; + +OLM_DLLEXPORT float +__ieee754_asinf(float x) +{ + double s; + float t,w,p,q; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3f800000) { /* |x| >= 1 */ + if(ix==0x3f800000) /* |x| == 1 */ + return x*pio2; /* asin(+-1) = +-pi/2 with inexact */ + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3f000000) { /* |x|<0.5 */ + if(ix<0x39800000) { /* |x| < 2**-12 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } + t = x*x; + p = t*(pS0+t*(pS1+t*pS2)); + q = one+t*qS1; + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabsf(x); + t = w*(float)0.5; + p = t*(pS0+t*(pS1+t*pS2)); + q = one+t*qS1; + s = sqrt(t); + w = p/q; + t = pio2-2.0*(s+s*w); + if(hx>0) return t; else return -t; +} diff --git a/openlibm/src/e_asinl.c b/openlibm/src/e_asinl.c new file mode 100644 index 0000000..521913a --- /dev/null +++ b/openlibm/src/e_asinl.c @@ -0,0 +1,77 @@ + +/* @(#)e_asin.c 1.3 95/01/18 */ +/* FreeBSD: head/lib/msun/src/e_asin.c 176451 2008-02-22 02:30:36Z das */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_asinl.c,v 1.2 2008/08/03 17:49:05 das Exp $"); + +/* + * See comments in e_asin.c. + * Converted to long double by David Schultz . + */ + +#include +#include + +#include "invtrig.h" +#include "math_private.h" + +static const long double +one = 1.00000000000000000000e+00, +huge = 1.000e+300; + +OLM_DLLEXPORT long double +asinl(long double x) +{ + union IEEEl2bits u; + long double t=0.0,w,p,q,c,r,s; + int16_t expsign, expt; + u.e = x; + expsign = u.xbits.expsign; + expt = expsign & 0x7fff; + if(expt >= BIAS) { /* |x|>= 1 */ + if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (exptone) return x;/* return x with inexact if x!=0*/ + } + t = x*x; + p = P(t); + q = Q(t); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabsl(x); + t = w*0.5; + p = P(t); + q = Q(t); + s = sqrtl(t); + if(u.bits.manh>=THRESH) { /* if |x| is close to 1 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + u.e = s; + u.bits.manl = 0; + w = u.e; + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(expsign>0) return t; else return -t; +} diff --git a/openlibm/src/e_atan2.c b/openlibm/src/e_atan2.c new file mode 100644 index 0000000..9b021b9 --- /dev/null +++ b/openlibm/src/e_atan2.c @@ -0,0 +1,129 @@ + +/* @(#)e_atan2.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_atan2.c,v 1.14 2008/08/02 19:17:00 das Exp $"); + +/* __ieee754_atan2(y,x) + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include + +#include "math_private.h" + +static volatile double +tiny = 1.0e-300; +static const double +zero = 0.0, +pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ +pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ +pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ +static volatile double +pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ + +OLM_DLLEXPORT double +__ieee754_atan2(double y, double x) +{ + double z; + int32_t k,m,hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + EXTRACT_WORDS(hy,ly,y); + iy = hy&0x7fffffff; + if(((ix|((lx|-lx)>>31))>0x7ff00000)|| + ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ + return x+y; + if(hx==0x3ff00000&&lx==0) return atan(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7ff00000) { + if(iy==0x7ff00000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>20; + if(k > 60) { /* |y/x| > 2**60 */ + z=pi_o_2+0.5*pi_lo; + m&=1; + } + else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */ + else z=atan(fabs(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: return -z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(atan2, atan2l); +#endif diff --git a/openlibm/src/e_atan2f.c b/openlibm/src/e_atan2f.c new file mode 100644 index 0000000..a52a581 --- /dev/null +++ b/openlibm/src/e_atan2f.c @@ -0,0 +1,97 @@ +/* e_atan2f.c -- float version of e_atan2.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_atan2f.c,v 1.12 2008/08/03 17:39:54 das Exp $"); + +#include + +#include "math_private.h" + +static volatile float +tiny = 1.0e-30; +static const float +zero = 0.0, +pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */ +pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */ +pi = 3.1415927410e+00; /* 0x40490fdb */ +static volatile float +pi_lo = -8.7422776573e-08; /* 0xb3bbbd2e */ + +OLM_DLLEXPORT float +__ieee754_atan2f(float y, float x) +{ + float z; + int32_t k,m,hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + GET_FLOAT_WORD(hy,y); + iy = hy&0x7fffffff; + if((ix>0x7f800000)|| + (iy>0x7f800000)) /* x or y is NaN */ + return x+y; + if(hx==0x3f800000) return atanf(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if(iy==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7f800000) { + if(iy==0x7f800000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>23; + if(k > 26) { /* |y/x| > 2**26 */ + z=pi_o_2+(float)0.5*pi_lo; + m&=1; + } + else if(k<-26&&hx<0) z=0.0; /* 0 > |y|/x > -2**-26 */ + else z=atanf(fabsf(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: return -z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/openlibm/src/e_atan2l.c b/openlibm/src/e_atan2l.c new file mode 100644 index 0000000..1c0a796 --- /dev/null +++ b/openlibm/src/e_atan2l.c @@ -0,0 +1,120 @@ + +/* @(#)e_atan2.c 1.3 95/01/18 */ +/* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_atan2l.c,v 1.3 2008/08/02 19:17:00 das Exp $"); + +/* + * See comments in e_atan2.c. + * Converted to long double by David Schultz . + */ + +#include +#include + +#include "invtrig.h" +#include "math_private.h" + +static volatile long double +tiny = 1.0e-300; +static const long double +zero = 0.0; + +#ifdef __i386__ +/* XXX Work around the fact that gcc truncates long double constants on i386 */ +static volatile double +pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ +pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ +#define pi ((long double)pi1 + pi2) +#else +static const long double +pi = 3.14159265358979323846264338327950280e+00L; +#endif + +OLM_DLLEXPORT long double +atan2l(long double y, long double x) +{ + union IEEEl2bits ux, uy; + long double z; + int32_t k,m; + int16_t exptx, expsignx, expty, expsigny; + + uy.e = y; + expsigny = uy.xbits.expsign; + expty = expsigny & 0x7fff; + ux.e = x; + expsignx = ux.xbits.expsign; + exptx = expsignx & 0x7fff; + + if ((exptx==BIAS+LDBL_MAX_EXP && + ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */ + (expty==BIAS+LDBL_MAX_EXP && + ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */ + return x+y; + if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) + return atanl(y); /* x=1.0 */ + m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) + return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; + + /* when x is INF */ + if(exptx==BIAS+LDBL_MAX_EXP) { + if(expty==BIAS+LDBL_MAX_EXP) { + switch(m) { + case 0: return pio2_hi*0.5+tiny;/* atan(+INF,+INF) */ + case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */ + case 2: return 1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/ + case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(expty==BIAS+LDBL_MAX_EXP) + return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny; + + /* compute y/x */ + k = expty-exptx; + if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */ + z=pio2_hi+pio2_lo; + m&=1; + } + else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; /* |y/x| tiny, x<0 */ + else z=atanl(fabsl(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: return -z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/openlibm/src/e_atanh.c b/openlibm/src/e_atanh.c new file mode 100644 index 0000000..5e1db91 --- /dev/null +++ b/openlibm/src/e_atanh.c @@ -0,0 +1,68 @@ + +/* @(#)e_atanh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_atanh.c,v 1.8 2008/02/22 02:30:34 das Exp $"); + +/* __ieee754_atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + +#include +#include + +#include "math_private.h" + +static const double one = 1.0, huge = 1e300; +static const double zero = 0.0; + +OLM_DLLEXPORT double +__ieee754_atanh(double x) +{ + double t; + int32_t hx,ix; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3ff00000) + return x/zero; + if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_HIGH_WORD(x,ix); + if(ix<0x3fe00000) { /* x < 0.5 */ + t = x+x; + t = 0.5*log1p(t+t*x/(one-x)); + } else + t = 0.5*log1p((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(atanh, atanhl); +#endif diff --git a/openlibm/src/e_atanhf.c b/openlibm/src/e_atanhf.c new file mode 100644 index 0000000..1ce329c --- /dev/null +++ b/openlibm/src/e_atanhf.c @@ -0,0 +1,46 @@ +/* e_atanhf.c -- float version of e_atanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_atanhf.c,v 1.7 2008/02/22 02:30:34 das Exp $"); + +#include + +#include "math_private.h" + +static const float one = 1.0, huge = 1e30; + +static const float zero = 0.0; + +OLM_DLLEXPORT float +__ieee754_atanhf(float x) +{ + float t; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if (ix>0x3f800000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3f800000) + return x/zero; + if(ix<0x31800000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_FLOAT_WORD(x,ix); + if(ix<0x3f000000) { /* x < 0.5 */ + t = x+x; + t = (float)0.5*log1pf(t+t*x/(one-x)); + } else + t = (float)0.5*log1pf((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff --git a/openlibm/src/e_cosh.c b/openlibm/src/e_cosh.c new file mode 100644 index 0000000..2e76570 --- /dev/null +++ b/openlibm/src/e_cosh.c @@ -0,0 +1,85 @@ + +/* @(#)e_cosh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_cosh.c,v 1.10 2011/10/21 06:28:47 das Exp $"); + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include +#include + +#include "math_private.h" + +static const double one = 1.0, half=0.5, huge = 1.0e300; + +OLM_DLLEXPORT double +__ieee754_cosh(double x) +{ + double t,w; + int32_t ix; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e43) { + t = expm1(fabs(x)); + w = one+t; + if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x40360000) { + t = __ieee754_exp(fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x408633CE) + return __ldexp_exp(fabs(x), -1); + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(cosh, coshl); +#endif diff --git a/openlibm/src/e_coshf.c b/openlibm/src/e_coshf.c new file mode 100644 index 0000000..e129659 --- /dev/null +++ b/openlibm/src/e_coshf.c @@ -0,0 +1,60 @@ +/* e_coshf.c -- float version of e_cosh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_coshf.c,v 1.9 2011/10/21 06:28:47 das Exp $"); + +#include + +#include "math_private.h" + +static const float one = 1.0, half=0.5, huge = 1.0e30; + +OLM_DLLEXPORT float +__ieee754_coshf(float x) +{ + float t,w; + int32_t ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3eb17218) { + t = expm1f(fabsf(x)); + w = one+t; + if (ix<0x39800000) return one; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,9], return (exp(|x|)+1/exp(|x|))/2; */ + if (ix < 0x41100000) { + t = __ieee754_expf(fabsf(x)); + return half*t+half/t; + } + + /* |x| in [9, log(maxfloat)] return half*exp(|x|) */ + if (ix < 0x42b17217) return half*__ieee754_expf(fabsf(x)); + + /* |x| in [log(maxfloat), overflowthresold] */ + if (ix<=0x42b2d4fc) + return __ldexp_expf(fabsf(x), -1); + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/openlibm/src/e_exp.c b/openlibm/src/e_exp.c new file mode 100644 index 0000000..639b9fe --- /dev/null +++ b/openlibm/src/e_exp.c @@ -0,0 +1,171 @@ + +/* @(#)e_exp.c 1.6 04/04/22 */ +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_exp.c,v 1.14 2011/10/21 06:26:38 das Exp $"); + +/* __ieee754_exp(x) + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better + * accuracy. + * + * 2. Approximation of exp(r) by a special rational function on + * the interval [0,0.34658]: + * Write + * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... + * We use a special Remes algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error + * of this polynomial approximation is bounded by 2**-59. In + * other words, + * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 + * (where z=r*r, and the values of P1 to P5 are listed below) + * and + * | 5 | -59 + * | 2.0+P1*z+...+P5*z - R(z) | <= 2 + * | | + * The computation of exp(r) thus becomes + * 2*r + * exp(r) = 1 + ------- + * R - r + * r*R1(r) + * = 1 + r + ----------- (for better accuracy) + * 2 - R1(r) + * where + * 2 4 10 + * R1(r) = r - (P1*r + P2*r + ... + P5*r ). + * + * 3. Scale back to obtain exp(x): + * From step 1, we have + * exp(x) = 2^k * exp(r) + * + * Special cases: + * exp(INF) is INF, exp(NaN) is NaN; + * exp(-INF) is 0, and + * for finite argument, only exp(0)=1 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then exp(x) overflow + * if x < -7.45133219101941108420e+02 then exp(x) underflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include + +#include "math_private.h" + +static const double +one = 1.0, +halF[2] = {0.5,-0.5,}, +huge = 1.0e+300, +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ +ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ + -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ +ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ + +static volatile double +twom1000= 9.33263618503218878990e-302; /* 2**-1000=0x01700000,0*/ + +OLM_DLLEXPORT double +__ieee754_exp(double x) /* default IEEE double exp */ +{ + double y,hi=0.0,lo=0.0,c,t,twopk; + int32_t k=0,xsb; + u_int32_t hx; + + GET_HIGH_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((hx&0xfffff)|lx)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom1000*twom1000; /* underflow */ + } + + /* this implementation gives 2.7182818284590455 for exp(1.0), + which is well within the allowable error. however, + 2.718281828459045 is closer to the true value so we prefer that + answer, given that 1.0 is such an important argument value. */ + if (x == 1.0) + return 2.718281828459045235360; + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = (int)(invln2*x+halF[xsb]); + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + STRICT_ASSIGN(double, x, hi - lo); + } + else if(hx < 0x3e300000) { /* when |x|<2**-28 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + if(k >= -1021) + INSERT_WORDS(twopk,0x3ff00000+(k<<20), 0); + else + INSERT_WORDS(twopk,0x3ff00000+((k+1000)<<20), 0); + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-2.0)-x); + else y = one-((lo-(x*c)/(2.0-c))-hi); + if(k >= -1021) { + if (k==1024) return y*2.0*0x1p1023; + return y*twopk; + } else { + return y*twopk*twom1000; + } +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(exp, expl); +#endif diff --git a/openlibm/src/e_expf.c b/openlibm/src/e_expf.c new file mode 100644 index 0000000..a239413 --- /dev/null +++ b/openlibm/src/e_expf.c @@ -0,0 +1,97 @@ +/* e_expf.c -- float version of e_exp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_expf.c,v 1.16 2011/10/21 06:26:38 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const float +one = 1.0, +halF[2] = {0.5,-0.5,}, +huge = 1.0e+30, +o_threshold= 8.8721679688e+01, /* 0x42b17180 */ +u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ +ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */ + -6.9314575195e-01,}, /* 0xbf317200 */ +ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */ + -1.4286067653e-06,}, /* 0xb5bfbe8e */ +invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ +/* + * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: + * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 + */ +P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ +P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ + +static volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ + +OLM_DLLEXPORT float +__ieee754_expf(float x) +{ + float y,hi=0.0,lo=0.0,c,t,twopk; + int32_t k=0,xsb; + u_int32_t hx; + + GET_FLOAT_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom100*twom100; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = invln2*x+halF[xsb]; + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + STRICT_ASSIGN(float, x, hi - lo); + } + else if(hx < 0x39000000) { /* when |x|<2**-14 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + if(k >= -125) + SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); + else + SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23)); + c = x - t*(P1+t*P2); + if(k==0) return one-((x*c)/(c-(float)2.0)-x); + else y = one-((lo-(x*c)/((float)2.0-c))-hi); + if(k >= -125) { + if(k==128) return y*2.0F*0x1p127F; + return y*twopk; + } else { + return y*twopk*twom100; + } +} diff --git a/openlibm/src/e_fmod.c b/openlibm/src/e_fmod.c new file mode 100644 index 0000000..285da8d --- /dev/null +++ b/openlibm/src/e_fmod.c @@ -0,0 +1,133 @@ + +/* @(#)e_fmod.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_fmod.c,v 1.10 2008/02/22 02:30:34 das Exp $"); + +/* + * __ieee754_fmod(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include + +#include "math_private.h" + +static const double one = 1.0, Zero[] = {0.0, -0.0,}; + +OLM_DLLEXPORT double +__ieee754_fmod(double x, double y) +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + u_int32_t lx,ly,lz; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ + ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<=hy) { + if((hx>31]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(hx<0x00100000) { /* subnormal x */ + if(hx==0) { + for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; + } else { + for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; + } + } else ix = (hx>>20)-1023; + + /* determine iy = ilogb(y) */ + if(hy<0x00100000) { /* subnormal y */ + if(hy==0) { + for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; + } else { + for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; + } + } else iy = (hy>>20)-1023; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -1022) + hx = 0x00100000|(0x000fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -1022-ix; + if(n<=31) { + hx = (hx<>(32-n)); + lx <<= n; + } else { + hx = lx<<(n-32); + lx = 0; + } + } + if(iy >= -1022) + hy = 0x00100000|(0x000fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -1022-iy; + if(n<=31) { + hy = (hy<>(32-n)); + ly <<= n; + } else { + hy = ly<<(n-32); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx>31); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + hx = hz+hz+(lz>>31); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00100000) { /* normalize x */ + hx = hx+hx+(lx>>31); lx = lx+lx; + iy -= 1; + } + if(iy>= -1022) { /* normalize output */ + hx = ((hx-0x00100000)|((iy+1023)<<20)); + INSERT_WORDS(x,hx|sx,lx); + } else { /* subnormal output */ + n = -1022 - iy; + if(n<=20) { + lx = (lx>>n)|((u_int32_t)hx<<(32-n)); + hx >>= n; + } else if (n<=31) { + lx = (hx<<(32-n))|(lx>>n); hx = sx; + } else { + lx = hx>>(n-32); hx = sx; + } + INSERT_WORDS(x,hx|sx,lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/openlibm/src/e_fmodf.c b/openlibm/src/e_fmodf.c new file mode 100644 index 0000000..88fd8ae --- /dev/null +++ b/openlibm/src/e_fmodf.c @@ -0,0 +1,105 @@ +/* e_fmodf.c -- float version of e_fmod.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_fmodf.c,v 1.7 2008/02/22 02:30:34 das Exp $"); + +/* + * __ieee754_fmodf(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include + +#include "math_private.h" + +static const float one = 1.0, Zero[] = {0.0, -0.0,}; + +OLM_DLLEXPORT float +__ieee754_fmodf(float x, float y) +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */ + (hy>0x7f800000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx>31]; /* |x|=|y| return x*0*/ + + /* determine ix = ilogb(x) */ + if(hx<0x00800000) { /* subnormal x */ + for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; + } else ix = (hx>>23)-127; + + /* determine iy = ilogb(y) */ + if(hy<0x00800000) { /* subnormal y */ + for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1; + } else iy = (hy>>23)-127; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -126) + hx = 0x00800000|(0x007fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -126-ix; + hx = hx<= -126) + hy = 0x00800000|(0x007fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -126-iy; + hy = hy<>31]; + hx = hz+hz; + } + } + hz=hx-hy; + if(hz>=0) {hx=hz;} + + /* convert back to floating value and restore the sign */ + if(hx==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00800000) { /* normalize x */ + hx = hx+hx; + iy -= 1; + } + if(iy>= -126) { /* normalize output */ + hx = ((hx-0x00800000)|((iy+127)<<23)); + SET_FLOAT_WORD(x,hx|sx); + } else { /* subnormal output */ + n = -126 - iy; + hx >>= n; + SET_FLOAT_WORD(x,hx|sx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/openlibm/src/e_fmodl.c b/openlibm/src/e_fmodl.c new file mode 100644 index 0000000..47d961b --- /dev/null +++ b/openlibm/src/e_fmodl.c @@ -0,0 +1,150 @@ +/* @(#)e_fmod.c 1.3 95/01/18 */ +/*- + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_fmodl.c,v 1.2 2008/07/31 20:09:47 das Exp $"); + +#include +#include +#include + +#include "fpmath.h" + +#include "math_private.h" + +#define BIAS (LDBL_MAX_EXP - 1) + +#if LDBL_MANL_SIZE > 32 +typedef u_int64_t manl_t; +#else +typedef u_int32_t manl_t; +#endif + +#if LDBL_MANH_SIZE > 32 +typedef u_int64_t manh_t; +#else +typedef u_int32_t manh_t; +#endif + +/* + * These macros add and remove an explicit integer bit in front of the + * fractional mantissa, if the architecture doesn't have such a bit by + * default already. + */ +#ifdef LDBL_IMPLICIT_NBIT +#define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) +#define HFRAC_BITS LDBL_MANH_SIZE +#else +#define SET_NBIT(hx) (hx) +#define HFRAC_BITS (LDBL_MANH_SIZE - 1) +#endif + +#define MANL_SHIFT (LDBL_MANL_SIZE - 1) + +static const long double one = 1.0, Zero[] = {0.0, -0.0,}; + +/* + * fmodl(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + * + * Assumptions: + * - The low part of the mantissa fits in a manl_t exactly. + * - The high part of the mantissa fits in an int64_t with enough room + * for an explicit integer bit in front of the fractional bits. + */ +OLM_DLLEXPORT long double +fmodl(long double x, long double y) +{ + union IEEEl2bits ux, uy; + int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ + manh_t hy; + manl_t lx,ly,lz; + int ix,iy,n,sx; + + ux.e = x; + uy.e = y; + sx = ux.bits.sign; + + /* purge off exception values */ + if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ + (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ + (uy.bits.exp == BIAS + LDBL_MAX_EXP && + ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ + return (x*y)/(x*y); + if(ux.bits.exp<=uy.bits.exp) { + if((ux.bits.exp>MANL_SHIFT); lx = lx+lx;} + else { + if ((hz|lz)==0) /* return sign(x)*0 */ + return Zero[sx]; + hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[sx]; + while(hx<(1ULL<>MANL_SHIFT); lx = lx+lx; + iy -= 1; + } + ux.bits.manh = hx; /* The mantissa is truncated here if needed. */ + ux.bits.manl = lx; + if (iy < LDBL_MIN_EXP) { + ux.bits.exp = iy + (BIAS + 512); + ux.e *= 0x1p-512; + } else { + ux.bits.exp = iy + BIAS; + } + x = ux.e * one; /* create necessary signal */ + return x; /* exact output */ +} diff --git a/openlibm/src/e_hypot.c b/openlibm/src/e_hypot.c new file mode 100644 index 0000000..3f4c1d1 --- /dev/null +++ b/openlibm/src/e_hypot.c @@ -0,0 +1,131 @@ + +/* @(#)e_hypot.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_hypot.c,v 1.14 2011/10/15 07:00:28 das Exp $"); + +/* __ieee754_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +__ieee754_hypot(double x, double y) +{ + double a,b,t1,t2,y1,y2,w; + int32_t j,k,ha,hb; + + GET_HIGH_WORD(ha,x); + ha &= 0x7fffffff; + GET_HIGH_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + a = fabs(a); + b = fabs(b); + if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ + k=0; + if(ha > 0x5f300000) { /* a>2**500 */ + if(ha >= 0x7ff00000) { /* Inf or NaN */ + u_int32_t low; + /* Use original arg order iff result is NaN; quieten sNaNs. */ + w = fabs(x+0.0)-fabs(y+0.0); + GET_LOW_WORD(low,a); + if(((ha&0xfffff)|low)==0) w = a; + GET_LOW_WORD(low,b); + if(((hb^0x7ff00000)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + if(hb < 0x20b00000) { /* b < 2**-500 */ + if(hb <= 0x000fffff) { /* subnormal b or 0 */ + u_int32_t low; + GET_LOW_WORD(low,b); + if((hb|low)==0) return a; + t1=0; + SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + } else { /* scale a and b by 2^600 */ + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_HIGH_WORD(t1,ha); + t2 = a-t1; + w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1 = 0; + SET_HIGH_WORD(y1,hb); + y2 = b - y1; + t1 = 0; + SET_HIGH_WORD(t1,ha+0x00100000); + t2 = a - t1; + w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int32_t high; + t1 = 1.0; + GET_HIGH_WORD(high,t1); + SET_HIGH_WORD(t1,high+(k<<20)); + return t1*w; + } else return w; +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(hypot, hypotl); +#endif diff --git a/openlibm/src/e_hypotf.c b/openlibm/src/e_hypotf.c new file mode 100644 index 0000000..e90fb5d --- /dev/null +++ b/openlibm/src/e_hypotf.c @@ -0,0 +1,84 @@ +/* e_hypotf.c -- float version of e_hypot.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_hypotf.c,v 1.14 2011/10/15 07:00:28 das Exp $"); + +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +__ieee754_hypotf(float x, float y) +{ + float a,b,t1,t2,y1,y2,w; + int32_t j,k,ha,hb; + + GET_FLOAT_WORD(ha,x); + ha &= 0x7fffffff; + GET_FLOAT_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + a = fabsf(a); + b = fabsf(b); + if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */ + k=0; + if(ha > 0x58800000) { /* a>2**50 */ + if(ha >= 0x7f800000) { /* Inf or NaN */ + /* Use original arg order iff result is NaN; quieten sNaNs. */ + w = fabsf(x+0.0F)-fabsf(y+0.0F); + if(ha == 0x7f800000) w = a; + if(hb == 0x7f800000) w = b; + return w; + } + /* scale a and b by 2**-68 */ + ha -= 0x22000000; hb -= 0x22000000; k += 68; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + if(hb < 0x26800000) { /* b < 2**-50 */ + if(hb <= 0x007fffff) { /* subnormal b or 0 */ + if(hb==0) return a; + SET_FLOAT_WORD(t1,0x7e800000); /* t1=2^126 */ + b *= t1; + a *= t1; + k -= 126; + } else { /* scale a and b by 2^68 */ + ha += 0x22000000; /* a *= 2^68 */ + hb += 0x22000000; /* b *= 2^68 */ + k -= 68; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + SET_FLOAT_WORD(t1,ha&0xfffff000); + t2 = a-t1; + w = __ieee754_sqrtf(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + SET_FLOAT_WORD(y1,hb&0xfffff000); + y2 = b - y1; + SET_FLOAT_WORD(t1,(ha+0x00800000)&0xfffff000); + t2 = a - t1; + w = __ieee754_sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + SET_FLOAT_WORD(t1,0x3f800000+(k<<23)); + return t1*w; + } else return w; +} diff --git a/openlibm/src/e_hypotl.c b/openlibm/src/e_hypotl.c new file mode 100644 index 0000000..2632774 --- /dev/null +++ b/openlibm/src/e_hypotl.c @@ -0,0 +1,124 @@ +/* From: @(#)e_hypot.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_hypotl.c,v 1.3 2011/10/16 05:36:39 das Exp $"); + +/* long double version of hypot(). See e_hypot.c for most comments. */ + +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#define GET_LDBL_MAN(h, l, v) do { \ + union IEEEl2bits uv; \ + \ + uv.e = v; \ + h = uv.bits.manh; \ + l = uv.bits.manl; \ +} while (0) + +#undef GET_HIGH_WORD +#define GET_HIGH_WORD(i, v) GET_LDBL_EXPSIGN(i, v) +#undef SET_HIGH_WORD +#define SET_HIGH_WORD(v, i) SET_LDBL_EXPSIGN(v, i) + +#define DESW(exp) (exp) /* delta expsign word */ +#define ESW(exp) (MAX_EXP - 1 + (exp)) /* expsign word */ +#define MANT_DIG LDBL_MANT_DIG +#define MAX_EXP LDBL_MAX_EXP + +#if LDBL_MANL_SIZE > 32 +typedef u_int64_t man_t; +#else +typedef u_int32_t man_t; +#endif + +OLM_DLLEXPORT long double +hypotl(long double x, long double y) +{ + long double a=x,b=y,t1,t2,y1,y2,w; + int32_t j,k,ha,hb; + + GET_HIGH_WORD(ha,x); + ha &= 0x7fff; + GET_HIGH_WORD(hb,y); + hb &= 0x7fff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + a = fabsl(a); + b = fabsl(b); + if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */ + k=0; + if(ha > ESW(MAX_EXP/2-12)) { /* a>2**(MAX_EXP/2-12) */ + if(ha >= ESW(MAX_EXP)) { /* Inf or NaN */ + man_t manh, manl; + /* Use original arg order iff result is NaN; quieten sNaNs. */ + w = fabsl(x+0.0)-fabsl(y+0.0); + GET_LDBL_MAN(manh,manl,a); + if (manh == LDBL_NBIT && manl == 0) w = a; + GET_LDBL_MAN(manh,manl,b); + if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b; + return w; + } + /* scale a and b by 2**-(MAX_EXP/2+88) */ + ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88); + k += MAX_EXP/2+88; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + if(hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */ + if(hb <= 0) { /* subnormal b or 0 */ + man_t manh, manl; + GET_LDBL_MAN(manh,manl,b); + if((manh|manl)==0) return a; + t1=1; + SET_HIGH_WORD(t1,ESW(MAX_EXP-2)); /* t1=2^(MAX_EXP-2) */ + b *= t1; + a *= t1; + k -= MAX_EXP-2; + } else { /* scale a and b by 2^(MAX_EXP/2+88) */ + ha += DESW(MAX_EXP/2+88); + hb += DESW(MAX_EXP/2+88); + k -= MAX_EXP/2+88; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = a; + union IEEEl2bits uv; + uv.e = t1; uv.bits.manl = 0; t1 = uv.e; + t2 = a-t1; + w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1 = b; + union IEEEl2bits uv; + uv.e = y1; uv.bits.manl = 0; y1 = uv.e; + y2 = b - y1; + t1 = a; + uv.e = t1; uv.bits.manl = 0; t1 = uv.e; + t2 = a - t1; + w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int32_t high; + t1 = 1.0; + GET_HIGH_WORD(high,t1); + SET_HIGH_WORD(t1,high+DESW(k)); + return t1*w; + } else return w; +} diff --git a/openlibm/src/e_j0.c b/openlibm/src/e_j0.c new file mode 100644 index 0000000..a2419d3 --- /dev/null +++ b/openlibm/src/e_j0.c @@ -0,0 +1,388 @@ + +/* @(#)e_j0.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_j0.c,v 1.9 2008/02/22 02:30:35 das Exp $"); + +/* __ieee754_j0(x), __ieee754_y0(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; + * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * where + * U(z) = u00 + u01*z + ... + u06*z^6 + * V(z) = 1 + v01*z + ... + v04*z^4 + * with absolute approximation error bounded by 2**-72. + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include + +#include "math_private.h" + +static double pzero(double), qzero(double); + +static const double +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ +R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ +R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ +R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ +S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ +S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ +S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ +S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ + +static const double zero = 0.0; + +OLM_DLLEXPORT double +__ieee754_j0(double x) +{ + double z, s,c,ss,cc,r,u,v; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/(x*x); + x = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c)0x48000000) z = (invsqrtpi*cc)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*cc-v*ss)/sqrt(x); + } + return z; + } + if(ix<0x3f200000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x3e400000) return one; /* |x|<2**-27 */ + else return one - 0.25*x*x; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3FF00000) { /* |x| < 1.00 */ + return one + z*(-0.25+(r/s)); + } else { + u = 0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +static const double +u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ +u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ +u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ +u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ +u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ +u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ +u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ +v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ +v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ +v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ +v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ + +OLM_DLLEXPORT double +__ieee754_y0(double x) +{ + double z, s,c,ss,cc,u,v; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c)0x48000000) z = (invsqrtpi*ss)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if(ix<=0x3e400000) { /* x < 2**-27 */ + return(u00 + tpi*__ieee754_log(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ + -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ + -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ + -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ + -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ +}; +static const double pS8[5] = { + 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ + 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ + 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ + 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ + 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ +}; + +static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ + -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ + -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ + -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ + -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ + -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ +}; +static const double pS5[5] = { + 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ + 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ + 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ + 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ + 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ +}; + +static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ + -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ + -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ + -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ + -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ + -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ +}; +static const double pS3[5] = { + 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ + 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ + 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ + 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ + 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ +}; + +static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ + -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ + -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ + -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ + -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ + -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ +}; +static const double pS2[5] = { + 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ + 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ + 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ + 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ + 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ +}; + + /* Note: This function is only called for ix>=0x40000000 (see above) */ + static double pzero(double x) +{ + const double *p,*q; + double z,r,s; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + assert(ix>=0x40000000 && ix<=0x48000000); + if(ix>=0x40200000) {p = pR8; q= pS8;} + else if(ix>=0x40122E8B){p = pR5; q= pS5;} + else if(ix>=0x4006DB6D){p = pR3; q= pS3;} + else {p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ + 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ + 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ + 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ + 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ +}; +static const double qS8[6] = { + 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ + 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ + 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ + 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ + 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ + -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ +}; + +static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ + 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ + 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ + 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ + 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ + 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ +}; +static const double qS5[6] = { + 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ + 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ + 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ + 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ + 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ + -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ +}; + +static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ + 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ + 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ + 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ + 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ + 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ +}; +static const double qS3[6] = { + 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ + 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ + 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ + 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ + 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ + -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ +}; + +static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ + 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ + 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ + 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ + 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ + 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ +}; +static const double qS2[6] = { + 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ + 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ + 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ + 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ + 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ + -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ +}; + + /* Note: This function is only called for ix>=0x40000000 (see above) */ + static double qzero(double x) +{ + const double *p,*q; + double s,r,z; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + assert(ix>=0x40000000 && ix<=0x48000000); + if(ix>=0x40200000) {p = qR8; q= qS8;} + else if(ix>=0x40122E8B){p = qR5; q= qS5;} + else if(ix>=0x4006DB6D){p = qR3; q= qS3;} + else {p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-.125 + r/s)/x; +} diff --git a/openlibm/src/e_j0f.c b/openlibm/src/e_j0f.c new file mode 100644 index 0000000..62258b1 --- /dev/null +++ b/openlibm/src/e_j0f.c @@ -0,0 +1,337 @@ +/* e_j0f.c -- float version of e_j0.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#include "cdefs-compat.h" + +#include +#include "math_private.h" + +static float pzerof(float), qzerof(float); + +static const float +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.5625000000e-02, /* 0x3c800000 */ +R03 = -1.8997929874e-04, /* 0xb947352e */ +R04 = 1.8295404516e-06, /* 0x35f58e88 */ +R05 = -4.6183270541e-09, /* 0xb19eaf3c */ +S01 = 1.5619102865e-02, /* 0x3c7fe744 */ +S02 = 1.1692678527e-04, /* 0x38f53697 */ +S03 = 5.1354652442e-07, /* 0x3509daa6 */ +S04 = 1.1661400734e-09; /* 0x30a045e8 */ + +static const float zero = 0.0; + +OLM_DLLEXPORT float +__ieee754_j0f(float x) +{ + float z, s,c,ss,cc,r,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/(x*x); + x = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(x); + c = cosf(x); + ss = s-c; + cc = s+c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -cosf(x+x); + if ((s*c)0x58000000) z = (invsqrtpi*cc)/sqrtf(x); /* |x|>2**49 */ + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*cc-v*ss)/sqrtf(x); + } + return z; + } + if(ix<0x3b000000) { /* |x| < 2**-9 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x39800000) return one; /* |x|<2**-12 */ + else return one - x*x/4; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3F800000) { /* |x| < 1.00 */ + return one + z*((float)-0.25+(r/s)); + } else { + u = (float)0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +static const float +u00 = -7.3804296553e-02, /* 0xbd9726b5 */ +u01 = 1.7666645348e-01, /* 0x3e34e80d */ +u02 = -1.3818567619e-02, /* 0xbc626746 */ +u03 = 3.4745343146e-04, /* 0x39b62a69 */ +u04 = -3.8140706238e-06, /* 0xb67ff53c */ +u05 = 1.9559013964e-08, /* 0x32a802ba */ +u06 = -3.9820518410e-11, /* 0xae2f21eb */ +v01 = 1.2730483897e-02, /* 0x3c509385 */ +v02 = 7.6006865129e-05, /* 0x389f65e0 */ +v03 = 2.5915085189e-07, /* 0x348b216c */ +v04 = 4.4111031494e-10; /* 0x2ff280c2 */ + +OLM_DLLEXPORT float +__ieee754_y0f(float x) +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = sinf(x); + c = cosf(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -cosf(x+x); + if ((s*c)0x58000000) z = (invsqrtpi*ss)/sqrtf(x); /* |x|>2**49 */ + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); + } + return z; + } + if(ix<=0x39000000) { /* x < 2**-13 */ + return(u00 + tpi*__ieee754_logf(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + -7.0312500000e-02, /* 0xbd900000 */ + -8.0816707611e+00, /* 0xc1014e86 */ + -2.5706311035e+02, /* 0xc3808814 */ + -2.4852163086e+03, /* 0xc51b5376 */ + -5.2530439453e+03, /* 0xc5a4285a */ +}; +static const float pS8[5] = { + 1.1653436279e+02, /* 0x42e91198 */ + 3.8337448730e+03, /* 0x456f9beb */ + 4.0597855469e+04, /* 0x471e95db */ + 1.1675296875e+05, /* 0x47e4087c */ + 4.7627726562e+04, /* 0x473a0bba */ +}; +static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.1412546255e-11, /* 0xad48c58a */ + -7.0312492549e-02, /* 0xbd8fffff */ + -4.1596107483e+00, /* 0xc0851b88 */ + -6.7674766541e+01, /* 0xc287597b */ + -3.3123129272e+02, /* 0xc3a59d9b */ + -3.4643338013e+02, /* 0xc3ad3779 */ +}; +static const float pS5[5] = { + 6.0753936768e+01, /* 0x42730408 */ + 1.0512523193e+03, /* 0x44836813 */ + 5.9789707031e+03, /* 0x45bad7c4 */ + 9.6254453125e+03, /* 0x461665c8 */ + 2.4060581055e+03, /* 0x451660ee */ +}; + +static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.5470459075e-09, /* 0xb12f081b */ + -7.0311963558e-02, /* 0xbd8fffb8 */ + -2.4090321064e+00, /* 0xc01a2d95 */ + -2.1965976715e+01, /* 0xc1afba52 */ + -5.8079170227e+01, /* 0xc2685112 */ + -3.1447946548e+01, /* 0xc1fb9565 */ +}; +static const float pS3[5] = { + 3.5856033325e+01, /* 0x420f6c94 */ + 3.6151397705e+02, /* 0x43b4c1ca */ + 1.1936077881e+03, /* 0x44953373 */ + 1.1279968262e+03, /* 0x448cffe6 */ + 1.7358093262e+02, /* 0x432d94b8 */ +}; + +static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.8753431271e-08, /* 0xb3be98b7 */ + -7.0303097367e-02, /* 0xbd8ffb12 */ + -1.4507384300e+00, /* 0xbfb9b1cc */ + -7.6356959343e+00, /* 0xc0f4579f */ + -1.1193166733e+01, /* 0xc1331736 */ + -3.2336456776e+00, /* 0xc04ef40d */ +}; +static const float pS2[5] = { + 2.2220300674e+01, /* 0x41b1c32d */ + 1.3620678711e+02, /* 0x430834f0 */ + 2.7047027588e+02, /* 0x43873c32 */ + 1.5387539673e+02, /* 0x4319e01a */ + 1.4657617569e+01, /* 0x416a859a */ +}; + + static float pzerof(float x) +{ + const float *p,*q; + float z,r,s; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pR8; q= pS8;} + else if(ix>=0x409173eb){p = pR5; q= pS5;} + else if(ix>=0x4036d917){p = pR3; q= pS3;} + else {p = pR2; q= pS2;} /* ix>=0x40000000 */ + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + 7.3242187500e-02, /* 0x3d960000 */ + 1.1768206596e+01, /* 0x413c4a93 */ + 5.5767340088e+02, /* 0x440b6b19 */ + 8.8591972656e+03, /* 0x460a6cca */ + 3.7014625000e+04, /* 0x471096a0 */ +}; +static const float qS8[6] = { + 1.6377603149e+02, /* 0x4323c6aa */ + 8.0983447266e+03, /* 0x45fd12c2 */ + 1.4253829688e+05, /* 0x480b3293 */ + 8.0330925000e+05, /* 0x49441ed4 */ + 8.4050156250e+05, /* 0x494d3359 */ + -3.4389928125e+05, /* 0xc8a7eb69 */ +}; + +static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.8408595828e-11, /* 0x2da1ec79 */ + 7.3242180049e-02, /* 0x3d95ffff */ + 5.8356351852e+00, /* 0x40babd86 */ + 1.3511157227e+02, /* 0x43071c90 */ + 1.0272437744e+03, /* 0x448067cd */ + 1.9899779053e+03, /* 0x44f8bf4b */ +}; +static const float qS5[6] = { + 8.2776611328e+01, /* 0x42a58da0 */ + 2.0778142090e+03, /* 0x4501dd07 */ + 1.8847289062e+04, /* 0x46933e94 */ + 5.6751113281e+04, /* 0x475daf1d */ + 3.5976753906e+04, /* 0x470c88c1 */ + -5.3543427734e+03, /* 0xc5a752be */ +}; + +static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.3774099900e-09, /* 0x3196681b */ + 7.3241114616e-02, /* 0x3d95ff70 */ + 3.3442313671e+00, /* 0x405607e3 */ + 4.2621845245e+01, /* 0x422a7cc5 */ + 1.7080809021e+02, /* 0x432acedf */ + 1.6673394775e+02, /* 0x4326bbe4 */ +}; +static const float qS3[6] = { + 4.8758872986e+01, /* 0x42430916 */ + 7.0968920898e+02, /* 0x44316c1c */ + 3.7041481934e+03, /* 0x4567825f */ + 6.4604252930e+03, /* 0x45c9e367 */ + 2.5163337402e+03, /* 0x451d4557 */ + -1.4924745178e+02, /* 0xc3153f59 */ +}; + +static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.5044444979e-07, /* 0x342189db */ + 7.3223426938e-02, /* 0x3d95f62a */ + 1.9981917143e+00, /* 0x3fffc4bf */ + 1.4495602608e+01, /* 0x4167edfd */ + 3.1666231155e+01, /* 0x41fd5471 */ + 1.6252708435e+01, /* 0x4182058c */ +}; +static const float qS2[6] = { + 3.0365585327e+01, /* 0x41f2ecb8 */ + 2.6934811401e+02, /* 0x4386ac8f */ + 8.4478375244e+02, /* 0x44533229 */ + 8.8293585205e+02, /* 0x445cbbe5 */ + 2.1266638184e+02, /* 0x4354aa98 */ + -5.3109550476e+00, /* 0xc0a9f358 */ +}; + + static float qzerof(float x) +{ + const float *p,*q; + float s,r,z; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = qR8; q= qS8;} + else if(ix>=0x409173eb){p = qR5; q= qS5;} + else if(ix>=0x4036d917){p = qR3; q= qS3;} + else {p = qR2; q= qS2;} /* ix>=0x40000000 */ + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-(float).125 + r/s)/x; +} diff --git a/openlibm/src/e_j1.c b/openlibm/src/e_j1.c new file mode 100644 index 0000000..4be57cd --- /dev/null +++ b/openlibm/src/e_j1.c @@ -0,0 +1,383 @@ + +/* @(#)e_j1.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_j1.c,v 1.9 2008/02/22 02:30:35 das Exp $"); + +/* __ieee754_j1(x), __ieee754_y1(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j1(x): + * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... + * 2. Reduce x to |x| since j1(x)=-j1(-x), and + * for x in (0,2) + * j1(x) = x/2 + x*z*R0/S0, where z = x*x; + * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) + * for x in (2,inf) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * as follow: + * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (sin(x) + cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j1(nan)= nan + * j1(0) = 0 + * j1(inf) = 0 + * + * Method -- y1(x): + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 2. For x<2. + * Since + * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) + * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. + * We use the following function to approximate y1, + * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 + * where for x in [0,2] (abs err less than 2**-65.89) + * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 + * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 + * Note: For tiny x, 1/x dominate y1 and hence + * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) + * 3. For x>=2. + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * by method mentioned above. + */ + +#include + +#include "math_private.h" + +static double pone(double), qone(double); + +static const double +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0,2] */ +r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ +r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ +r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ +r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ +s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ +s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ +s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ +s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ +s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ + +static const double zero = 0.0; + +OLM_DLLEXPORT double +__ieee754_j1(double x) +{ + double z, s,c,ss,cc,r,u,v,y; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/x; + y = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(y); + c = cos(y); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure y+y not overflow */ + z = cos(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); + else { + u = pone(y); v = qone(y); + z = invsqrtpi*(u*cc-v*ss)/sqrt(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x3e400000) { /* |x|<2**-27 */ + if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*0.5+r/s); +} + +static const double U0[5] = { + -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ + 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ + -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ + 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ + -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ +}; +static const double V0[5] = { + 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ + 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ + 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ + 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ + 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ +}; + +OLM_DLLEXPORT double +__ieee754_y1(double x) +{ + double z, s,c,ss,cc,u,v; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = cos(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); + else { + u = pone(x); v = qone(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if(ix<=0x3c900000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ + 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ + 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ + 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ + 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ +}; +static const double ps8[5] = { + 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ + 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ + 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ + 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ + 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ +}; + +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ + 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ + 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ + 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ + 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ + 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ +}; +static const double ps5[5] = { + 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ + 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ + 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ + 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ + 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ +}; + +static const double pr3[6] = { + 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ + 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ + 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ + 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ + 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ + 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ +}; +static const double ps3[5] = { + 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ + 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ + 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ + 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ + 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ +}; + +static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ + 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ + 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ + 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ + 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ + 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ +}; +static const double ps2[5] = { + 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ + 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ + 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ + 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ + 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ +}; + + /* Note: This function is only called for ix>=0x40000000 (see above) */ + static double pone(double x) +{ + const double *p,*q; + double z,r,s; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + assert(ix>=0x40000000 && ix<=0x48000000); + if(ix>=0x40200000) {p = pr8; q= ps8;} + else if(ix>=0x40122E8B){p = pr5; q= ps5;} + else if(ix>=0x4006DB6D){p = pr3; q= ps3;} + else {p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ + -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ + -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ + -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ + -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ +}; +static const double qs8[6] = { + 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ + 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ + 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ + 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ + 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ + -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ +}; + +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ + -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ + -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ + -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ + -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ + -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ +}; +static const double qs5[6] = { + 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ + 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ + 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ + 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ + 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ + -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ +}; + +static const double qr3[6] = { + -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ + -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ + -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ + -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ + -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ + -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ +}; +static const double qs3[6] = { + 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ + 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ + 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ + 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ + 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ + -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ +}; + +static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ + -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ + -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ + -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ + -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ + -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ +}; +static const double qs2[6] = { + 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ + 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ + 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ + 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ + 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ + -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ +}; + + /* Note: This function is only called for ix>=0x40000000 (see above) */ + static double qone(double x) +{ + const double *p,*q; + double s,r,z; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + assert(ix>=0x40000000 && ix<=0x48000000); + if(ix>=0x40200000) {p = qr8; q= qs8;} + else if(ix>=0x40122E8B){p = qr5; q= qs5;} + else if(ix>=0x4006DB6D){p = qr3; q= qs3;} + else {p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (.375 + r/s)/x; +} diff --git a/openlibm/src/e_j1f.c b/openlibm/src/e_j1f.c new file mode 100644 index 0000000..ac32c6f --- /dev/null +++ b/openlibm/src/e_j1f.c @@ -0,0 +1,332 @@ +/* e_j1f.c -- float version of e_j1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#include "cdefs-compat.h" +#include +#include "math_private.h" + +static float ponef(float), qonef(float); + +static const float +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0,2] */ +r00 = -6.2500000000e-02, /* 0xbd800000 */ +r01 = 1.4070566976e-03, /* 0x3ab86cfd */ +r02 = -1.5995563444e-05, /* 0xb7862e36 */ +r03 = 4.9672799207e-08, /* 0x335557d2 */ +s01 = 1.9153760746e-02, /* 0x3c9ce859 */ +s02 = 1.8594678841e-04, /* 0x3942fab6 */ +s03 = 1.1771846857e-06, /* 0x359dffc2 */ +s04 = 5.0463624390e-09, /* 0x31ad6446 */ +s05 = 1.2354227016e-11; /* 0x2d59567e */ + +static const float zero = 0.0; + +OLM_DLLEXPORT float +__ieee754_j1f(float x) +{ + float z, s,c,ss,cc,r,u,v,y; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/x; + y = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(y); + c = cosf(y); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure y+y not overflow */ + z = cosf(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if(ix>0x58000000) z = (invsqrtpi*cc)/sqrtf(y); /* |x|>2**49 */ + else { + u = ponef(y); v = qonef(y); + z = invsqrtpi*(u*cc-v*ss)/sqrtf(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x39000000) { /* |x|<2**-13 */ + if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*(float)0.5+r/s); +} + +static const float U0[5] = { + -1.9605709612e-01, /* 0xbe48c331 */ + 5.0443872809e-02, /* 0x3d4e9e3c */ + -1.9125689287e-03, /* 0xbafaaf2a */ + 2.3525259166e-05, /* 0x37c5581c */ + -9.1909917899e-08, /* 0xb3c56003 */ +}; +static const float V0[5] = { + 1.9916731864e-02, /* 0x3ca3286a */ + 2.0255257550e-04, /* 0x3954644b */ + 1.3560879779e-06, /* 0x35b602d4 */ + 6.2274145840e-09, /* 0x31d5f8eb */ + 1.6655924903e-11, /* 0x2d9281cf */ +}; + +OLM_DLLEXPORT float +__ieee754_y1f(float x) +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(x); + c = cosf(x); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = cosf(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x58000000) z = (invsqrtpi*ss)/sqrtf(x); /* |x|>2**49 */ + else { + u = ponef(x); v = qonef(x); + z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); + } + return z; + } + if(ix<=0x33000000) { /* x < 2**-25 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + 1.1718750000e-01, /* 0x3df00000 */ + 1.3239480972e+01, /* 0x4153d4ea */ + 4.1205184937e+02, /* 0x43ce06a3 */ + 3.8747453613e+03, /* 0x45722bed */ + 7.9144794922e+03, /* 0x45f753d6 */ +}; +static const float ps8[5] = { + 1.1420736694e+02, /* 0x42e46a2c */ + 3.6509309082e+03, /* 0x45642ee5 */ + 3.6956207031e+04, /* 0x47105c35 */ + 9.7602796875e+04, /* 0x47bea166 */ + 3.0804271484e+04, /* 0x46f0a88b */ +}; + +static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.3199052094e-11, /* 0x2d68333f */ + 1.1718749255e-01, /* 0x3defffff */ + 6.8027510643e+00, /* 0x40d9b023 */ + 1.0830818176e+02, /* 0x42d89dca */ + 5.1763616943e+02, /* 0x440168b7 */ + 5.2871520996e+02, /* 0x44042dc6 */ +}; +static const float ps5[5] = { + 5.9280597687e+01, /* 0x426d1f55 */ + 9.9140142822e+02, /* 0x4477d9b1 */ + 5.3532670898e+03, /* 0x45a74a23 */ + 7.8446904297e+03, /* 0x45f52586 */ + 1.5040468750e+03, /* 0x44bc0180 */ +}; + +static const float pr3[6] = { + 3.0250391081e-09, /* 0x314fe10d */ + 1.1718686670e-01, /* 0x3defffab */ + 3.9329774380e+00, /* 0x407bb5e7 */ + 3.5119403839e+01, /* 0x420c7a45 */ + 9.1055007935e+01, /* 0x42b61c2a */ + 4.8559066772e+01, /* 0x42423c7c */ +}; +static const float ps3[5] = { + 3.4791309357e+01, /* 0x420b2a4d */ + 3.3676245117e+02, /* 0x43a86198 */ + 1.0468714600e+03, /* 0x4482dbe3 */ + 8.9081134033e+02, /* 0x445eb3ed */ + 1.0378793335e+02, /* 0x42cf936c */ +}; + +static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.0771083225e-07, /* 0x33e74ea8 */ + 1.1717621982e-01, /* 0x3deffa16 */ + 2.3685150146e+00, /* 0x401795c0 */ + 1.2242610931e+01, /* 0x4143e1bc */ + 1.7693971634e+01, /* 0x418d8d41 */ + 5.0735230446e+00, /* 0x40a25a4d */ +}; +static const float ps2[5] = { + 2.1436485291e+01, /* 0x41ab7dec */ + 1.2529022980e+02, /* 0x42fa9499 */ + 2.3227647400e+02, /* 0x436846c7 */ + 1.1767937469e+02, /* 0x42eb5bd7 */ + 8.3646392822e+00, /* 0x4105d590 */ +}; + + static float ponef(float x) +{ + const float *p,*q; + float z,r,s; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pr8; q= ps8;} + else if(ix>=0x409173eb){p = pr5; q= ps5;} + else if(ix>=0x4036d917){p = pr3; q= ps3;} + else {p = pr2; q= ps2;} /* ix>=0x40000000 */ + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + -1.0253906250e-01, /* 0xbdd20000 */ + -1.6271753311e+01, /* 0xc1822c8d */ + -7.5960174561e+02, /* 0xc43de683 */ + -1.1849806641e+04, /* 0xc639273a */ + -4.8438511719e+04, /* 0xc73d3683 */ +}; +static const float qs8[6] = { + 1.6139537048e+02, /* 0x43216537 */ + 7.8253862305e+03, /* 0x45f48b17 */ + 1.3387534375e+05, /* 0x4802bcd6 */ + 7.1965775000e+05, /* 0x492fb29c */ + 6.6660125000e+05, /* 0x4922be94 */ + -2.9449025000e+05, /* 0xc88fcb48 */ +}; + +static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.0897993405e-11, /* 0xadb7d219 */ + -1.0253904760e-01, /* 0xbdd1fffe */ + -8.0564479828e+00, /* 0xc100e736 */ + -1.8366960144e+02, /* 0xc337ab6b */ + -1.3731937256e+03, /* 0xc4aba633 */ + -2.6124443359e+03, /* 0xc523471c */ +}; +static const float qs5[6] = { + 8.1276550293e+01, /* 0x42a28d98 */ + 1.9917987061e+03, /* 0x44f8f98f */ + 1.7468484375e+04, /* 0x468878f8 */ + 4.9851425781e+04, /* 0x4742bb6d */ + 2.7948074219e+04, /* 0x46da5826 */ + -4.7191835938e+03, /* 0xc5937978 */ +}; + +static const float qr3[6] = { + -5.0783124372e-09, /* 0xb1ae7d4f */ + -1.0253783315e-01, /* 0xbdd1ff5b */ + -4.6101160049e+00, /* 0xc0938612 */ + -5.7847221375e+01, /* 0xc267638e */ + -2.2824453735e+02, /* 0xc3643e9a */ + -2.1921012878e+02, /* 0xc35b35cb */ +}; +static const float qs3[6] = { + 4.7665153503e+01, /* 0x423ea91e */ + 6.7386511230e+02, /* 0x4428775e */ + 3.3801528320e+03, /* 0x45534272 */ + 5.5477290039e+03, /* 0x45ad5dd5 */ + 1.9031191406e+03, /* 0x44ede3d0 */ + -1.3520118713e+02, /* 0xc3073381 */ +}; + +static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.7838172539e-07, /* 0xb43f8932 */ + -1.0251704603e-01, /* 0xbdd1f475 */ + -2.7522056103e+00, /* 0xc0302423 */ + -1.9663616180e+01, /* 0xc19d4f16 */ + -4.2325313568e+01, /* 0xc2294d1f */ + -2.1371921539e+01, /* 0xc1aaf9b2 */ +}; +static const float qs2[6] = { + 2.9533363342e+01, /* 0x41ec4454 */ + 2.5298155212e+02, /* 0x437cfb47 */ + 7.5750280762e+02, /* 0x443d602e */ + 7.3939318848e+02, /* 0x4438d92a */ + 1.5594900513e+02, /* 0x431bf2f2 */ + -4.9594988823e+00, /* 0xc09eb437 */ +}; + + static float qonef(float x) +{ + const float *p,*q; + float s,r,z; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = qr8; q= qs8;} + else if(ix>=0x409173eb){p = qr5; q= qs5;} + else if(ix>=0x4036d917){p = qr3; q= qs3;} + else {p = qr2; q= qs2;} /* ix>=0x40000000 */ + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return ((float).375 + r/s)/x; +} diff --git a/openlibm/src/e_jn.c b/openlibm/src/e_jn.c new file mode 100644 index 0000000..1a53965 --- /dev/null +++ b/openlibm/src/e_jn.c @@ -0,0 +1,271 @@ + +/* @(#)e_jn.c 1.4 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_jn.c,v 1.11 2010/11/13 10:54:10 uqs Exp $"); + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for nx, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include + +#include "math_private.h" + +static const double +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ +one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ + +static const double zero = 0.00000000000000000000e+00; + +OLM_DLLEXPORT double +__ieee754_jn(int n, double x) +{ + int32_t i,hx,ix,lx, sgn; + double a, b, temp, di; + double z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0(x)); + if(n==1) return(__ieee754_j1(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabs(x); + if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ + b = zero; + else if((double)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = cos(x)+sin(x); break; + case 1: temp = -cos(x)+sin(x); break; + case 2: temp = -cos(x)-sin(x); break; + case 3: temp = cos(x)-sin(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + a = __ieee754_j0(x); + b = __ieee754_j1(x); + for(i=1;i33) /* underflow */ + b = zero; + else { + temp = x*0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (double)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + double t,v; + double q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(double)x; h = 2.0/(double)x; + q0 = w; z = w+h; q1 = w*z - 1.0; k=1; + while(q1<1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_log(fabs(v*tmp)); + if(tmp<7.09782712893383973096e+02) { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>1e100) { + a /= b; + t /= b; + b = one; + } + } + } + z = __ieee754_j0(x); + w = __ieee754_j1(x); + if (fabs(z) >= fabs(w)) + b = (t*z/b); + else + b = (t*w/a); + } + } + if(sgn==1) return -b; else return b; +} + +OLM_DLLEXPORT double +__ieee754_yn(int n, double x) +{ + int32_t i,hx,ix,lx; + int32_t sign; + double a, b, temp; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0(x)); + if(n==1) return(sign*__ieee754_y1(x)); + if(ix==0x7ff00000) return zero; + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = sin(x)-cos(x); break; + case 1: temp = -sin(x)-cos(x); break; + case 2: temp = -sin(x)+cos(x); break; + case 3: temp = sin(x)+cos(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + u_int32_t high; + a = __ieee754_y0(x); + b = __ieee754_y1(x); + /* quit if b is -inf */ + GET_HIGH_WORD(high,b); + for(i=1;i0) return b; else return -b; +} diff --git a/openlibm/src/e_jnf.c b/openlibm/src/e_jnf.c new file mode 100644 index 0000000..cb73e86 --- /dev/null +++ b/openlibm/src/e_jnf.c @@ -0,0 +1,200 @@ +/* e_jnf.c -- float version of e_jn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_jnf.c,v 1.11 2010/11/13 10:54:10 uqs Exp $"); + +#include + +#include "math_private.h" + +static const float +two = 2.0000000000e+00, /* 0x40000000 */ +one = 1.0000000000e+00; /* 0x3F800000 */ + +static const float zero = 0.0000000000e+00; + +OLM_DLLEXPORT float +__ieee754_jnf(int n, float x) +{ + int32_t i,hx,ix, sgn; + float a, b, temp, di; + float z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0f(x)); + if(n==1) return(__ieee754_j1f(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabsf(x); + if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */ + b = zero; + else if((float)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + a = __ieee754_j0f(x); + b = __ieee754_j1f(x); + for(i=1;i33) /* underflow */ + b = zero; + else { + temp = x*(float)0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (float)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + float t,v; + float q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(float)x; h = (float)2.0/(float)x; + q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1; + while(q1<(float)1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_logf(fabsf(v*tmp)); + if(tmp<(float)8.8721679688e+01) { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>(float)1e10) { + a /= b; + t /= b; + b = one; + } + } + } + z = __ieee754_j0f(x); + w = __ieee754_j1f(x); + if (fabsf(z) >= fabsf(w)) + b = (t*z/b); + else + b = (t*w/a); + } + } + if(sgn==1) return -b; else return b; +} + +OLM_DLLEXPORT float +__ieee754_ynf(int n, float x) +{ + int32_t i,hx,ix,ib; + int32_t sign; + float a, b, temp; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0f(x)); + if(n==1) return(sign*__ieee754_y1f(x)); + if(ix==0x7f800000) return zero; + + a = __ieee754_y0f(x); + b = __ieee754_y1f(x); + /* quit if b is -inf */ + GET_FLOAT_WORD(ib,b); + for(i=1;i0) return b; else return -b; +} diff --git a/openlibm/src/e_lgamma.c b/openlibm/src/e_lgamma.c new file mode 100644 index 0000000..d316796 --- /dev/null +++ b/openlibm/src/e_lgamma.c @@ -0,0 +1,36 @@ + +/* @(#)e_lgamma.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_lgamma.c,v 1.9 2008/02/22 02:30:35 das Exp $"); + +/* __ieee754_lgamma(x) + * Return the logarithm of the Gamma function of x. + * + * Method: call __ieee754_lgamma_r + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +__ieee754_lgamma(double x) +{ +#ifdef OPENLIBM_ONLY_THREAD_SAFE + int signgam; +#endif + + return __ieee754_lgamma_r(x,&signgam); +} diff --git a/openlibm/src/e_lgamma_r.c b/openlibm/src/e_lgamma_r.c new file mode 100644 index 0000000..df3ae23 --- /dev/null +++ b/openlibm/src/e_lgamma_r.c @@ -0,0 +1,298 @@ + +/* @(#)e_lgamma_r.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_lgamma_r.c,v 1.11 2011/10/15 07:00:28 das Exp $"); + +/* __ieee754_lgamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * where + * poly(z) is a 14 degree polynomial. + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * with accuracy + * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * where + * |w - f(z)| < 2**-58.74 + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1) = lgamma(2) = 0 + * lgamma(x) ~ -log(|x|) for tiny x + * lgamma(0) = lgamma(neg.integer) = inf and raise divide-by-zero + * lgamma(inf) = inf + * lgamma(-inf) = inf (bug for bug compatible with C99!?) + * + */ + +#include + +#include "math_private.h" + +static const double +two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ +a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ +a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ +a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ +a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ +a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ +a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ +a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ +a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ +a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ +a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ +a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ +tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ +tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ +/* tt = -(tail of tf) */ +tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ +t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ +t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ +t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ +t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ +t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ +t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ +t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ +t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ +t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ +t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ +t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ +t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ +t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ +t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ +t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ +u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ +u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ +u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ +u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ +u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ +v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ +v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ +v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ +v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ +v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ +s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ +s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ +s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ +s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ +s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ +s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ +r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ +r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ +r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ +r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ +r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ +r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ +w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ +w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ +w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ +w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ +w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ +w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ +w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ + +static const double zero= 0.00000000000000000000e+00; + + static double sin_pi(double x) +{ + double y,z; + int n,ix; + + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floor(y); + if(z!=y) { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */ + n = (int) (y*4.0); + } else { + if(ix>=0x43400000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x43300000) z = y+two52; /* exact */ + GET_LOW_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sin(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cos(pi*(0.5-y),zero); break; + case 3: + case 4: y = __kernel_sin(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; + default: y = __kernel_sin(pi*(y-2.0),zero,0); break; + } + return -y; +} + + +OLM_DLLEXPORT double +__ieee754_lgamma_r(double x, int *signgamp) +{ + double t,y,z,nadj,p,p1,p2,p3,q,r,w; + int32_t hx; + int i,lx,ix; + + EXTRACT_WORDS(hx,lx,x); + + /* purge off +-inf, NaN, +-0, tiny and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x*x; + if((ix|lx)==0) return one/zero; + if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_log(-x); + } else return -__ieee754_log(x); + } + if(hx<0) { + if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ + return one/zero; + t = sin_pi(x); + if(t==zero) return one/zero; /* -integer */ + nadj = __ieee754_log(pi/fabs(t*x)); + if(t=0x3FE76944) {y = one-x; i= 0;} + else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-0.5*y + p1/p2); + } + } + else if(ix<0x40200000) { /* x < 8.0 */ + i = (int)x; + y = x-(double)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6.0); /* FALLTHRU */ + case 6: z *= (y+5.0); /* FALLTHRU */ + case 5: z *= (y+4.0); /* FALLTHRU */ + case 4: z *= (y+3.0); /* FALLTHRU */ + case 3: z *= (y+2.0); /* FALLTHRU */ + r += __ieee754_log(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x43900000) { + t = __ieee754_log(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(__ieee754_log(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/openlibm/src/e_lgammaf.c b/openlibm/src/e_lgammaf.c new file mode 100644 index 0000000..5b95f02 --- /dev/null +++ b/openlibm/src/e_lgammaf.c @@ -0,0 +1,37 @@ +/* e_lgammaf.c -- float version of e_lgamma.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_lgammaf.c,v 1.8 2008/02/22 02:30:35 das Exp $"); + +/* __ieee754_lgammaf(x) + * Return the logarithm of the Gamma function of x. + * + * Method: call __ieee754_lgammaf_r + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +__ieee754_lgammaf(float x) +{ +#ifdef OPENLIBM_ONLY_THREAD_SAFE + int signgam; +#endif + + return __ieee754_lgammaf_r(x,&signgam); +} diff --git a/openlibm/src/e_lgammaf_r.c b/openlibm/src/e_lgammaf_r.c new file mode 100644 index 0000000..7446dfc --- /dev/null +++ b/openlibm/src/e_lgammaf_r.c @@ -0,0 +1,231 @@ +/* e_lgammaf_r.c -- float version of e_lgamma_r.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_lgammaf_r.c,v 1.12 2011/10/15 07:00:28 das Exp $"); + +#include + +#include "math_private.h" + +static const float +two23= 8.3886080000e+06, /* 0x4b000000 */ +half= 5.0000000000e-01, /* 0x3f000000 */ +one = 1.0000000000e+00, /* 0x3f800000 */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +a0 = 7.7215664089e-02, /* 0x3d9e233f */ +a1 = 3.2246702909e-01, /* 0x3ea51a66 */ +a2 = 6.7352302372e-02, /* 0x3d89f001 */ +a3 = 2.0580807701e-02, /* 0x3ca89915 */ +a4 = 7.3855509982e-03, /* 0x3bf2027e */ +a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ +a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ +a7 = 5.1006977446e-04, /* 0x3a05b634 */ +a8 = 2.2086278477e-04, /* 0x39679767 */ +a9 = 1.0801156895e-04, /* 0x38e28445 */ +a10 = 2.5214456400e-05, /* 0x37d383a2 */ +a11 = 4.4864096708e-05, /* 0x383c2c75 */ +tc = 1.4616321325e+00, /* 0x3fbb16c3 */ +tf = -1.2148628384e-01, /* 0xbdf8cdcd */ +/* tt = -(tail of tf) */ +tt = 6.6971006518e-09, /* 0x31e61c52 */ +t0 = 4.8383611441e-01, /* 0x3ef7b95e */ +t1 = -1.4758771658e-01, /* 0xbe17213c */ +t2 = 6.4624942839e-02, /* 0x3d845a15 */ +t3 = -3.2788541168e-02, /* 0xbd064d47 */ +t4 = 1.7970675603e-02, /* 0x3c93373d */ +t5 = -1.0314224288e-02, /* 0xbc28fcfe */ +t6 = 6.1005386524e-03, /* 0x3bc7e707 */ +t7 = -3.6845202558e-03, /* 0xbb7177fe */ +t8 = 2.2596477065e-03, /* 0x3b141699 */ +t9 = -1.4034647029e-03, /* 0xbab7f476 */ +t10 = 8.8108185446e-04, /* 0x3a66f867 */ +t11 = -5.3859531181e-04, /* 0xba0d3085 */ +t12 = 3.1563205994e-04, /* 0x39a57b6b */ +t13 = -3.1275415677e-04, /* 0xb9a3f927 */ +t14 = 3.3552918467e-04, /* 0x39afe9f7 */ +u0 = -7.7215664089e-02, /* 0xbd9e233f */ +u1 = 6.3282704353e-01, /* 0x3f2200f4 */ +u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ +u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ +u4 = 2.2896373272e-01, /* 0x3e6a7578 */ +u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ +v1 = 2.4559779167e+00, /* 0x401d2ebe */ +v2 = 2.1284897327e+00, /* 0x4008392d */ +v3 = 7.6928514242e-01, /* 0x3f44efdf */ +v4 = 1.0422264785e-01, /* 0x3dd572af */ +v5 = 3.2170924824e-03, /* 0x3b52d5db */ +s0 = -7.7215664089e-02, /* 0xbd9e233f */ +s1 = 2.1498242021e-01, /* 0x3e5c245a */ +s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ +s3 = 1.4635047317e-01, /* 0x3e15dce6 */ +s4 = 2.6642270386e-02, /* 0x3cda40e4 */ +s5 = 1.8402845599e-03, /* 0x3af135b4 */ +s6 = 3.1947532989e-05, /* 0x3805ff67 */ +r1 = 1.3920053244e+00, /* 0x3fb22d3b */ +r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ +r3 = 1.7193385959e-01, /* 0x3e300f6e */ +r4 = 1.8645919859e-02, /* 0x3c98bf54 */ +r5 = 7.7794247773e-04, /* 0x3a4beed6 */ +r6 = 7.3266842264e-06, /* 0x36f5d7bd */ +w0 = 4.1893854737e-01, /* 0x3ed67f1d */ +w1 = 8.3333335817e-02, /* 0x3daaaaab */ +w2 = -2.7777778450e-03, /* 0xbb360b61 */ +w3 = 7.9365057172e-04, /* 0x3a500cfd */ +w4 = -5.9518753551e-04, /* 0xba1c065c */ +w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ +w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ + +static const float zero= 0.0000000000e+00; + + static float sin_pif(float x) +{ + float y,z; + int n,ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3e800000) return __kernel_sindf(pi*x); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floorf(y); + if(z!=y) { /* inexact anyway */ + y *= (float)0.5; + y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ + n = (int) (y*(float)4.0); + } else { + if(ix>=0x4b800000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x4b000000) z = y+two23; /* exact */ + GET_FLOAT_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sindf(pi*y); break; + case 1: + case 2: y = __kernel_cosdf(pi*((float)0.5-y)); break; + case 3: + case 4: y = __kernel_sindf(pi*(one-y)); break; + case 5: + case 6: y = -__kernel_cosdf(pi*(y-(float)1.5)); break; + default: y = __kernel_sindf(pi*(y-(float)2.0)); break; + } + return -y; +} + + +OLM_DLLEXPORT float +__ieee754_lgammaf_r(float x, int *signgamp) +{ + float t,y,z,nadj,p,p1,p2,p3,q,r,w; + int32_t hx; + int i,ix; + + GET_FLOAT_WORD(hx,x); + + /* purge off +-inf, NaN, +-0, tiny and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x*x; + if(ix==0) return one/zero; + if(ix<0x35000000) { /* |x|<2**-21, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_logf(-x); + } else return -__ieee754_logf(x); + } + if(hx<0) { + if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ + return one/zero; + t = sin_pif(x); + if(t==zero) return one/zero; /* -integer */ + nadj = __ieee754_logf(pi/fabsf(t*x)); + if(t=0x3f3b4a20) {y = one-x; i= 0;} + else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-(float)0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-(float)0.5*y + p1/p2); + } + } + else if(ix<0x41000000) { /* x < 8.0 */ + i = (int)x; + y = x-(float)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+(float)6.0); /* FALLTHRU */ + case 6: z *= (y+(float)5.0); /* FALLTHRU */ + case 5: z *= (y+(float)4.0); /* FALLTHRU */ + case 4: z *= (y+(float)3.0); /* FALLTHRU */ + case 3: z *= (y+(float)2.0); /* FALLTHRU */ + r += __ieee754_logf(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x5c800000) { + t = __ieee754_logf(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(__ieee754_logf(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/openlibm/src/e_lgammal.c b/openlibm/src/e_lgammal.c new file mode 100644 index 0000000..c1bfb25 --- /dev/null +++ b/openlibm/src/e_lgammal.c @@ -0,0 +1,15 @@ +#include "cdefs-compat.h" + +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double +lgammal(long double x) +{ +#ifdef OPENLIBM_ONLY_THREAD_SAFE + int signgam; +#endif + + return (lgammal_r(x, &signgam)); +} diff --git a/openlibm/src/e_log.c b/openlibm/src/e_log.c new file mode 100644 index 0000000..29584bb --- /dev/null +++ b/openlibm/src/e_log.c @@ -0,0 +1,146 @@ + +/* @(#)e_log.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_log.c,v 1.15 2008/03/29 16:37:59 das Exp $"); + +/* __ieee754_log(x) + * Return the logrithm of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include + +#include "math_private.h" + +static const double +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +OLM_DLLEXPORT double +__ieee754_log(double x) +{ + double hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,hx,i,j; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* -2**-20 <= f < 2**-20 */ + if(f==zero) { + if(k==0) { + return zero; + } else { + dk=(double)k; + return dk*ln2_hi+dk*ln2_lo; + } + } + R = f*f*(0.5-0.33333333333333333*f); + if(k==0) return f-R; else {dk=(double)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/(2.0+f); + dk = (double)k; + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(log, logl); +#endif diff --git a/openlibm/src/e_log10.c b/openlibm/src/e_log10.c new file mode 100644 index 0000000..8e3c4e0 --- /dev/null +++ b/openlibm/src/e_log10.c @@ -0,0 +1,93 @@ + +/* @(#)e_log10.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_log10.c,v 1.15 2011/10/15 05:23:28 das Exp $"); + +/* + * Return the base 10 logarithm of x. See e_log.c and k_log.h for most + * comments. + * + * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2) + * in not-quite-routine extra precision. + */ + +#include +#include + +#include "math_private.h" +#include "k_log.h" + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ +ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ +log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ +log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +static const double zero = 0.0; + +OLM_DLLEXPORT double +__ieee754_log10(double x) +{ + double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2; + int32_t i,k,hx; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + if (hx == 0x3ff00000 && lx == 0) + return zero; /* log(1) = +0 */ + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + y = (double)k; + f = x - 1.0; + hfsq = 0.5*f*f; + r = k_log1p(f); + + /* See e_log2.c for most details. */ + hi = f - hfsq; + SET_LOW_WORD(hi,0); + lo = (f - hi) - hfsq + r; + val_hi = hi*ivln10hi; + y2 = y*log10_2hi; + val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; + + /* + * Extra precision in for adding y*log10_2hi is not strictly needed + * since there is no very large cancellation near x = sqrt(2) or + * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs + * with some parallelism and it reduces the error for many args. + */ + w = y2 + val_hi; + val_lo += (y2 - w) + val_hi; + val_hi = w; + + return val_lo + val_hi; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(log10, log10l); +#endif diff --git a/openlibm/src/e_log10f.c b/openlibm/src/e_log10f.c new file mode 100644 index 0000000..1f6e31a --- /dev/null +++ b/openlibm/src/e_log10f.c @@ -0,0 +1,75 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_log10f.c,v 1.13 2011/10/16 05:36:23 das Exp $"); + +/* + * Float version of e_log10.c. See the latter for most comments. + */ + +#include + +#include "math_private.h" +#include "k_logf.h" + +// VBS +#define float_t float + +static const float +two25 = 3.3554432000e+07, /* 0x4c000000 */ +ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */ +ivln10lo = -3.1689971365e-05, /* 0xb804ead9 */ +log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */ +log10_2lo = 7.9034151668e-07; /* 0x355427db */ + +static const float zero = 0.0; + +OLM_DLLEXPORT float +__ieee754_log10f(float x) +{ + float f,hfsq,hi,lo,r,y; + int32_t i,k,hx; + + GET_FLOAT_WORD(hx,x); + + k=0; + if (hx < 0x00800000) { /* x < 2**-126 */ + if ((hx&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(hx,x); + } + if (hx >= 0x7f800000) return x+x; + if (hx == 0x3f800000) + return zero; /* log(1) = +0 */ + k += (hx>>23)-127; + hx &= 0x007fffff; + i = (hx+(0x4afb0d))&0x800000; + SET_FLOAT_WORD(x,hx|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + y = (float)k; + f = x - (float)1.0; + hfsq = (float)0.5*f*f; + r = k_log1pf(f); + + /* See e_log2f.c and e_log2.c for details. */ + if (sizeof(float_t) > sizeof(float)) + return (r - hfsq + f) * ((float_t)ivln10lo + ivln10hi) + + y * ((float_t)log10_2lo + log10_2hi); + hi = f - hfsq; + GET_FLOAT_WORD(hx,hi); + SET_FLOAT_WORD(hi,hx&0xfffff000); + lo = (f - hi) - hfsq + r; + return y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi + hi*ivln10hi + + y*log10_2hi; +} diff --git a/openlibm/src/e_log2.c b/openlibm/src/e_log2.c new file mode 100644 index 0000000..1570233 --- /dev/null +++ b/openlibm/src/e_log2.c @@ -0,0 +1,116 @@ + +/* @(#)e_log10.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_log2.c,v 1.4 2011/10/15 05:23:28 das Exp $"); + +/* + * Return the base 2 logarithm of x. See e_log.c and k_log.h for most + * comments. + * + * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel, + * then does the combining and scaling steps + * log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k + * in not-quite-routine extra precision. + */ + +#include +#include + +#include "math_private.h" +#include "k_log.h" + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +ivln2hi = 1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */ +ivln2lo = 1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */ + +static const double zero = 0.0; + +OLM_DLLEXPORT double +__ieee754_log2(double x) +{ + double f,hfsq,hi,lo,r,val_hi,val_lo,w,y; + int32_t i,k,hx; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + if (hx == 0x3ff00000 && lx == 0) + return zero; /* log(1) = +0 */ + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + y = (double)k; + f = x - 1.0; + hfsq = 0.5*f*f; + r = k_log1p(f); + + /* + * f-hfsq must (for args near 1) be evaluated in extra precision + * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2). + * This is fairly efficient since f-hfsq only depends on f, so can + * be evaluated in parallel with R. Not combining hfsq with R also + * keeps R small (though not as small as a true `lo' term would be), + * so that extra precision is not needed for terms involving R. + * + * Compiler bugs involving extra precision used to break Dekker's + * theorem for spitting f-hfsq as hi+lo, unless double_t was used + * or the multi-precision calculations were avoided when double_t + * has extra precision. These problems are now automatically + * avoided as a side effect of the optimization of combining the + * Dekker splitting step with the clear-low-bits step. + * + * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra + * precision to avoid a very large cancellation when x is very near + * these values. Unlike the above cancellations, this problem is + * specific to base 2. It is strange that adding +-1 is so much + * harder than adding +-ln2 or +-log10_2. + * + * This uses Dekker's theorem to normalize y+val_hi, so the + * compiler bugs are back in some configurations, sigh. And I + * don't want to used double_t to avoid them, since that gives a + * pessimization and the support for avoiding the pessimization + * is not yet available. + * + * The multi-precision calculations for the multiplications are + * routine. + */ + hi = f - hfsq; + SET_LOW_WORD(hi,0); + lo = (f - hi) - hfsq + r; + val_hi = hi*ivln2hi; + val_lo = (lo+hi)*ivln2lo + lo*ivln2hi; + + /* spadd(val_hi, val_lo, y), except for not using double_t: */ + w = y + val_hi; + val_lo += (y - w) + val_hi; + val_hi = w; + + return val_lo + val_hi; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(log2, log2l); +#endif diff --git a/openlibm/src/e_log2f.c b/openlibm/src/e_log2f.c new file mode 100644 index 0000000..58977ac --- /dev/null +++ b/openlibm/src/e_log2f.c @@ -0,0 +1,85 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_log2f.c,v 1.5 2011/10/15 05:23:28 das Exp $"); + +/* + * Float version of e_log2.c. See the latter for most comments. + */ + +#include + +#include "math_private.h" +#include "k_logf.h" + +// VBS +#define float_t float + +static const float +two25 = 3.3554432000e+07, /* 0x4c000000 */ +ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */ +ivln2lo = -1.7605285393e-04; /* 0xb9389ad4 */ + +static const float zero = 0.0; + +OLM_DLLEXPORT float +__ieee754_log2f(float x) +{ + float f,hfsq,hi,lo,r,y; + int32_t i,k,hx; + + GET_FLOAT_WORD(hx,x); + + k=0; + if (hx < 0x00800000) { /* x < 2**-126 */ + if ((hx&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(hx,x); + } + if (hx >= 0x7f800000) return x+x; + if (hx == 0x3f800000) + return zero; /* log(1) = +0 */ + k += (hx>>23)-127; + hx &= 0x007fffff; + i = (hx+(0x4afb0d))&0x800000; + SET_FLOAT_WORD(x,hx|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + y = (float)k; + f = x - (float)1.0; + hfsq = (float)0.5*f*f; + r = k_log1pf(f); + + /* + * We no longer need to avoid falling into the multi-precision + * calculations due to compiler bugs breaking Dekker's theorem. + * Keep avoiding this as an optimization. See e_log2.c for more + * details (some details are here only because the optimization + * is not yet available in double precision). + * + * Another compiler bug turned up. With gcc on i386, + * (ivln2lo + ivln2hi) would be evaluated in float precision + * despite runtime evaluations using double precision. So we + * must cast one of its terms to float_t. This makes the whole + * expression have type float_t, so return is forced to waste + * time clobbering its extra precision. + */ + if (sizeof(float_t) > sizeof(float)) + return (r - hfsq + f) * ((float_t)ivln2lo + ivln2hi) + y; + + hi = f - hfsq; + GET_FLOAT_WORD(hx,hi); + SET_FLOAT_WORD(hi,hx&0xfffff000); + lo = (f - hi) - hfsq + r; + return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + y; +} diff --git a/openlibm/src/e_logf.c b/openlibm/src/e_logf.c new file mode 100644 index 0000000..dc5e151 --- /dev/null +++ b/openlibm/src/e_logf.c @@ -0,0 +1,89 @@ +/* e_logf.c -- float version of e_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_logf.c,v 1.11 2008/03/29 16:37:59 das Exp $"); + +#include + +#include "math_private.h" + +static const float +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ +Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ +Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ +Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ +Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ + +static const float zero = 0.0; + +OLM_DLLEXPORT float +__ieee754_logf(float x) +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if ((ix&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (ix >= 0x7f800000) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + f = x-(float)1.0; + if((0x007fffff&(0x8000+ix))<0xc000) { /* -2**-9 <= f < 2**-9 */ + if(f==zero) { + if(k==0) { + return zero; + } else { + dk=(float)k; + return dk*ln2_hi+dk*ln2_lo; + } + } + R = f*f*((float)0.5-(float)0.33333333333333333*f); + if(k==0) return f-R; else {dk=(float)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/((float)2.0+f); + dk = (float)k; + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + t1= w*(Lg2+w*Lg4); + t2= z*(Lg1+w*Lg3); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=(float)0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/openlibm/src/e_pow.c b/openlibm/src/e_pow.c new file mode 100644 index 0000000..a891552 --- /dev/null +++ b/openlibm/src/e_pow.c @@ -0,0 +1,317 @@ +/* @(#)e_pow.c 1.5 04/04/22 SMI */ +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_pow.c,v 1.14 2011/10/21 06:26:07 das Exp $"); + +/* __ieee754_pow(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 53-24 = 29 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular + * pow(integer,integer) + * always returns the correct integer provided it is + * representable. + * + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include + +#include "math_private.h" + +static const double +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ +dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ +zero = 0.0, +one = 1.0, +two = 2.0, +two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ +huge = 1.0e300, +tiny = 1.0e-300, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ +L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ +L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ +L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ +L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ +L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ +lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ +lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ +ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ +cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ +cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ +cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ +ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ +ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ +ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ + +OLM_DLLEXPORT double +__ieee754_pow(double x, double y) +{ + double z,ax,z_h,z_l,p_h,p_l; + double y1,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if((iy|ly)==0) return one; + + /* x==1: 1**y = 1, even if y is NaN */ + if (hx==0x3ff00000 && lx == 0) return one; + + /* y!=zero: result is NaN if either arg is NaN */ + if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || + iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) + return (x+0.0)+(y+0.0); + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x43400000) yisint = 2; /* even integer y */ + else if(iy>=0x3ff00000) { + k = (iy>>20)-0x3ff; /* exponent */ + if(k>20) { + j = ly>>(52-k); + if((j<<(52-k))==ly) yisint = 2-(j&1); + } else if(ly==0) { + j = iy>>(20-k); + if((j<<(20-k))==iy) yisint = 2-(j&1); + } + } + } + + /* special value of y */ + if(ly==0) { + if (iy==0x7ff00000) { /* y is +-inf */ + if(((ix-0x3ff00000)|lx)==0) + return one; /* (-1)**+-inf is NaN */ + else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3ff00000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x40080000) return x*x*x; /* y is 3 */ + if(hy==0x40100000) { /* y is 4 */ + u = x*x; + return u*u; + } + if(hy==0x3fe00000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return sqrt(x); + } + } + + ax = fabs(x); + /* special value of x */ + if(lx==0) { + if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3ff00000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be + n = (hx>>31)+1; + but ANSI C says a right shift of a signed negative quantity is + implementation defined. */ + n = ((u_int32_t)hx>>31)-1; + + /* (x<0)**(non-int) is NaN */ + if((n|yisint)==0) return (x-x)/(x-x); + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ + + /* |y| is huge */ + if(iy>0x41e00000) { /* if |y| > 2**31 */ + if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ + if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; + if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; + } + /* over/underflow if x is not close to one */ + if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny; + if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-one; /* t has 20 trailing zeros */ + w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); + u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + SET_LOW_WORD(t1,0); + t2 = v-(t1-u); + } else { + double ss,s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00100000) + {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } + n += ((ix)>>20)-0x3ff; + j = ix&0x000fffff; + /* determine interval */ + ix = j|0x3ff00000; /* normalize ix */ + if(j<=0x3988E) k=0; /* |x|>1)|0x20000000)+0x00080000+(k<<18)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = ss*ss; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+ss); + s2 = s_h*s_h; + t_h = 3.0+s2+r; + SET_LOW_WORD(t_h,0); + t_l = r-((t_h-3.0)-s2); + /* u+v = ss*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*ss; + /* 2/(3log2)*(ss+...) */ + p_h = u+v; + SET_LOW_WORD(p_h,0); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (double)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + SET_LOW_WORD(t1,0); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + y1 = y; + SET_LOW_WORD(y1,0); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + EXTRACT_WORDS(j,i,z); + if (j>=0x40900000) { /* z >= 1024 */ + if(((j-0x40900000)|i)!=0) /* if z > 1024 */ + return s*huge*huge; /* overflow */ + else { + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ + if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ + return s*tiny*tiny; /* underflow */ + else { + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>20)-0x3ff; + n = 0; + if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00100000>>(k+1)); + k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ + t = zero; + SET_HIGH_WORD(t,n&~(0x000fffff>>k)); + n = ((n&0x000fffff)|0x00100000)>>(20-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + SET_LOW_WORD(t,0); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_HIGH_WORD(j,z); + j += (n<<20); + if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ + else SET_HIGH_WORD(z,j); + return s*z; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(pow, powl); +#endif diff --git a/openlibm/src/e_powf.c b/openlibm/src/e_powf.c new file mode 100644 index 0000000..9527ef0 --- /dev/null +++ b/openlibm/src/e_powf.c @@ -0,0 +1,253 @@ +/* e_powf.c -- float version of e_pow.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_powf.c,v 1.16 2011/10/21 06:26:07 das Exp $"); + +#include + +#include "math_private.h" + +static const float +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ +dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ +zero = 0.0, +half = 0.5, +qrtr = 0.25, +thrd = 3.33333343e-01, /* 0x3eaaaaab */ +one = 1.0, +two = 2.0, +two24 = 16777216.0, /* 0x4b800000 */ +huge = 1.0e30, +tiny = 1.0e-30, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 6.0000002384e-01, /* 0x3f19999a */ +L2 = 4.2857143283e-01, /* 0x3edb6db7 */ +L3 = 3.3333334327e-01, /* 0x3eaaaaab */ +L4 = 2.7272811532e-01, /* 0x3e8ba305 */ +L5 = 2.3066075146e-01, /* 0x3e6c3255 */ +L6 = 2.0697501302e-01, /* 0x3e53f142 */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08, /* 0x3331bb4c */ +lg2 = 6.9314718246e-01, /* 0x3f317218 */ +lg2_h = 6.93145752e-01, /* 0x3f317200 */ +lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ +ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ +cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ +cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */ +cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */ +ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ +ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ +ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ + +OLM_DLLEXPORT float +__ieee754_powf(float x, float y) +{ + float z,ax,z_h,z_l,p_h,p_l; + float y1,t1,t2,r,s,sn,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy,is; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if(iy==0) return one; + + /* x==1: 1**y = 1, even if y is NaN */ + if (hx==0x3f800000) return one; + + /* y!=zero: result is NaN if either arg is NaN */ + if(ix > 0x7f800000 || + iy > 0x7f800000) + return nan_mix(x, y); + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x4b800000) yisint = 2; /* even integer y */ + else if(iy>=0x3f800000) { + k = (iy>>23)-0x7f; /* exponent */ + j = iy>>(23-k); + if((j<<(23-k))==iy) yisint = 2-(j&1); + } + } + + /* special value of y */ + if (iy==0x7f800000) { /* y is +-inf */ + if (ix==0x3f800000) + return one; /* (-1)**+-inf is NaN */ + else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3f800000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3f000000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return __ieee754_sqrtf(x); + } + + ax = fabsf(x); + /* special value of x */ + if(ix==0x7f800000||ix==0||ix==0x3f800000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3f800000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + + n = ((u_int32_t)hx>>31)-1; + + /* (x<0)**(non-int) is NaN */ + if((n|yisint)==0) return (x-x)/(x-x); + + sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */ + + /* |y| is huge */ + if(iy>0x4d000000) { /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + if(ix<0x3f7ffff6) return (hy<0)? sn*huge*huge:sn*tiny*tiny; + if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-1; /* t has 20 trailing zeros */ + w = (t*t)*(half-t*(thrd-t*qrtr)); + u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = v-(t1-u); + } else { + float s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00800000) + {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); } + n += ((ix)>>23)-0x7f; + j = ix&0x007fffff; + /* determine interval */ + ix = j|0x3f800000; /* normalize ix */ + if(j<=0x1cc471) k=0; /* |x|>1)&0xfffff000)|0x20000000; + SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = s*s; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = 3+s2+r; + GET_FLOAT_WORD(is,t_h); + SET_FLOAT_WORD(t_h,is&0xfffff000); + t_l = r-((t_h-3)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + p_h = u+v; + GET_FLOAT_WORD(is,p_h); + SET_FLOAT_WORD(p_h,is&0xfffff000); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = n; + t1 = (((z_h+z_l)+dp_h[k])+t); + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + GET_FLOAT_WORD(is,y); + SET_FLOAT_WORD(y1,is&0xfffff000); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + GET_FLOAT_WORD(j,z); + if (j>0x43000000) /* if z > 128 */ + return sn*huge*huge; /* overflow */ + else if (j==0x43000000) { /* if z == 128 */ + if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */ + } + else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */ + return sn*tiny*tiny; /* underflow */ + else if (j==0xc3160000){ /* z == -150 */ + if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */ + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>23)-0x7f; + n = 0; + if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00800000>>(k+1)); + k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ + SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); + n = ((n&0x007fffff)|0x00800000)>>(23-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + GET_FLOAT_WORD(is,t); + SET_FLOAT_WORD(t,is&0xffff8000); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_FLOAT_WORD(j,z); + j += (n<<23); + if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */ + else SET_FLOAT_WORD(z,j); + return sn*z; +} diff --git a/openlibm/src/e_rem_pio2.c b/openlibm/src/e_rem_pio2.c new file mode 100644 index 0000000..c09e38a --- /dev/null +++ b/openlibm/src/e_rem_pio2.c @@ -0,0 +1,183 @@ + +/* @(#)e_rem_pio2.c 1.4 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_rem_pio2.c,v 1.22 2011/06/19 17:07:58 kargl Exp $"); + +/* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include +#include + +#include "math_private.h" + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const double +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ +pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ +pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ +pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ +pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ +pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + +__inline int +__ieee754_rem_pio2(double x, double *y) +{ + double z,w,t,r,fn; + double tx[3],ty[2]; + int32_t e0,i,j,nx,n,ix,hx; + u_int32_t low; + + GET_HIGH_WORD(hx,x); /* high word of x */ + ix = hx&0x7fffffff; +#if 0 /* Must be handled in caller. */ + if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} +#endif + if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ + if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ + goto medium; /* cancellation -- use medium case */ + if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ + if (hx > 0) { + z = x - pio2_1; /* one round good to 85 bits */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + return 1; + } else { + z = x + pio2_1; + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + return -1; + } + } else { + if (hx > 0) { + z = x - 2*pio2_1; + y[0] = z - 2*pio2_1t; + y[1] = (z-y[0])-2*pio2_1t; + return 2; + } else { + z = x + 2*pio2_1; + y[0] = z + 2*pio2_1t; + y[1] = (z-y[0])+2*pio2_1t; + return -2; + } + } + } + if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ + if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ + if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ + goto medium; + if (hx > 0) { + z = x - 3*pio2_1; + y[0] = z - 3*pio2_1t; + y[1] = (z-y[0])-3*pio2_1t; + return 3; + } else { + z = x + 3*pio2_1; + y[0] = z + 3*pio2_1t; + y[1] = (z-y[0])+3*pio2_1t; + return -3; + } + } else { + if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ + goto medium; + if (hx > 0) { + z = x - 4*pio2_1; + y[0] = z - 4*pio2_1t; + y[1] = (z-y[0])-4*pio2_1t; + return 4; + } else { + z = x + 4*pio2_1; + y[0] = z + 4*pio2_1t; + y[1] = (z-y[0])+4*pio2_1t; + return -4; + } + } + } + if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ +medium: + /* Use a specialized rint() to get fn. Assume round-to-nearest. */ + STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52); + fn = fn-0x1.8p52; +#ifdef HAVE_EFFICIENT_IRINT + n = irint(fn); +#else + n = (int32_t)fn; +#endif + r = x-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 85 bit */ + { + u_int32_t high; + j = ix>>20; + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>16) { /* 2nd iteration needed, good to 118 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>49) { /* 3rd iteration need, 151 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7ff00000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + GET_LOW_WORD(low,x); + e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ + INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low); + for(i=0;i<2;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,ty,e0,nx,1); + if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} + y[0] = ty[0]; y[1] = ty[1]; return n; +} diff --git a/openlibm/src/e_rem_pio2f.c b/openlibm/src/e_rem_pio2f.c new file mode 100644 index 0000000..9861bb9 --- /dev/null +++ b/openlibm/src/e_rem_pio2f.c @@ -0,0 +1,81 @@ +/* e_rem_pio2f.c -- float version of e_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Debugged and optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_rem_pio2f.c,v 1.32 2009/06/03 08:16:34 ed Exp $"); + +/* __ieee754_rem_pio2f(x,y) + * + * return the remainder of x rem pi/2 in *y + * use double precision for everything except passing x + * use __kernel_rem_pio2() for large x + */ + +#include +#include + +#include "math_private.h" + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + */ + +static const double +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */ +pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */ + +__inline int +__ieee754_rem_pio2f(float x, double *y) +{ + double w,r,fn; + double tx[1],ty[1]; + float z; + int32_t e0,n,ix,hx; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + /* 33+53 bit pi is good enough for medium size */ + if(ix<0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */ + /* Use a specialized rint() to get fn. Assume round-to-nearest. */ + STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52); + fn = fn-0x1.8p52; +#ifdef HAVE_EFFICIENT_IRINT + n = irint(fn); +#else + n = (int32_t)fn; +#endif + r = x-fn*pio2_1; + w = fn*pio2_1t; + *y = r-w; + return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7f800000) { /* x is inf or NaN */ + *y=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(|x|)-23) */ + e0 = (ix>>23)-150; /* e0 = ilogb(|x|)-23; */ + SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); + tx[0] = z; + n = __kernel_rem_pio2(tx,ty,e0,1,0); + if(hx<0) {*y = -ty[0]; return -n;} + *y = ty[0]; return n; +} diff --git a/openlibm/src/e_remainder.c b/openlibm/src/e_remainder.c new file mode 100644 index 0000000..a72631c --- /dev/null +++ b/openlibm/src/e_remainder.c @@ -0,0 +1,79 @@ + +/* @(#)e_remainder.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_remainder.c,v 1.12 2008/03/30 20:47:42 das Exp $"); + +/* __ieee754_remainder(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmod() return x-[x/p]chopped*p exactlp. + */ + +#include +#include + +#include "math_private.h" + +static const double zero = 0.0; + + +OLM_DLLEXPORT double +__ieee754_remainder(double x, double p) +{ + int32_t hx,hp; + u_int32_t sx,lx,lp; + double p_half; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hp,lp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7ff00000)|| /* x not finite */ + ((hp>=0x7ff00000)&& /* p is NaN */ + (((hp-0x7ff00000)|lp)!=0))) + return ((long double)x*p)/((long double)x*p); + + + if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabs(x); + p = fabs(p); + if (hp<0x00200000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_HIGH_WORD(hx,x); + if ((hx&0x7fffffff)==0) hx = 0; + SET_HIGH_WORD(x,hx^sx); + return x; +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(remainder, remainderl); +#endif diff --git a/openlibm/src/e_remainderf.c b/openlibm/src/e_remainderf.c new file mode 100644 index 0000000..ac0d153 --- /dev/null +++ b/openlibm/src/e_remainderf.c @@ -0,0 +1,66 @@ +/* e_remainderf.c -- float version of e_remainder.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_remainderf.c,v 1.8 2008/02/12 17:11:36 bde Exp $"); + +#include + +#include "math_private.h" + +static const float zero = 0.0; + + +OLM_DLLEXPORT float +__ieee754_remainderf(float x, float p) +{ + int32_t hx,hp; + u_int32_t sx; + float p_half; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if(hp==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7f800000)|| /* x not finite */ + ((hp>0x7f800000))) /* p is NaN */ + return ((long double)x*p)/((long double)x*p); + + + if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p); /* now x < 2p */ + if ((hx-hp)==0) return zero*x; + x = fabsf(x); + p = fabsf(p); + if (hp<0x01000000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = (float)0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_FLOAT_WORD(hx,x); + if ((hx&0x7fffffff)==0) hx = 0; + SET_FLOAT_WORD(x,hx^sx); + return x; +} diff --git a/openlibm/src/e_remainderl.c b/openlibm/src/e_remainderl.c new file mode 100644 index 0000000..5f1ee61 --- /dev/null +++ b/openlibm/src/e_remainderl.c @@ -0,0 +1,39 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_remainderl.c,v 1.1 2008/03/30 20:47:42 das Exp $"); + +#include +#include "math_private.h" + +OLM_DLLEXPORT long double +remainderl(long double x, long double y) +{ + int quo; + + return (remquol(x, y, &quo)); +} diff --git a/openlibm/src/e_sinh.c b/openlibm/src/e_sinh.c new file mode 100644 index 0000000..7f3a2bf --- /dev/null +++ b/openlibm/src/e_sinh.c @@ -0,0 +1,79 @@ + +/* @(#)e_sinh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_sinh.c,v 1.11 2011/10/21 06:28:47 das Exp $"); + +/* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include +#include + +#include "math_private.h" + +static const double one = 1.0, shuge = 1.0e307; + +OLM_DLLEXPORT double +__ieee754_sinh(double x) +{ + double t,h; + int32_t ix,jx; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3e300000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1(fabs(x)); + if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x408633CE) + return h*2.0*__ldexp_exp(fabs(x), -1); + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(sinh, sinhl); +#endif diff --git a/openlibm/src/e_sinhf.c b/openlibm/src/e_sinhf.c new file mode 100644 index 0000000..6e5e06d --- /dev/null +++ b/openlibm/src/e_sinhf.c @@ -0,0 +1,57 @@ +/* e_sinhf.c -- float version of e_sinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_sinhf.c,v 1.10 2011/10/21 06:28:47 das Exp $"); + +#include + +#include "math_private.h" + +static const float one = 1.0, shuge = 1.0e37; + +OLM_DLLEXPORT float +__ieee754_sinhf(float x) +{ + float t,h; + int32_t ix,jx; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,9], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x41100000) { /* |x|<9 */ + if (ix<0x39800000) /* |x|<2**-12 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1f(fabsf(x)); + if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [9, logf(maxfloat)] return 0.5*exp(|x|) */ + if (ix < 0x42b17217) return h*__ieee754_expf(fabsf(x)); + + /* |x| in [logf(maxfloat), overflowthresold] */ + if (ix<=0x42b2d4fc) + return h*2.0F*__ldexp_expf(fabsf(x), -1); + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff --git a/openlibm/src/e_sqrt.c b/openlibm/src/e_sqrt.c new file mode 100644 index 0000000..2eb4a1a --- /dev/null +++ b/openlibm/src/e_sqrt.c @@ -0,0 +1,451 @@ + +/* @(#)e_sqrt.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_sqrt.c,v 1.11 2008/03/02 01:47:58 das Exp $"); + +/* __ieee754_sqrt(x) + * Return correctly rounded sqrt. + * ------------------------------------------ + * | Use the hardware sqrt if you have one | + * ------------------------------------------ + * Method: + * Bit by bit method using integer arithmetic. (Slow, but portable) + * 1. Normalization + * Scale x to y in [1,4) with even powers of 2: + * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then + * sqrt(x) = 2^k * sqrt(y) + * 2. Bit by bit computation + * Let q = sqrt(y) truncated to i bit after binary point (q = 1), + * i 0 + * i+1 2 + * s = 2*q , and y = 2 * ( y - q ). (1) + * i i i i + * + * To compute q from q , one checks whether + * i+1 i + * + * -(i+1) 2 + * (q + 2 ) <= y. (2) + * i + * -(i+1) + * If (2) is false, then q = q ; otherwise q = q + 2 . + * i+1 i i+1 i + * + * With some algebric manipulation, it is not difficult to see + * that (2) is equivalent to + * -(i+1) + * s + 2 <= y (3) + * i i + * + * The advantage of (3) is that s and y can be computed by + * i i + * the following recurrence formula: + * if (3) is false + * + * s = s , y = y ; (4) + * i+1 i i+1 i + * + * otherwise, + * -i -(i+1) + * s = s + 2 , y = y - s - 2 (5) + * i+1 i i+1 i i + * + * One may easily use induction to prove (4) and (5). + * Note. Since the left hand side of (3) contain only i+2 bits, + * it does not necessary to do a full (53-bit) comparison + * in (3). + * 3. Final rounding + * After generating the 53 bits result, we compute one more bit. + * Together with the remainder, we can decide whether the + * result is exact, bigger than 1/2ulp, or less than 1/2ulp + * (it will never equal to 1/2ulp). + * The rounding mode can be detected by checking whether + * huge + tiny is equal to huge, and whether huge - tiny is + * equal to huge for some floating point number "huge" and "tiny". + * + * Special cases: + * sqrt(+-0) = +-0 ... exact + * sqrt(inf) = inf + * sqrt(-ve) = NaN ... with invalid signal + * sqrt(NaN) = NaN ... with invalid signal for signaling NaN + * + * Other methods : see the appended file at the end of the program below. + *--------------- + */ + +#include +#include + +#include "math_private.h" + +static const double one = 1.0, tiny=1.0e-300; + +OLM_DLLEXPORT double +__ieee754_sqrt(double x) +{ + double z; + int32_t sign = (int)0x80000000; + int32_t ix0,s0,q,m,t,i; + u_int32_t r,t1,s1,ix1,q1; + + EXTRACT_WORDS(ix0,ix1,x); + + /* take care of Inf and NaN */ + if((ix0&0x7ff00000)==0x7ff00000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix0<=0) { + if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix0<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix0>>20); + if(m==0) { /* subnormal x */ + while(ix0==0) { + m -= 21; + ix0 |= (ix1>>11); ix1 <<= 21; + } + for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1; + m -= i-1; + ix0 |= (ix1>>(32-i)); + ix1 <<= i; + } + m -= 1023; /* unbias exponent */ + ix0 = (ix0&0x000fffff)|0x00100000; + if(m&1){ /* odd m, double x to make it even */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + } + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ + r = 0x00200000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s0+r; + if(t<=ix0) { + s0 = t+r; + ix0 -= t; + q += r; + } + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + r>>=1; + } + + r = sign; + while(r!=0) { + t1 = s1+r; + t = s0; + if((t>31); + ix1 += ix1; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if((ix0|ix1)!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;} + else if (z>one) { + if (q1==(u_int32_t)0xfffffffe) q+=1; + q1+=2; + } else + q1 += (q1&1); + } + } + ix0 = (q>>1)+0x3fe00000; + ix1 = q1>>1; + if ((q&1)==1) ix1 |= sign; + ix0 += (m <<20); + INSERT_WORDS(z,ix0,ix1); + return z; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(sqrt, sqrtl); +#endif + +/* +Other methods (use floating-point arithmetic) +------------- +(This is a copy of a drafted paper by Prof W. Kahan +and K.C. Ng, written in May, 1986) + + Two algorithms are given here to implement sqrt(x) + (IEEE double precision arithmetic) in software. + Both supply sqrt(x) correctly rounded. The first algorithm (in + Section A) uses newton iterations and involves four divisions. + The second one uses reciproot iterations to avoid division, but + requires more multiplications. Both algorithms need the ability + to chop results of arithmetic operations instead of round them, + and the INEXACT flag to indicate when an arithmetic operation + is executed exactly with no roundoff error, all part of the + standard (IEEE 754-1985). The ability to perform shift, add, + subtract and logical AND operations upon 32-bit words is needed + too, though not part of the standard. + +A. sqrt(x) by Newton Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + + 1 11 52 ...widths + ------------------------------------------------------ + x: |s| e | f | + ------------------------------------------------------ + msb lsb msb lsb ...order + + + ------------------------ ------------------------ + x0: |s| e | f1 | x1: | f2 | + ------------------------ ------------------------ + + By performing shifts and subtracts on x0 and x1 (both regarded + as integers), we obtain an 8-bit approximation of sqrt(x) as + follows. + + k := (x0>>1) + 0x1ff80000; + y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits + Here k is a 32-bit integer and T1[] is an integer array containing + correction terms. Now magically the floating value of y (y's + leading 32-bit word is y0, the value of its trailing word is 0) + approximates sqrt(x) to almost 8-bit. + + Value of T1: + static int T1[32]= { + 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592, + 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, + 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, + 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,}; + + (2) Iterative refinement + + Apply Heron's rule three times to y, we have y approximates + sqrt(x) to within 1 ulp (Unit in the Last Place): + + y := (y+x/y)/2 ... almost 17 sig. bits + y := (y+x/y)/2 ... almost 35 sig. bits + y := y-(y-x/y)/2 ... within 1 ulp + + + Remark 1. + Another way to improve y to within 1 ulp is: + + y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x) + y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x) + + 2 + (x-y )*y + y := y + 2* ---------- ...within 1 ulp + 2 + 3y + x + + + This formula has one division fewer than the one above; however, + it requires more multiplications and additions. Also x must be + scaled in advance to avoid spurious overflow in evaluating the + expression 3y*y+x. Hence it is not recommended uless division + is slow. If division is very slow, then one should use the + reciproot algorithm given in section B. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + I := FALSE; ... reset INEXACT flag I + R := RZ; ... set rounding mode to round-toward-zero + z := x/y; ... chopped quotient, possibly inexact + If(not I) then { ... if the quotient is exact + if(z=y) { + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + } else { + z := z - ulp; ... special rounding + } + } + i := TRUE; ... sqrt(x) is inexact + If (r=RN) then z=z+ulp ... rounded-to-nearest + If (r=RP) then { ... round-toward-+inf + y = y+ulp; z=z+ulp; + } + y := y+z; ... chopped sum + y0:=y0-0x00100000; ... y := y/2 is correctly rounded. + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + + (4) Special cases + + Square root of +inf, +-0, or NaN is itself; + Square root of a negative number is NaN with invalid signal. + + +B. sqrt(x) by Reciproot Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + (see section A). By performing shifs and subtracts on x0 and y0, + we obtain a 7.8-bit approximation of 1/sqrt(x) as follows. + + k := 0x5fe80000 - (x0>>1); + y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits + + Here k is a 32-bit integer and T2[] is an integer array + containing correction terms. Now magically the floating + value of y (y's leading 32-bit word is y0, the value of + its trailing word y1 is set to zero) approximates 1/sqrt(x) + to almost 7.8-bit. + + Value of T2: + static int T2[64]= { + 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, + 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, + 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, + 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, + 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, + 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, + 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, + 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,}; + + (2) Iterative refinement + + Apply Reciproot iteration three times to y and multiply the + result by x to get an approximation z that matches sqrt(x) + to about 1 ulp. To be exact, we will have + -1ulp < sqrt(x)-z<1.0625ulp. + + ... set rounding mode to Round-to-nearest + y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x) + y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x) + ... special arrangement for better accuracy + z := x*y ... 29 bits to sqrt(x), with z*y<1 + z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x) + + Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that + (a) the term z*y in the final iteration is always less than 1; + (b) the error in the final result is biased upward so that + -1 ulp < sqrt(x) - z < 1.0625 ulp + instead of |sqrt(x)-z|<1.03125ulp. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + R := RZ; ... set rounding mode to round-toward-zero + switch(r) { + case RN: ... round-to-nearest + if(x<= z*(z-ulp)...chopped) z = z - ulp; else + if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp; + break; + case RZ:case RM: ... round-to-zero or round-to--inf + R:=RP; ... reset rounding mod to round-to-+inf + if(x=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp; + break; + case RP: ... round-to-+inf + if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else + if(x>z*z ...chopped) z = z+ulp; + break; + } + + Remark 3. The above comparisons can be done in fixed point. For + example, to compare x and w=z*z chopped, it suffices to compare + x1 and w1 (the trailing parts of x and w), regarding them as + two's complement integers. + + ...Is z an exact square root? + To determine whether z is an exact square root of x, let z1 be the + trailing part of z, and also let x0 and x1 be the leading and + trailing parts of x. + + If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0 + I := 1; ... Raise Inexact flag: z is not exact + else { + j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2 + k := z1 >> 26; ... get z's 25-th and 26-th + fraction bits + I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); + } + R:= r ... restore rounded mode + return sqrt(x):=z. + + If multiplication is cheaper then the foregoing red tape, the + Inexact flag can be evaluated by + + I := i; + I := (z*z!=x) or I. + + Note that z*z can overwrite I; this value must be sensed if it is + True. + + Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be + zero. + + -------------------- + z1: | f2 | + -------------------- + bit 31 bit 0 + + Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd + or even of logb(x) have the following relations: + + ------------------------------------------------- + bit 27,26 of z1 bit 1,0 of x1 logb(x) + ------------------------------------------------- + 00 00 odd and even + 01 01 even + 10 10 odd + 10 00 even + 11 01 even + ------------------------------------------------- + + (4) Special cases (see (4) of Section A). + + */ + diff --git a/openlibm/src/e_sqrtf.c b/openlibm/src/e_sqrtf.c new file mode 100644 index 0000000..2aeaa9f --- /dev/null +++ b/openlibm/src/e_sqrtf.c @@ -0,0 +1,86 @@ +/* e_sqrtf.c -- float version of e_sqrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include + +#include "math_private.h" + +static const float one = 1.0, tiny=1.0e-30; + +OLM_DLLEXPORT float +__ieee754_sqrtf(float x) +{ + float z; + int32_t sign = (int)0x80000000; + int32_t ix,s,q,m,t,i; + u_int32_t r; + + GET_FLOAT_WORD(ix,x); + + /* take care of Inf and NaN */ + if((ix&0x7f800000)==0x7f800000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix<=0) { + if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix>>23); + if(m==0) { /* subnormal x */ + for(i=0;(ix&0x00800000)==0;i++) ix<<=1; + m -= i-1; + } + m -= 127; /* unbias exponent */ + ix = (ix&0x007fffff)|0x00800000; + if(m&1) /* odd m, double x to make it even */ + ix += ix; + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix += ix; + q = s = 0; /* q = sqrt(x) */ + r = 0x01000000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s+r; + if(t<=ix) { + s = t+r; + ix -= t; + q += r; + } + ix += ix; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if(ix!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (z>one) + q += 2; + else + q += (q&1); + } + } + ix = (q>>1)+0x3f000000; + ix += (m <<23); + SET_FLOAT_WORD(z,ix); + return z; +} diff --git a/openlibm/src/e_sqrtl.c b/openlibm/src/e_sqrtl.c new file mode 100644 index 0000000..a073bf9 --- /dev/null +++ b/openlibm/src/e_sqrtl.c @@ -0,0 +1,162 @@ +/*- + * Copyright (c) 2007 Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/e_sqrtl.c,v 1.1 2008/03/02 01:47:58 das Exp $"); + +#include +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +/* Return (x + ulp) for normal positive x. Assumes no overflow. */ +static inline long double +inc(long double x) +{ + union IEEEl2bits u; + + u.e = x; + if (++u.bits.manl == 0) { + if (++u.bits.manh == 0) { + u.bits.exp++; + u.bits.manh |= LDBL_NBIT; + } + } + return (u.e); +} + +/* Return (x - ulp) for normal positive x. Assumes no underflow. */ +static inline long double +dec(long double x) +{ + union IEEEl2bits u; + + u.e = x; + if (u.bits.manl-- == 0) { + if (u.bits.manh-- == LDBL_NBIT) { + u.bits.exp--; + u.bits.manh |= LDBL_NBIT; + } + } + return (u.e); +} + +#ifndef __GNUC__ +#pragma STDC FENV_ACCESS ON +#endif + +/* + * This is slow, but simple and portable. You should use hardware sqrt + * if possible. + */ + +OLM_DLLEXPORT long double +sqrtl(long double x) +{ + union IEEEl2bits u; + int k, r; + long double lo, xn; + fenv_t env; + + u.e = x; + + /* If x = NaN, then sqrt(x) = NaN. */ + /* If x = Inf, then sqrt(x) = Inf. */ + /* If x = -Inf, then sqrt(x) = NaN. */ + if (u.bits.exp == LDBL_MAX_EXP * 2 - 1) + return (x * x + x); + + /* If x = +-0, then sqrt(x) = +-0. */ + if ((u.bits.manh | u.bits.manl | u.bits.exp) == 0) + return (x); + + /* If x < 0, then raise invalid and return NaN */ + if (u.bits.sign) + return ((x - x) / (x - x)); + + feholdexcept(&env); + + if (u.bits.exp == 0) { + /* Adjust subnormal numbers. */ + u.e *= 0x1.0p514; + k = -514; + } else { + k = 0; + } + /* + * u.e is a normal number, so break it into u.e = e*2^n where + * u.e = (2*e)*2^2k for odd n and u.e = (4*e)*2^2k for even n. + */ + if ((u.bits.exp - 0x3ffe) & 1) { /* n is odd. */ + k += u.bits.exp - 0x3fff; /* 2k = n - 1. */ + u.bits.exp = 0x3fff; /* u.e in [1,2). */ + } else { + k += u.bits.exp - 0x4000; /* 2k = n - 2. */ + u.bits.exp = 0x4000; /* u.e in [2,4). */ + } + + /* + * Newton's iteration. + * Split u.e into a high and low part to achieve additional precision. + */ + xn = sqrt(u.e); /* 53-bit estimate of sqrtl(x). */ +#if LDBL_MANT_DIG > 100 + xn = (xn + (u.e / xn)) * 0.5; /* 106-bit estimate. */ +#endif + lo = u.e; + u.bits.manl = 0; /* Zero out lower bits. */ + lo = (lo - u.e) / xn; /* Low bits divided by xn. */ + xn = xn + (u.e / xn); /* High portion of estimate. */ + u.e = xn + lo; /* Combine everything. */ + u.bits.exp += (k >> 1) - 1; + + feclearexcept(FE_INEXACT); + r = fegetround(); + fesetround(FE_TOWARDZERO); /* Set to round-toward-zero. */ + xn = x / u.e; /* Chopped quotient (inexact?). */ + + if (!fetestexcept(FE_INEXACT)) { /* Quotient is exact. */ + if (xn == u.e) { + fesetenv(&env); + return (u.e); + } + /* Round correctly for inputs like x = y**2 - ulp. */ + xn = dec(xn); /* xn = xn - ulp. */ + } + + if (r == FE_TONEAREST) { + xn = inc(xn); /* xn = xn + ulp. */ + } else if (r == FE_UPWARD) { + u.e = inc(u.e); /* u.e = u.e + ulp. */ + xn = inc(xn); /* xn = xn + ulp. */ + } + u.e = u.e + xn; /* Chopped sum. */ + feupdateenv(&env); /* Restore env and raise inexact */ + u.bits.exp--; + return (u.e); +} diff --git a/openlibm/src/fpmath.h b/openlibm/src/fpmath.h new file mode 100644 index 0000000..eb824d7 --- /dev/null +++ b/openlibm/src/fpmath.h @@ -0,0 +1,124 @@ +/*- + * Copyright (c) 2003 Mike Barcroft + * Copyright (c) 2002 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/libc/include/fpmath.h,v 1.4 2008/12/23 22:20:59 marcel Exp $ + */ +#ifndef _FPMATH_H_ +#define _FPMATH_H_ + +#if defined(__aarch64__) +#include "aarch64_fpmath.h" +#elif defined(__i386__) || defined(__x86_64__) +#ifdef __LP64__ +#include "amd64_fpmath.h" +#else +#include "i386_fpmath.h" +#endif +#elif defined(__powerpc__) || defined(__POWERPC__) +#include "powerpc_fpmath.h" +#elif defined(__mips__) +#include "mips_fpmath.h" +#elif defined(__s390__) +#include "s390_fpmath.h" +#elif defined(__riscv) +#include "riscv_fpmath.h" +#elif defined(__loongarch64) +#include "loongarch64_fpmath.h" +#endif + +/* Definitions provided directly by GCC and Clang. */ +#if !(defined(__BYTE_ORDER__) && defined(__ORDER_LITTLE_ENDIAN__) && defined(__ORDER_BIG_ENDIAN__)) + +#if defined(__GLIBC__) + +#include +#include +#define __ORDER_LITTLE_ENDIAN__ __LITTLE_ENDIAN +#define __ORDER_BIG_ENDIAN__ __BIG_ENDIAN +#define __BYTE_ORDER__ __BYTE_ORDER + +#elif defined(__APPLE__) + +#include +#define __ORDER_LITTLE_ENDIAN__ LITTLE_ENDIAN +#define __ORDER_BIG_ENDIAN__ BIG_ENDIAN +#define __BYTE_ORDER__ BYTE_ORDER + +#elif defined(_WIN32) + +#define __ORDER_LITTLE_ENDIAN__ 1234 +#define __ORDER_BIG_ENDIAN__ 4321 +#define __BYTE_ORDER__ __ORDER_LITTLE_ENDIAN__ + +#endif + +#endif /* __BYTE_ORDER__, __ORDER_LITTLE_ENDIAN__ and __ORDER_BIG_ENDIAN__ */ + +#ifndef __FLOAT_WORD_ORDER__ +#define __FLOAT_WORD_ORDER__ __BYTE_ORDER__ +#endif + +union IEEEf2bits { + float f; + struct { +#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ + unsigned int man :23; + unsigned int exp :8; + unsigned int sign :1; +#else /* _BIG_ENDIAN */ + unsigned int sign :1; + unsigned int exp :8; + unsigned int man :23; +#endif + } bits; +}; + +#define DBL_MANH_SIZE 20 +#define DBL_MANL_SIZE 32 + +union IEEEd2bits { + double d; + struct { +#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ +#if __FLOAT_WORD_ORDER__ == __ORDER_LITTLE_ENDIAN__ + unsigned int manl :32; +#endif + unsigned int manh :20; + unsigned int exp :11; + unsigned int sign :1; +#if __FLOAT_WORD_ORDER__ == __ORDER_BIG_ENDIAN__ + unsigned int manl :32; +#endif +#else /* _BIG_ENDIAN */ + unsigned int sign :1; + unsigned int exp :11; + unsigned int manh :20; + unsigned int manl :32; +#endif + } bits; +}; + +#endif diff --git a/openlibm/src/i386_fpmath.h b/openlibm/src/i386_fpmath.h new file mode 100644 index 0000000..455631c --- /dev/null +++ b/openlibm/src/i386_fpmath.h @@ -0,0 +1,54 @@ +/*- + * Copyright (c) 2002, 2003 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/libc/i386/_fpmath.h,v 1.6 2008/01/17 16:39:06 bde Exp $ + */ + +union IEEEl2bits { + long double e; + struct { + unsigned int manl :32; + unsigned int manh :32; + unsigned int exp :15; + unsigned int sign :1; + unsigned int junk :16; + } bits; + struct { + unsigned long long man :64; + unsigned int expsign :16; + unsigned int junk :16; + } xbits; +}; + +#define LDBL_NBIT 0x80000000 +#define mask_nbit_l(u) ((u).bits.manh &= ~LDBL_NBIT) + +#define LDBL_MANH_SIZE 32 +#define LDBL_MANL_SIZE 32 + +#define LDBL_TO_ARRAY32(u, a) do { \ + (a)[0] = (uint32_t)(u).bits.manl; \ + (a)[1] = (uint32_t)(u).bits.manh; \ +} while (0) diff --git a/openlibm/src/k_cos.c b/openlibm/src/k_cos.c new file mode 100644 index 0000000..f3054ef --- /dev/null +++ b/openlibm/src/k_cos.c @@ -0,0 +1,80 @@ + +/* @(#)k_cos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_cos.c,v 1.12 2008/02/19 12:54:14 bde Exp $"); + +/* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm + * 1. Since cos(-x) = cos(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. + * 3. cos(x) is approximated by a polynomial of degree 14 on + * [0,pi/4] + * 4 14 + * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x + * where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 + * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 + * | | + * + * 4 6 8 10 12 14 + * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then + * cos(x) ~ 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y + * ~ cos(x) - x*y, + * a correction term is necessary in cos(x) and hence + * cos(x+y) = 1 - (x*x/2 - (r - x*y)) + * For better accuracy, rearrange to + * cos(x+y) ~ w + (tmp + (r-x*y)) + * where w = 1 - x*x/2 and tmp is a tiny correction term + * (1 - x*x/2 == w + tmp exactly in infinite precision). + * The exactness of w + tmp in infinite precision depends on w + * and tmp having the same precision as x. If they have extra + * precision due to compiler bugs, then the extra precision is + * only good provided it is retained in all terms of the final + * expression for cos(). Retention happens in all cases tested + * under FreeBSD, so don't pessimize things by forcibly clipping + * any extra precision in w. + */ + +#include + +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ +C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ +C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ +C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ +C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ + +OLM_DLLEXPORT double +__kernel_cos(double x, double y) +{ + double hz,z,r,w; + + z = x*x; + w = z*z; + r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6)); + hz = 0.5*z; + w = one-hz; + return w + (((one-w)-hz) + (z*r-x*y)); +} diff --git a/openlibm/src/k_cosf.c b/openlibm/src/k_cosf.c new file mode 100644 index 0000000..6774db4 --- /dev/null +++ b/openlibm/src/k_cosf.c @@ -0,0 +1,48 @@ +/* k_cosf.c -- float version of k_cos.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Debugged and optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#ifndef INLINE_KERNEL_COSDF +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_cosf.c,v 1.18 2009/06/03 08:16:34 ed Exp $"); +#endif + +#include + +#include "math_private.h" + +/* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */ +static const double +one = 1.0, +C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */ +C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */ +C2 = -0x16c087e80f1e27.0p-62, /* -0.00138867637746099294692 */ +C3 = 0x199342e0ee5069.0p-68; /* 0.0000243904487962774090654 */ + +#ifndef INLINE_KERNEL_COSDF +extern +#endif +//__inline float +OLM_DLLEXPORT float +__kernel_cosdf(double x) +{ + double r, w, z; + + /* Try to optimize for parallel evaluation as in k_tanf.c. */ + z = x*x; + w = z*z; + r = C2+z*C3; + return ((one+z*C0) + w*C1) + (w*z)*r; +} diff --git a/openlibm/src/k_exp.c b/openlibm/src/k_exp.c new file mode 100644 index 0000000..4739e20 --- /dev/null +++ b/openlibm/src/k_exp.c @@ -0,0 +1,108 @@ +/*- + * Copyright (c) 2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_exp.c,v 1.1 2011/10/21 06:27:56 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const u_int32_t k = 1799; /* constant for reduction */ +static const double kln2 = 1246.97177782734161156; /* k * ln2 */ + +/* + * Compute exp(x), scaled to avoid spurious overflow. An exponent is + * returned separately in 'expt'. + * + * Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91 + * Output: 2**1023 <= y < 2**1024 + */ +static double +__frexp_exp(double x, int *expt) +{ + double exp_x; + u_int32_t hx; + + /* + * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to + * minimize |exp(kln2) - 2**k|. We also scale the exponent of + * exp_x to MAX_EXP so that the result can be multiplied by + * a tiny number without losing accuracy due to denormalization. + */ + exp_x = exp(x - kln2); + GET_HIGH_WORD(hx, exp_x); + *expt = (hx >> 20) - (0x3ff + 1023) + k; + SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20)); + return (exp_x); +} + +/* + * __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt. + * They are intended for large arguments (real part >= ln(DBL_MAX)) + * where care is needed to avoid overflow. + * + * The present implementation is narrowly tailored for our hyperbolic and + * exponential functions. We assume expt is small (0 or -1), and the caller + * has filtered out very large x, for which overflow would be inevitable. + */ + +OLM_DLLEXPORT double +__ldexp_exp(double x, int expt) +{ + double exp_x, scale; + int ex_expt; + + exp_x = __frexp_exp(x, &ex_expt); + expt += ex_expt; + INSERT_WORDS(scale, (0x3ff + expt) << 20, 0); + return (exp_x * scale); +} + +OLM_DLLEXPORT double complex +__ldexp_cexp(double complex z, int expt) +{ + double x, y, exp_x, scale1, scale2; + int ex_expt, half_expt; + + x = creal(z); + y = cimag(z); + exp_x = __frexp_exp(x, &ex_expt); + expt += ex_expt; + + /* + * Arrange so that scale1 * scale2 == 2**expt. We use this to + * compensate for scalbn being horrendously slow. + */ + half_expt = expt / 2; + INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0); + half_expt = expt - half_expt; + INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0); + + return (CMPLX(cos(y) * exp_x * scale1 * scale2, + sin(y) * exp_x * scale1 * scale2)); +} diff --git a/openlibm/src/k_expf.c b/openlibm/src/k_expf.c new file mode 100644 index 0000000..bbf094c --- /dev/null +++ b/openlibm/src/k_expf.c @@ -0,0 +1,87 @@ +/*- + * Copyright (c) 2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_expf.c,v 1.1 2011/10/21 06:27:56 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const u_int32_t k = 235; /* constant for reduction */ +static const float kln2 = 162.88958740F; /* k * ln2 */ + +/* + * See k_exp.c for details. + * + * Input: ln(FLT_MAX) <= x < ln(2 * FLT_MAX / FLT_MIN_DENORM) ~= 192.7 + * Output: 2**127 <= y < 2**128 + */ +static float +__frexp_expf(float x, int *expt) +{ + double exp_x; + u_int32_t hx; + + exp_x = expf(x - kln2); + GET_FLOAT_WORD(hx, exp_x); + *expt = (hx >> 23) - (0x7f + 127) + k; + SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 127) << 23)); + return (exp_x); +} + +OLM_DLLEXPORT float +__ldexp_expf(float x, int expt) +{ + float exp_x, scale; + int ex_expt; + + exp_x = __frexp_expf(x, &ex_expt); + expt += ex_expt; + SET_FLOAT_WORD(scale, (0x7f + expt) << 23); + return (exp_x * scale); +} + +OLM_DLLEXPORT float complex +__ldexp_cexpf(float complex z, int expt) +{ + float x, y, exp_x, scale1, scale2; + int ex_expt, half_expt; + + x = crealf(z); + y = cimagf(z); + exp_x = __frexp_expf(x, &ex_expt); + expt += ex_expt; + + half_expt = expt / 2; + SET_FLOAT_WORD(scale1, (0x7f + half_expt) << 23); + half_expt = expt - half_expt; + SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23); + + return (CMPLXF(cosf(y) * exp_x * scale1 * scale2, + sinf(y) * exp_x * scale1 * scale2)); +} diff --git a/openlibm/src/k_log.h b/openlibm/src/k_log.h new file mode 100644 index 0000000..a0943c4 --- /dev/null +++ b/openlibm/src/k_log.h @@ -0,0 +1,100 @@ + +/* @(#)e_log.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_log.h,v 1.2 2011/10/15 05:23:28 das Exp $"); + +/* + * k_log1p(f): + * Return log(1+f) - f for 1+f in ~[sqrt(2)/2, sqrt(2)]. + * + * The following describes the overall strategy for computing + * logarithms in base e. The argument reduction and adding the final + * term of the polynomial are done by the caller for increased accuracy + * when different bases are used. + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +static const double +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +/* + * We always inline k_log1p(), since doing so produces a + * substantial performance improvement (~40% on amd64). + */ +static inline double +k_log1p(double f) +{ + double hfsq,s,z,R,w,t1,t2; + + s = f/(2.0+f); + z = s*s; + w = z*z; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + R = t2+t1; + hfsq=0.5*f*f; + return s*(hfsq+R); +} diff --git a/openlibm/src/k_logf.h b/openlibm/src/k_logf.h new file mode 100644 index 0000000..1b665ae --- /dev/null +++ b/openlibm/src/k_logf.h @@ -0,0 +1,39 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_logf.h,v 1.3 2011/10/15 05:23:28 das Exp $"); + +/* + * Float version of k_log.h. See the latter for most comments. + */ + +static const float +/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ +Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ +Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ +Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ +Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ + +static inline float +k_log1pf(float f) +{ + float hfsq,s,z,R,w,t1,t2; + + s = f/((float)2.0+f); + z = s*s; + w = z*z; + t1= w*(Lg2+w*Lg4); + t2= z*(Lg1+w*Lg3); + R = t2+t1; + hfsq=(float)0.5*f*f; + return s*(hfsq+R); +} diff --git a/openlibm/src/k_rem_pio2.c b/openlibm/src/k_rem_pio2.c new file mode 100644 index 0000000..9555d3a --- /dev/null +++ b/openlibm/src/k_rem_pio2.c @@ -0,0 +1,444 @@ + +/* @(#)k_rem_pio2.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_rem_pio2.c,v 1.11 2008/02/25 11:43:20 bde Exp $"); + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec) + * double x[],y[]; int e0,nx,prec; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] ouput result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precison, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0]. Must be <= 16360 or you need to + * expand the ipio2 table. + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The minimum and recommended value + * for jk is 3,4,4,6 for single, double, extended, and quad. + * jk+1 must be 2 larger than you might expect so that our + * recomputation test works. (Up to 24 bits in the integer + * part (the 24 bits of it that we compute) and 23 bits in + * the fraction part may be lost to cancelation before we + * recompute.) + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include + +#include "math_private.h" + +static const int init_jk[] = {3,4,4,6}; /* initial value for jk */ + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + * + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * NB: This table must have at least (e0-3)/24 + jk terms. + * For quad precision (e0 <= 16360, jk = 6), this is 686. + */ +static const int32_t ipio2[] = { +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, + +#if LDBL_MAX_EXP > 1024 +#if LDBL_MAX_EXP > 16384 +#error "ipio2 table needs to be expanded" +#endif +0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6, +0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, +0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35, +0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30, +0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C, +0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4, +0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770, +0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, +0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19, +0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522, +0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16, +0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6, +0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E, +0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, +0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3, +0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF, +0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, +0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612, +0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929, +0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC, +0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B, +0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C, +0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, +0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB, +0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC, +0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C, +0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F, +0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5, +0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, +0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B, +0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA, +0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD, +0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3, +0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3, +0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, +0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F, +0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61, +0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, +0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51, +0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0, +0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C, +0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6, +0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC, +0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, +0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328, +0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D, +0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0, +0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B, +0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4, +0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, +0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F, +0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD, +0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B, +0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4, +0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761, +0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, +0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30, +0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262, +0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E, +0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1, +0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C, +0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4, +0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08, +0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196, +0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, +0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4, +0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC, +0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C, +0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0, +0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C, +0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, +0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC, +0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22, +0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893, +0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7, +0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5, +0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, +0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4, +0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF, +0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, +0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2, +0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138, +0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E, +0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569, +0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34, +0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, +0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D, +0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F, +0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855, +0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569, +0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B, +0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, +0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41, +0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49, +0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F, +0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110, +0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8, +0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, +0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A, +0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270, +0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, +0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616, +0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B, +0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0, +#endif + +}; + +static const double PIo2[] = { + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ +}; + +static const double +zero = 0.0, +one = 1.0, +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ + +OLM_DLLEXPORT int +__kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec) +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + double z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/24; if(jv<0) jv=0; + q0 = e0-24*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (double)((int32_t)(twon24* z)); + iq[i] = (int32_t)(z-two24*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbn(z,q0); /* actual value of z */ + z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (double)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(24-q0)); n += i; + iq[jz-1] -= i<<(24-q0); + ih = iq[jz-1]>>(23-q0); + } + else if(q0==0) ih = iq[jz-1]>>23; + else if(z>=0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7fffff; break; + case 2: + iq[jz-1] &= 0x3fffff; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbn(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (double) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==0.0) { + jz -= 1; q0 -= 24; + while(iq[jz]==0) { jz--; q0-=24;} + } else { /* break z into 24-bit if necessary */ + z = scalbn(z,-q0); + if(z>=two24) { + fw = (double)((int32_t)(twon24*z)); + iq[jz] = (int32_t)(z-two24*fw); + jz += 1; q0 += 24; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbn(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(double)iq[i]; fw*=twon24; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + STRICT_ASSIGN(double,fw,fw); + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/openlibm/src/k_sin.c b/openlibm/src/k_sin.c new file mode 100644 index 0000000..0b3de39 --- /dev/null +++ b/openlibm/src/k_sin.c @@ -0,0 +1,71 @@ + +/* @(#)k_sin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_sin.c,v 1.11 2008/02/19 12:54:14 bde Exp $"); + +/* __kernel_sin( x, y, iy) + * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. Callers must return sin(-0) = -0 without calling here since our + * odd polynomial is not evaluated in a way that preserves -0. + * Callers may do the optimization sin(x) ~ x for tiny x. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include + +#include "math_private.h" + +static const double +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ +S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ +S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ +S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ +S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ +S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ + +OLM_DLLEXPORT double +__kernel_sin(double x, double y, int iy) +{ + double z,r,v,w; + + z = x*x; + w = z*z; + r = S2+z*(S3+z*S4) + z*w*(S5+z*S6); + v = z*x; + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/openlibm/src/k_sinf.c b/openlibm/src/k_sinf.c new file mode 100644 index 0000000..15c8e03 --- /dev/null +++ b/openlibm/src/k_sinf.c @@ -0,0 +1,48 @@ +/* k_sinf.c -- float version of k_sin.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#ifndef INLINE_KERNEL_SINDF +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_sinf.c,v 1.16 2009/06/03 08:16:34 ed Exp $"); +#endif + +#include + +#include "math_private.h" + +/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */ +static const double +S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */ +S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */ +S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */ +S4 = 0x16cd878c3b46a7.0p-71; /* 0.0000027183114939898219064 */ + +#ifndef INLINE_KERNEL_SINDF +extern +#endif +//__inline float +OLM_DLLEXPORT float +__kernel_sindf(double x) +{ + double r, s, w, z; + + /* Try to optimize for parallel evaluation as in k_tanf.c. */ + z = x*x; + w = z*z; + r = S3+z*S4; + s = z*x; + return (x + s*(S1+z*S2)) + s*w*r; +} diff --git a/openlibm/src/k_tan.c b/openlibm/src/k_tan.c new file mode 100644 index 0000000..41f754b --- /dev/null +++ b/openlibm/src/k_tan.c @@ -0,0 +1,134 @@ +/* @(#)k_tan.c 1.5 04/04/22 SMI */ + +/* + * ==================================================== + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* INDENT OFF */ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_tan.c,v 1.13 2008/02/22 02:30:35 das Exp $"); + +/* __kernel_tan( x, y, k ) + * kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. Callers must return tan(-0) = -0 without calling here since our + * odd polynomial is not evaluated in a way that preserves -0. + * Callers may do the optimization tan(x) ~ x for tiny x. + * 3. tan(x) is approximated by a odd polynomial of degree 27 on + * [0,0.67434] + * 3 27 + * tan(x) ~ x + T1*x + ... + T13*x + * where + * + * |tan(x) 2 4 26 | -59.2 + * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 + * | x | + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * 3 2 2 2 2 + * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) + * then + * 3 2 + * tan(x+y) = x + (T1*x + (x *(r+y)+y)) + * + * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include + +#include "math_private.h" + +static const double xxx[] = { + 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ + 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ + 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ + 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ + 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ + 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ + 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ + 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ + 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ + 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ + 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ + -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ + 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ +/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ +/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ +/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */ +}; +#define one xxx[13] +#define pio4 xxx[14] +#define pio4lo xxx[15] +#define T xxx +/* INDENT ON */ + +double +__kernel_tan(double x, double y, int iy) { + double z, r, v, w, s; + int32_t ix, hx; + + GET_HIGH_WORD(hx,x); + ix = hx & 0x7fffffff; /* high word of |x| */ + if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ + if (hx < 0) { + x = -x; + y = -y; + } + z = pio4 - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + } + z = x * x; + w = z * z; + /* + * Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + + w * T[11])))); + v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + + w * T[12]))))); + s = z * x; + r = y + z * (s * (r + v) + y); + r += T[0] * s; + w = x + r; + if (ix >= 0x3FE59428) { + v = (double) iy; + return (double) (1 - ((hx >> 30) & 2)) * + (v - 2.0 * (x - (w * w / (w + v) - r))); + } + if (iy == 1) + return w; + else { + /* + * if allow error up to 2 ulp, simply return + * -1.0 / (x+r) here + */ + /* compute -1.0 / (x+r) accurately */ + double a, t; + z = w; + SET_LOW_WORD(z,0); + v = r - (z - x); /* z+v = r+x */ + t = a = -1.0 / w; /* a = -1.0/w */ + SET_LOW_WORD(t,0); + s = 1.0 + t * z; + return t + a * (s + t * v); + } +} diff --git a/openlibm/src/k_tanf.c b/openlibm/src/k_tanf.c new file mode 100644 index 0000000..9c17d1b --- /dev/null +++ b/openlibm/src/k_tanf.c @@ -0,0 +1,68 @@ +/* k_tanf.c -- float version of k_tan.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#ifndef INLINE_KERNEL_TANDF +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/k_tanf.c,v 1.23 2009/06/03 08:16:34 ed Exp $"); +#endif + +#include + +#include "math_private.h" + +/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */ +static const double +T[] = { + 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */ + 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */ + 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */ + 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */ + 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */ + 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */ +}; + +#ifndef INLINE_KERNEL_TANDF +extern +#endif +//__inline float +OLM_DLLEXPORT float +__kernel_tandf(double x, int iy) +{ + double z,r,w,s,t,u; + + z = x*x; + /* + * Split up the polynomial into small independent terms to give + * opportunities for parallel evaluation. The chosen splitting is + * micro-optimized for Athlons (XP, X64). It costs 2 multiplications + * relative to Horner's method on sequential machines. + * + * We add the small terms from lowest degree up for efficiency on + * non-sequential machines (the lowest degree terms tend to be ready + * earlier). Apart from this, we don't care about order of + * operations, and don't need to to care since we have precision to + * spare. However, the chosen splitting is good for accuracy too, + * and would give results as accurate as Horner's method if the + * small terms were added from highest degree down. + */ + r = T[4]+z*T[5]; + t = T[2]+z*T[3]; + w = z*z; + s = z*x; + u = T[0]+z*T[1]; + r = (x+s*u)+(s*w)*(t+w*r); + if(iy==1) return r; + else return -1.0/r; +} diff --git a/openlibm/src/loongarch64_fpmath.h b/openlibm/src/loongarch64_fpmath.h new file mode 100644 index 0000000..31ea131 --- /dev/null +++ b/openlibm/src/loongarch64_fpmath.h @@ -0,0 +1,56 @@ +/*- + * Copyright (c) 2023 Yifan An + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include + +union IEEEl2bits { + long double e; + struct { + uint64_t manl :64; + uint64_t manh :48; + unsigned int exp :15; + unsigned int sign :1; + } bits; + struct { + uint64_t manl :64; + uint64_t manh :48; + unsigned int expsign :16; + } xbits; +}; + +#define LDBL_NBIT 0 +#define LDBL_IMPLICIT_NBIT +#define mask_nbit_l(u) ((void)0) + +#define LDBL_MANH_SIZE 48 +#define LDBL_MANL_SIZE 64 + +#define LDBL_TO_ARRAY32(u, a) do { \ + (a)[0] = (uint32_t)(u).bits.manl; \ + (a)[1] = (uint32_t)((u).bits.manl >> 32); \ + (a)[2] = (uint32_t)(u).bits.manh; \ + (a)[3] = (uint32_t)((u).bits.manh >> 32); \ +} while(0) diff --git a/openlibm/src/math_private.h b/openlibm/src/math_private.h new file mode 100644 index 0000000..15a27b2 --- /dev/null +++ b/openlibm/src/math_private.h @@ -0,0 +1,375 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $FreeBSD: src/lib/msun/src/math_private.h,v 1.34 2011/10/21 06:27:56 das Exp $ + */ + +#ifndef _MATH_PRIVATE_H_ +#define _MATH_PRIVATE_H_ + +#include +#include +#include "cdefs-compat.h" +#include "types-compat.h" +#include "fpmath.h" +#include +#include "math_private_openbsd.h" + +/* + * The original fdlibm code used statements like: + * n0 = ((*(int*)&one)>>29)^1; * index of high word * + * ix0 = *(n0+(int*)&x); * high word of x * + * ix1 = *((1-n0)+(int*)&x); * low word of x * + * to dig two 32 bit words out of the 64 bit IEEE floating point + * value. That is non-ANSI, and, moreover, the gcc instruction + * scheduler gets it wrong. We instead use the following macros. + * Unlike the original code, we determine the endianness at compile + * time, not at run time; I don't see much benefit to selecting + * endianness at run time. + */ + +/* + * A union which permits us to convert between a double and two 32 bit + * ints. + */ + +#if __FLOAT_WORD_ORDER__ == __ORDER_BIG_ENDIAN__ + +typedef union +{ + double value; + struct + { + u_int32_t msw; + u_int32_t lsw; + } parts; + struct + { + u_int64_t w; + } xparts; +} ieee_double_shape_type; + +#endif + +#if __FLOAT_WORD_ORDER__ == __ORDER_LITTLE_ENDIAN__ + +typedef union +{ + double value; + struct + { + u_int32_t lsw; + u_int32_t msw; + } parts; + struct + { + u_int64_t w; + } xparts; +} ieee_double_shape_type; + +#endif + +/* Get two 32 bit ints from a double. */ + +#define EXTRACT_WORDS(ix0,ix1,d) \ +do { \ + ieee_double_shape_type ew_u; \ + ew_u.value = (d); \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (0) + +/* Get a 64-bit int from a double. */ +#define EXTRACT_WORD64(ix,d) \ +do { \ + ieee_double_shape_type ew_u; \ + ew_u.value = (d); \ + (ix) = ew_u.xparts.w; \ +} while (0) + +/* Get the more significant 32 bit int from a double. */ + +#define GET_HIGH_WORD(i,d) \ +do { \ + ieee_double_shape_type gh_u; \ + gh_u.value = (d); \ + (i) = gh_u.parts.msw; \ +} while (0) + +/* Get the less significant 32 bit int from a double. */ + +#define GET_LOW_WORD(i,d) \ +do { \ + ieee_double_shape_type gl_u; \ + gl_u.value = (d); \ + (i) = gl_u.parts.lsw; \ +} while (0) + +/* Set a double from two 32 bit ints. */ + +#define INSERT_WORDS(d,ix0,ix1) \ +do { \ + ieee_double_shape_type iw_u; \ + iw_u.parts.msw = (ix0); \ + iw_u.parts.lsw = (ix1); \ + (d) = iw_u.value; \ +} while (0) + +/* Set a double from a 64-bit int. */ +#define INSERT_WORD64(d,ix) \ +do { \ + ieee_double_shape_type iw_u; \ + iw_u.xparts.w = (ix); \ + (d) = iw_u.value; \ +} while (0) + +/* Set the more significant 32 bits of a double from an int. */ + +#define SET_HIGH_WORD(d,v) \ +do { \ + ieee_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Set the less significant 32 bits of a double from an int. */ + +#define SET_LOW_WORD(d,v) \ +do { \ + ieee_double_shape_type sl_u; \ + sl_u.value = (d); \ + sl_u.parts.lsw = (v); \ + (d) = sl_u.value; \ +} while (0) + +/* + * A union which permits us to convert between a float and a 32 bit + * int. + */ + +typedef union +{ + float value; + /* FIXME: Assumes 32 bit int. */ + unsigned int word; +} ieee_float_shape_type; + +/* Get a 32 bit int from a float. */ + +#define GET_FLOAT_WORD(i,d) \ +do { \ + ieee_float_shape_type gf_u; \ + gf_u.value = (d); \ + (i) = gf_u.word; \ +} while (0) + +/* Set a float from a 32 bit int. */ + +#define SET_FLOAT_WORD(d,i) \ +do { \ + ieee_float_shape_type sf_u; \ + sf_u.word = (i); \ + (d) = sf_u.value; \ +} while (0) + +/* Get expsign as a 16 bit int from a long double. */ + +#define GET_LDBL_EXPSIGN(i,d) \ +do { \ + union IEEEl2bits ge_u; \ + ge_u.e = (d); \ + (i) = ge_u.xbits.expsign; \ +} while (0) + +/* Set expsign of a long double from a 16 bit int. */ + +#define SET_LDBL_EXPSIGN(d,v) \ +do { \ + union IEEEl2bits se_u; \ + se_u.e = (d); \ + se_u.xbits.expsign = (v); \ + (d) = se_u.e; \ +} while (0) + + +#ifndef __FreeBSD__ +#define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) +#else +#ifdef FLT_EVAL_METHOD +// Attempt to get strict C99 semantics for assignment with non-C99 compilers. +#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0 +#define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) +#else +#define STRICT_ASSIGN(type, lval, rval) do { \ + volatile type __lval; \ + \ + if (sizeof(type) >= sizeof(long double)) \ + (lval) = (rval); \ + else { \ + __lval = (rval); \ + (lval) = __lval; \ + } \ +} while (0) +#endif +#endif +#endif + +/* + * Common routine to process the arguments to nan(), nanf(), and nanl(). + */ +void __scan_nan(u_int32_t *__words, int __num_words, const char *__s); + +/* + * Mix 1 or 2 NaNs. First add 0 to each arg. This normally just turns + * signaling NaNs into quiet NaNs by setting a quiet bit. We do this + * because we want to never return a signaling NaN, and also because we + * don't want the quiet bit to affect the result. Then mix the converted + * args using addition. The result is typically the arg whose mantissa + * bits (considered as in integer) are largest. + * + * Technical complications: the result in bits might depend on the precision + * and/or on compiler optimizations, especially when different register sets + * are used for different precisions. Try to make the result not depend on + * at least the precision by always doing the main mixing step in long double + * precision. Try to reduce dependencies on optimizations by adding the + * the 0's in different precisions (unless everything is in long double + * precision). + */ +#define nan_mix(x, y) (((x) + 0.0L) + ((y) + 0)) + +#ifdef __GNUCLIKE_ASM + +/* Asm versions of some functions. */ + +#ifdef __amd64__ +static __inline int +irint(double x) +{ + int n; + + __asm__("cvtsd2si %1,%0" : "=r" (n) : "x" (x)); + return (n); +} +#define HAVE_EFFICIENT_IRINT +#endif + +#ifdef __i386__ +static __inline int +irint(double x) +{ + int n; + + __asm__("fistl %0" : "=m" (n) : "t" (x)); + return (n); +} +#define HAVE_EFFICIENT_IRINT +#endif + +#endif /* __GNUCLIKE_ASM */ + +/* + * ieee style elementary functions + * + * We rename functions here to improve other sources' diffability + * against fdlibm. + */ +#define __ieee754_sqrt sqrt +#define __ieee754_acos acos +#define __ieee754_acosh acosh +#define __ieee754_log log +#define __ieee754_log2 log2 +#define __ieee754_atanh atanh +#define __ieee754_asin asin +#define __ieee754_atan2 atan2 +#define __ieee754_exp exp +#define __ieee754_cosh cosh +#define __ieee754_fmod fmod +#define __ieee754_pow pow +#define __ieee754_lgamma lgamma +#define __ieee754_lgamma_r lgamma_r +#define __ieee754_log10 log10 +#define __ieee754_sinh sinh +#define __ieee754_hypot hypot +#define __ieee754_j0 j0 +#define __ieee754_j1 j1 +#define __ieee754_y0 y0 +#define __ieee754_y1 y1 +#define __ieee754_jn jn +#define __ieee754_yn yn +#define __ieee754_remainder remainder +#define __ieee754_sqrtf sqrtf +#define __ieee754_acosf acosf +#define __ieee754_acoshf acoshf +#define __ieee754_logf logf +#define __ieee754_atanhf atanhf +#define __ieee754_asinf asinf +#define __ieee754_atan2f atan2f +#define __ieee754_expf expf +#define __ieee754_coshf coshf +#define __ieee754_fmodf fmodf +#define __ieee754_powf powf +#define __ieee754_lgammaf lgammaf +#define __ieee754_lgammaf_r lgammaf_r +#define __ieee754_log10f log10f +#define __ieee754_log2f log2f +#define __ieee754_sinhf sinhf +#define __ieee754_hypotf hypotf +#define __ieee754_j0f j0f +#define __ieee754_j1f j1f +#define __ieee754_y0f y0f +#define __ieee754_y1f y1f +#define __ieee754_jnf jnf +#define __ieee754_ynf ynf +#define __ieee754_remainderf remainderf + +/* fdlibm kernel function */ +int __kernel_rem_pio2(double*,double*,int,int,int); + +/* double precision kernel functions */ +#ifdef INLINE_REM_PIO2 +__inline +#endif +int __ieee754_rem_pio2(double,double*); +double __kernel_sin(double,double,int); +double __kernel_cos(double,double); +double __kernel_tan(double,double,int); +double __ldexp_exp(double,int); +double complex __ldexp_cexp(double complex,int); + +/* float precision kernel functions */ +#ifdef INLINE_REM_PIO2F +__inline +#endif +int __ieee754_rem_pio2f(float,double*); +#ifdef INLINE_KERNEL_SINDF +__inline +#endif +float __kernel_sindf(double); +#ifdef INLINE_KERNEL_COSDF +__inline +#endif +float __kernel_cosdf(double); +#ifdef INLINE_KERNEL_TANDF +__inline +#endif +float __kernel_tandf(double,int); +float __ldexp_expf(float,int); +float complex __ldexp_cexpf(float complex,int); + +/* long double precision kernel functions */ +long double __kernel_sinl(long double, long double, int); +long double __kernel_cosl(long double, long double); +long double __kernel_tanl(long double, long double, int); + +#endif /* !_MATH_PRIVATE_H_ */ diff --git a/openlibm/src/math_private_openbsd.h b/openlibm/src/math_private_openbsd.h new file mode 100644 index 0000000..021670f --- /dev/null +++ b/openlibm/src/math_private_openbsd.h @@ -0,0 +1,218 @@ +/* $OpenBSD: math_private.h,v 1.17 2014/06/02 19:31:17 kettenis Exp $ */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * from: @(#)fdlibm.h 5.1 93/09/24 + */ + +#ifndef _MATH_PRIVATE_OPENBSD_H_ +#define _MATH_PRIVATE_OPENBSD_H_ + +#if __FLOAT_WORD_ORDER__ == __ORDER_BIG_ENDIAN__ + +typedef union +{ + long double value; + struct { + u_int32_t mswhi; + u_int32_t mswlo; + u_int32_t lswhi; + u_int32_t lswlo; + } parts32; + struct { + u_int64_t msw; + u_int64_t lsw; + } parts64; +} ieee_quad_shape_type; + +#endif + +#if __FLOAT_WORD_ORDER__ == __ORDER_LITTLE_ENDIAN__ + +typedef union +{ + long double value; + struct { + u_int32_t lswlo; + u_int32_t lswhi; + u_int32_t mswlo; + u_int32_t mswhi; + } parts32; + struct { + u_int64_t lsw; + u_int64_t msw; + } parts64; +} ieee_quad_shape_type; + +#endif + +/* Get two 64 bit ints from a long double. */ + +#define GET_LDOUBLE_WORDS64(ix0,ix1,d) \ +do { \ + ieee_quad_shape_type qw_u; \ + qw_u.value = (d); \ + (ix0) = qw_u.parts64.msw; \ + (ix1) = qw_u.parts64.lsw; \ +} while (0) + +/* Set a long double from two 64 bit ints. */ + +#define SET_LDOUBLE_WORDS64(d,ix0,ix1) \ +do { \ + ieee_quad_shape_type qw_u; \ + qw_u.parts64.msw = (ix0); \ + qw_u.parts64.lsw = (ix1); \ + (d) = qw_u.value; \ +} while (0) + +/* Get the more significant 64 bits of a long double mantissa. */ + +#define GET_LDOUBLE_MSW64(v,d) \ +do { \ + ieee_quad_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts64.msw; \ +} while (0) + +/* Set the more significant 64 bits of a long double mantissa from an int. */ + +#define SET_LDOUBLE_MSW64(d,v) \ +do { \ + ieee_quad_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts64.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Get the least significant 64 bits of a long double mantissa. */ + +#define GET_LDOUBLE_LSW64(v,d) \ +do { \ + ieee_quad_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts64.lsw; \ +} while (0) + +/* A union which permits us to convert between a long double and + three 32 bit ints. */ + +#if __FLOAT_WORD_ORDER__ == __ORDER_BIG_ENDIAN__ + +typedef union +{ + long double value; + struct { +#ifdef __LP64__ + int padh:32; +#endif + int exp:16; + int padl:16; + u_int32_t msw; + u_int32_t lsw; + } parts; +} ieee_extended_shape_type; + +#endif + +#if __FLOAT_WORD_ORDER__ == __ORDER_LITTLE_ENDIAN__ + +typedef union +{ + long double value; + struct { + u_int32_t lsw; + u_int32_t msw; + int exp:16; + int padl:16; +#ifdef __LP64__ + int padh:32; +#endif + } parts; +} ieee_extended_shape_type; + +#endif + +/* Get three 32 bit ints from a double. */ + +#define GET_LDOUBLE_WORDS(se,ix0,ix1,d) \ +do { \ + ieee_extended_shape_type ew_u; \ + ew_u.value = (d); \ + (se) = ew_u.parts.exp; \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (0) + +/* Set a double from two 32 bit ints. */ + +#define SET_LDOUBLE_WORDS(d,se,ix0,ix1) \ +do { \ + ieee_extended_shape_type iw_u; \ + iw_u.parts.exp = (se); \ + iw_u.parts.msw = (ix0); \ + iw_u.parts.lsw = (ix1); \ + (d) = iw_u.value; \ +} while (0) + +/* Get the more significant 32 bits of a long double mantissa. */ + +#define GET_LDOUBLE_MSW(v,d) \ +do { \ + ieee_extended_shape_type sh_u; \ + sh_u.value = (d); \ + (v) = sh_u.parts.msw; \ +} while (0) + +/* Set the more significant 32 bits of a long double mantissa from an int. */ + +#define SET_LDOUBLE_MSW(d,v) \ +do { \ + ieee_extended_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Get int from the exponent of a long double. */ + +#define GET_LDOUBLE_EXP(se,d) \ +do { \ + ieee_extended_shape_type ge_u; \ + ge_u.value = (d); \ + (se) = ge_u.parts.exp; \ +} while (0) + +/* Set exponent of a long double from an int. */ + +#define SET_LDOUBLE_EXP(d,se) \ +do { \ + ieee_extended_shape_type se_u; \ + se_u.value = (d); \ + se_u.parts.exp = (se); \ + (d) = se_u.value; \ +} while (0) + +/* + * Common routine to process the arguments to nan(), nanf(), and nanl(). + */ +void __scan_nan(uint32_t *__words, int __num_words, const char *__s); + +/* + * Functions internal to the math package, yet not static. + */ +double __exp__D(double, double); +struct Double __log__D(double); +long double __p1evll(long double, void *, int); +long double __polevll(long double, void *, int); + +#endif /* _MATH_PRIVATE_OPENBSD_H_ */ diff --git a/openlibm/src/mips_fpmath.h b/openlibm/src/mips_fpmath.h new file mode 100644 index 0000000..50f119f --- /dev/null +++ b/openlibm/src/mips_fpmath.h @@ -0,0 +1,57 @@ +/*- + * Copyright (c) 2002, 2003 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + */ + +union IEEEl2bits { + long double e; + struct { +#ifndef __MIPSEB__ + unsigned int manl :32; + unsigned int manh :20; + unsigned int exp :11; + unsigned int sign :1; +#else + unsigned int sign :1; + unsigned int exp :11; + unsigned int manh :20; + unsigned int manl :32; +#endif + } bits; +}; + +#define LDBL_NBIT 0 +#define mask_nbit_l(u) ((void)0) +#define LDBL_IMPLICIT_NBIT + +#define LDBL_MANH_SIZE 20 +#define LDBL_MANL_SIZE 32 + +#define LDBL_TO_ARRAY32(u, a) do { \ + (a)[0] = (uint32_t)(u).bits.manl; \ + (a)[1] = (uint32_t)(u).bits.manh; \ +} while(0) + diff --git a/openlibm/src/polevll.c b/openlibm/src/polevll.c new file mode 100644 index 0000000..1c785d8 --- /dev/null +++ b/openlibm/src/polevll.c @@ -0,0 +1,104 @@ +/* $OpenBSD: polevll.c,v 1.2 2013/11/12 20:35:09 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* polevll.c + * p1evll.c + * + * Evaluate polynomial + * + * + * + * SYNOPSIS: + * + * int N; + * long double x, y, coef[N+1], polevl[]; + * + * y = polevll( x, coef, N ); + * + * + * + * DESCRIPTION: + * + * Evaluates polynomial of degree N: + * + * 2 N + * y = C + C x + C x +...+ C x + * 0 1 2 N + * + * Coefficients are stored in reverse order: + * + * coef[0] = C , ..., coef[N] = C . + * N 0 + * + * The function p1evll() assumes that coef[N] = 1.0 and is + * omitted from the array. Its calling arguments are + * otherwise the same as polevll(). + * + * + * SPEED: + * + * In the interest of speed, there are no checks for out + * of bounds arithmetic. This routine is used by most of + * the functions in the library. Depending on available + * equipment features, the user may wish to rewrite the + * program in microcode or assembly language. + * + */ + +#include + +#include "math_private.h" + +/* + * Polynomial evaluator: + * P[0] x^n + P[1] x^(n-1) + ... + P[n] + */ +long double +__polevll(long double x, void *PP, int n) +{ + long double y; + long double *P; + + P = (long double *)PP; + y = *P++; + do { + y = y * x + *P++; + } while (--n); + + return (y); +} + +/* + * Polynomial evaluator: + * x^n + P[0] x^(n-1) + P[1] x^(n-2) + ... + P[n] + */ +long double +__p1evll(long double x, void *PP, int n) +{ + long double y; + long double *P; + + P = (long double *)PP; + n -= 1; + y = x + *P++; + do { + y = y * x + *P++; + } while (--n); + + return (y); +} diff --git a/openlibm/src/powerpc_fpmath.h b/openlibm/src/powerpc_fpmath.h new file mode 100644 index 0000000..6d80eb4 --- /dev/null +++ b/openlibm/src/powerpc_fpmath.h @@ -0,0 +1,49 @@ +/*- + * Copyright (c) 2003 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + */ + +union IEEEl2bits { + long double e; + struct { + unsigned int sign :1; + unsigned int exp :11; + unsigned int manh :20; + unsigned int manl :32; + } bits; +}; + +#define mask_nbit_l(u) ((void)0) +#define LDBL_IMPLICIT_NBIT +#define LDBL_NBIT 0 + +#define LDBL_MANH_SIZE 20 +#define LDBL_MANL_SIZE 32 + +#define LDBL_TO_ARRAY32(u, a) do { \ + (a)[0] = (uint32_t)(u).bits.manl; \ + (a)[1] = (uint32_t)(u).bits.manh; \ +} while(0) diff --git a/openlibm/src/riscv_fpmath.h b/openlibm/src/riscv_fpmath.h new file mode 100644 index 0000000..cfa85ff --- /dev/null +++ b/openlibm/src/riscv_fpmath.h @@ -0,0 +1,58 @@ +/*- + * Copyright (c) 2002, 2003 David Schultz + * Copyright (c) 2014 The FreeBSD Foundation + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: head/lib/libc/riscv/_fpmath.h 362788 2020-06-29 19:30:35Z mhorne $ + */ + +union IEEEl2bits { + long double e; + struct { + unsigned long manl :64; + unsigned long manh :48; + unsigned int exp :15; + unsigned int sign :1; + } bits; + struct { + unsigned long manl :64; + unsigned long manh :48; + unsigned int expsign :16; + } xbits; +}; + +#define LDBL_NBIT 0 +#define LDBL_IMPLICIT_NBIT +#define mask_nbit_l(u) ((void)0) + +#define LDBL_MANH_SIZE 48 +#define LDBL_MANL_SIZE 64 + +#define LDBL_TO_ARRAY32(u, a) do { \ + (a)[0] = (uint32_t)(u).bits.manl; \ + (a)[1] = (uint32_t)((u).bits.manl >> 32); \ + (a)[2] = (uint32_t)(u).bits.manh; \ + (a)[3] = (uint32_t)((u).bits.manh >> 32); \ +} while(0) + diff --git a/openlibm/src/s390_fpmath.h b/openlibm/src/s390_fpmath.h new file mode 100644 index 0000000..1e7787c --- /dev/null +++ b/openlibm/src/s390_fpmath.h @@ -0,0 +1,51 @@ +/*- + * Copyright (c) 2016 Dan Horák + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD$ + * + * cloned from powerpc_fpmath.h + */ + +union IEEEl2bits { + long double e; + struct { + unsigned int sign :1; + unsigned int exp :11; + unsigned int manh :20; + unsigned int manl :32; + } bits; +}; + +#define mask_nbit_l(u) ((void)0) +#define LDBL_IMPLICIT_NBIT +#define LDBL_NBIT 0 + +#define LDBL_MANH_SIZE 20 +#define LDBL_MANL_SIZE 32 + +#define LDBL_TO_ARRAY32(u, a) do { \ + (a)[0] = (uint32_t)(u).bits.manl; \ + (a)[1] = (uint32_t)(u).bits.manh; \ +} while(0) diff --git a/openlibm/src/s_asinh.c b/openlibm/src/s_asinh.c new file mode 100644 index 0000000..ca7937c --- /dev/null +++ b/openlibm/src/s_asinh.c @@ -0,0 +1,62 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_asinh.c,v 1.9 2008/02/22 02:30:35 das Exp $"); + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include +#include + +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +huge= 1.00000000000000000000e+300; + +OLM_DLLEXPORT double +asinh(double x) +{ + double t,w; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = __ieee754_log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); + w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); + } + if(hx>0) return w; else return -w; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(asinh, asinhl); +#endif diff --git a/openlibm/src/s_asinhf.c b/openlibm/src/s_asinhf.c new file mode 100644 index 0000000..c9d3694 --- /dev/null +++ b/openlibm/src/s_asinhf.c @@ -0,0 +1,49 @@ +/* s_asinhf.c -- float version of s_asinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_asinhf.c,v 1.9 2008/02/22 02:30:35 das Exp $"); + +#include + +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +ln2 = 6.9314718246e-01, /* 0x3f317218 */ +huge= 1.0000000000e+30; + +OLM_DLLEXPORT float +asinhf(float x) +{ + float t,w; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x+x; /* x is inf or NaN */ + if(ix< 0x31800000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x4d800000) { /* |x| > 2**28 */ + w = __ieee754_logf(fabsf(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabsf(x); + w = __ieee754_logf((float)2.0*t+one/(__ieee754_sqrtf(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1pf(fabsf(x)+t/(one+__ieee754_sqrtf(one+t))); + } + if(hx>0) return w; else return -w; +} diff --git a/openlibm/src/s_atan.c b/openlibm/src/s_atan.c new file mode 100644 index 0000000..23a2949 --- /dev/null +++ b/openlibm/src/s_atan.c @@ -0,0 +1,124 @@ +/* @(#)s_atan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_atan.c,v 1.13 2011/02/10 07:37:50 das Exp $"); + +/* atan(x) + * Method + * 1. Reduce x to positive by atan(x) = -atan(-x). + * 2. According to the integer k=4t+0.25 chopped, t=x, the argument + * is further reduced to one of the following intervals and the + * arctangent of t is evaluated by the corresponding formula: + * + * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) + * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) + * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) + * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) + * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include + +#include "math_private.h" + +static const double atanhi[] = { + 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ + 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ + 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ + 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ +}; + +static const double atanlo[] = { + 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ + 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ + 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ + 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ +}; + +static const double aT[] = { + 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ + -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ + 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ + -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ + 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ + -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ + 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ + -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ + 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ + -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ + 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ +}; + + static const double +one = 1.0, +huge = 1.0e300; + +OLM_DLLEXPORT double +atan(double x) +{ + double w,s1,s2,z; + int32_t ix,hx,id; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x44100000) { /* if |x| >= 2^66 */ + u_int32_t low; + GET_LOW_WORD(low,x); + if(ix>0x7ff00000|| + (ix==0x7ff00000&&(low!=0))) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+*(volatile double *)&atanlo[3]; + else return -atanhi[3]-*(volatile double *)&atanlo[3]; + } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ + if (ix < 0x3e400000) { /* |x| < 2^-27 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabs(x); + if (ix < 0x3ff30000) { /* |x| < 1.1875 */ + if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = (2.0*x-one)/(2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x40038000) { /* |x| < 2.4375 */ + id = 2; x = (x-1.5)/(one+1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(atan, atanl); +#endif diff --git a/openlibm/src/s_atanf.c b/openlibm/src/s_atanf.c new file mode 100644 index 0000000..cdba6a3 --- /dev/null +++ b/openlibm/src/s_atanf.c @@ -0,0 +1,93 @@ +/* s_atanf.c -- float version of s_atan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_atanf.c,v 1.10 2008/08/01 01:24:25 das Exp $"); + +#include + +#include "math_private.h" + +static const float atanhi[] = { + 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ + 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ + 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ + 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ +}; + +static const float atanlo[] = { + 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ + 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ + 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ + 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ +}; + +static const float aT[] = { + 3.3333328366e-01, + -1.9999158382e-01, + 1.4253635705e-01, + -1.0648017377e-01, + 6.1687607318e-02, +}; + +static const float +one = 1.0, +huge = 1.0e30; + +OLM_DLLEXPORT float +atanf(float x) +{ + float w,s1,s2,z; + int32_t ix,hx,id; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x4c800000) { /* if |x| >= 2**26 */ + if(ix>0x7f800000) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+*(volatile float *)&atanlo[3]; + else return -atanhi[3]-*(volatile float *)&atanlo[3]; + } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ + if (ix < 0x39800000) { /* |x| < 2**-12 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabsf(x); + if (ix < 0x3f980000) { /* |x| < 1.1875 */ + if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = ((float)2.0*x-one)/((float)2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x401c0000) { /* |x| < 2.4375 */ + id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); + } else { /* 2.4375 <= |x| < 2**26 */ + id = 3; x = -(float)1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*aT[4])); + s2 = w*(aT[1]+w*aT[3]); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} diff --git a/openlibm/src/s_atanl.c b/openlibm/src/s_atanl.c new file mode 100644 index 0000000..4edfa5a --- /dev/null +++ b/openlibm/src/s_atanl.c @@ -0,0 +1,85 @@ +/* @(#)s_atan.c 5.1 93/09/24 */ +/* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_atanl.c,v 1.1 2008/07/31 22:41:26 das Exp $"); + +/* + * See comments in s_atan.c. + * Converted to long double by David Schultz . + */ + +#include +#include + +#include "invtrig.h" +#include "math_private.h" + +static const long double +one = 1.0, +huge = 1.0e300; + +OLM_DLLEXPORT long double +atanl(long double x) +{ + union IEEEl2bits u; + long double w,s1,s2,z; + int id; + int16_t expsign, expt; + int32_t expman; + + u.e = x; + expsign = u.xbits.expsign; + expt = expsign & 0x7fff; + if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */ + if(expt == BIAS + LDBL_MAX_EXP && + ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) + return x+x; /* NaN */ + if(expsign>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } + /* Extract the exponent and the first few bits of the mantissa. */ + /* XXX There should be a more convenient way to do this. */ + expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff); + if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */ + if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabsl(x); + if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */ + if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */ + id = 0; x = (2.0*x-one)/(2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */ + id = 2; x = (x-1.5)/(one+1.5*x); + } else { /* 2.4375 <= |x| < 2^ATAN_CONST */ + id = 3; x = -1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum aT[i]z**(i+1) into odd and even poly */ + s1 = z*T_even(w); + s2 = w*T_odd(w); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (expsign<0)? -z:z; + } +} diff --git a/openlibm/src/s_cabs.c b/openlibm/src/s_cabs.c new file mode 100644 index 0000000..481632a --- /dev/null +++ b/openlibm/src/s_cabs.c @@ -0,0 +1,32 @@ +/* $OpenBSD: s_cabs.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Martynas Venckus + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#include +#include +#include + +#include "math_private.h" + +double +cabs(double complex z) +{ + return hypot(__real__ z, __imag__ z); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(cabs, cabsl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_cabsf.c b/openlibm/src/s_cabsf.c new file mode 100644 index 0000000..8d9bd96 --- /dev/null +++ b/openlibm/src/s_cabsf.c @@ -0,0 +1,25 @@ +/* $OpenBSD: s_cabsf.c,v 1.1 2008/09/07 20:36:09 martynas Exp $ */ +/* + * Copyright (c) 2008 Martynas Venckus + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#include +#include + +float +cabsf(float complex z) +{ + return hypotf(__real__ z, __imag__ z); +} diff --git a/openlibm/src/s_cabsl.c b/openlibm/src/s_cabsl.c new file mode 100644 index 0000000..847ded7 --- /dev/null +++ b/openlibm/src/s_cabsl.c @@ -0,0 +1,26 @@ +/* $OpenBSD: s_cabsl.c,v 1.1 2011/07/08 19:25:31 martynas Exp $ */ + +/* + * Copyright (c) 2011 Martynas Venckus + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +#include +#include + +long double +cabsl(long double complex z) +{ + return hypotl(__real__ z, __imag__ z); +} diff --git a/openlibm/src/s_cacos.c b/openlibm/src/s_cacos.c new file mode 100644 index 0000000..e29717b --- /dev/null +++ b/openlibm/src/s_cacos.c @@ -0,0 +1,67 @@ +/* $OpenBSD: s_cacos.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cacos() + * + * Complex circular arc cosine + * + * + * + * SYNOPSIS: + * + * double complex cacos(); + * double complex z, w; + * + * w = cacos (z); + * + * + * + * DESCRIPTION: + * + * + * w = arccos z = PI/2 - arcsin z. + * + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 5200 1.6e-15 2.8e-16 + * IEEE -10,+10 30000 1.8e-14 2.2e-15 + */ + +#include +#include +#include + +#include "math_private.h" + +double complex +cacos(double complex z) +{ + double complex w; + + w = casin (z); + w = (M_PI_2 - creal (w)) - cimag (w) * I; + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(cacos, cacosl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_cacosf.c b/openlibm/src/s_cacosf.c new file mode 100644 index 0000000..f3c0eb9 --- /dev/null +++ b/openlibm/src/s_cacosf.c @@ -0,0 +1,60 @@ +/* $OpenBSD: s_cacosf.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cacosf() + * + * Complex circular arc cosine + * + * + * + * SYNOPSIS: + * + * void cacosf(); + * cmplxf z, w; + * + * cacosf( &z, &w ); + * + * + * + * DESCRIPTION: + * + * + * w = arccos z = PI/2 - arcsin z. + * + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 9.2e-6 1.2e-6 + * + */ + +#include +#include + +float complex +cacosf(float complex z) +{ + float complex w; + + w = casinf( z ); + w = ((float)M_PI_2 - crealf (w)) - cimagf (w) * I; + return (w); +} diff --git a/openlibm/src/s_cacosh.c b/openlibm/src/s_cacosh.c new file mode 100644 index 0000000..f16c14c --- /dev/null +++ b/openlibm/src/s_cacosh.c @@ -0,0 +1,62 @@ +/* $OpenBSD: s_cacosh.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cacosh + * + * Complex inverse hyperbolic cosine + * + * + * + * SYNOPSIS: + * + * double complex cacosh(); + * double complex z, w; + * + * w = cacosh (z); + * + * + * + * DESCRIPTION: + * + * acosh z = i acos z . + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.6e-14 2.1e-15 + * + */ + +#include +#include +#include + +#include "math_private.h" + +double complex +cacosh(double complex z) +{ + double complex w; + + w = I * cacos (z); + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(cacosh, cacoshl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_cacoshf.c b/openlibm/src/s_cacoshf.c new file mode 100644 index 0000000..f3c40ae --- /dev/null +++ b/openlibm/src/s_cacoshf.c @@ -0,0 +1,55 @@ +/* $OpenBSD: s_cacoshf.c,v 1.1 2008/09/07 20:36:09 martynas Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cacoshf + * + * Complex inverse hyperbolic cosine + * + * + * + * SYNOPSIS: + * + * float complex cacoshf(); + * float complex z, w; + * + * w = cacoshf (z); + * + * + * + * DESCRIPTION: + * + * acosh z = i acos z . + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.6e-14 2.1e-15 + * + */ + +#include +#include + +float complex +cacoshf(float complex z) +{ + float complex w; + + w = I * cacosf (z); + return (w); +} diff --git a/openlibm/src/s_cacoshl.c b/openlibm/src/s_cacoshl.c new file mode 100644 index 0000000..5e5ae31 --- /dev/null +++ b/openlibm/src/s_cacoshl.c @@ -0,0 +1,56 @@ +/* $OpenBSD: s_cacoshl.c,v 1.1 2011/07/08 19:25:31 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cacoshl + * + * Complex inverse hyperbolic cosine + * + * + * + * SYNOPSIS: + * + * long double complex cacoshl(); + * long double complex z, w; + * + * w = cacoshl (z); + * + * + * + * DESCRIPTION: + * + * acosh z = i acos z . + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.6e-14 2.1e-15 + * + */ + +#include +#include + +long double complex +cacoshl(long double complex z) +{ + long double complex w; + + w = I * cacosl(z); + return (w); +} diff --git a/openlibm/src/s_cacosl.c b/openlibm/src/s_cacosl.c new file mode 100644 index 0000000..8a7b8a1 --- /dev/null +++ b/openlibm/src/s_cacosl.c @@ -0,0 +1,63 @@ +/* $OpenBSD: s_cacosl.c,v 1.3 2011/07/20 21:02:51 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cacosl() + * + * Complex circular arc cosine + * + * + * + * SYNOPSIS: + * + * long double complex cacosl(); + * long double complex z, w; + * + * w = cacosl( z ); + * + * + * + * DESCRIPTION: + * + * + * w = arccos z = PI/2 - arcsin z. + * + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 5200 1.6e-15 2.8e-16 + * IEEE -10,+10 30000 1.8e-14 2.2e-15 + */ + +#include +#include + +static const long double PIO2L = 1.570796326794896619231321691639751442098585L; + +long double complex +cacosl(long double complex z) +{ + long double complex w; + + w = casinl(z); + w = (PIO2L - creall(w)) - cimagl(w) * I; + return (w); +} diff --git a/openlibm/src/s_carg.c b/openlibm/src/s_carg.c new file mode 100644 index 0000000..2ebfe17 --- /dev/null +++ b/openlibm/src/s_carg.c @@ -0,0 +1,40 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_carg.c,v 1.1 2007/12/12 23:43:51 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +carg(double complex z) +{ + + return (atan2(cimag(z), creal(z))); +} diff --git a/openlibm/src/s_cargf.c b/openlibm/src/s_cargf.c new file mode 100644 index 0000000..41e320b --- /dev/null +++ b/openlibm/src/s_cargf.c @@ -0,0 +1,40 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cargf.c,v 1.1 2007/12/12 23:43:51 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +cargf(float complex z) +{ + + return (atan2f(cimagf(z), crealf(z))); +} diff --git a/openlibm/src/s_cargl.c b/openlibm/src/s_cargl.c new file mode 100644 index 0000000..5052133 --- /dev/null +++ b/openlibm/src/s_cargl.c @@ -0,0 +1,40 @@ +/*- + * Copyright (c) 2005-2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cargl.c,v 1.1 2008/07/31 22:41:26 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double +cargl(long double complex z) +{ + + return (atan2l(cimagl(z), creall(z))); +} diff --git a/openlibm/src/s_casin.c b/openlibm/src/s_casin.c new file mode 100644 index 0000000..4e5daaa --- /dev/null +++ b/openlibm/src/s_casin.c @@ -0,0 +1,136 @@ +/* $OpenBSD: s_casin.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* casin() + * + * Complex circular arc sine + * + * + * + * SYNOPSIS: + * + * double complex casin(); + * double complex z, w; + * + * w = casin (z); + * + * + * + * DESCRIPTION: + * + * Inverse complex sine: + * + * 2 + * w = -i clog( iz + csqrt( 1 - z ) ). + * + * casin(z) = -i casinh(iz) + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 10100 2.1e-15 3.4e-16 + * IEEE -10,+10 30000 2.2e-14 2.7e-15 + * Larger relative error can be observed for z near zero. + * Also tested by csin(casin(z)) = z. + */ + +#include +#include +#include + +#include "math_private.h" + +double complex +casin(double complex z) +{ + double complex w; + static double complex ca, ct, zz, z2; + double x, y; + + x = creal (z); + y = cimag (z); + + if (y == 0.0) { + if (fabs(x) > 1.0) { + w = M_PI_2 + 0.0 * I; + /*mtherr ("casin", DOMAIN);*/ + } + else { + w = asin (x) + 0.0 * I; + } + return (w); + } + + /* Power series expansion */ + /* + b = cabs(z); + if( b < 0.125 ) { + z2.r = (x - y) * (x + y); + z2.i = 2.0 * x * y; + + cn = 1.0; + n = 1.0; + ca.r = x; + ca.i = y; + sum.r = x; + sum.i = y; + do { + ct.r = z2.r * ca.r - z2.i * ca.i; + ct.i = z2.r * ca.i + z2.i * ca.r; + ca.r = ct.r; + ca.i = ct.i; + + cn *= n; + n += 1.0; + cn /= n; + n += 1.0; + b = cn/n; + + ct.r *= b; + ct.i *= b; + sum.r += ct.r; + sum.i += ct.i; + b = fabs(ct.r) + fabs(ct.i); + } + while( b > MACHEP ); + w->r = sum.r; + w->i = sum.i; + return; + } + */ + + ca = x + y * I; + ct = ca * I; + /* sqrt( 1 - z*z) */ + /* cmul( &ca, &ca, &zz ) */ + /*x * x - y * y */ + zz = (x - y) * (x + y) + (2.0 * x * y) * I; + + zz = 1.0 - creal(zz) - cimag(zz) * I; + z2 = csqrt (zz); + + zz = ct + z2; + zz = clog (zz); + /* multiply by 1/i = -i */ + w = zz * (-1.0 * I); + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(casin, casinl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_casinf.c b/openlibm/src/s_casinf.c new file mode 100644 index 0000000..1573264 --- /dev/null +++ b/openlibm/src/s_casinf.c @@ -0,0 +1,132 @@ +/* $OpenBSD: s_casinf.c,v 1.3 2011/07/20 19:28:33 martynas Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* casinf() + * + * Complex circular arc sine + * + * + * + * SYNOPSIS: + * + * void casinf(); + * cmplxf z, w; + * + * casinf( &z, &w ); + * + * + * + * DESCRIPTION: + * + * Inverse complex sine: + * + * 2 + * w = -i clog( iz + csqrt( 1 - z ) ). + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.1e-5 1.5e-6 + * Larger relative error can be observed for z near zero. + * + */ + +#include +#include + +float complex +casinf(float complex z) +{ + float complex w; + float x, y; + static float complex ca, ct, zz, z2; + /* + float cn, n; + static float a, b, s, t, u, v, y2; + static cmplxf sum; + */ + + x = crealf(z); + y = cimagf(z); + + if(y == 0.0f) { + if(fabsf(x) > 1.0f) { + w = (float)M_PI_2 + 0.0f * I; + /*mtherr( "casinf", DOMAIN );*/ + } + else { + w = asinf (x) + 0.0f * I; + } + return (w); + } + + /* Power series expansion */ + /* + b = cabsf(z); + if(b < 0.125) { + z2.r = (x - y) * (x + y); + z2.i = 2.0 * x * y; + + cn = 1.0; + n = 1.0; + ca.r = x; + ca.i = y; + sum.r = x; + sum.i = y; + do { + ct.r = z2.r * ca.r - z2.i * ca.i; + ct.i = z2.r * ca.i + z2.i * ca.r; + ca.r = ct.r; + ca.i = ct.i; + + cn *= n; + n += 1.0; + cn /= n; + n += 1.0; + b = cn/n; + + ct.r *= b; + ct.i *= b; + sum.r += ct.r; + sum.i += ct.i; + b = fabsf(ct.r) + fabsf(ct.i); + } + while(b > MACHEPF); + w->r = sum.r; + w->i = sum.i; + return; + } + */ + + + ca = x + y * I; + ct = ca * I; /* iz */ + /* sqrt( 1 - z*z) */ + /* cmul( &ca, &ca, &zz ) */ + /*x * x - y * y */ + zz = (x - y) * (x + y) + (2.0f * x * y) * I; + zz = 1.0f - crealf(zz) - cimagf(zz) * I; + z2 = csqrtf (zz); + + zz = ct + z2; + zz = clogf (zz); + /* multiply by 1/i = -i */ + w = zz * (-1.0f * I); + return (w); +} diff --git a/openlibm/src/s_casinh.c b/openlibm/src/s_casinh.c new file mode 100644 index 0000000..4b1154d --- /dev/null +++ b/openlibm/src/s_casinh.c @@ -0,0 +1,62 @@ +/* $OpenBSD: s_casinh.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* casinh + * + * Complex inverse hyperbolic sine + * + * + * + * SYNOPSIS: + * + * double complex casinh(); + * double complex z, w; + * + * w = casinh (z); + * + * + * + * DESCRIPTION: + * + * casinh z = -i casin iz . + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.8e-14 2.6e-15 + * + */ + +#include +#include +#include + +#include "math_private.h" + +double complex +casinh(double complex z) +{ + double complex w; + + w = -1.0 * I * casin (z * I); + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(casinh, casinhl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_casinhf.c b/openlibm/src/s_casinhf.c new file mode 100644 index 0000000..8894624 --- /dev/null +++ b/openlibm/src/s_casinhf.c @@ -0,0 +1,55 @@ +/* $OpenBSD: s_casinhf.c,v 1.1 2008/09/07 20:36:09 martynas Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* casinhf + * + * Complex inverse hyperbolic sine + * + * + * + * SYNOPSIS: + * + * float complex casinhf(); + * float complex z, w; + * + * w = casinhf (z); + * + * + * + * DESCRIPTION: + * + * casinh z = -i casin iz . + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.8e-14 2.6e-15 + * + */ + +#include +#include + +float complex +casinhf(float complex z) +{ + float complex w; + + w = -1.0f * I * casinf (z * I); + return (w); +} diff --git a/openlibm/src/s_casinhl.c b/openlibm/src/s_casinhl.c new file mode 100644 index 0000000..33ae217 --- /dev/null +++ b/openlibm/src/s_casinhl.c @@ -0,0 +1,56 @@ +/* $OpenBSD: s_casinhl.c,v 1.1 2011/07/08 19:25:31 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* casinhl + * + * Complex inverse hyperbolic sine + * + * + * + * SYNOPSIS: + * + * long double complex casinhf(); + * long double complex z, w; + * + * w = casinhl (z); + * + * + * + * DESCRIPTION: + * + * casinh z = -i casin iz . + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.8e-14 2.6e-15 + * + */ + +#include +#include + +long double complex +casinhl(long double complex z) +{ + long double complex w; + + w = -1.0L * I * casinl(z * I); + return (w); +} diff --git a/openlibm/src/s_casinl.c b/openlibm/src/s_casinl.c new file mode 100644 index 0000000..b346272 --- /dev/null +++ b/openlibm/src/s_casinl.c @@ -0,0 +1,130 @@ +/* $OpenBSD: s_casinl.c,v 1.3 2011/07/20 21:02:51 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* casinl() + * + * Complex circular arc sine + * + * + * + * SYNOPSIS: + * + * long double complex casinl(); + * long double complex z, w; + * + * w = casinl( z ); + * + * + * + * DESCRIPTION: + * + * Inverse complex sine: + * + * 2 + * w = -i clog( iz + csqrt( 1 - z ) ). + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 10100 2.1e-15 3.4e-16 + * IEEE -10,+10 30000 2.2e-14 2.7e-15 + * Larger relative error can be observed for z near zero. + * Also tested by csin(casin(z)) = z. + */ + +#include +#include +#include + +#if LDBL_MANT_DIG == 64 +static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L; +#elif LDBL_MANT_DIG == 113 +static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L; +#endif + +static const long double PIO2L = 1.570796326794896619231321691639751442098585L; + +long double complex +casinl(long double complex z) +{ + long double complex w; + long double x, y, b; + static long double complex ca, ct, zz, z2; + + x = creall(z); + y = cimagl(z); + + if (y == 0.0L) { + if (fabsl(x) > 1.0L) { + w = PIO2L + 0.0L * I; + /*mtherr( "casinl", DOMAIN );*/ + } + else { + w = asinl(x) + 0.0L * I; + } + return (w); + } + + /* Power series expansion */ + b = cabsl(z); + if (b < 0.125L) { + long double complex sum; + long double n, cn; + + z2 = (x - y) * (x + y) + (2.0L * x * y) * I; + cn = 1.0L; + n = 1.0L; + ca = x + y * I; + sum = x + y * I; + do { + ct = z2 * ca; + ca = ct; + + cn *= n; + n += 1.0L; + cn /= n; + n += 1.0L; + b = cn/n; + + ct *= b; + sum += ct; + b = cabsl(ct); + } + + while (b > MACHEPL); + w = sum; + return w; + } + + ca = x + y * I; + ct = ca * I; /* iz */ + /* sqrt(1 - z*z) */ + /* cmul(&ca, &ca, &zz) */ + /* x * x - y * y */ + zz = (x - y) * (x + y) + (2.0L * x * y) * I; + zz = 1.0L - creall(zz) - cimagl(zz) * I; + z2 = csqrtl(zz); + + zz = ct + z2; + zz = clogl(zz); + /* multiply by 1/i = -i */ + w = zz * (-1.0L * I); + return (w); +} diff --git a/openlibm/src/s_catan.c b/openlibm/src/s_catan.c new file mode 100644 index 0000000..9ee3dbb --- /dev/null +++ b/openlibm/src/s_catan.c @@ -0,0 +1,133 @@ +/* $OpenBSD: s_catan.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* catan() + * + * Complex circular arc tangent + * + * + * + * SYNOPSIS: + * + * double complex catan(); + * double complex z, w; + * + * w = catan (z); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * 1 ( 2x ) + * Re w = - arctan(-----------) + k PI + * 2 ( 2 2) + * (1 - x - y ) + * + * ( 2 2) + * 1 (x + (y+1) ) + * Im w = - log(------------) + * 4 ( 2 2) + * (x + (y-1) ) + * + * Where k is an arbitrary integer. + * + * catan(z) = -i catanh(iz). + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 5900 1.3e-16 7.8e-18 + * IEEE -10,+10 30000 2.3e-15 8.5e-17 + * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, + * had peak relative error 1.5e-16, rms relative error + * 2.9e-17. See also clog(). + */ + +#include +#include +#include + +#include "math_private.h" + +#define MAXNUM 1.0e308 + +static const double DP1 = 3.14159265160560607910E0; +static const double DP2 = 1.98418714791870343106E-9; +static const double DP3 = 1.14423774522196636802E-17; + +static double +_redupi(double x) +{ + double t; + long i; + + t = x/M_PI; + if(t >= 0.0) + t += 0.5; + else + t -= 0.5; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return (t); +} + +double complex +catan(double complex z) +{ + double complex w; + double a, t, x, x2, y; + + x = creal (z); + y = cimag (z); + + if ((x == 0.0) && (y > 1.0)) + goto ovrf; + + x2 = x * x; + a = 1.0 - x2 - (y * y); + if (a == 0.0) + goto ovrf; + + t = 0.5 * atan2 (2.0 * x, a); + w = _redupi (t); + + t = y - 1.0; + a = x2 + (t * t); + if (a == 0.0) + goto ovrf; + + t = y + 1.0; + a = (x2 + (t * t))/a; + w = w + (0.25 * log (a)) * I; + return (w); + +ovrf: + /*mtherr ("catan", OVERFLOW);*/ + w = MAXNUM + MAXNUM * I; + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(catan, catanl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_catanf.c b/openlibm/src/s_catanf.c new file mode 100644 index 0000000..d40cb56 --- /dev/null +++ b/openlibm/src/s_catanf.c @@ -0,0 +1,124 @@ +/* $OpenBSD: s_catanf.c,v 1.2 2010/07/18 18:42:26 guenther Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* catanf() + * + * Complex circular arc tangent + * + * + * + * SYNOPSIS: + * + * float complex catanf(); + * float complex z, w; + * + * w = catanf( z ); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * 1 ( 2x ) + * Re w = - arctan(-----------) + k PI + * 2 ( 2 2) + * (1 - x - y ) + * + * ( 2 2) + * 1 (x + (y+1) ) + * Im w = - log(------------) + * 4 ( 2 2) + * (x + (y-1) ) + * + * Where k is an arbitrary integer. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 2.3e-6 5.2e-8 + * + */ + +#include +#include + +#define MAXNUMF 1.0e38F + +static const double DP1 = 3.140625; +static const double DP2 = 9.67502593994140625E-4; +static const double DP3 = 1.509957990978376432E-7; + +static float +_redupif(float xx) +{ + float x, t; + long i; + + x = xx; + t = x/(float)M_PI; + if(t >= 0.0) + t += 0.5; + else + t -= 0.5; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return(t); +} + +float complex +catanf(float complex z) +{ + float complex w; + float a, t, x, x2, y; + + x = crealf(z); + y = cimagf(z); + + if((x == 0.0f) && (y > 1.0f)) + goto ovrf; + + x2 = x * x; + a = 1.0f - x2 - (y * y); + if (a == 0.0f) + goto ovrf; + + t = 0.5f * atan2f(2.0f * x, a); + w = _redupif(t); + + t = y - 1.0f; + a = x2 + (t * t); + if(a == 0.0f) + goto ovrf; + + t = y + 1.0f; + a = (x2 + (t * t))/a; + w = w + (0.25f * logf (a)) * I; + return (w); + +ovrf: + /*mtherr( "catanf", OVERFLOW );*/ + w = MAXNUMF + MAXNUMF * I; + return (w); +} diff --git a/openlibm/src/s_catanh.c b/openlibm/src/s_catanh.c new file mode 100644 index 0000000..3e3eeaf --- /dev/null +++ b/openlibm/src/s_catanh.c @@ -0,0 +1,62 @@ +/* $OpenBSD: s_catanh.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* catanh + * + * Complex inverse hyperbolic tangent + * + * + * + * SYNOPSIS: + * + * double complex catanh(); + * double complex z, w; + * + * w = catanh (z); + * + * + * + * DESCRIPTION: + * + * Inverse tanh, equal to -i catan (iz); + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 2.3e-16 6.2e-17 + * + */ + +#include +#include +#include + +#include "math_private.h" + +double complex +catanh(double complex z) +{ + double complex w; + + w = -1.0 * I * catan (z * I); + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(catanh, catanhl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_catanhf.c b/openlibm/src/s_catanhf.c new file mode 100644 index 0000000..7d43825 --- /dev/null +++ b/openlibm/src/s_catanhf.c @@ -0,0 +1,55 @@ +/* $OpenBSD: s_catanhf.c,v 1.1 2008/09/07 20:36:09 martynas Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* catanhf + * + * Complex inverse hyperbolic tangent + * + * + * + * SYNOPSIS: + * + * float complex catanhf(); + * float complex z, w; + * + * w = catanhf (z); + * + * + * + * DESCRIPTION: + * + * Inverse tanh, equal to -i catan (iz); + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 2.3e-16 6.2e-17 + * + */ + +#include +#include + +float complex +catanhf(float complex z) +{ + float complex w; + + w = -1.0f * I * catanf (z * I); + return (w); +} diff --git a/openlibm/src/s_catanhl.c b/openlibm/src/s_catanhl.c new file mode 100644 index 0000000..711a268 --- /dev/null +++ b/openlibm/src/s_catanhl.c @@ -0,0 +1,56 @@ +/* $OpenBSD: s_catanhl.c,v 1.1 2011/07/08 19:25:31 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* catanhl + * + * Complex inverse hyperbolic tangent + * + * + * + * SYNOPSIS: + * + * long double complex catanhl(); + * long double complex z, w; + * + * w = catanhl (z); + * + * + * + * DESCRIPTION: + * + * Inverse tanh, equal to -i catan (iz); + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 2.3e-16 6.2e-17 + * + */ + +#include +#include + +long double complex +catanhl(long double complex z) +{ + long double complex w; + + w = -1.0L * I * catanl(z * I); + return (w); +} diff --git a/openlibm/src/s_catanl.c b/openlibm/src/s_catanl.c new file mode 100644 index 0000000..acd51b0 --- /dev/null +++ b/openlibm/src/s_catanl.c @@ -0,0 +1,127 @@ +/* $OpenBSD: s_catanl.c,v 1.3 2011/07/20 21:02:51 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* catanl() + * + * Complex circular arc tangent + * + * + * + * SYNOPSIS: + * + * long double complex catanl(); + * long double complex z, w; + * + * w = catanl( z ); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * 1 ( 2x ) + * Re w = - arctan(-----------) + k PI + * 2 ( 2 2) + * (1 - x - y ) + * + * ( 2 2) + * 1 (x + (y+1) ) + * Im w = - log(------------) + * 4 ( 2 2) + * (x + (y-1) ) + * + * Where k is an arbitrary integer. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 5900 1.3e-16 7.8e-18 + * IEEE -10,+10 30000 2.3e-15 8.5e-17 + * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, + * had peak relative error 1.5e-16, rms relative error + * 2.9e-17. See also clog(). + */ + +#include +#include +#include + +static const long double PIL = 3.141592653589793238462643383279502884197169L; +static const long double DP1 = 3.14159265358979323829596852490908531763125L; +static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; +static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; + +static long double +redupil(long double x) +{ + long double t; + long i; + + t = x / PIL; + if (t >= 0.0L) + t += 0.5L; + else + t -= 0.5L; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return (t); +} + +long double complex +catanl(long double complex z) +{ + long double complex w; + long double a, t, x, x2, y; + + x = creall(z); + y = cimagl(z); + + if ((x == 0.0L) && (y > 1.0L)) + goto ovrf; + + x2 = x * x; + a = 1.0L - x2 - (y * y); + if (a == 0.0L) + goto ovrf; + + t = atan2l(2.0L * x, a) * 0.5L; + w = redupil(t); + + t = y - 1.0L; + a = x2 + (t * t); + if (a == 0.0L) + goto ovrf; + + t = y + 1.0L; + a = (x2 + (t * t)) / a; + w = w + (0.25L * logl(a)) * I; + return (w); + +ovrf: + /*mtherr( "catanl", OVERFLOW );*/ + w = LDBL_MAX + LDBL_MAX * I; + return (w); +} diff --git a/openlibm/src/s_cbrt.c b/openlibm/src/s_cbrt.c new file mode 100644 index 0000000..b6316ad --- /dev/null +++ b/openlibm/src/s_cbrt.c @@ -0,0 +1,118 @@ +/* @(#)s_cbrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cbrt.c,v 1.17 2011/03/12 16:50:39 kargl Exp $"); + +#include + +#include "math_private.h" + +/* cbrt(x) + * Return cube root of x + */ +static const u_int32_t + B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */ + B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */ + +/* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */ +static const double +P0 = 1.87595182427177009643, /* 0x3ffe03e6, 0x0f61e692 */ +P1 = -1.88497979543377169875, /* 0xbffe28e0, 0x92f02420 */ +P2 = 1.621429720105354466140, /* 0x3ff9f160, 0x4a49d6c2 */ +P3 = -0.758397934778766047437, /* 0xbfe844cb, 0xbee751d9 */ +P4 = 0.145996192886612446982; /* 0x3fc2b000, 0xd4e4edd7 */ + +OLM_DLLEXPORT double +cbrt(double x) +{ + int32_t hx; + union { + double value; + u_int64_t bits; + } u; + double r,s,t=0.0,w; + u_int32_t sign; + u_int32_t high,low; + + EXTRACT_WORDS(hx,low,x); + sign=hx&0x80000000; /* sign= sign(x) */ + hx ^=sign; + if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ + + /* + * Rough cbrt to 5 bits: + * cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3) + * where e is integral and >= 0, m is real and in [0, 1), and "/" and + * "%" are integer division and modulus with rounding towards minus + * infinity. The RHS is always >= the LHS and has a maximum relative + * error of about 1 in 16. Adding a bias of -0.03306235651 to the + * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE + * floating point representation, for finite positive normal values, + * ordinary integer divison of the value in bits magically gives + * almost exactly the RHS of the above provided we first subtract the + * exponent bias (1023 for doubles) and later add it back. We do the + * subtraction virtually to keep e >= 0 so that ordinary integer + * division rounds towards minus infinity; this is also efficient. + */ + if(hx<0x00100000) { /* zero or subnormal? */ + if((hx|low)==0) + return(x); /* cbrt(0) is itself */ + SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ + t*=x; + GET_HIGH_WORD(high,t); + INSERT_WORDS(t,sign|((high&0x7fffffff)/3+B2),0); + } else + INSERT_WORDS(t,sign|(hx/3+B1),0); + + /* + * New cbrt to 23 bits: + * cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x) + * where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r) + * to within 2**-23.5 when |r - 1| < 1/10. The rough approximation + * has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this + * gives us bounds for r = t**3/x. + * + * Try to optimize for parallel evaluation as in k_tanf.c. + */ + r=(t*t)*(t/x); + t=t*((P0+r*(P1+r*P2))+((r*r)*r)*(P3+r*P4)); + + /* + * Round t away from zero to 23 bits (sloppily except for ensuring that + * the result is larger in magnitude than cbrt(x) but not much more than + * 2 23-bit ulps larger). With rounding towards zero, the error bound + * would be ~5/6 instead of ~4/6. With a maximum error of 2 23-bit ulps + * in the rounded t, the infinite-precision error in the Newton + * approximation barely affects third digit in the final error + * 0.667; the error in the rounded t can be up to about 3 23-bit ulps + * before the final error is larger than 0.667 ulps. + */ + u.value=t; + u.bits=(u.bits+0x80000000)&0xffffffffc0000000ULL; + t=u.value; + + /* one step Newton iteration to 53 bits with error < 0.667 ulps */ + s=t*t; /* t*t is exact */ + r=x/s; /* error <= 0.5 ulps; |r| < |t| */ + w=t+t; /* t+t is exact */ + r=(r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */ + t=t+t*r; /* error <= 0.5 + 0.5/3 + epsilon */ + + return(t); +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(cbrt, cbrtl); +#endif diff --git a/openlibm/src/s_cbrtf.c b/openlibm/src/s_cbrtf.c new file mode 100644 index 0000000..6a3a762 --- /dev/null +++ b/openlibm/src/s_cbrtf.c @@ -0,0 +1,74 @@ +/* s_cbrtf.c -- float version of s_cbrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Debugged and optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cbrtf.c,v 1.18 2008/02/22 02:30:35 das Exp $"); + +#include + +#include "math_private.h" + +/* cbrtf(x) + * Return cube root of x + */ +static const unsigned + B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */ + B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */ + +OLM_DLLEXPORT float +cbrtf(float x) +{ + double r,T; + float t; + int32_t hx; + u_int32_t sign; + u_int32_t high; + + GET_FLOAT_WORD(hx,x); + sign=hx&0x80000000; /* sign= sign(x) */ + hx ^=sign; + if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */ + + /* rough cbrt to 5 bits */ + if(hx<0x00800000) { /* zero or subnormal? */ + if(hx==0) + return(x); /* cbrt(+-0) is itself */ + SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */ + t*=x; + GET_FLOAT_WORD(high,t); + SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2)); + } else + SET_FLOAT_WORD(t,sign|(hx/3+B1)); + + /* + * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In + * double precision so that its terms can be arranged for efficiency + * without causing overflow or underflow. + */ + T=t; + r=T*T*T; + T=T*((double)x+x+r)/(x+r+r); + + /* + * Second step Newton iteration to 47 bits. In double precision for + * efficiency and accuracy. + */ + r=T*T*T; + T=T*((double)x+x+r)/(x+r+r); + + /* rounding to 24 bits is perfect in round-to-nearest mode */ + return(T); +} diff --git a/openlibm/src/s_cbrtl.c b/openlibm/src/s_cbrtl.c new file mode 100644 index 0000000..2fe0360 --- /dev/null +++ b/openlibm/src/s_cbrtl.c @@ -0,0 +1,161 @@ +/*- + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Copyright (c) 2009-2011, Bruce D. Evans, Steven G. Kargl, David Schultz. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * The argument reduction and testing for exceptional cases was + * written by Steven G. Kargl with input from Bruce D. Evans + * and David A. Schultz. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cbrtl.c,v 1.1 2011/03/12 19:37:35 kargl Exp $"); + +#include +#include +// VBS +//#include + +#include "fpmath.h" +#include "math_private.h" +#if defined(__i386__) +#include "i387/bsd_ieeefp.h" +#endif + +#define BIAS (LDBL_MAX_EXP - 1) + +static const unsigned + B1 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */ + +OLM_DLLEXPORT long double +cbrtl(long double x) +{ + union IEEEl2bits u, v; + long double r, s, t, w; + double dr, dt, dx; + float ft, fx; + u_int32_t hx; + u_int16_t expsign; + int k; + + u.e = x; + expsign = u.xbits.expsign; + k = expsign & 0x7fff; + + /* + * If x = +-Inf, then cbrt(x) = +-Inf. + * If x = NaN, then cbrt(x) = NaN. + */ + if (k == BIAS + LDBL_MAX_EXP) + return (x + x); + +#ifdef __i386__ + fp_prec_t oprec; + + oprec = fpgetprec(); + if (oprec != FP_PE) + fpsetprec(FP_PE); +#endif + + if (k == 0) { + /* If x = +-0, then cbrt(x) = +-0. */ + if ((u.bits.manh | u.bits.manl) == 0) { +#ifdef __i386__ + if (oprec != FP_PE) + fpsetprec(oprec); +#endif + return (x); + } + /* Adjust subnormal numbers. */ + u.e *= 0x1.0p514; + k = u.bits.exp; + k -= BIAS + 514; + } else + k -= BIAS; + u.xbits.expsign = BIAS; + v.e = 1; + + x = u.e; + switch (k % 3) { + case 1: + case -2: + x = 2*x; + k--; + break; + case 2: + case -1: + x = 4*x; + k -= 2; + break; + } + v.xbits.expsign = (expsign & 0x8000) | (BIAS + k / 3); + + /* + * The following is the guts of s_cbrtf, with the handling of + * special values removed and extra care for accuracy not taken, + * but with most of the extra accuracy not discarded. + */ + + /* ~5-bit estimate: */ + fx = x; + GET_FLOAT_WORD(hx, fx); + SET_FLOAT_WORD(ft, ((hx & 0x7fffffff) / 3 + B1)); + + /* ~16-bit estimate: */ + dx = x; + dt = ft; + dr = dt * dt * dt; + dt = dt * (dx + dx + dr) / (dx + dr + dr); + + /* ~47-bit estimate: */ + dr = dt * dt * dt; + dt = dt * (dx + dx + dr) / (dx + dr + dr); + +#if LDBL_MANT_DIG == 64 + /* + * dt is cbrtl(x) to ~47 bits (after x has been reduced to 1 <= x < 8). + * Round it away from zero to 32 bits (32 so that t*t is exact, and + * away from zero for technical reasons). + */ + volatile double vd2 = 0x1.0p32; + volatile double vd1 = 0x1.0p-31; + #define vd ((long double)vd2 + vd1) + + t = dt + vd - 0x1.0p32; +#elif LDBL_MANT_DIG == 113 + /* + * Round dt away from zero to 47 bits. Since we don't trust the 47, + * add 2 47-bit ulps instead of 1 to round up. Rounding is slow and + * might be avoidable in this case, since on most machines dt will + * have been evaluated in 53-bit precision and the technical reasons + * for rounding up might not apply to either case in cbrtl() since + * dt is much more accurate than needed. + */ + t = dt + 0x2.0p-46 + 0x1.0p60L - 0x1.0p60; +#else +#error "Unsupported long double format" +#endif + + /* + * Final step Newton iteration to 64 or 113 bits with + * error < 0.667 ulps + */ + s=t*t; /* t*t is exact */ + r=x/s; /* error <= 0.5 ulps; |r| < |t| */ + w=t+t; /* t+t is exact */ + r=(r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */ + t=t+t*r; /* error <= 0.5 + 0.5/3 + epsilon */ + + t *= v.e; +#ifdef __i386__ + if (oprec != FP_PE) + fpsetprec(oprec); +#endif + return (t); +} diff --git a/openlibm/src/s_ccos.c b/openlibm/src/s_ccos.c new file mode 100644 index 0000000..faafdb0 --- /dev/null +++ b/openlibm/src/s_ccos.c @@ -0,0 +1,91 @@ +/* $OpenBSD: s_ccos.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* ccos() + * + * Complex circular cosine + * + * + * + * SYNOPSIS: + * + * double complex ccos(); + * double complex z, w; + * + * w = ccos (z); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * + * w = cos x cosh y - i sin x sinh y. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 8400 4.5e-17 1.3e-17 + * IEEE -10,+10 30000 3.8e-16 1.0e-16 + */ + +#include +#include +#include + +#include "math_private.h" + +/* calculate cosh and sinh */ + +static void +_cchsh(double x, double *c, double *s) +{ + double e, ei; + + if (fabs(x) <= 0.5) { + *c = cosh(x); + *s = sinh(x); + } + else { + e = exp(x); + ei = 0.5/e; + e = 0.5 * e; + *s = e - ei; + *c = e + ei; + } +} + +double complex +ccos(double complex z) +{ + double complex w; + double ch, sh; + + _cchsh( cimag(z), &ch, &sh ); + w = cos(creal (z)) * ch - (sin (creal (z)) * sh) * I; + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(ccos, ccosl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_ccosf.c b/openlibm/src/s_ccosf.c new file mode 100644 index 0000000..ce382f0 --- /dev/null +++ b/openlibm/src/s_ccosf.c @@ -0,0 +1,84 @@ +/* $OpenBSD: s_ccosf.c,v 1.2 2010/07/18 18:42:26 guenther Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* ccosf() + * + * Complex circular cosine + * + * + * + * SYNOPSIS: + * + * void ccosf(); + * cmplxf z, w; + * + * ccosf( &z, &w ); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * + * w = cos x cosh y - i sin x sinh y. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.8e-7 5.5e-8 + */ + +#include +#include + +/* calculate cosh and sinh */ + +static void +_cchshf(float xx, float *c, float *s) +{ + float x, e, ei; + + x = xx; + if(fabsf(x) <= 0.5f) { + *c = coshf(x); + *s = sinhf(x); + } + else { + e = expf(x); + ei = 0.5f/e; + e = 0.5f * e; + *s = e - ei; + *c = e + ei; + } +} + +float complex +ccosf(float complex z) +{ + float complex w; + float ch, sh; + + _cchshf( cimagf(z), &ch, &sh ); + w = cosf( crealf(z) ) * ch + ( -sinf( crealf(z) ) * sh) * I; + return (w); +} diff --git a/openlibm/src/s_ccosh.c b/openlibm/src/s_ccosh.c new file mode 100644 index 0000000..110494a --- /dev/null +++ b/openlibm/src/s_ccosh.c @@ -0,0 +1,155 @@ +/*- + * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/* + * Hyperbolic cosine of a complex argument z = x + i y. + * + * cosh(z) = cosh(x+iy) + * = cosh(x) cos(y) + i sinh(x) sin(y). + * + * Exceptional values are noted in the comments within the source code. + * These values and the return value were taken from n1124.pdf. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_ccosh.c,v 1.2 2011/10/21 06:29:32 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const double huge = 0x1p1023; + +OLM_DLLEXPORT double complex +ccosh(double complex z) +{ + double x, y, h; + int32_t hx, hy, ix, iy, lx, ly; + + x = creal(z); + y = cimag(z); + + EXTRACT_WORDS(hx, lx, x); + EXTRACT_WORDS(hy, ly, y); + + ix = 0x7fffffff & hx; + iy = 0x7fffffff & hy; + + /* Handle the nearly-non-exceptional cases where x and y are finite. */ + if (ix < 0x7ff00000 && iy < 0x7ff00000) { + if ((iy | ly) == 0) + return (CMPLX(cosh(x), x * y)); + if (ix < 0x40360000) /* small x: normal case */ + return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y))); + + /* |x| >= 22, so cosh(x) ~= exp(|x|) */ + if (ix < 0x40862e42) { + /* x < 710: exp(|x|) won't overflow */ + h = exp(fabs(x)) * 0.5; + return (CMPLX(h * cos(y), copysign(h, x) * sin(y))); + } else if (ix < 0x4096bbaa) { + /* x < 1455: scale to avoid overflow */ + z = __ldexp_cexp(CMPLX(fabs(x), y), -1); + return (CMPLX(creal(z), cimag(z) * copysign(1, x))); + } else { + /* x >= 1455: the result always overflows */ + h = huge * x; + return (CMPLX(h * h * cos(y), h * sin(y))); + } + } + + /* + * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0. + * The sign of 0 in the result is unspecified. Choice = normally + * the same as dNaN. Raise the invalid floating-point exception. + * + * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0. + * The sign of 0 in the result is unspecified. Choice = normally + * the same as d(NaN). + */ + if ((ix | lx) == 0 && iy >= 0x7ff00000) + return (CMPLX(y - y, copysign(0, x * (y - y)))); + + /* + * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0. + * + * cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0. + * The sign of 0 in the result is unspecified. + */ + if ((iy | ly) == 0 && ix >= 0x7ff00000) { + if (((hx & 0xfffff) | lx) == 0) + return (CMPLX(x * x, copysign(0, x) * y)); + return (CMPLX(x * x, copysign(0, (x + x) * y))); + } + + /* + * cosh(x +- I Inf) = dNaN + I dNaN. + * Raise the invalid floating-point exception for finite nonzero x. + * + * cosh(x + I NaN) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero x. Choice = don't raise (except for signaling NaNs). + */ + if (ix < 0x7ff00000 && iy >= 0x7ff00000) + return (CMPLX(y - y, x * (y - y))); + + /* + * cosh(+-Inf + I NaN) = +Inf + I d(NaN). + * + * cosh(+-Inf +- I Inf) = +Inf + I dNaN. + * The sign of Inf in the result is unspecified. Choice = always +. + * Raise the invalid floating-point exception. + * + * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y) + */ + if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { + if (iy >= 0x7ff00000) + return (CMPLX(x * x, x * (y - y))); + return (CMPLX((x * x) * cos(y), x * sin(y))); + } + + /* + * cosh(NaN + I NaN) = d(NaN) + I d(NaN). + * + * cosh(NaN +- I Inf) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception. + * Choice = raise. + * + * cosh(NaN + I y) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero y. Choice = don't raise (except for signaling NaNs). + */ + return (CMPLX((x * x) * (y - y), (x + x) * (y - y))); +} + +OLM_DLLEXPORT double complex +ccos(double complex z) +{ + + /* ccos(z) = ccosh(I * z) */ + return (ccosh(CMPLX(-cimag(z), creal(z)))); +} diff --git a/openlibm/src/s_ccoshf.c b/openlibm/src/s_ccoshf.c new file mode 100644 index 0000000..53c8e7a --- /dev/null +++ b/openlibm/src/s_ccoshf.c @@ -0,0 +1,104 @@ +/*- + * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/* + * Hyperbolic cosine of a complex argument. See s_ccosh.c for details. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_ccoshf.c,v 1.2 2011/10/21 06:29:32 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const float huge = 0x1p127; + +OLM_DLLEXPORT float complex +ccoshf(float complex z) +{ + float x, y, h; + int32_t hx, hy, ix, iy; + + x = crealf(z); + y = cimagf(z); + + GET_FLOAT_WORD(hx, x); + GET_FLOAT_WORD(hy, y); + + ix = 0x7fffffff & hx; + iy = 0x7fffffff & hy; + + if (ix < 0x7f800000 && iy < 0x7f800000) { + if (iy == 0) + return (CMPLXF(coshf(x), x * y)); + if (ix < 0x41100000) /* small x: normal case */ + return (CMPLXF(coshf(x) * cosf(y), sinhf(x) * sinf(y))); + + /* |x| >= 9, so cosh(x) ~= exp(|x|) */ + if (ix < 0x42b17218) { + /* x < 88.7: expf(|x|) won't overflow */ + h = expf(fabsf(x)) * 0.5f; + return (CMPLXF(h * cosf(y), copysignf(h, x) * sinf(y))); + } else if (ix < 0x4340b1e7) { + /* x < 192.7: scale to avoid overflow */ + z = __ldexp_cexpf(CMPLXF(fabsf(x), y), -1); + return (CMPLXF(crealf(z), cimagf(z) * copysignf(1, x))); + } else { + /* x >= 192.7: the result always overflows */ + h = huge * x; + return (CMPLXF(h * h * cosf(y), h * sinf(y))); + } + } + + if (ix == 0 && iy >= 0x7f800000) + return (CMPLXF(y - y, copysignf(0, x * (y - y)))); + + if (iy == 0 && ix >= 0x7f800000) { + if ((hx & 0x7fffff) == 0) + return (CMPLXF(x * x, copysignf(0, x) * y)); + return (CMPLXF(x * x, copysignf(0, (x + x) * y))); + } + + if (ix < 0x7f800000 && iy >= 0x7f800000) + return (CMPLXF(y - y, x * (y - y))); + + if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) { + if (iy >= 0x7f800000) + return (CMPLXF(x * x, x * (y - y))); + return (CMPLXF((x * x) * cosf(y), x * sinf(y))); + } + + return (CMPLXF((x * x) * (y - y), (x + x) * (y - y))); +} + +OLM_DLLEXPORT float complex +ccosf(float complex z) +{ + + return (ccoshf(CMPLXF(-cimagf(z), crealf(z)))); +} diff --git a/openlibm/src/s_ccoshl.c b/openlibm/src/s_ccoshl.c new file mode 100644 index 0000000..0233d19 --- /dev/null +++ b/openlibm/src/s_ccoshl.c @@ -0,0 +1,59 @@ +/* $OpenBSD: s_ccoshl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* ccoshl + * + * Complex hyperbolic cosine + * + * + * + * SYNOPSIS: + * + * long double complex ccoshl(); + * long double complex z, w; + * + * w = ccoshl (z); + * + * + * + * DESCRIPTION: + * + * ccosh(z) = cosh x cos y + i sinh x sin y . + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 2.9e-16 8.1e-17 + * + */ + +#include +#include + +long double complex +ccoshl(long double complex z) +{ + long double complex w; + long double x, y; + + x = creall(z); + y = cimagl(z); + w = coshl(x) * cosl(y) + (sinhl(x) * sinl(y)) * I; + return (w); +} diff --git a/openlibm/src/s_ccosl.c b/openlibm/src/s_ccosl.c new file mode 100644 index 0000000..0d50483 --- /dev/null +++ b/openlibm/src/s_ccosl.c @@ -0,0 +1,82 @@ +/* $OpenBSD: s_ccosl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* ccosl() + * + * Complex circular cosine + * + * + * + * SYNOPSIS: + * + * long double complex ccosl(); + * long double complex z, w; + * + * w = ccosl( z ); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * + * w = cos x cosh y - i sin x sinh y. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 8400 4.5e-17 1.3e-17 + * IEEE -10,+10 30000 3.8e-16 1.0e-16 + */ + +#include +#include + +static void +cchshl(long double x, long double *c, long double *s) +{ + long double e, ei; + + if(fabsl(x) <= 0.5L) { + *c = coshl(x); + *s = sinhl(x); + } else { + e = expl(x); + ei = 0.5L/e; + e = 0.5L * e; + *s = e - ei; + *c = e + ei; + } +} + +long double complex +ccosl(long double complex z) +{ + long double complex w; + long double ch, sh; + + cchshl(cimagl(z), &ch, &sh); + w = cosl(creall(z)) * ch + (-sinl(creall(z)) * sh) * I; + return (w); +} diff --git a/openlibm/src/s_ceil.c b/openlibm/src/s_ceil.c new file mode 100644 index 0000000..9c70a97 --- /dev/null +++ b/openlibm/src/s_ceil.c @@ -0,0 +1,77 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_ceil.c,v 1.11 2008/02/15 07:01:40 bde Exp $"); + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include +#include + +#include "math_private.h" + +static const double huge = 1.0e300; + +OLM_DLLEXPORT double +ceil(double x) +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;i1=0;} + else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) { + if(j0==20) i0+=1; + else { + j = i1 + (1<<(52-j0)); + if(j + +#include "math_private.h" + +static const float huge = 1.0e30; + +OLM_DLLEXPORT float +ceilf(float x) +{ + int32_t i0,j0; + u_int32_t i; + + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;} + else if(i0!=0) { i0=0x3f800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/openlibm/src/s_ceill.c b/openlibm/src/s_ceill.c new file mode 100644 index 0000000..f525411 --- /dev/null +++ b/openlibm/src/s_ceill.c @@ -0,0 +1,102 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * From: @(#)s_ceil.c 5.1 93/09/24 + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_ceill.c,v 1.9 2008/02/14 15:10:33 bde Exp $"); + +/* + * ceill(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceill(x). + */ + +#include +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#ifdef LDBL_IMPLICIT_NBIT +#define MANH_SIZE (LDBL_MANH_SIZE + 1) +#define INC_MANH(u, c) do { \ + u_int64_t o = u.bits.manh; \ + u.bits.manh += (c); \ + if (u.bits.manh < o) \ + u.bits.exp++; \ +} while (0) +#else +#define MANH_SIZE LDBL_MANH_SIZE +#define INC_MANH(u, c) do { \ + u_int64_t o = u.bits.manh; \ + u.bits.manh += (c); \ + if (u.bits.manh < o) { \ + u.bits.exp++; \ + u.bits.manh |= 1llu << (LDBL_MANH_SIZE - 1); \ + } \ +} while (0) +#endif + +static const long double huge = 1.0e300; + +OLM_DLLEXPORT long double +ceill(long double x) +{ + union IEEEl2bits u = { .e = x }; + int e = u.bits.exp - LDBL_MAX_EXP + 1; + + if (e < MANH_SIZE - 1) { + if (e < 0) { /* raise inexact if x != 0 */ + if (huge + x > 0.0) + if (u.bits.exp > 0 || + (u.bits.manh | u.bits.manl) != 0) + u.e = u.bits.sign ? -0.0 : 1.0; + } else { + u_int64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1); + if (((u.bits.manh & m) | u.bits.manl) == 0) + return (x); /* x is integral */ + if (!u.bits.sign) { +#ifdef LDBL_IMPLICIT_NBIT + if (e == 0) + u.bits.exp++; + else +#endif + INC_MANH(u, 1llu << (MANH_SIZE - e - 1)); + } + if (huge + x > 0.0) { /* raise inexact flag */ + u.bits.manh &= ~m; + u.bits.manl = 0; + } + } + } else if (e < LDBL_MANT_DIG - 1) { + u_int64_t m = (u_int64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1); + if ((u.bits.manl & m) == 0) + return (x); /* x is integral */ + if (!u.bits.sign) { + if (e == MANH_SIZE - 1) + INC_MANH(u, 1); + else { + u_int64_t o = u.bits.manl; + u.bits.manl += 1llu << (LDBL_MANT_DIG - e - 1); + if (u.bits.manl < o) /* got a carry */ + INC_MANH(u, 1); + } + } + if (huge + x > 0.0) /* raise inexact flag */ + u.bits.manl &= ~m; + } + return (u.e); +} diff --git a/openlibm/src/s_cexp.c b/openlibm/src/s_cexp.c new file mode 100644 index 0000000..1510721 --- /dev/null +++ b/openlibm/src/s_cexp.c @@ -0,0 +1,89 @@ +/*- + * Copyright (c) 2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cexp.c,v 1.3 2011/10/21 06:27:56 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const u_int32_t +exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ +cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ + +OLM_DLLEXPORT double complex +cexp(double complex z) +{ + double x, y, exp_x; + u_int32_t hx, hy, lx, ly; + + x = creal(z); + y = cimag(z); + + EXTRACT_WORDS(hy, ly, y); + hy &= 0x7fffffff; + + /* cexp(x + I 0) = exp(x) + I 0 */ + if ((hy | ly) == 0) + return (CMPLX(exp(x), y)); + EXTRACT_WORDS(hx, lx, x); + /* cexp(0 + I y) = cos(y) + I sin(y) */ + if (((hx & 0x7fffffff) | lx) == 0) + return (CMPLX(cos(y), sin(y))); + + if (hy >= 0x7ff00000) { + if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { + /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ + return (CMPLX(y - y, y - y)); + } else if (hx & 0x80000000) { + /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ + return (CMPLX(0.0, 0.0)); + } else { + /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ + return (CMPLX(x, y - y)); + } + } + + if (hx >= exp_ovfl && hx <= cexp_ovfl) { + /* + * x is between 709.7 and 1454.3, so we must scale to avoid + * overflow in exp(x). + */ + return (__ldexp_cexp(z, 0)); + } else { + /* + * Cases covered here: + * - x < exp_ovfl and exp(x) won't overflow (common case) + * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 + * - x = +-Inf (generated by exp()) + * - x = NaN (spurious inexact exception from y) + */ + exp_x = exp(x); + return (CMPLX(exp_x * cos(y), exp_x * sin(y))); + } +} diff --git a/openlibm/src/s_cexpf.c b/openlibm/src/s_cexpf.c new file mode 100644 index 0000000..05f4544 --- /dev/null +++ b/openlibm/src/s_cexpf.c @@ -0,0 +1,89 @@ +/*- + * Copyright (c) 2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cexpf.c,v 1.3 2011/10/21 06:27:56 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const u_int32_t +exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */ +cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ + +OLM_DLLEXPORT float complex +cexpf(float complex z) +{ + float x, y, exp_x; + u_int32_t hx, hy; + + x = crealf(z); + y = cimagf(z); + + GET_FLOAT_WORD(hy, y); + hy &= 0x7fffffff; + + /* cexp(x + I 0) = exp(x) + I 0 */ + if (hy == 0) + return (CMPLXF(expf(x), y)); + GET_FLOAT_WORD(hx, x); + /* cexp(0 + I y) = cos(y) + I sin(y) */ + if ((hx & 0x7fffffff) == 0) + return (CMPLXF(cosf(y), sinf(y))); + + if (hy >= 0x7f800000) { + if ((hx & 0x7fffffff) != 0x7f800000) { + /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ + return (CMPLXF(y - y, y - y)); + } else if (hx & 0x80000000) { + /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ + return (CMPLXF(0.0, 0.0)); + } else { + /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ + return (CMPLXF(x, y - y)); + } + } + + if (hx >= exp_ovfl && hx <= cexp_ovfl) { + /* + * x is between 88.7 and 192, so we must scale to avoid + * overflow in expf(x). + */ + return (__ldexp_cexpf(z, 0)); + } else { + /* + * Cases covered here: + * - x < exp_ovfl and exp(x) won't overflow (common case) + * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 + * - x = +-Inf (generated by exp()) + * - x = NaN (spurious inexact exception from y) + */ + exp_x = expf(x); + return (CMPLXF(exp_x * cosf(y), exp_x * sinf(y))); + } +} diff --git a/openlibm/src/s_cexpl.c b/openlibm/src/s_cexpl.c new file mode 100644 index 0000000..f143d88 --- /dev/null +++ b/openlibm/src/s_cexpl.c @@ -0,0 +1,69 @@ +/* $OpenBSD: s_cexpl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cexpl() + * + * Complex exponential function + * + * + * + * SYNOPSIS: + * + * long double complex cexpl(); + * long double complex z, w; + * + * w = cexpl( z ); + * + * + * + * DESCRIPTION: + * + * Returns the exponential of the complex argument z + * into the complex result w. + * + * If + * z = x + iy, + * r = exp(x), + * + * then + * + * w = r cos y + i r sin y. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 8700 3.7e-17 1.1e-17 + * IEEE -10,+10 30000 3.0e-16 8.7e-17 + * + */ + +#include +#include + +long double complex +cexpl(long double complex z) +{ + long double complex w; + long double r; + + r = expl(creall(z)); + w = r * cosl(cimagl(z)) + (r * sinl(cimagl(z))) * I; + return (w); +} diff --git a/openlibm/src/s_cimag.c b/openlibm/src/s_cimag.c new file mode 100644 index 0000000..456ae99 --- /dev/null +++ b/openlibm/src/s_cimag.c @@ -0,0 +1,37 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_cimag.c,v 1.3 2009/03/14 18:24:15 das Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +cimag(double complex z) +{ + return (__imag__ z); +} diff --git a/openlibm/src/s_cimagf.c b/openlibm/src/s_cimagf.c new file mode 100644 index 0000000..8287412 --- /dev/null +++ b/openlibm/src/s_cimagf.c @@ -0,0 +1,37 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_cimagf.c,v 1.3 2009/03/14 18:24:15 das Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +cimagf(float complex z) +{ + return (__imag__ z); +} diff --git a/openlibm/src/s_cimagl.c b/openlibm/src/s_cimagl.c new file mode 100644 index 0000000..588c6a3 --- /dev/null +++ b/openlibm/src/s_cimagl.c @@ -0,0 +1,37 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_cimagl.c,v 1.3 2009/03/14 18:24:15 das Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double +cimagl(long double complex z) +{ + return (__imag__ z); +} diff --git a/openlibm/src/s_clog.c b/openlibm/src/s_clog.c new file mode 100644 index 0000000..6412df7 --- /dev/null +++ b/openlibm/src/s_clog.c @@ -0,0 +1,79 @@ +/* $OpenBSD: s_clog.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* clog.c + * + * Complex natural logarithm + * + * + * + * SYNOPSIS: + * + * double complex clog(); + * double complex z, w; + * + * w = clog (z); + * + * + * + * DESCRIPTION: + * + * Returns complex logarithm to the base e (2.718...) of + * the complex argument x. + * + * If z = x + iy, r = sqrt( x**2 + y**2 ), + * then + * w = log(r) + i arctan(y/x). + * + * The arctangent ranges from -PI to +PI. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 7000 8.5e-17 1.9e-17 + * IEEE -10,+10 30000 5.0e-15 1.1e-16 + * + * Larger relative error can be observed for z near 1 +i0. + * In IEEE arithmetic the peak absolute error is 5.2e-16, rms + * absolute error 1.0e-16. + */ + +#include +#include +#include + +#include "math_private.h" + +double complex +clog(double complex z) +{ + double complex w; + double p, rr; + + /*rr = sqrt( z->r * z->r + z->i * z->i );*/ + rr = cabs(z); + p = log(rr); + rr = atan2 (cimag (z), creal (z)); + w = p + rr * I; + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(clog, clogl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_clogf.c b/openlibm/src/s_clogf.c new file mode 100644 index 0000000..e157aae --- /dev/null +++ b/openlibm/src/s_clogf.c @@ -0,0 +1,72 @@ +/* $OpenBSD: s_clogf.c,v 1.2 2010/07/18 18:42:26 guenther Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* clogf.c + * + * Complex natural logarithm + * + * + * + * SYNOPSIS: + * + * void clogf(); + * cmplxf z, w; + * + * clogf( &z, &w ); + * + * + * + * DESCRIPTION: + * + * Returns complex logarithm to the base e (2.718...) of + * the complex argument x. + * + * If z = x + iy, r = sqrt( x**2 + y**2 ), + * then + * w = log(r) + i arctan(y/x). + * + * The arctangent ranges from -PI to +PI. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.9e-6 6.2e-8 + * + * Larger relative error can be observed for z near 1 +i0. + * In IEEE arithmetic the peak absolute error is 3.1e-7. + * + */ + +#include +#include + +float complex +clogf(float complex z) +{ + float complex w; + float p, rr, x, y; + + x = crealf(z); + y = cimagf(z); + rr = atan2f(y, x); + p = cabsf(z); + p = logf(p); + w = p + rr * I; + return (w); +} diff --git a/openlibm/src/s_clogl.c b/openlibm/src/s_clogl.c new file mode 100644 index 0000000..c337103 --- /dev/null +++ b/openlibm/src/s_clogl.c @@ -0,0 +1,73 @@ +/* $OpenBSD: s_clogl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* clogl.c + * + * Complex natural logarithm + * + * + * + * SYNOPSIS: + * + * long double complex clogl(); + * long double complex z, w; + * + * w = clogl( z ); + * + * + * + * DESCRIPTION: + * + * Returns complex logarithm to the base e (2.718...) of + * the complex argument x. + * + * If z = x + iy, r = sqrt( x**2 + y**2 ), + * then + * w = log(r) + i arctan(y/x). + * + * The arctangent ranges from -PI to +PI. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 7000 8.5e-17 1.9e-17 + * IEEE -10,+10 30000 5.0e-15 1.1e-16 + * + * Larger relative error can be observed for z near 1 +i0. + * In IEEE arithmetic the peak absolute error is 5.2e-16, rms + * absolute error 1.0e-16. + */ + +#include +#include + +long double complex +clogl(long double complex z) +{ + long double complex w; + long double p, rr; + + /*rr = sqrt(z->r * z->r + z->i * z->i);*/ + p = cabsl(z); + p = logl(p); + rr = atan2l(cimagl(z), creall(z)); + w = p + rr * I; + return (w); +} diff --git a/openlibm/src/s_conj.c b/openlibm/src/s_conj.c new file mode 100644 index 0000000..a7c0940 --- /dev/null +++ b/openlibm/src/s_conj.c @@ -0,0 +1,38 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_conj.c,v 1.2 2008/08/07 14:39:56 das Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT double complex +conj(double complex z) +{ + + return (CMPLX(creal(z), -cimag(z))); +} diff --git a/openlibm/src/s_conjf.c b/openlibm/src/s_conjf.c new file mode 100644 index 0000000..d2ff743 --- /dev/null +++ b/openlibm/src/s_conjf.c @@ -0,0 +1,38 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_conjf.c,v 1.2 2008/08/07 14:39:56 das Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT float complex +conjf(float complex z) +{ + + return (CMPLXF(crealf(z), -cimagf(z))); +} diff --git a/openlibm/src/s_conjl.c b/openlibm/src/s_conjl.c new file mode 100644 index 0000000..e4d7a01 --- /dev/null +++ b/openlibm/src/s_conjl.c @@ -0,0 +1,38 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_conjl.c,v 1.2 2008/08/07 14:39:56 das Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double complex +conjl(long double complex z) +{ + + return (CMPLXL(creall(z), -cimagl(z))); +} diff --git a/openlibm/src/s_copysign.c b/openlibm/src/s_copysign.c new file mode 100644 index 0000000..a52701f --- /dev/null +++ b/openlibm/src/s_copysign.c @@ -0,0 +1,34 @@ +/* @(#)s_copysign.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_copysign.c,v 1.10 2008/02/22 02:30:35 das Exp $"); + +/* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +copysign(double x, double y) +{ + u_int32_t hx,hy; + GET_HIGH_WORD(hx,x); + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000)); + return x; +} diff --git a/openlibm/src/s_copysignf.c b/openlibm/src/s_copysignf.c new file mode 100644 index 0000000..945b3fd --- /dev/null +++ b/openlibm/src/s_copysignf.c @@ -0,0 +1,37 @@ +/* s_copysignf.c -- float version of s_copysign.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_copysignf.c,v 1.10 2008/02/22 02:30:35 das Exp $"); + +/* + * copysignf(float x, float y) + * copysignf(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +copysignf(float x, float y) +{ + u_int32_t ix,iy; + GET_FLOAT_WORD(ix,x); + GET_FLOAT_WORD(iy,y); + SET_FLOAT_WORD(x,(ix&0x7fffffff)|(iy&0x80000000)); + return x; +} diff --git a/openlibm/src/s_copysignl.c b/openlibm/src/s_copysignl.c new file mode 100644 index 0000000..6cae5d3 --- /dev/null +++ b/openlibm/src/s_copysignl.c @@ -0,0 +1,43 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_copysignl.c,v 1.2 2007/01/07 07:54:21 das Exp $ + */ + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT long double +copysignl(long double x, long double y) +{ + union IEEEl2bits ux, uy; + + ux.e = x; + uy.e = y; + ux.bits.sign = uy.bits.sign; + return (ux.e); +} diff --git a/openlibm/src/s_cos.c b/openlibm/src/s_cos.c new file mode 100644 index 0000000..9896bd8 --- /dev/null +++ b/openlibm/src/s_cos.c @@ -0,0 +1,89 @@ +/* @(#)s_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cos.c,v 1.13 2011/02/10 07:37:50 das Exp $"); + +/* cos(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include +#include + +//#define INLINE_REM_PIO2 +#include "math_private.h" +//#include "e_rem_pio2.c" + +OLM_DLLEXPORT double +cos(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) { + if(ix<0x3e46a09e) /* if x < 2**-27 * sqrt(2) */ + if(((int)x)==0) return 1.0; /* generate inexact */ + return __kernel_cos(x,z); + } + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_cos(y[0],y[1]); + case 1: return -__kernel_sin(y[0],y[1],1); + case 2: return -__kernel_cos(y[0],y[1]); + default: + return __kernel_sin(y[0],y[1],1); + } + } +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(cos, cosl); +#endif diff --git a/openlibm/src/s_cosf.c b/openlibm/src/s_cosf.c new file mode 100644 index 0000000..57ec7c7 --- /dev/null +++ b/openlibm/src/s_cosf.c @@ -0,0 +1,85 @@ +/* s_cosf.c -- float version of s_cos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cosf.c,v 1.18 2008/02/25 22:19:17 bde Exp $"); + +#include +#include + +//#define INLINE_KERNEL_COSDF +//#define INLINE_KERNEL_SINDF +//#define INLINE_REM_PIO2F +#include "math_private.h" +//#include "e_rem_pio2f.c" +//#include "k_cosf.c" +//#include "k_sinf.c" + +/* Small multiples of pi/2 rounded to double precision. */ +static const double +c1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ +c2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ +c3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ +c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ + +OLM_DLLEXPORT float +cosf(float x) +{ + double y; + int32_t n, hx, ix; + + GET_FLOAT_WORD(hx,x); + ix = hx & 0x7fffffff; + + if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ + if(ix<0x39800000) /* |x| < 2**-12 */ + if(((int)x)==0) return 1.0; /* 1 with inexact if x != 0 */ + return __kernel_cosdf(x); + } + if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */ + if(ix<=0x4016cbe3) { /* |x| ~> 3*pi/4 */ + if(hx>0) + return __kernel_sindf(c1pio2 - x); + else + return __kernel_sindf(x + c1pio2); + } else + return -__kernel_cosdf(x + (hx > 0 ? -c2pio2 : c2pio2)); + } + if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4 */ + if(ix<=0x40afeddf) { /* |x| ~> 7*pi/4 */ + if(hx>0) + return __kernel_sindf(x - c3pio2); + else + return __kernel_sindf(-c3pio2 - x); + } else + return __kernel_cosdf(x + (hx > 0 ? -c4pio2 : c4pio2)); + } + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* general argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,&y); + switch(n&3) { + case 0: return __kernel_cosdf(y); + case 1: return __kernel_sindf(-y); + case 2: return -__kernel_cosdf(y); + default: + return __kernel_sindf(y); + } + } +} diff --git a/openlibm/src/s_cosl.c b/openlibm/src/s_cosl.c new file mode 100644 index 0000000..886d3e3 --- /dev/null +++ b/openlibm/src/s_cosl.c @@ -0,0 +1,90 @@ +/*- + * Copyright (c) 2007 Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cosl.c,v 1.3 2011/05/30 19:41:28 kargl Exp $"); + +/* + * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows + * an accuracy of <= 0.7412 ULP. + */ + +#include +#include + +#include "math_private.h" +#if LDBL_MANT_DIG == 64 +#include "../ld80/e_rem_pio2l.h" +#elif LDBL_MANT_DIG == 113 +#include "../ld128/e_rem_pio2l.h" +#else +#error "Unsupported long double format" +#endif + +OLM_DLLEXPORT long double +cosl(long double x) +{ + union IEEEl2bits z; + int e0; + long double y[2]; + long double hi, lo; + + z.e = x; + z.bits.sign = 0; + + /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */ + if (z.bits.exp == 0) + return (1.0); + + /* If x = NaN or Inf, then cos(x) = NaN. */ + if (z.bits.exp == 32767) + return ((x - x) / (x - x)); + + /* Optimize the case where x is already within range. */ + if (z.e < M_PI_4) + return (__kernel_cosl(z.e, 0)); + + e0 = __ieee754_rem_pio2l(x, y); + hi = y[0]; + lo = y[1]; + + switch (e0 & 3) { + case 0: + hi = __kernel_cosl(hi, lo); + break; + case 1: + hi = - __kernel_sinl(hi, lo, 1); + break; + case 2: + hi = - __kernel_cosl(hi, lo); + break; + case 3: + hi = __kernel_sinl(hi, lo, 1); + break; + } + + return (hi); +} diff --git a/openlibm/src/s_cpow.c b/openlibm/src/s_cpow.c new file mode 100644 index 0000000..dae6251 --- /dev/null +++ b/openlibm/src/s_cpow.c @@ -0,0 +1,78 @@ +/* $OpenBSD: s_cpow.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cpow + * + * Complex power function + * + * + * + * SYNOPSIS: + * + * double complex cpow(); + * double complex a, z, w; + * + * w = cpow (a, z); + * + * + * + * DESCRIPTION: + * + * Raises complex A to the complex Zth power. + * Definition is per AMS55 # 4.2.8, + * analytically equivalent to cpow(a,z) = cexp(z clog(a)). + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 9.4e-15 1.5e-15 + * + */ + +#include +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT double complex +cpow(double complex a, double complex z) +{ + double complex w; + double x, y, r, theta, absa, arga; + + x = creal (z); + y = cimag (z); + absa = cabs (a); + if (absa == 0.0) { + return (0.0 + 0.0 * I); + } + arga = carg (a); + r = pow (absa, x); + theta = x * arga; + if (y != 0.0) { + r = r * exp (-y * arga); + theta = theta + y * log (absa); + } + w = r * cos (theta) + (r * sin (theta)) * I; + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(cpow, cpowl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_cpowf.c b/openlibm/src/s_cpowf.c new file mode 100644 index 0000000..764053d --- /dev/null +++ b/openlibm/src/s_cpowf.c @@ -0,0 +1,73 @@ +/* $OpenBSD: s_cpowf.c,v 1.2 2010/07/18 18:42:26 guenther Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cpowf + * + * Complex power function + * + * + * + * SYNOPSIS: + * + * float complex cpowf(); + * float complex a, z, w; + * + * w = cpowf (a, z); + * + * + * + * DESCRIPTION: + * + * Raises complex A to the complex Zth power. + * Definition is per AMS55 # 4.2.8, + * analytically equivalent to cpow(a,z) = cexp(z clog(a)). + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 9.4e-15 1.5e-15 + * + */ + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT float complex +cpowf(float complex a, float complex z) +{ + float complex w; + float x, y, r, theta, absa, arga; + + x = crealf(z); + y = cimagf(z); + absa = cabsf (a); + if (absa == 0.0f) { + return (0.0f + 0.0f * I); + } + arga = cargf (a); + r = powf (absa, x); + theta = x * arga; + if (y != 0.0f) { + r = r * expf (-y * arga); + theta = theta + y * logf (absa); + } + w = r * cosf (theta) + (r * sinf (theta)) * I; + return (w); +} diff --git a/openlibm/src/s_cpowl.c b/openlibm/src/s_cpowl.c new file mode 100644 index 0000000..81c9afd --- /dev/null +++ b/openlibm/src/s_cpowl.c @@ -0,0 +1,74 @@ +/* $OpenBSD: s_cpowl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* cpowl + * + * Complex power function + * + * + * + * SYNOPSIS: + * + * long double complex cpowl(); + * long double complex a, z, w; + * + * w = cpowl (a, z); + * + * + * + * DESCRIPTION: + * + * Raises complex A to the complex Zth power. + * Definition is per AMS55 # 4.2.8, + * analytically equivalent to cpow(a,z) = cexp(z clog(a)). + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 9.4e-15 1.5e-15 + * + */ + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double complex +cpowl(long double complex a, long double complex z) +{ + long double complex w; + long double x, y, r, theta, absa, arga; + + x = creall(z); + y = cimagl(z); + absa = cabsl(a); + if (absa == 0.0L) { + return (0.0L + 0.0L * I); + } + arga = cargl(a); + r = powl(absa, x); + theta = x * arga; + if (y != 0.0L) { + r = r * expl(-y * arga); + theta = theta + y * logl(absa); + } + w = r * cosl(theta) + (r * sinl(theta)) * I; + return (w); +} diff --git a/openlibm/src/s_cproj.c b/openlibm/src/s_cproj.c new file mode 100644 index 0000000..b9faa24 --- /dev/null +++ b/openlibm/src/s_cproj.c @@ -0,0 +1,47 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cproj.c,v 1.1 2008/08/07 15:07:48 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT double complex +cproj(double complex z) +{ + + if (!isinf(creal(z)) && !isinf(cimag(z))) + return (z); + else + return (CMPLX(INFINITY, copysign(0.0, cimag(z)))); +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(cproj, cprojl); +#endif diff --git a/openlibm/src/s_cprojf.c b/openlibm/src/s_cprojf.c new file mode 100644 index 0000000..717c165 --- /dev/null +++ b/openlibm/src/s_cprojf.c @@ -0,0 +1,43 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cprojf.c,v 1.1 2008/08/07 15:07:48 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT float complex +cprojf(float complex z) +{ + + if (!isinf(crealf(z)) && !isinf(cimagf(z))) + return (z); + else + return (CMPLXF(INFINITY, copysignf(0.0, cimagf(z)))); +} diff --git a/openlibm/src/s_cprojl.c b/openlibm/src/s_cprojl.c new file mode 100644 index 0000000..753ab4c --- /dev/null +++ b/openlibm/src/s_cprojl.c @@ -0,0 +1,43 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_cprojl.c,v 1.1 2008/08/07 15:07:48 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double complex +cprojl(long double complex z) +{ + + if (!isinf(creall(z)) && !isinf(cimagl(z))) + return (z); + else + return (CMPLXL(INFINITY, copysignl(0.0, cimagl(z)))); +} diff --git a/openlibm/src/s_creal.c b/openlibm/src/s_creal.c new file mode 100644 index 0000000..28a0fbf --- /dev/null +++ b/openlibm/src/s_creal.c @@ -0,0 +1,37 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_creal.c,v 1.1 2004/05/30 09:21:56 stefanf Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +creal(double complex z) +{ + return z; +} diff --git a/openlibm/src/s_crealf.c b/openlibm/src/s_crealf.c new file mode 100644 index 0000000..9aaed5f --- /dev/null +++ b/openlibm/src/s_crealf.c @@ -0,0 +1,37 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_crealf.c,v 1.1 2004/05/30 09:21:56 stefanf Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +crealf(float complex z) +{ + return z; +} diff --git a/openlibm/src/s_creall.c b/openlibm/src/s_creall.c new file mode 100644 index 0000000..576666e --- /dev/null +++ b/openlibm/src/s_creall.c @@ -0,0 +1,37 @@ +/*- + * Copyright (c) 2004 Stefan Farfeleder + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_creall.c,v 1.1 2004/05/30 09:21:56 stefanf Exp $ + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double +creall(long double complex z) +{ + return z; +} diff --git a/openlibm/src/s_csin.c b/openlibm/src/s_csin.c new file mode 100644 index 0000000..a905991 --- /dev/null +++ b/openlibm/src/s_csin.c @@ -0,0 +1,93 @@ +/* $OpenBSD: s_csin.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* csin() + * + * Complex circular sine + * + * + * + * SYNOPSIS: + * + * double complex csin(); + * double complex z, w; + * + * w = csin (z); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * + * w = sin x cosh y + i cos x sinh y. + * + * csin(z) = -i csinh(iz). + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 8400 5.3e-17 1.3e-17 + * IEEE -10,+10 30000 3.8e-16 1.0e-16 + * Also tested by csin(casin(z)) = z. + * + */ + +#include +#include +#include + +#include "math_private.h" + +/* calculate cosh and sinh */ + +static void +cchsh(double x, double *c, double *s) +{ + double e, ei; + + if (fabs(x) <= 0.5) { + *c = cosh(x); + *s = sinh(x); + } + else { + e = exp(x); + ei = 0.5/e; + e = 0.5 * e; + *s = e - ei; + *c = e + ei; + } +} + +double complex +csin(double complex z) +{ + double complex w; + double ch, sh; + + cchsh( cimag (z), &ch, &sh ); + w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I; + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(csin, csinl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_csinf.c b/openlibm/src/s_csinf.c new file mode 100644 index 0000000..42aa981 --- /dev/null +++ b/openlibm/src/s_csinf.c @@ -0,0 +1,85 @@ +/* $OpenBSD: s_csinf.c,v 1.2 2010/07/18 18:42:26 guenther Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* csinf() + * + * Complex circular sine + * + * + * + * SYNOPSIS: + * + * void csinf(); + * cmplxf z, w; + * + * csinf( &z, &w ); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * + * w = sin x cosh y + i cos x sinh y. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.9e-7 5.5e-8 + * + */ + +#include +#include + +/* calculate cosh and sinh */ + +static void +cchshf(float xx, float *c, float *s) +{ + float x, e, ei; + + x = xx; + if(fabsf(x) <= 0.5f) { + *c = coshf(x); + *s = sinhf(x); + } + else { + e = expf(x); + ei = 0.5f/e; + e = 0.5f * e; + *s = e - ei; + *c = e + ei; + } +} + +float complex +csinf(float complex z) +{ + float complex w; + float ch, sh; + + cchshf(cimagf(z), &ch, &sh); + w = sinf(crealf(z)) * ch + (cosf(crealf(z)) * sh) * I; + return (w); +} diff --git a/openlibm/src/s_csinh.c b/openlibm/src/s_csinh.c new file mode 100644 index 0000000..3838f25 --- /dev/null +++ b/openlibm/src/s_csinh.c @@ -0,0 +1,157 @@ +/*- + * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/* + * Hyperbolic sine of a complex argument z = x + i y. + * + * sinh(z) = sinh(x+iy) + * = sinh(x) cos(y) + i cosh(x) sin(y). + * + * Exceptional values are noted in the comments within the source code. + * These values and the return value were taken from n1124.pdf. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_csinh.c,v 1.2 2011/10/21 06:29:32 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const double huge = 0x1p1023; + +OLM_DLLEXPORT double complex +csinh(double complex z) +{ + double x, y, h; + int32_t hx, hy, ix, iy, lx, ly; + + x = creal(z); + y = cimag(z); + + EXTRACT_WORDS(hx, lx, x); + EXTRACT_WORDS(hy, ly, y); + + ix = 0x7fffffff & hx; + iy = 0x7fffffff & hy; + + /* Handle the nearly-non-exceptional cases where x and y are finite. */ + if (ix < 0x7ff00000 && iy < 0x7ff00000) { + if ((iy | ly) == 0) + return (CMPLX(sinh(x), y)); + if (ix < 0x40360000) /* small x: normal case */ + return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y))); + + /* |x| >= 22, so cosh(x) ~= exp(|x|) */ + if (ix < 0x40862e42) { + /* x < 710: exp(|x|) won't overflow */ + h = exp(fabs(x)) * 0.5; + return (CMPLX(copysign(h, x) * cos(y), h * sin(y))); + } else if (ix < 0x4096bbaa) { + /* x < 1455: scale to avoid overflow */ + z = __ldexp_cexp(CMPLX(fabs(x), y), -1); + return (CMPLX(creal(z) * copysign(1, x), cimag(z))); + } else { + /* x >= 1455: the result always overflows */ + h = huge * x; + return (CMPLX(h * cos(y), h * h * sin(y))); + } + } + + /* + * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. + * The sign of 0 in the result is unspecified. Choice = normally + * the same as dNaN. Raise the invalid floating-point exception. + * + * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). + * The sign of 0 in the result is unspecified. Choice = normally + * the same as d(NaN). + */ + if ((ix | lx) == 0 && iy >= 0x7ff00000) + return (CMPLX(copysign(0, x * (y - y)), y - y)); + + /* + * sinh(+-Inf +- I 0) = +-Inf + I +-0. + * + * sinh(NaN +- I 0) = d(NaN) + I +-0. + */ + if ((iy | ly) == 0 && ix >= 0x7ff00000) { + if (((hx & 0xfffff) | lx) == 0) + return (CMPLX(x, y)); + return (CMPLX(x, copysign(0, y))); + } + + /* + * sinh(x +- I Inf) = dNaN + I dNaN. + * Raise the invalid floating-point exception for finite nonzero x. + * + * sinh(x + I NaN) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero x. Choice = don't raise (except for signaling NaNs). + */ + if (ix < 0x7ff00000 && iy >= 0x7ff00000) + return (CMPLX(y - y, x * (y - y))); + + /* + * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). + * The sign of Inf in the result is unspecified. Choice = normally + * the same as d(NaN). + * + * sinh(+-Inf +- I Inf) = +Inf + I dNaN. + * The sign of Inf in the result is unspecified. Choice = always +. + * Raise the invalid floating-point exception. + * + * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) + */ + if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { + if (iy >= 0x7ff00000) + return (CMPLX(x * x, x * (y - y))); + return (CMPLX(x * cos(y), INFINITY * sin(y))); + } + + /* + * sinh(NaN + I NaN) = d(NaN) + I d(NaN). + * + * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception. + * Choice = raise. + * + * sinh(NaN + I y) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero y. Choice = don't raise (except for signaling NaNs). + */ + return (CMPLX((x * x) * (y - y), (x + x) * (y - y))); +} + +OLM_DLLEXPORT double complex +csin(double complex z) +{ + + /* csin(z) = -I * csinh(I * z) */ + z = csinh(CMPLX(-cimag(z), creal(z))); + return (CMPLX(cimag(z), -creal(z))); +} diff --git a/openlibm/src/s_csinhf.c b/openlibm/src/s_csinhf.c new file mode 100644 index 0000000..94954b0 --- /dev/null +++ b/openlibm/src/s_csinhf.c @@ -0,0 +1,105 @@ +/*- + * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/* + * Hyperbolic sine of a complex argument z. See s_csinh.c for details. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_csinhf.c,v 1.2 2011/10/21 06:29:32 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const float huge = 0x1p127; + +OLM_DLLEXPORT float complex +csinhf(float complex z) +{ + float x, y, h; + int32_t hx, hy, ix, iy; + + x = crealf(z); + y = cimagf(z); + + GET_FLOAT_WORD(hx, x); + GET_FLOAT_WORD(hy, y); + + ix = 0x7fffffff & hx; + iy = 0x7fffffff & hy; + + if (ix < 0x7f800000 && iy < 0x7f800000) { + if (iy == 0) + return (CMPLXF(sinhf(x), y)); + if (ix < 0x41100000) /* small x: normal case */ + return (CMPLXF(sinhf(x) * cosf(y), coshf(x) * sinf(y))); + + /* |x| >= 9, so cosh(x) ~= exp(|x|) */ + if (ix < 0x42b17218) { + /* x < 88.7: expf(|x|) won't overflow */ + h = expf(fabsf(x)) * 0.5f; + return (CMPLXF(copysignf(h, x) * cosf(y), h * sinf(y))); + } else if (ix < 0x4340b1e7) { + /* x < 192.7: scale to avoid overflow */ + z = __ldexp_cexpf(CMPLXF(fabsf(x), y), -1); + return (CMPLXF(crealf(z) * copysignf(1, x), cimagf(z))); + } else { + /* x >= 192.7: the result always overflows */ + h = huge * x; + return (CMPLXF(h * cosf(y), h * h * sinf(y))); + } + } + + if (ix == 0 && iy >= 0x7f800000) + return (CMPLXF(copysignf(0, x * (y - y)), y - y)); + + if (iy == 0 && ix >= 0x7f800000) { + if ((hx & 0x7fffff) == 0) + return (CMPLXF(x, y)); + return (CMPLXF(x, copysignf(0, y))); + } + + if (ix < 0x7f800000 && iy >= 0x7f800000) + return (CMPLXF(y - y, x * (y - y))); + + if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) { + if (iy >= 0x7f800000) + return (CMPLXF(x * x, x * (y - y))); + return (CMPLXF(x * cosf(y), INFINITY * sinf(y))); + } + + return (CMPLXF((x * x) * (y - y), (x + x) * (y - y))); +} + +OLM_DLLEXPORT float complex +csinf(float complex z) +{ + + z = csinhf(CMPLXF(-cimagf(z), crealf(z))); + return (CMPLXF(cimagf(z), -crealf(z))); +} diff --git a/openlibm/src/s_csinhl.c b/openlibm/src/s_csinhl.c new file mode 100644 index 0000000..57b577f --- /dev/null +++ b/openlibm/src/s_csinhl.c @@ -0,0 +1,58 @@ +/* $OpenBSD: s_csinhl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* csinhl + * + * Complex hyperbolic sine + * + * + * + * SYNOPSIS: + * + * long double complex csinhl(); + * long double complex z, w; + * + * w = csinhl (z); + * + * DESCRIPTION: + * + * csinh z = (cexp(z) - cexp(-z))/2 + * = sinh x * cos y + i cosh x * sin y . + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 3.1e-16 8.2e-17 + * + */ + +#include +#include + +long double complex +csinhl(long double complex z) +{ + long double complex w; + long double x, y; + + x = creall(z); + y = cimagl(z); + w = sinhl(x) * cosl(y) + (coshl(x) * sinl(y)) * I; + return (w); +} diff --git a/openlibm/src/s_csinl.c b/openlibm/src/s_csinl.c new file mode 100644 index 0000000..3470ac5 --- /dev/null +++ b/openlibm/src/s_csinl.c @@ -0,0 +1,84 @@ +/* $OpenBSD: s_csinl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* csinl() + * + * Complex circular sine + * + * + * + * SYNOPSIS: + * + * long double complex csinl(); + * long double complex z, w; + * + * w = csinl( z ); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * + * w = sin x cosh y + i cos x sinh y. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 8400 5.3e-17 1.3e-17 + * IEEE -10,+10 30000 3.8e-16 1.0e-16 + * Also tested by csin(casin(z)) = z. + * + */ + +#include +#include + +static void +cchshl(long double x, long double *c, long double *s) +{ + long double e, ei; + + if(fabsl(x) <= 0.5L) { + *c = coshl(x); + *s = sinhl(x); + } else { + e = expl(x); + ei = 0.5L/e; + e = 0.5L * e; + *s = e - ei; + *c = e + ei; + } +} + +long double complex +csinl(long double complex z) +{ + long double complex w; + long double ch, sh; + + cchshl(cimagl(z), &ch, &sh); + w = sinl(creall(z)) * ch + (cosl(creall(z)) * sh) * I; + return (w); +} diff --git a/openlibm/src/s_csqrt.c b/openlibm/src/s_csqrt.c new file mode 100644 index 0000000..9cf4255 --- /dev/null +++ b/openlibm/src/s_csqrt.c @@ -0,0 +1,114 @@ +/*- + * Copyright (c) 2007 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_csqrt.c,v 1.4 2008/08/08 00:15:16 das Exp $"); + +#include +#include +#include + +#include "math_private.h" + +/* + * gcc doesn't implement complex multiplication or division correctly, + * so we need to handle infinities specially. We turn on this pragma to + * notify conforming c99 compilers that the fast-but-incorrect code that + * gcc generates is acceptable, since the special cases have already been + * handled. + */ +#ifndef __GNUC__ +#pragma STDC CX_LIMITED_RANGE ON +#endif + +/* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */ +#define THRESH 0x1.a827999fcef32p+1022 + +OLM_DLLEXPORT double complex +csqrt(double complex z) +{ + double complex result; + double a, b; + double t; + int scale; + + a = creal(z); + b = cimag(z); + + /* Handle special cases. */ + if (z == 0) + return (CMPLX(0, b)); + if (isinf(b)) + return (CMPLX(INFINITY, b)); + if (isnan(a)) { + t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ + return (CMPLX(a, t)); /* return NaN + NaN i */ + } + if (isinf(a)) { + /* + * csqrt(inf + NaN i) = inf + NaN i + * csqrt(inf + y i) = inf + 0 i + * csqrt(-inf + NaN i) = NaN +- inf i + * csqrt(-inf + y i) = 0 + inf i + */ + if (signbit(a)) + return (CMPLX(fabs(b - b), copysign(a, b))); + else + return (CMPLX(a, copysign(b - b, b))); + } + /* + * The remaining special case (b is NaN) is handled just fine by + * the normal code path below. + */ + + /* Scale to avoid overflow. */ + if (fabs(a) >= THRESH || fabs(b) >= THRESH) { + a *= 0.25; + b *= 0.25; + scale = 1; + } else { + scale = 0; + } + + /* Algorithm 312, CACM vol 10, Oct 1967. */ + if (a >= 0) { + t = sqrt((a + hypot(a, b)) * 0.5); + result = CMPLX(t, b / (2 * t)); + } else { + t = sqrt((-a + hypot(a, b)) * 0.5); + result = CMPLX(fabs(b) / (2 * t), copysign(t, b)); + } + + /* Rescale. */ + if (scale) + return (result * 2); + else + return (result); +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(csqrt, csqrtl); +#endif diff --git a/openlibm/src/s_csqrtf.c b/openlibm/src/s_csqrtf.c new file mode 100644 index 0000000..a131829 --- /dev/null +++ b/openlibm/src/s_csqrtf.c @@ -0,0 +1,90 @@ +/*- + * Copyright (c) 2007 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_csqrtf.c,v 1.3 2008/08/08 00:15:16 das Exp $"); + +#include +#include + +#include "math_private.h" + +/* + * gcc doesn't implement complex multiplication or division correctly, + * so we need to handle infinities specially. We turn on this pragma to + * notify conforming c99 compilers that the fast-but-incorrect code that + * gcc generates is acceptable, since the special cases have already been + * handled. + */ +#ifndef __GNUC__ +#pragma STDC CX_LIMITED_RANGE ON +#endif + +OLM_DLLEXPORT float complex +csqrtf(float complex z) +{ + float a = crealf(z), b = cimagf(z); + double t; + + /* Handle special cases. */ + if (z == 0) + return (CMPLXF(0, b)); + if (isinf(b)) + return (CMPLXF(INFINITY, b)); + if (isnan(a)) { + t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ + return (CMPLXF(a, t)); /* return NaN + NaN i */ + } + if (isinf(a)) { + /* + * csqrtf(inf + NaN i) = inf + NaN i + * csqrtf(inf + y i) = inf + 0 i + * csqrtf(-inf + NaN i) = NaN +- inf i + * csqrtf(-inf + y i) = 0 + inf i + */ + if (signbit(a)) + return (CMPLXF(fabsf(b - b), copysignf(a, b))); + else + return (CMPLXF(a, copysignf(b - b, b))); + } + /* + * The remaining special case (b is NaN) is handled just fine by + * the normal code path below. + */ + + /* + * We compute t in double precision to avoid overflow and to + * provide correct rounding in nearly all cases. + * This is Algorithm 312, CACM vol 10, Oct 1967. + */ + if (a >= 0) { + t = sqrt((a + hypot(a, b)) * 0.5); + return (CMPLXF(t, b / (2.0 * t))); + } else { + t = sqrt((-a + hypot(a, b)) * 0.5); + return (CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b))); + } +} diff --git a/openlibm/src/s_csqrtl.c b/openlibm/src/s_csqrtl.c new file mode 100644 index 0000000..da97fb2 --- /dev/null +++ b/openlibm/src/s_csqrtl.c @@ -0,0 +1,109 @@ +/*- + * Copyright (c) 2007-2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" + +#include +#include +#include + +#include "math_private.h" + +/* + * gcc doesn't implement complex multiplication or division correctly, + * so we need to handle infinities specially. We turn on this pragma to + * notify conforming c99 compilers that the fast-but-incorrect code that + * gcc generates is acceptable, since the special cases have already been + * handled. + */ +#ifndef __GNUC__ +#pragma STDC CX_LIMITED_RANGE ON +#endif + +/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */ +#define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L) + +OLM_DLLEXPORT long double complex +csqrtl(long double complex z) +{ + long double complex result; + long double a, b; + long double t; + int scale; + + a = creall(z); + b = cimagl(z); + + /* Handle special cases. */ + if (z == 0) + return (CMPLXL(0, b)); + if (isinf(b)) + return (CMPLXL(INFINITY, b)); + if (isnan(a)) { + t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ + return (CMPLXL(a, t)); /* return NaN + NaN i */ + } + if (isinf(a)) { + /* + * csqrt(inf + NaN i) = inf + NaN i + * csqrt(inf + y i) = inf + 0 i + * csqrt(-inf + NaN i) = NaN +- inf i + * csqrt(-inf + y i) = 0 + inf i + */ + if (signbit(a)) + return (CMPLXL(fabsl(b - b), copysignl(a, b))); + else + return (CMPLXL(a, copysignl(b - b, b))); + } + /* + * The remaining special case (b is NaN) is handled just fine by + * the normal code path below. + */ + + /* Scale to avoid overflow. */ + if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { + a *= 0.25; + b *= 0.25; + scale = 1; + } else { + scale = 0; + } + + /* Algorithm 312, CACM vol 10, Oct 1967. */ + if (a >= 0) { + t = sqrtl((a + hypotl(a, b)) * 0.5); + result = CMPLXL(t, b / (2 * t)); + } else { + t = sqrtl((-a + hypotl(a, b)) * 0.5); + result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b)); + } + + /* Rescale. */ + if (scale) + return (result * 2); + else + return (result); +} diff --git a/openlibm/src/s_ctan.c b/openlibm/src/s_ctan.c new file mode 100644 index 0000000..9420095 --- /dev/null +++ b/openlibm/src/s_ctan.c @@ -0,0 +1,159 @@ +/* $OpenBSD: s_ctan.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* ctan() + * + * Complex circular tangent + * + * + * + * SYNOPSIS: + * + * double complex ctan(); + * double complex z, w; + * + * w = ctan (z); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * + * sin 2x + i sinh 2y + * w = --------------------. + * cos 2x + cosh 2y + * + * On the real axis the denominator is zero at odd multiples + * of PI/2. The denominator is evaluated by its Taylor + * series near these points. + * + * ctan(z) = -i ctanh(iz). + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 5200 7.1e-17 1.6e-17 + * IEEE -10,+10 30000 7.2e-16 1.2e-16 + * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z. + */ + +#include +#include +#include + +#include "math_private.h" + +#define MACHEP 1.1e-16 +#define MAXNUM 1.0e308 + +static const double DP1 = 3.14159265160560607910E0; +static const double DP2 = 1.98418714791870343106E-9; +static const double DP3 = 1.14423774522196636802E-17; + +static double +_redupi(double x) +{ + double t; + long i; + + t = x/M_PI; + if (t >= 0.0) + t += 0.5; + else + t -= 0.5; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return (t); +} + +/* Taylor series expansion for cosh(2y) - cos(2x) */ + +static double +_ctans(double complex z) +{ + double f, x, x2, y, y2, rn, t; + double d; + + x = fabs (2.0 * creal (z)); + y = fabs (2.0 * cimag(z)); + + x = _redupi(x); + + x = x * x; + y = y * y; + x2 = 1.0; + y2 = 1.0; + f = 1.0; + rn = 0.0; + d = 0.0; + do { + rn += 1.0; + f *= rn; + rn += 1.0; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 + x2; + t /= f; + d += t; + + rn += 1.0; + f *= rn; + rn += 1.0; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 - x2; + t /= f; + d += t; + } + while (fabs(t/d) > MACHEP) + ; + return (d); +} + +double complex +ctan(double complex z) +{ + double complex w; + double d; + + d = cos (2.0 * creal (z)) + cosh (2.0 * cimag (z)); + + if (fabs(d) < 0.25) + d = _ctans (z); + + if (d == 0.0) { + /*mtherr ("ctan", OVERFLOW);*/ + w = MAXNUM + MAXNUM * I; + return (w); + } + + w = sin (2.0 * creal(z)) / d + (sinh (2.0 * cimag(z)) / d) * I; + return (w); +} + +#if LDBL_MANT_DIG == DBL_MANT_DIG +openlibm_strong_reference(ctan, ctanl); +#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ diff --git a/openlibm/src/s_ctanf.c b/openlibm/src/s_ctanf.c new file mode 100644 index 0000000..3bb3742 --- /dev/null +++ b/openlibm/src/s_ctanf.c @@ -0,0 +1,148 @@ +/* $OpenBSD: s_ctanf.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* ctanf() + * + * Complex circular tangent + * + * + * + * SYNOPSIS: + * + * void ctanf(); + * cmplxf z, w; + * + * ctanf( &z, &w ); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * + * sin 2x + i sinh 2y + * w = --------------------. + * cos 2x + cosh 2y + * + * On the real axis the denominator is zero at odd multiples + * of PI/2. The denominator is evaluated by its Taylor + * series near these points. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 3.3e-7 5.1e-8 + */ + +#include +#include + +#define MACHEPF 3.0e-8 +#define MAXNUMF 1.0e38f + +static const double DP1 = 3.140625; +static const double DP2 = 9.67502593994140625E-4; +static const double DP3 = 1.509957990978376432E-7; + +static float +_redupif(float xx) +{ + float x, t; + long i; + + x = xx; + t = x/(float)M_PI; + if(t >= 0.0) + t += 0.5; + else + t -= 0.5; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return(t); +} + +/* Taylor series expansion for cosh(2y) - cos(2x) */ + +static float +_ctansf(float complex z) +{ + float f, x, x2, y, y2, rn, t, d; + + x = fabsf(2.0f * crealf(z)); + y = fabsf(2.0f * cimagf(z)); + + x = _redupif(x); + + x = x * x; + y = y * y; + x2 = 1.0f; + y2 = 1.0f; + f = 1.0f; + rn = 0.0f; + d = 0.0f; + do { + rn += 1.0f; + f *= rn; + rn += 1.0f; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 + x2; + t /= f; + d += t; + + rn += 1.0f; + f *= rn; + rn += 1.0f; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 - x2; + t /= f; + d += t; + } + while (fabsf(t/d) > MACHEPF) + ; + return(d); +} + +float complex +ctanf(float complex z) +{ + float complex w; + float d; + + d = cosf( 2.0f * crealf(z) ) + coshf( 2.0f * cimagf(z) ); + + if(fabsf(d) < 0.25f) + d = _ctansf(z); + + if (d == 0.0f) { + /*mtherr( "ctanf", OVERFLOW );*/ + w = MAXNUMF + MAXNUMF * I; + return (w); + } + w = sinf (2.0f * crealf(z)) / d + (sinhf (2.0f * cimagf(z)) / d) * I; + return (w); +} diff --git a/openlibm/src/s_ctanh.c b/openlibm/src/s_ctanh.c new file mode 100644 index 0000000..8d452ee --- /dev/null +++ b/openlibm/src/s_ctanh.c @@ -0,0 +1,144 @@ +/*- + * Copyright (c) 2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/* + * Hyperbolic tangent of a complex argument z = x + i y. + * + * The algorithm is from: + * + * W. Kahan. Branch Cuts for Complex Elementary Functions or Much + * Ado About Nothing's Sign Bit. In The State of the Art in + * Numerical Analysis, pp. 165 ff. Iserles and Powell, eds., 1987. + * + * Method: + * + * Let t = tan(x) + * beta = 1/cos^2(y) + * s = sinh(x) + * rho = cosh(x) + * + * We have: + * + * tanh(z) = sinh(z) / cosh(z) + * + * sinh(x) cos(y) + i cosh(x) sin(y) + * = --------------------------------- + * cosh(x) cos(y) + i sinh(x) sin(y) + * + * cosh(x) sinh(x) / cos^2(y) + i tan(y) + * = ------------------------------------- + * 1 + sinh^2(x) / cos^2(y) + * + * beta rho s + i t + * = ---------------- + * 1 + beta s^2 + * + * Modifications: + * + * I omitted the original algorithm's handling of overflow in tan(x) after + * verifying with nearpi.c that this can't happen in IEEE single or double + * precision. I also handle large x differently. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_ctanh.c,v 1.2 2011/10/21 06:30:16 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT double complex +ctanh(double complex z) +{ + double x, y; + double t, beta, s, rho, denom; + u_int32_t hx, ix, lx; + + x = creal(z); + y = cimag(z); + + EXTRACT_WORDS(hx, lx, x); + ix = hx & 0x7fffffff; + + /* + * ctanh(NaN + i 0) = NaN + i 0 + * + * ctanh(NaN + i y) = NaN + i NaN for y != 0 + * + * The imaginary part has the sign of x*sin(2*y), but there's no + * special effort to get this right. + * + * ctanh(+-Inf +- i Inf) = +-1 +- 0 + * + * ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite + * + * The imaginary part of the sign is unspecified. This special + * case is only needed to avoid a spurious invalid exception when + * y is infinite. + */ + if (ix >= 0x7ff00000) { + if ((ix & 0xfffff) | lx) /* x is NaN */ + return (CMPLX(x, (y == 0 ? y : x * y))); + SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */ + return (CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y)))); + } + + /* + * ctanh(x + i NAN) = NaN + i NaN + * ctanh(x +- i Inf) = NaN + i NaN + */ + if (!isfinite(y)) + return (CMPLX(y - y, y - y)); + + /* + * ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the + * approximation sinh^2(huge) ~= exp(2*huge) / 4. + * We use a modified formula to avoid spurious overflow. + */ + if (ix >= 0x40360000) { /* x >= 22 */ + double exp_mx = exp(-fabs(x)); + return (CMPLX(copysign(1, x), + 4 * sin(y) * cos(y) * exp_mx * exp_mx)); + } + + /* Kahan's algorithm */ + t = tan(y); + beta = 1.0 + t * t; /* = 1 / cos^2(y) */ + s = sinh(x); + rho = sqrt(1 + s * s); /* = cosh(x) */ + denom = 1 + beta * s * s; + return (CMPLX((beta * rho * s) / denom, t / denom)); +} + +OLM_DLLEXPORT double complex +ctan(double complex z) +{ + + /* ctan(z) = -I * ctanh(I * z) */ + z = ctanh(CMPLX(-cimag(z), creal(z))); + return (CMPLX(cimag(z), -creal(z))); +} diff --git a/openlibm/src/s_ctanhf.c b/openlibm/src/s_ctanhf.c new file mode 100644 index 0000000..b2f8f19 --- /dev/null +++ b/openlibm/src/s_ctanhf.c @@ -0,0 +1,84 @@ +/*- + * Copyright (c) 2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/* + * Hyperbolic tangent of a complex argument z. See s_ctanh.c for details. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_ctanhf.c,v 1.2 2011/10/21 06:30:16 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT float complex +ctanhf(float complex z) +{ + float x, y; + float t, beta, s, rho, denom; + u_int32_t hx, ix; + + x = crealf(z); + y = cimagf(z); + + GET_FLOAT_WORD(hx, x); + ix = hx & 0x7fffffff; + + if (ix >= 0x7f800000) { + if (ix & 0x7fffff) + return (CMPLXF(x, (y == 0 ? y : x * y))); + SET_FLOAT_WORD(x, hx - 0x40000000); + return (CMPLXF(x, + copysignf(0, isinf(y) ? y : sinf(y) * cosf(y)))); + } + + if (!isfinite(y)) + return (CMPLXF(y - y, y - y)); + + if (ix >= 0x41300000) { /* x >= 11 */ + float exp_mx = expf(-fabsf(x)); + return (CMPLXF(copysignf(1, x), + 4 * sinf(y) * cosf(y) * exp_mx * exp_mx)); + } + + t = tanf(y); + beta = 1.0 + t * t; + s = sinhf(x); + rho = sqrtf(1 + s * s); + denom = 1 + beta * s * s; + return (CMPLXF((beta * rho * s) / denom, t / denom)); +} + +OLM_DLLEXPORT float complex +ctanf(float complex z) +{ + + z = ctanhf(CMPLXF(-cimagf(z), crealf(z))); + return (CMPLXF(cimagf(z), -crealf(z))); +} + diff --git a/openlibm/src/s_ctanhl.c b/openlibm/src/s_ctanhl.c new file mode 100644 index 0000000..6d996d4 --- /dev/null +++ b/openlibm/src/s_ctanhl.c @@ -0,0 +1,60 @@ +/* $OpenBSD: s_ctanhl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* ctanhl + * + * Complex hyperbolic tangent + * + * + * + * SYNOPSIS: + * + * long double complex ctanhl(); + * long double complex z, w; + * + * w = ctanhl (z); + * + * + * + * DESCRIPTION: + * + * tanh z = (sinh 2x + i sin 2y) / (cosh 2x + cos 2y) . + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 1.7e-14 2.4e-16 + * + */ + +#include +#include + +long double complex +ctanhl(long double complex z) +{ + long double complex w; + long double x, y, d; + + x = creall(z); + y = cimagl(z); + d = coshl(2.0L * x) + cosl(2.0L * y); + w = sinhl(2.0L * x) / d + (sinl(2.0L * y) / d) * I; + return (w); +} diff --git a/openlibm/src/s_ctanl.c b/openlibm/src/s_ctanl.c new file mode 100644 index 0000000..cf33ced --- /dev/null +++ b/openlibm/src/s_ctanl.c @@ -0,0 +1,157 @@ +/* $OpenBSD: s_ctanl.c,v 1.3 2011/07/20 21:02:51 martynas Exp $ */ + +/* + * Copyright (c) 2008 Stephen L. Moshier + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ + +/* ctanl() + * + * Complex circular tangent + * + * + * + * SYNOPSIS: + * + * long double complex ctanl(); + * long double complex z, w; + * + * w = ctanl( z ); + * + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * + * sin 2x + i sinh 2y + * w = --------------------. + * cos 2x + cosh 2y + * + * On the real axis the denominator is zero at odd multiples + * of PI/2. The denominator is evaluated by its Taylor + * series near these points. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 5200 7.1e-17 1.6e-17 + * IEEE -10,+10 30000 7.2e-16 1.2e-16 + * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z. + */ + +#include +#include +#include + +#if LDBL_MANT_DIG == 64 +static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L; +#elif LDBL_MANT_DIG == 113 +static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L; +#endif + +static const long double PIL = 3.141592653589793238462643383279502884197169L; +static const long double DP1 = 3.14159265358979323829596852490908531763125L; +static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; +static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; + +static long double +redupil(long double x) +{ + long double t; + long i; + + t = x / PIL; + if (t >= 0.0L) + t += 0.5L; + else + t -= 0.5L; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return (t); +} + +static long double +ctansl(long double complex z) +{ + long double f, x, x2, y, y2, rn, t; + long double d; + + x = fabsl(2.0L * creall(z)); + y = fabsl(2.0L * cimagl(z)); + + x = redupil(x); + + x = x * x; + y = y * y; + x2 = 1.0L; + y2 = 1.0L; + f = 1.0L; + rn = 0.0L; + d = 0.0L; + do { + rn += 1.0L; + f *= rn; + rn += 1.0L; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 + x2; + t /= f; + d += t; + + rn += 1.0L; + f *= rn; + rn += 1.0L; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 - x2; + t /= f; + d += t; + } + while (fabsl(t/d) > MACHEPL); + return(d); +} + +long double complex +ctanl(long double complex z) +{ + long double complex w; + long double d, x, y; + + x = creall(z); + y = cimagl(z); + d = cosl(2.0L * x) + coshl(2.0L * y); + + if (fabsl(d) < 0.25L) { + d = fabsl(d); + d = ctansl(z); + } + if (d == 0.0L) { + /*mtherr( "ctan", OVERFLOW );*/ + w = LDBL_MAX + LDBL_MAX * I; + return (w); + } + + w = sinl(2.0L * x) / d + (sinhl(2.0L * y) / d) * I; + return (w); +} diff --git a/openlibm/src/s_erf.c b/openlibm/src/s_erf.c new file mode 100644 index 0000000..67068c4 --- /dev/null +++ b/openlibm/src/s_erf.c @@ -0,0 +1,307 @@ +/* @(#)s_erf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_erf.c,v 1.8 2008/02/22 02:30:35 das Exp $"); + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * where R = P/Q where P is an odd poly of degree 8 and + * Q is an odd poly of degree 10. + * -57.90 + * | R - (erf(x)-x)/x | <= 2 + * + * + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * That is, we use rational approximation to approximate + * erf(1+s) - (c = (single)0.84506291151) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * where + * P1(s) = degree 6 poly in s + * Q1(s) = degree 6 poly in s + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) + * erf(x) = 1 - erfc(x) + * where + * R1(z) = degree 7 poly in z, (z=1/x^2) + * S1(z) = degree 8 poly in z + * + * 4. For x in [1/0.35,28] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6 x >= 28 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + +#include +#include + +#include "math_private.h" + +static const double +tiny = 1e-300, +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ + /* c = (float)0.84506291151 */ +erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ +efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ +pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ +pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ +pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ +pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ +pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ +qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ +qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ +qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ +qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ +qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ +pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ +pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ +pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ +pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ +pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ +pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ +qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ +qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ +qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ +qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ +qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ +qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ +ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ +ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ +ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ +ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ +ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ +ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ +ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ +sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ +sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ +sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ +sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ +sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ +sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ +sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ +sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ +rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ +rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ +rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ +rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ +rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ +rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ +sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ +sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ +sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ +sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ +sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ +sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ +sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ + +OLM_DLLEXPORT double +erf(double x) +{ + int32_t hx,ix,i; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3e300000) { /* |x|<2**-28 */ + if (ix < 0x00800000) + return 0.125*(8.0*x+efx8*x); /*avoid underflow */ + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40180000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} + +OLM_DLLEXPORT double +erfc(double x) +{ + int32_t hx,ix; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (double)(((u_int32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3c700000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3fd00000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x403c0000) { /* |x|<28 */ + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)* + __ieee754_exp((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(erf, erfl); +openlibm_weak_reference(erfc, erfcl); +#endif diff --git a/openlibm/src/s_erff.c b/openlibm/src/s_erff.c new file mode 100644 index 0000000..ed6030f --- /dev/null +++ b/openlibm/src/s_erff.c @@ -0,0 +1,184 @@ +/* s_erff.c -- float version of s_erf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_erff.c,v 1.8 2008/02/22 02:30:35 das Exp $"); + +#include + +#include "math_private.h" + +static const float +tiny = 1e-30, +half= 5.0000000000e-01, /* 0x3F000000 */ +one = 1.0000000000e+00, /* 0x3F800000 */ +two = 2.0000000000e+00, /* 0x40000000 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.2837916613e-01, /* 0x3e0375d4 */ +efx8= 1.0270333290e+00, /* 0x3f8375d4 */ +/* + * Domain [0, 0.84375], range ~[-5.4446e-10,5.5197e-10]: + * |(erf(x) - x)/x - p(x)/q(x)| < 2**-31. + */ +pp0 = 1.28379166e-01F, /* 0x1.06eba8p-3 */ +pp1 = -3.36030394e-01F, /* -0x1.58185ap-2 */ +pp2 = -1.86260219e-03F, /* -0x1.e8451ep-10 */ +qq1 = 3.12324286e-01F, /* 0x1.3fd1f0p-2 */ +qq2 = 2.16070302e-02F, /* 0x1.620274p-6 */ +qq3 = -1.98859419e-03F, /* -0x1.04a626p-9 */ +/* + * Domain [0.84375, 1.25], range ~[-1.953e-11,1.940e-11]: + * |(erf(x) - erx) - p(x)/q(x)| < 2**-36. + */ +erx = 8.42697144e-01F, /* 0x1.af7600p-1. erf(1) rounded to 16 bits. */ +pa0 = 3.64939137e-06F, /* 0x1.e9d022p-19 */ +pa1 = 4.15109694e-01F, /* 0x1.a91284p-2 */ +pa2 = -1.65179938e-01F, /* -0x1.5249dcp-3 */ +pa3 = 1.10914491e-01F, /* 0x1.c64e46p-4 */ +qa1 = 6.02074385e-01F, /* 0x1.344318p-1 */ +qa2 = 5.35934687e-01F, /* 0x1.126608p-1 */ +qa3 = 1.68576106e-01F, /* 0x1.593e6ep-3 */ +qa4 = 5.62181212e-02F, /* 0x1.cc89f2p-5 */ +/* + * Domain [1.25,1/0.35], range ~[-7.043e-10,7.457e-10]: + * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-30 + */ +ra0 = -9.87132732e-03F, /* -0x1.4376b2p-7 */ +ra1 = -5.53605914e-01F, /* -0x1.1b723cp-1 */ +ra2 = -2.17589188e+00F, /* -0x1.1683a0p+1 */ +ra3 = -1.43268085e+00F, /* -0x1.6ec42cp+0 */ +sa1 = 5.45995426e+00F, /* 0x1.5d6fe4p+2 */ +sa2 = 6.69798088e+00F, /* 0x1.acabb8p+2 */ +sa3 = 1.43113089e+00F, /* 0x1.6e5e98p+0 */ +sa4 = -5.77397496e-02F, /* -0x1.d90108p-5 */ +/* + * Domain [1/0.35, 11], range ~[-2.264e-13,2.336e-13]: + * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-42 + */ +rb0 = -9.86494310e-03F, /* -0x1.434124p-7 */ +rb1 = -6.25171244e-01F, /* -0x1.401672p-1 */ +rb2 = -6.16498327e+00F, /* -0x1.8a8f16p+2 */ +rb3 = -1.66696873e+01F, /* -0x1.0ab70ap+4 */ +rb4 = -9.53764343e+00F, /* -0x1.313460p+3 */ +sb1 = 1.26884899e+01F, /* 0x1.96081cp+3 */ +sb2 = 4.51839523e+01F, /* 0x1.6978bcp+5 */ +sb3 = 4.72810211e+01F, /* 0x1.7a3f88p+5 */ +sb4 = 8.93033314e+00F; /* 0x1.1dc54ap+3 */ + + +OLM_DLLEXPORT float +erff(float x) +{ + int32_t hx,ix,i; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x38800000) { /* |x|<2**-14 */ + if (ix < 0x04000000) /* |x|<0x1p-119 */ + return (8*x+efx8*x)/8; /* avoid spurious underflow */ + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*pp2); + s = one+z*(qq1+z*(qq2+z*qq3)); + y = r/s; + return x + x*y; + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*pa3)); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40800000) { /* inf>|x|>=4 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*ra3)); + S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4))); + } + SET_FLOAT_WORD(z,hx&0xffffe000); + r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} + +OLM_DLLEXPORT float +erfcf(float x) +{ + int32_t hx,ix; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (float)(((u_int32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x33800000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*pp2); + s = one+z*(qq1+z*(qq2+z*qq3)); + y = r/s; + if(hx < 0x3e800000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*pa3)); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x41300000) { /* |x|<28 */ + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*ra3)); + S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4))); + } + SET_FLOAT_WORD(z,hx&0xffffe000); + r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} diff --git a/openlibm/src/s_exp2.c b/openlibm/src/s_exp2.c new file mode 100644 index 0000000..d643dbb --- /dev/null +++ b/openlibm/src/s_exp2.c @@ -0,0 +1,396 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2.c,v 1.7 2008/02/22 02:27:34 das Exp $"); + +#include +#include + +#include "math_private.h" + +#define TBLBITS 8 +#define TBLSIZE (1 << TBLBITS) + +static const double + huge = 0x1p1000, + redux = 0x1.8p52 / TBLSIZE, + P1 = 0x1.62e42fefa39efp-1, + P2 = 0x1.ebfbdff82c575p-3, + P3 = 0x1.c6b08d704a0a6p-5, + P4 = 0x1.3b2ab88f70400p-7, + P5 = 0x1.5d88003875c74p-10; + +static volatile double twom1000 = 0x1p-1000; + +static const double tbl[TBLSIZE * 2] = { +/* exp2(z + eps) eps */ + 0x1.6a09e667f3d5dp-1, 0x1.9880p-44, + 0x1.6b052fa751744p-1, 0x1.8000p-50, + 0x1.6c012750bd9fep-1, -0x1.8780p-45, + 0x1.6cfdcddd476bfp-1, 0x1.ec00p-46, + 0x1.6dfb23c651a29p-1, -0x1.8000p-50, + 0x1.6ef9298593ae3p-1, -0x1.c000p-52, + 0x1.6ff7df9519386p-1, -0x1.fd80p-45, + 0x1.70f7466f42da3p-1, -0x1.c880p-45, + 0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46, + 0x1.72f8286eacf05p-1, -0x1.8300p-44, + 0x1.73f9a48a58152p-1, -0x1.0c00p-47, + 0x1.74fbd35d7ccfcp-1, 0x1.f880p-45, + 0x1.75feb564267f1p-1, 0x1.3e00p-47, + 0x1.77024b1ab6d48p-1, -0x1.7d00p-45, + 0x1.780694fde5d38p-1, -0x1.d000p-50, + 0x1.790b938ac1d00p-1, 0x1.3000p-49, + 0x1.7a11473eb0178p-1, -0x1.d000p-49, + 0x1.7b17b0976d060p-1, 0x1.0400p-45, + 0x1.7c1ed0130c133p-1, 0x1.0000p-53, + 0x1.7d26a62ff8636p-1, -0x1.6900p-45, + 0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47, + 0x1.7f3878491c3e8p-1, -0x1.4580p-45, + 0x1.80427543e1b4ep-1, 0x1.3000p-44, + 0x1.814d2add1071ap-1, 0x1.f000p-47, + 0x1.82589994ccd7ep-1, -0x1.1c00p-45, + 0x1.8364c1eb942d0p-1, 0x1.9d00p-45, + 0x1.8471a4623cab5p-1, 0x1.7100p-43, + 0x1.857f4179f5bbcp-1, 0x1.2600p-45, + 0x1.868d99b4491afp-1, -0x1.2c40p-44, + 0x1.879cad931a395p-1, -0x1.3000p-45, + 0x1.88ac7d98a65b8p-1, -0x1.a800p-45, + 0x1.89bd0a4785800p-1, -0x1.d000p-49, + 0x1.8ace5422aa223p-1, 0x1.3280p-44, + 0x1.8be05bad619fap-1, 0x1.2b40p-43, + 0x1.8cf3216b54383p-1, -0x1.ed00p-45, + 0x1.8e06a5e08664cp-1, -0x1.0500p-45, + 0x1.8f1ae99157807p-1, 0x1.8280p-45, + 0x1.902fed0282c0ep-1, -0x1.cb00p-46, + 0x1.9145b0b91ff96p-1, -0x1.5e00p-47, + 0x1.925c353aa2ff9p-1, 0x1.5400p-48, + 0x1.93737b0cdc64ap-1, 0x1.7200p-46, + 0x1.948b82b5f98aep-1, -0x1.9000p-47, + 0x1.95a44cbc852cbp-1, 0x1.5680p-45, + 0x1.96bdd9a766f21p-1, -0x1.6d00p-44, + 0x1.97d829fde4e2ap-1, -0x1.1000p-47, + 0x1.98f33e47a23a3p-1, 0x1.d000p-45, + 0x1.9a0f170ca0604p-1, -0x1.8a40p-44, + 0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44, + 0x1.9c49182a3f15bp-1, 0x1.6b80p-45, + 0x1.9d674194bb8c5p-1, -0x1.c000p-49, + 0x1.9e86319e3238ep-1, 0x1.7d00p-46, + 0x1.9fa5e8d07f302p-1, 0x1.6400p-46, + 0x1.a0c667b5de54dp-1, -0x1.5000p-48, + 0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47, + 0x1.a309bec4a2e27p-1, 0x1.ad80p-45, + 0x1.a42c980460a5dp-1, -0x1.af00p-46, + 0x1.a5503b23e259bp-1, 0x1.b600p-47, + 0x1.a674a8af46213p-1, 0x1.8880p-44, + 0x1.a799e1330b3a7p-1, 0x1.1200p-46, + 0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47, + 0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45, + 0x1.ab0e521356fb8p-1, 0x1.b700p-45, + 0x1.ac36bbfd3f381p-1, 0x1.9000p-50, + 0x1.ad5ff3a3c2780p-1, 0x1.4000p-49, + 0x1.ae89f995ad2a3p-1, -0x1.c900p-45, + 0x1.afb4ce622f367p-1, 0x1.6500p-46, + 0x1.b0e07298db790p-1, 0x1.fd40p-45, + 0x1.b20ce6c9a89a9p-1, 0x1.2700p-46, + 0x1.b33a2b84f1a4bp-1, 0x1.d470p-43, + 0x1.b468415b747e7p-1, -0x1.8380p-44, + 0x1.b59728de5593ap-1, 0x1.8000p-54, + 0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47, + 0x1.b7f76f2fb5e50p-1, 0x1.e800p-50, + 0x1.b928cf22749b2p-1, -0x1.4c00p-47, + 0x1.ba5b030a10603p-1, -0x1.d700p-47, + 0x1.bb8e0b79a6f66p-1, 0x1.d900p-47, + 0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47, + 0x1.bdf69c3f3a16fp-1, -0x1.f780p-46, + 0x1.bf2c25bd71db8p-1, -0x1.0a00p-46, + 0x1.c06286141b2e9p-1, -0x1.1400p-46, + 0x1.c199bdd8552e0p-1, 0x1.be00p-47, + 0x1.c2d1cd9fa64eep-1, -0x1.9400p-47, + 0x1.c40ab5fffd02fp-1, -0x1.ed00p-47, + 0x1.c544778fafd15p-1, 0x1.9660p-44, + 0x1.c67f12e57d0cbp-1, -0x1.a100p-46, + 0x1.c7ba88988c1b6p-1, -0x1.8458p-42, + 0x1.c8f6d9406e733p-1, -0x1.a480p-46, + 0x1.ca3405751c4dfp-1, 0x1.b000p-51, + 0x1.cb720dcef9094p-1, 0x1.1400p-47, + 0x1.ccb0f2e6d1689p-1, 0x1.0200p-48, + 0x1.cdf0b555dc412p-1, 0x1.3600p-48, + 0x1.cf3155b5bab3bp-1, -0x1.6900p-47, + 0x1.d072d4a0789bcp-1, 0x1.9a00p-47, + 0x1.d1b532b08c8fap-1, -0x1.5e00p-46, + 0x1.d2f87080d8a85p-1, 0x1.d280p-46, + 0x1.d43c8eacaa203p-1, 0x1.1a00p-47, + 0x1.d5818dcfba491p-1, 0x1.f000p-50, + 0x1.d6c76e862e6a1p-1, -0x1.3a00p-47, + 0x1.d80e316c9834ep-1, -0x1.cd80p-47, + 0x1.d955d71ff6090p-1, 0x1.4c00p-48, + 0x1.da9e603db32aep-1, 0x1.f900p-48, + 0x1.dbe7cd63a8325p-1, 0x1.9800p-49, + 0x1.dd321f301b445p-1, -0x1.5200p-48, + 0x1.de7d5641c05bfp-1, -0x1.d700p-46, + 0x1.dfc97337b9aecp-1, -0x1.6140p-46, + 0x1.e11676b197d5ep-1, 0x1.b480p-47, + 0x1.e264614f5a3e7p-1, 0x1.0ce0p-43, + 0x1.e3b333b16ee5cp-1, 0x1.c680p-47, + 0x1.e502ee78b3fb4p-1, -0x1.9300p-47, + 0x1.e653924676d68p-1, -0x1.5000p-49, + 0x1.e7a51fbc74c44p-1, -0x1.7f80p-47, + 0x1.e8f7977cdb726p-1, -0x1.3700p-48, + 0x1.ea4afa2a490e8p-1, 0x1.5d00p-49, + 0x1.eb9f4867ccae4p-1, 0x1.61a0p-46, + 0x1.ecf482d8e680dp-1, 0x1.5500p-48, + 0x1.ee4aaa2188514p-1, 0x1.6400p-51, + 0x1.efa1bee615a13p-1, -0x1.e800p-49, + 0x1.f0f9c1cb64106p-1, -0x1.a880p-48, + 0x1.f252b376bb963p-1, -0x1.c900p-45, + 0x1.f3ac948dd7275p-1, 0x1.a000p-53, + 0x1.f50765b6e4524p-1, -0x1.4f00p-48, + 0x1.f6632798844fdp-1, 0x1.a800p-51, + 0x1.f7bfdad9cbe38p-1, 0x1.abc0p-48, + 0x1.f91d802243c82p-1, -0x1.4600p-50, + 0x1.fa7c1819e908ep-1, -0x1.b0c0p-47, + 0x1.fbdba3692d511p-1, -0x1.0e00p-51, + 0x1.fd3c22b8f7194p-1, -0x1.0de8p-46, + 0x1.fe9d96b2a23eep-1, 0x1.e430p-49, + 0x1.0000000000000p+0, 0x0.0000p+0, + 0x1.00b1afa5abcbep+0, -0x1.3400p-52, + 0x1.0163da9fb3303p+0, -0x1.2170p-46, + 0x1.02168143b0282p+0, 0x1.a400p-52, + 0x1.02c9a3e77806cp+0, 0x1.f980p-49, + 0x1.037d42e11bbcap+0, -0x1.7400p-51, + 0x1.04315e86e7f89p+0, 0x1.8300p-50, + 0x1.04e5f72f65467p+0, -0x1.a3f0p-46, + 0x1.059b0d315855ap+0, -0x1.2840p-47, + 0x1.0650a0e3c1f95p+0, 0x1.1600p-48, + 0x1.0706b29ddf71ap+0, 0x1.5240p-46, + 0x1.07bd42b72a82dp+0, -0x1.9a00p-49, + 0x1.0874518759bd0p+0, 0x1.6400p-49, + 0x1.092bdf66607c8p+0, -0x1.0780p-47, + 0x1.09e3ecac6f383p+0, -0x1.8000p-54, + 0x1.0a9c79b1f3930p+0, 0x1.fa00p-48, + 0x1.0b5586cf988fcp+0, -0x1.ac80p-48, + 0x1.0c0f145e46c8ap+0, 0x1.9c00p-50, + 0x1.0cc922b724816p+0, 0x1.5200p-47, + 0x1.0d83b23395dd8p+0, -0x1.ad00p-48, + 0x1.0e3ec32d3d1f3p+0, 0x1.bac0p-46, + 0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47, + 0x1.0fb66affed2f0p+0, -0x1.d300p-47, + 0x1.1073028d7234bp+0, 0x1.1500p-48, + 0x1.11301d0125b5bp+0, 0x1.c000p-49, + 0x1.11edbab5e2af9p+0, 0x1.6bc0p-46, + 0x1.12abdc06c31d5p+0, 0x1.8400p-49, + 0x1.136a814f2047dp+0, -0x1.ed00p-47, + 0x1.1429aaea92de9p+0, 0x1.8e00p-49, + 0x1.14e95934f3138p+0, 0x1.b400p-49, + 0x1.15a98c8a58e71p+0, 0x1.5300p-47, + 0x1.166a45471c3dfp+0, 0x1.3380p-47, + 0x1.172b83c7d5211p+0, 0x1.8d40p-45, + 0x1.17ed48695bb9fp+0, -0x1.5d00p-47, + 0x1.18af9388c8d93p+0, -0x1.c880p-46, + 0x1.1972658375d66p+0, 0x1.1f00p-46, + 0x1.1a35beb6fcba7p+0, 0x1.0480p-46, + 0x1.1af99f81387e3p+0, -0x1.7390p-43, + 0x1.1bbe084045d54p+0, 0x1.4e40p-45, + 0x1.1c82f95281c43p+0, -0x1.a200p-47, + 0x1.1d4873168b9b2p+0, 0x1.3800p-49, + 0x1.1e0e75eb44031p+0, 0x1.ac00p-49, + 0x1.1ed5022fcd938p+0, 0x1.1900p-47, + 0x1.1f9c18438cdf7p+0, -0x1.b780p-46, + 0x1.2063b88628d8fp+0, 0x1.d940p-45, + 0x1.212be3578a81ep+0, 0x1.8000p-50, + 0x1.21f49917ddd41p+0, 0x1.b340p-45, + 0x1.22bdda2791323p+0, 0x1.9f80p-46, + 0x1.2387a6e7561e7p+0, -0x1.9c80p-46, + 0x1.2451ffb821427p+0, 0x1.2300p-47, + 0x1.251ce4fb2a602p+0, -0x1.3480p-46, + 0x1.25e85711eceb0p+0, 0x1.2700p-46, + 0x1.26b4565e27d16p+0, 0x1.1d00p-46, + 0x1.2780e341de00fp+0, 0x1.1ee0p-44, + 0x1.284dfe1f5633ep+0, -0x1.4c00p-46, + 0x1.291ba7591bb30p+0, -0x1.3d80p-46, + 0x1.29e9df51fdf09p+0, 0x1.8b00p-47, + 0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45, + 0x1.2b87fd0dada3ap+0, 0x1.a340p-45, + 0x1.2c57e39771af9p+0, -0x1.0800p-46, + 0x1.2d285a6e402d9p+0, -0x1.ed00p-47, + 0x1.2df961f641579p+0, -0x1.4200p-48, + 0x1.2ecafa93e2ecfp+0, -0x1.4980p-45, + 0x1.2f9d24abd8822p+0, -0x1.6300p-46, + 0x1.306fe0a31b625p+0, -0x1.2360p-44, + 0x1.31432edeea50bp+0, -0x1.0df8p-40, + 0x1.32170fc4cd7b8p+0, -0x1.2480p-45, + 0x1.32eb83ba8e9a2p+0, -0x1.5980p-45, + 0x1.33c08b2641766p+0, 0x1.ed00p-46, + 0x1.3496266e3fa27p+0, -0x1.c000p-50, + 0x1.356c55f929f0fp+0, -0x1.0d80p-44, + 0x1.36431a2de88b9p+0, 0x1.2c80p-45, + 0x1.371a7373aaa39p+0, 0x1.0600p-45, + 0x1.37f26231e74fep+0, -0x1.6600p-46, + 0x1.38cae6d05d838p+0, -0x1.ae00p-47, + 0x1.39a401b713ec3p+0, -0x1.4720p-43, + 0x1.3a7db34e5a020p+0, 0x1.8200p-47, + 0x1.3b57fbfec6e95p+0, 0x1.e800p-44, + 0x1.3c32dc313a8f2p+0, 0x1.f800p-49, + 0x1.3d0e544ede122p+0, -0x1.7a00p-46, + 0x1.3dea64c1234bbp+0, 0x1.6300p-45, + 0x1.3ec70df1c4eccp+0, -0x1.8a60p-43, + 0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44, + 0x1.40822c367a0bbp+0, 0x1.5b80p-45, + 0x1.4160a21f72e95p+0, 0x1.ec00p-46, + 0x1.423fb27094646p+0, -0x1.3600p-46, + 0x1.431f5d950a920p+0, 0x1.3980p-45, + 0x1.43ffa3f84b9ebp+0, 0x1.a000p-48, + 0x1.44e0860618919p+0, -0x1.6c00p-48, + 0x1.45c2042a7d201p+0, -0x1.bc00p-47, + 0x1.46a41ed1d0016p+0, -0x1.2800p-46, + 0x1.4786d668b3326p+0, 0x1.0e00p-44, + 0x1.486a2b5c13c00p+0, -0x1.d400p-45, + 0x1.494e1e192af04p+0, 0x1.c200p-47, + 0x1.4a32af0d7d372p+0, -0x1.e500p-46, + 0x1.4b17dea6db801p+0, 0x1.7800p-47, + 0x1.4bfdad53629e1p+0, -0x1.3800p-46, + 0x1.4ce41b817c132p+0, 0x1.0800p-47, + 0x1.4dcb299fddddbp+0, 0x1.c700p-45, + 0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46, + 0x1.4f9b2769d2d02p+0, 0x1.9200p-46, + 0x1.508417f4531c1p+0, -0x1.8c00p-47, + 0x1.516daa2cf662ap+0, -0x1.a000p-48, + 0x1.5257de83f51eap+0, 0x1.a080p-43, + 0x1.5342b569d4edap+0, -0x1.6d80p-45, + 0x1.542e2f4f6ac1ap+0, -0x1.2440p-44, + 0x1.551a4ca5d94dbp+0, 0x1.83c0p-43, + 0x1.56070dde9116bp+0, 0x1.4b00p-45, + 0x1.56f4736b529dep+0, 0x1.15a0p-43, + 0x1.57e27dbe2c40ep+0, -0x1.9e00p-45, + 0x1.58d12d497c76fp+0, -0x1.3080p-45, + 0x1.59c0827ff0b4cp+0, 0x1.dec0p-43, + 0x1.5ab07dd485427p+0, -0x1.4000p-51, + 0x1.5ba11fba87af4p+0, 0x1.0080p-44, + 0x1.5c9268a59460bp+0, -0x1.6c80p-45, + 0x1.5d84590998e3fp+0, 0x1.69a0p-43, + 0x1.5e76f15ad20e1p+0, -0x1.b400p-46, + 0x1.5f6a320dcebcap+0, 0x1.7700p-46, + 0x1.605e1b976dcb8p+0, 0x1.6f80p-45, + 0x1.6152ae6cdf715p+0, 0x1.1000p-47, + 0x1.6247eb03a5531p+0, -0x1.5d00p-46, + 0x1.633dd1d1929b5p+0, -0x1.2d00p-46, + 0x1.6434634ccc313p+0, -0x1.a800p-49, + 0x1.652b9febc8efap+0, -0x1.8600p-45, + 0x1.6623882553397p+0, 0x1.1fe0p-40, + 0x1.671c1c708328ep+0, -0x1.7200p-44, + 0x1.68155d44ca97ep+0, 0x1.6800p-49, + 0x1.690f4b19e9471p+0, -0x1.9780p-45, +}; + +/* + * exp2(x): compute the base 2 exponential of x + * + * Accuracy: Peak error < 0.503 ulp for normalized results. + * + * Method: (accurate tables) + * + * Reduce x: + * x = 2**k + y, for integer k and |y| <= 1/2. + * Thus we have exp2(x) = 2**k * exp2(y). + * + * Reduce y: + * y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE. + * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]), + * with |z - eps[i]| <= 2**-9 + 2**-39 for the table used. + * + * We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via + * a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61. + * The values in exp2t[] and eps[] are chosen such that + * exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such + * that exp2t[i] is accurate to 2**-64. + * + * Note that the range of i is +-TBLSIZE/2, so we actually index the tables + * by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are + * virtual tables, interleaved in the real table tbl[]. + * + * This method is due to Gal, with many details due to Gal and Bachelis: + * + * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library + * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). + */ +OLM_DLLEXPORT double +exp2(double x) +{ + double r, t, twopk, twopkp1000, z; + u_int32_t hx, ix, lx, i0; + int k; + + /* Filter out exceptional cases. */ + GET_HIGH_WORD(hx,x); + ix = hx & 0x7fffffff; /* high word of |x| */ + if(ix >= 0x40900000) { /* |x| >= 1024 */ + if(ix >= 0x7ff00000) { + GET_LOW_WORD(lx,x); + if(((ix & 0xfffff) | lx) != 0 || (hx & 0x80000000) == 0) + return (x + x); /* x is NaN or +Inf */ + else + return (0.0); /* x is -Inf */ + } + if(x >= 0x1.0p10) + return (huge * huge); /* overflow */ + if(x <= -0x1.0ccp10) + return (twom1000 * twom1000); /* underflow */ + } else if (ix < 0x3c900000) { /* |x| < 0x1p-54 */ + return (1.0 + x); + } + + /* Reduce x, computing z, i0, and k. */ + STRICT_ASSIGN(double, t, x + redux); + GET_LOW_WORD(i0, t); + i0 += TBLSIZE / 2; + k = (i0 >> TBLBITS) << 20; + i0 = (i0 & (TBLSIZE - 1)) << 1; + t -= redux; + z = x - t; + + /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ + t = tbl[i0]; /* exp2t[i0] */ + z -= tbl[i0 + 1]; /* eps[i0] */ + if (k >= -(1021 << 20)) + INSERT_WORDS(twopk, 0x3ff00000 + k, 0); + else + INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0); + r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5)))); + + /* Scale by 2**(k>>20). */ + if(k >= -(1021 << 20)) { + if (k == 1024 << 20) + return (r * 2.0 * 0x1p1023); + return (r * twopk); + } else { + return (r * twopkp1000 * twom1000); + } +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(exp2, exp2l); +#endif diff --git a/openlibm/src/s_exp2f.c b/openlibm/src/s_exp2f.c new file mode 100644 index 0000000..74bc9f3 --- /dev/null +++ b/openlibm/src/s_exp2f.c @@ -0,0 +1,136 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2f.c,v 1.9 2008/02/22 02:27:34 das Exp $"); + +#include +#include + +#include "math_private.h" + +#define TBLBITS 4 +#define TBLSIZE (1 << TBLBITS) + +static const float + huge = 0x1p100f, + redux = 0x1.8p23f / TBLSIZE, + P1 = 0x1.62e430p-1f, + P2 = 0x1.ebfbe0p-3f, + P3 = 0x1.c6b348p-5f, + P4 = 0x1.3b2c9cp-7f; + +static volatile float twom100 = 0x1p-100f; + +static const double exp2ft[TBLSIZE] = { + 0x1.6a09e667f3bcdp-1, + 0x1.7a11473eb0187p-1, + 0x1.8ace5422aa0dbp-1, + 0x1.9c49182a3f090p-1, + 0x1.ae89f995ad3adp-1, + 0x1.c199bdd85529cp-1, + 0x1.d5818dcfba487p-1, + 0x1.ea4afa2a490dap-1, + 0x1.0000000000000p+0, + 0x1.0b5586cf9890fp+0, + 0x1.172b83c7d517bp+0, + 0x1.2387a6e756238p+0, + 0x1.306fe0a31b715p+0, + 0x1.3dea64c123422p+0, + 0x1.4bfdad5362a27p+0, + 0x1.5ab07dd485429p+0, +}; + +/* + * exp2f(x): compute the base 2 exponential of x + * + * Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927. + * + * Method: (equally-spaced tables) + * + * Reduce x: + * x = 2**k + y, for integer k and |y| <= 1/2. + * Thus we have exp2f(x) = 2**k * exp2(y). + * + * Reduce y: + * y = i/TBLSIZE + z for integer i near y * TBLSIZE. + * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z), + * with |z| <= 2**-(TBLSIZE+1). + * + * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a + * degree-4 minimax polynomial with maximum error under 1.4 * 2**-33. + * Using double precision for everything except the reduction makes + * roundoff error insignificant and simplifies the scaling step. + * + * This method is due to Tang, but I do not use his suggested parameters: + * + * Tang, P. Table-driven Implementation of the Exponential Function + * in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989). + */ +OLM_DLLEXPORT float +exp2f(float x) +{ + double tv, twopk, u, z; + float t; + u_int32_t hx, ix, i0; + int32_t k; + + /* Filter out exceptional cases. */ + GET_FLOAT_WORD(hx, x); + ix = hx & 0x7fffffff; /* high word of |x| */ + if(ix >= 0x43000000) { /* |x| >= 128 */ + if(ix >= 0x7f800000) { + if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0) + return (x + x); /* x is NaN or +Inf */ + else + return (0.0); /* x is -Inf */ + } + if(x >= 0x1.0p7f) + return (huge * huge); /* overflow */ + if(x <= -0x1.2cp7f) + return (twom100 * twom100); /* underflow */ + } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */ + return (1.0f + x); + } + + /* Reduce x, computing z, i0, and k. */ + STRICT_ASSIGN(float, t, x + redux); + GET_FLOAT_WORD(i0, t); + i0 += TBLSIZE / 2; + k = (i0 >> TBLBITS) << 20; + i0 &= TBLSIZE - 1; + t -= redux; + z = x - t; + INSERT_WORDS(twopk, 0x3ff00000 + k, 0); + + /* Compute r = exp2(y) = exp2ft[i0] * p(z). */ + tv = exp2ft[i0]; + u = tv * z; + tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4); + + /* Scale by 2**(k>>20). */ + return (tv * twopk); +} diff --git a/openlibm/src/s_expm1.c b/openlibm/src/s_expm1.c new file mode 100644 index 0000000..5798714 --- /dev/null +++ b/openlibm/src/s_expm1.c @@ -0,0 +1,221 @@ +/* @(#)s_expm1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_expm1.c,v 1.12 2011/10/21 06:26:38 das Exp $"); + +/* expm1(x) + * Returns exp(x)-1, the exponential of x minus 1. + * + * Method + * 1. Argument reduction: + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * + * Here a correction term c will be computed to compensate + * the error in r when rounded to a floating-point number. + * + * 2. Approximating expm1(r) by a special rational function on + * the interval [0,0.34658]: + * Since + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... + * we define R1(r*r) by + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) + * That is, + * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) + * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) + * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... + * We use a special Reme algorithm on [0,0.347] to generate + * a polynomial of degree 5 in r*r to approximate R1. The + * maximum error of this polynomial approximation is bounded + * by 2**-61. In other words, + * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 + * where Q1 = -1.6666666666666567384E-2, + * Q2 = 3.9682539681370365873E-4, + * Q3 = -9.9206344733435987357E-6, + * Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; + * z = r*r, + * with error bounded by + * | 5 | -61 + * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 + * | | + * + * expm1(r) = exp(r)-1 is then computed by the following + * specific way which minimize the accumulation rounding error: + * 2 3 + * r r [ 3 - (R1 + R1*r/2) ] + * expm1(r) = r + --- + --- * [--------------------] + * 2 2 [ 6 - r*(3 - R1*r/2) ] + * + * To compensate the error in the argument reduction, we use + * expm1(r+c) = expm1(r) + c + expm1(r)*c + * ~ expm1(r) + c + r*c + * Thus c+r*c will be added in as the correction terms for + * expm1(r+c). Now rearrange the term to avoid optimization + * screw up: + * ( 2 2 ) + * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) + * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) + * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) + * ( ) + * + * = r - E + * 3. Scale back to obtain expm1(x): + * From step 1, we have + * expm1(x) = either 2^k*[expm1(r)+1] - 1 + * = or 2^k*[expm1(r) + (1-2^-k)] + * 4. Implementation notes: + * (A). To save one multiplication, we scale the coefficient Qi + * to Qi*2^i, and replace z by (x^2)/2. + * (B). To achieve maximum accuracy, we compute expm1(x) by + * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) + * (ii) if k=0, return r-E + * (iii) if k=-1, return 0.5*(r-E)-0.5 + * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) + * else return 1.0+2.0*(r-E); + * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) + * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else + * (vii) return 2^k(1-((E+2^-k)-r)) + * + * Special cases: + * expm1(INF) is INF, expm1(NaN) is NaN; + * expm1(-INF) is -1, and + * for finite argument, only expm1(0)=0 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then expm1(x) overflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include +#include + +#include "math_private.h" + +static const double +one = 1.0, +huge = 1.0e+300, +tiny = 1.0e-300, +o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ +ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ +ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */ +/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */ +Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ +Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ +Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ +Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ +Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ + +OLM_DLLEXPORT double +expm1(double x) +{ + double y,hi,lo,c,t,e,hxs,hfx,r1,twopk; + int32_t k,xsb; + u_int32_t hx; + + GET_HIGH_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t low; + GET_LOW_WORD(low,x); + if(((hx&0xfffff)|low)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:-1.0;/* exp(+-inf)-1={inf,-1} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ + if(x+tiny<0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?0.5:-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + STRICT_ASSIGN(double, x, hi - lo); + c = (hi-x)-lo; + } + else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = 0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = 3.0-r1*hfx; + e = hxs*((r1-t)/(6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + INSERT_WORDS(twopk,0x3ff00000+(k<<20),0); /* 2^k */ + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return 0.5*(x-e)-0.5; + if(k==1) { + if(x < -0.25) return -2.0*(e-(x+0.5)); + else return one+2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + y = one-(e-x); + if (k == 1024) y = y*2.0*0x1p1023; + else y = y*twopk; + return y-one; + } + t = one; + if(k<20) { + SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ + y = t-(e-x); + y = y*twopk; + } else { + SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ + y = x-(e+t); + y += one; + y = y*twopk; + } + } + return y; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(expm1, expm1l); +#endif diff --git a/openlibm/src/s_expm1f.c b/openlibm/src/s_expm1f.c new file mode 100644 index 0000000..cb7ceec --- /dev/null +++ b/openlibm/src/s_expm1f.c @@ -0,0 +1,123 @@ +/* s_expm1f.c -- float version of s_expm1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_expm1f.c,v 1.12 2011/10/21 06:26:38 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const float +one = 1.0, +huge = 1.0e+30, +tiny = 1.0e-30, +o_threshold = 8.8721679688e+01,/* 0x42b17180 */ +ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ +ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ +invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ +/* + * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]: + * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04 + * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c): + */ +Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */ +Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */ + +OLM_DLLEXPORT float +expm1f(float x) +{ + float y,hi,lo,c,t,e,hxs,hfx,r1,twopk; + int32_t k,xsb; + u_int32_t hx; + + GET_FLOAT_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ + if(x+tiny<(float)0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + STRICT_ASSIGN(float, x, hi - lo); + c = (hi-x)-lo; + } + else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = (float)0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*Q2); + t = (float)3.0-r1*hfx; + e = hxs*((r1-t)/((float)6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); /* 2^k */ + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return (float)0.5*(x-e)-(float)0.5; + if(k==1) { + if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); + else return one+(float)2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + y = one-(e-x); + if (k == 128) y = y*2.0F*0x1p127F; + else y = y*twopk; + return y-one; + } + t = one; + if(k<23) { + SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ + y = t-(e-x); + y = y*twopk; + } else { + SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ + y = x-(e+t); + y += one; + y = y*twopk; + } + } + return y; +} diff --git a/openlibm/src/s_fabs.c b/openlibm/src/s_fabs.c new file mode 100644 index 0000000..43ffc1a --- /dev/null +++ b/openlibm/src/s_fabs.c @@ -0,0 +1,28 @@ +/* @(#)s_fabs.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * fabs(x) returns the absolute value of x. + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +fabs(double x) +{ + u_int32_t high; + GET_HIGH_WORD(high,x); + SET_HIGH_WORD(x,high&0x7fffffff); + return x; +} diff --git a/openlibm/src/s_fabsf.c b/openlibm/src/s_fabsf.c new file mode 100644 index 0000000..eeceee4 --- /dev/null +++ b/openlibm/src/s_fabsf.c @@ -0,0 +1,34 @@ +/* s_fabsf.c -- float version of s_fabs.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fabsf.c,v 1.8 2008/02/22 02:30:35 das Exp $"); + +/* + * fabsf(x) returns the absolute value of x. + */ + +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +fabsf(float x) +{ + u_int32_t ix; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x7fffffff); + return x; +} diff --git a/openlibm/src/s_fabsl.c b/openlibm/src/s_fabsl.c new file mode 100644 index 0000000..6bc1971 --- /dev/null +++ b/openlibm/src/s_fabsl.c @@ -0,0 +1,43 @@ +/*- + * Copyright (c) 2003 Dag-Erling Coïdan Smørgrav + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer + * in this position and unchanged. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. The name of the author may not be used to endorse or promote products + * derived from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_fabsl.c,v 1.2 2003/10/25 19:53:28 des Exp $ + */ + +#include +#include "math_private.h" +#include "fpmath.h" + +OLM_DLLEXPORT long double +fabsl(long double x) +{ + union IEEEl2bits u; + + u.e = x; + u.bits.sign = 0; + return (u.e); +} diff --git a/openlibm/src/s_fdim.c b/openlibm/src/s_fdim.c new file mode 100644 index 0000000..2f05347 --- /dev/null +++ b/openlibm/src/s_fdim.c @@ -0,0 +1,48 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fdim.c,v 1.1 2004/06/30 07:04:01 das Exp $"); +#include +#include "math_private.h" + +#define DECL(type, fn) \ +OLM_DLLEXPORT type \ +fn(type x, type y) \ +{ \ + \ + if (isnan(x)) \ + return (x); \ + if (isnan(y)) \ + return (y); \ + return (x > y ? x - y : 0.0); \ +} + +DECL(double, fdim) +DECL(float, fdimf) +#ifdef OLM_LONG_DOUBLE +DECL(long double, fdiml) +#endif diff --git a/openlibm/src/s_floor.c b/openlibm/src/s_floor.c new file mode 100644 index 0000000..4a44bd5 --- /dev/null +++ b/openlibm/src/s_floor.c @@ -0,0 +1,78 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_floor.c,v 1.11 2008/02/15 07:01:40 bde Exp $"); + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include +#include + +#include "math_private.h" + +static const double huge = 1.0e300; + +OLM_DLLEXPORT double +floor(double x) +{ + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffff)|i1)!=0) + { i0=0xbff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) { + if(j0==20) i0+=1; + else { + j = i1+(1<<(52-j0)); + if(j + +#include "math_private.h" + +static const float huge = 1.0e30; + +OLM_DLLEXPORT float +floorf(float x) +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffff)!=0) + { i0=0xbf800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/openlibm/src/s_floorl.c b/openlibm/src/s_floorl.c new file mode 100644 index 0000000..8427edb --- /dev/null +++ b/openlibm/src/s_floorl.c @@ -0,0 +1,102 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * From: @(#)s_floor.c 5.1 93/09/24 + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_floorl.c,v 1.8 2008/02/14 15:10:34 bde Exp $"); + +/* + * floorl(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floorl(x). + */ + +#include +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#ifdef LDBL_IMPLICIT_NBIT +#define MANH_SIZE (LDBL_MANH_SIZE + 1) +#define INC_MANH(u, c) do { \ + uint64_t o = u.bits.manh; \ + u.bits.manh += (c); \ + if (u.bits.manh < o) \ + u.bits.exp++; \ +} while (0) +#else +#define MANH_SIZE LDBL_MANH_SIZE +#define INC_MANH(u, c) do { \ + uint64_t o = u.bits.manh; \ + u.bits.manh += (c); \ + if (u.bits.manh < o) { \ + u.bits.exp++; \ + u.bits.manh |= 1llu << (LDBL_MANH_SIZE - 1); \ + } \ +} while (0) +#endif + +static const long double huge = 1.0e300; + +OLM_DLLEXPORT long double +floorl(long double x) +{ + union IEEEl2bits u = { .e = x }; + int e = u.bits.exp - LDBL_MAX_EXP + 1; + + if (e < MANH_SIZE - 1) { + if (e < 0) { /* raise inexact if x != 0 */ + if (huge + x > 0.0) + if (u.bits.exp > 0 || + (u.bits.manh | u.bits.manl) != 0) + u.e = u.bits.sign ? -1.0 : 0.0; + } else { + uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1); + if (((u.bits.manh & m) | u.bits.manl) == 0) + return (x); /* x is integral */ + if (u.bits.sign) { +#ifdef LDBL_IMPLICIT_NBIT + if (e == 0) + u.bits.exp++; + else +#endif + INC_MANH(u, 1llu << (MANH_SIZE - e - 1)); + } + if (huge + x > 0.0) { /* raise inexact flag */ + u.bits.manh &= ~m; + u.bits.manl = 0; + } + } + } else if (e < LDBL_MANT_DIG - 1) { + uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1); + if ((u.bits.manl & m) == 0) + return (x); /* x is integral */ + if (u.bits.sign) { + if (e == MANH_SIZE - 1) + INC_MANH(u, 1); + else { + uint64_t o = u.bits.manl; + u.bits.manl += 1llu << (LDBL_MANT_DIG - e - 1); + if (u.bits.manl < o) /* got a carry */ + INC_MANH(u, 1); + } + } + if (huge + x > 0.0) /* raise inexact flag */ + u.bits.manl &= ~m; + } + return (u.e); +} diff --git a/openlibm/src/s_fma.c b/openlibm/src/s_fma.c new file mode 100644 index 0000000..63e529e --- /dev/null +++ b/openlibm/src/s_fma.c @@ -0,0 +1,284 @@ +/*- + * Copyright (c) 2005-2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fma.c,v 1.8 2011/10/21 06:30:43 das Exp $"); + +#include +#include +#include + +#include "math_private.h" + +/* + * A struct dd represents a floating-point number with twice the precision + * of a double. We maintain the invariant that "hi" stores the 53 high-order + * bits of the result. + */ +struct dd { + double hi; + double lo; +}; + +/* + * Compute a+b exactly, returning the exact result in a struct dd. We assume + * that both a and b are finite, but make no assumptions about their relative + * magnitudes. + */ +static inline struct dd +dd_add(double a, double b) +{ + struct dd ret; + double s; + + ret.hi = a + b; + s = ret.hi - a; + ret.lo = (a - (ret.hi - s)) + (b - s); + return (ret); +} + +/* + * Compute a+b, with a small tweak: The least significant bit of the + * result is adjusted into a sticky bit summarizing all the bits that + * were lost to rounding. This adjustment negates the effects of double + * rounding when the result is added to another number with a higher + * exponent. For an explanation of round and sticky bits, see any reference + * on FPU design, e.g., + * + * J. Coonen. An Implementation Guide to a Proposed Standard for + * Floating-Point Arithmetic. Computer, vol. 13, no. 1, Jan 1980. + */ +static inline double +add_adjusted(double a, double b) +{ + struct dd sum; + u_int64_t hibits, lobits; + + sum = dd_add(a, b); + if (sum.lo != 0) { + EXTRACT_WORD64(hibits, sum.hi); + if ((hibits & 1) == 0) { + /* hibits += (int)copysign(1.0, sum.hi * sum.lo) */ + EXTRACT_WORD64(lobits, sum.lo); + hibits += 1 - ((hibits ^ lobits) >> 62); + INSERT_WORD64(sum.hi, hibits); + } + } + return (sum.hi); +} + +/* + * Compute ldexp(a+b, scale) with a single rounding error. It is assumed + * that the result will be subnormal, and care is taken to ensure that + * double rounding does not occur. + */ +static inline double +add_and_denormalize(double a, double b, int scale) +{ + struct dd sum; + u_int64_t hibits, lobits; + int bits_lost; + + sum = dd_add(a, b); + + /* + * If we are losing at least two bits of accuracy to denormalization, + * then the first lost bit becomes a round bit, and we adjust the + * lowest bit of sum.hi to make it a sticky bit summarizing all the + * bits in sum.lo. With the sticky bit adjusted, the hardware will + * break any ties in the correct direction. + * + * If we are losing only one bit to denormalization, however, we must + * break the ties manually. + */ + if (sum.lo != 0) { + EXTRACT_WORD64(hibits, sum.hi); + bits_lost = -((int)(hibits >> 52) & 0x7ff) - scale + 1; + if ((bits_lost != 1) ^ (int)(hibits & 1)) { + /* hibits += (int)copysign(1.0, sum.hi * sum.lo) */ + EXTRACT_WORD64(lobits, sum.lo); + hibits += 1 - (((hibits ^ lobits) >> 62) & 2); + INSERT_WORD64(sum.hi, hibits); + } + } + return (ldexp(sum.hi, scale)); +} + +/* + * Compute a*b exactly, returning the exact result in a struct dd. We assume + * that both a and b are normalized, so no underflow or overflow will occur. + * The current rounding mode must be round-to-nearest. + */ +static inline struct dd +dd_mul(double a, double b) +{ + static const double split = 0x1p27 + 1.0; + struct dd ret; + double ha, hb, la, lb, p, q; + + p = a * split; + ha = a - p; + ha += p; + la = a - ha; + + p = b * split; + hb = b - p; + hb += p; + lb = b - hb; + + p = ha * hb; + q = ha * lb + la * hb; + + ret.hi = p + q; + ret.lo = p - ret.hi + q + la * lb; + return (ret); +} + +/* + * Fused multiply-add: Compute x * y + z with a single rounding error. + * + * We use scaling to avoid overflow/underflow, along with the + * canonical precision-doubling technique adapted from: + * + * Dekker, T. A Floating-Point Technique for Extending the + * Available Precision. Numer. Math. 18, 224-242 (1971). + * + * This algorithm is sensitive to the rounding precision. FPUs such + * as the i387 must be set in double-precision mode if variables are + * to be stored in FP registers in order to avoid incorrect results. + * This is the default on FreeBSD, but not on many other systems. + * + * Hardware instructions should be used on architectures that support it, + * since this implementation will likely be several times slower. + */ +OLM_DLLEXPORT double +fma(double x, double y, double z) +{ + double xs, ys, zs, adj; + struct dd xy, r; + int oround; + int ex, ey, ez; + int spread; + + /* + * Handle special cases. The order of operations and the particular + * return values here are crucial in handling special cases involving + * infinities, NaNs, overflows, and signed zeroes correctly. + */ + if (x == 0.0 || y == 0.0) + return (x * y + z); + if (z == 0.0) + return (x * y); + if (!isfinite(x) || !isfinite(y)) + return (x * y + z); + if (!isfinite(z)) + return (z); + + xs = frexp(x, &ex); + ys = frexp(y, &ey); + zs = frexp(z, &ez); + oround = fegetround(); + spread = ex + ey - ez; + + /* + * If x * y and z are many orders of magnitude apart, the scaling + * will overflow, so we handle these cases specially. Rounding + * modes other than FE_TONEAREST are painful. + */ + if (spread < -DBL_MANT_DIG) { + feraiseexcept(FE_INEXACT); + if (!isnormal(z)) + feraiseexcept(FE_UNDERFLOW); + switch (oround) { + case FE_TONEAREST: + return (z); + case FE_TOWARDZERO: + if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0)) + return (z); + else + return (nextafter(z, 0)); + case FE_DOWNWARD: + if ((x > 0.0) ^ (y < 0.0)) + return (z); + else + return (nextafter(z, -INFINITY)); + default: /* FE_UPWARD */ + if ((x > 0.0) ^ (y < 0.0)) + return (nextafter(z, INFINITY)); + else + return (z); + } + } + if (spread <= DBL_MANT_DIG * 2) + zs = ldexp(zs, -spread); + else + zs = copysign(DBL_MIN, zs); + + fesetround(FE_TONEAREST); + + /* + * Basic approach for round-to-nearest: + * + * (xy.hi, xy.lo) = x * y (exact) + * (r.hi, r.lo) = xy.hi + z (exact) + * adj = xy.lo + r.lo (inexact; low bit is sticky) + * result = r.hi + adj (correctly rounded) + */ + xy = dd_mul(xs, ys); + r = dd_add(xy.hi, zs); + + spread = ex + ey; + + if (r.hi == 0.0) { + /* + * When the addends cancel to 0, ensure that the result has + * the correct sign. + */ + fesetround(oround); + volatile double vzs = zs; /* XXX gcc CSE bug workaround */ + return (xy.hi + vzs + ldexp(xy.lo, spread)); + } + + if (oround != FE_TONEAREST) { + /* + * There is no need to worry about double rounding in directed + * rounding modes. + */ + fesetround(oround); + adj = r.lo + xy.lo; + return (ldexp(r.hi + adj, spread)); + } + + adj = add_adjusted(r.lo, xy.lo); + if (spread + ilogb(r.hi) > -1023) + return (ldexp(r.hi + adj, spread)); + else + return (add_and_denormalize(r.hi, adj, spread)); +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(fma, fmal); +#endif diff --git a/openlibm/src/s_fmaf.c b/openlibm/src/s_fmaf.c new file mode 100644 index 0000000..b3c8efb --- /dev/null +++ b/openlibm/src/s_fmaf.c @@ -0,0 +1,69 @@ +/*- + * Copyright (c) 2005-2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fmaf.c,v 1.3 2011/10/15 04:16:58 das Exp $"); + +#include +#include + +#include "math_private.h" + +/* + * Fused multiply-add: Compute x * y + z with a single rounding error. + * + * A double has more than twice as much precision than a float, so + * direct double-precision arithmetic suffices, except where double + * rounding occurs. + */ +OLM_DLLEXPORT float +fmaf(float x, float y, float z) +{ + double xy, result; + u_int32_t hr, lr; + + xy = (double)x * y; + result = xy + z; + EXTRACT_WORDS(hr, lr, result); + /* Common case: The double precision result is fine. */ + if ((lr & 0x1fffffff) != 0x10000000 || /* not a halfway case */ + (hr & 0x7ff00000) == 0x7ff00000 || /* NaN */ + result - xy == z || /* exact */ + fegetround() != FE_TONEAREST) /* not round-to-nearest */ + return (result); + + /* + * If result is inexact, and exactly halfway between two float values, + * we need to adjust the low-order bit in the direction of the error. + */ + fesetround(FE_TOWARDZERO); + volatile double vxy = xy; /* XXX work around gcc CSE bug */ + double adjusted_result = vxy + z; + fesetround(FE_TONEAREST); + if (result == adjusted_result) + SET_LOW_WORD(adjusted_result, lr + 1); + return (adjusted_result); +} diff --git a/openlibm/src/s_fmal.c b/openlibm/src/s_fmal.c new file mode 100644 index 0000000..2fe30c6 --- /dev/null +++ b/openlibm/src/s_fmal.c @@ -0,0 +1,269 @@ +/*- + * Copyright (c) 2005-2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fmal.c,v 1.7 2011/10/21 06:30:43 das Exp $"); + +#include +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +/* + * A struct dd represents a floating-point number with twice the precision + * of a long double. We maintain the invariant that "hi" stores the high-order + * bits of the result. + */ +struct dd { + long double hi; + long double lo; +}; + +/* + * Compute a+b exactly, returning the exact result in a struct dd. We assume + * that both a and b are finite, but make no assumptions about their relative + * magnitudes. + */ +static inline struct dd +dd_add(long double a, long double b) +{ + struct dd ret; + long double s; + + ret.hi = a + b; + s = ret.hi - a; + ret.lo = (a - (ret.hi - s)) + (b - s); + return (ret); +} + +/* + * Compute a+b, with a small tweak: The least significant bit of the + * result is adjusted into a sticky bit summarizing all the bits that + * were lost to rounding. This adjustment negates the effects of double + * rounding when the result is added to another number with a higher + * exponent. For an explanation of round and sticky bits, see any reference + * on FPU design, e.g., + * + * J. Coonen. An Implementation Guide to a Proposed Standard for + * Floating-Point Arithmetic. Computer, vol. 13, no. 1, Jan 1980. + */ +static inline long double +add_adjusted(long double a, long double b) +{ + struct dd sum; + union IEEEl2bits u; + + sum = dd_add(a, b); + if (sum.lo != 0) { + u.e = sum.hi; + if ((u.bits.manl & 1) == 0) + sum.hi = nextafterl(sum.hi, INFINITY * sum.lo); + } + return (sum.hi); +} + +/* + * Compute ldexp(a+b, scale) with a single rounding error. It is assumed + * that the result will be subnormal, and care is taken to ensure that + * double rounding does not occur. + */ +static inline long double +add_and_denormalize(long double a, long double b, int scale) +{ + struct dd sum; + int bits_lost; + union IEEEl2bits u; + + sum = dd_add(a, b); + + /* + * If we are losing at least two bits of accuracy to denormalization, + * then the first lost bit becomes a round bit, and we adjust the + * lowest bit of sum.hi to make it a sticky bit summarizing all the + * bits in sum.lo. With the sticky bit adjusted, the hardware will + * break any ties in the correct direction. + * + * If we are losing only one bit to denormalization, however, we must + * break the ties manually. + */ + if (sum.lo != 0) { + u.e = sum.hi; + bits_lost = -u.bits.exp - scale + 1; + if ((bits_lost != 1) ^ (int)(u.bits.manl & 1)) + sum.hi = nextafterl(sum.hi, INFINITY * sum.lo); + } + return (ldexp(sum.hi, scale)); +} + +/* + * Compute a*b exactly, returning the exact result in a struct dd. We assume + * that both a and b are normalized, so no underflow or overflow will occur. + * The current rounding mode must be round-to-nearest. + */ +static inline struct dd +dd_mul(long double a, long double b) +{ +#if LDBL_MANT_DIG == 64 + static const long double split = 0x1p32L + 1.0; +#elif LDBL_MANT_DIG == 113 + static const long double split = 0x1p57L + 1.0; +#endif + struct dd ret; + long double ha, hb, la, lb, p, q; + + p = a * split; + ha = a - p; + ha += p; + la = a - ha; + + p = b * split; + hb = b - p; + hb += p; + lb = b - hb; + + p = ha * hb; + q = ha * lb + la * hb; + + ret.hi = p + q; + ret.lo = p - ret.hi + q + la * lb; + return (ret); +} + +/* + * Fused multiply-add: Compute x * y + z with a single rounding error. + * + * We use scaling to avoid overflow/underflow, along with the + * canonical precision-doubling technique adapted from: + * + * Dekker, T. A Floating-Point Technique for Extending the + * Available Precision. Numer. Math. 18, 224-242 (1971). + */ +OLM_DLLEXPORT long double +fmal(long double x, long double y, long double z) +{ + long double xs, ys, zs, adj; + struct dd xy, r; + int oround; + int ex, ey, ez; + int spread; + + /* + * Handle special cases. The order of operations and the particular + * return values here are crucial in handling special cases involving + * infinities, NaNs, overflows, and signed zeroes correctly. + */ + if (x == 0.0 || y == 0.0) + return (x * y + z); + if (z == 0.0) + return (x * y); + if (!isfinite(x) || !isfinite(y)) + return (x * y + z); + if (!isfinite(z)) + return (z); + + xs = frexpl(x, &ex); + ys = frexpl(y, &ey); + zs = frexpl(z, &ez); + oround = fegetround(); + spread = ex + ey - ez; + + /* + * If x * y and z are many orders of magnitude apart, the scaling + * will overflow, so we handle these cases specially. Rounding + * modes other than FE_TONEAREST are painful. + */ + if (spread < -LDBL_MANT_DIG) { + feraiseexcept(FE_INEXACT); + if (!isnormal(z)) + feraiseexcept(FE_UNDERFLOW); + switch (oround) { + case FE_TONEAREST: + return (z); + case FE_TOWARDZERO: + if ((x > 0.0) ^ (y < 0.0) ^ (z < 0.0)) + return (z); + else + return (nextafterl(z, 0)); + case FE_DOWNWARD: + if ((x > 0.0) ^ (y < 0.0)) + return (z); + else + return (nextafterl(z, -INFINITY)); + default: /* FE_UPWARD */ + if ((x > 0.0) ^ (y < 0.0)) + return (nextafterl(z, INFINITY)); + else + return (z); + } + } + if (spread <= LDBL_MANT_DIG * 2) + zs = ldexpl(zs, -spread); + else + zs = copysignl(LDBL_MIN, zs); + + fesetround(FE_TONEAREST); + + /* + * Basic approach for round-to-nearest: + * + * (xy.hi, xy.lo) = x * y (exact) + * (r.hi, r.lo) = xy.hi + z (exact) + * adj = xy.lo + r.lo (inexact; low bit is sticky) + * result = r.hi + adj (correctly rounded) + */ + xy = dd_mul(xs, ys); + r = dd_add(xy.hi, zs); + + spread = ex + ey; + + if (r.hi == 0.0) { + /* + * When the addends cancel to 0, ensure that the result has + * the correct sign. + */ + fesetround(oround); + volatile long double vzs = zs; /* XXX gcc CSE bug workaround */ + return (xy.hi + vzs + ldexpl(xy.lo, spread)); + } + + if (oround != FE_TONEAREST) { + /* + * There is no need to worry about double rounding in directed + * rounding modes. + */ + fesetround(oround); + adj = r.lo + xy.lo; + return (ldexpl(r.hi + adj, spread)); + } + + adj = add_adjusted(r.lo, xy.lo); + if (spread + ilogbl(r.hi) > -16383) + return (ldexpl(r.hi + adj, spread)); + else + return (add_and_denormalize(r.hi, adj, spread)); +} diff --git a/openlibm/src/s_fmax.c b/openlibm/src/s_fmax.c new file mode 100644 index 0000000..73919c6 --- /dev/null +++ b/openlibm/src/s_fmax.c @@ -0,0 +1,54 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fmax.c,v 1.1 2004/06/30 07:04:01 das Exp $"); + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT double +fmax(double x, double y) +{ + union IEEEd2bits u[2]; + + u[0].d = x; + u[1].d = y; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].bits.exp == 2047 && (u[0].bits.manh | u[0].bits.manl) != 0) + return (y); + if (u[1].bits.exp == 2047 && (u[1].bits.manh | u[1].bits.manl) != 0) + return (x); + + /* Handle comparisons of signed zeroes. */ + if (u[0].bits.sign != u[1].bits.sign) + return (u[u[0].bits.sign].d); + + return (x > y ? x : y); +} diff --git a/openlibm/src/s_fmaxf.c b/openlibm/src/s_fmaxf.c new file mode 100644 index 0000000..a803461 --- /dev/null +++ b/openlibm/src/s_fmaxf.c @@ -0,0 +1,54 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fmaxf.c,v 1.1 2004/06/30 07:04:01 das Exp $"); + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT float +fmaxf(float x, float y) +{ + union IEEEf2bits u[2]; + + u[0].f = x; + u[1].f = y; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].bits.exp == 255 && u[0].bits.man != 0) + return (y); + if (u[1].bits.exp == 255 && u[1].bits.man != 0) + return (x); + + /* Handle comparisons of signed zeroes. */ + if (u[0].bits.sign != u[1].bits.sign) + return (u[u[0].bits.sign].f); + + return (x > y ? x : y); +} diff --git a/openlibm/src/s_fmaxl.c b/openlibm/src/s_fmaxl.c new file mode 100644 index 0000000..48de991 --- /dev/null +++ b/openlibm/src/s_fmaxl.c @@ -0,0 +1,56 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fmaxl.c,v 1.1 2004/06/30 07:04:01 das Exp $"); + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT long double +fmaxl(long double x, long double y) +{ + union IEEEl2bits u[2]; + + u[0].e = x; + mask_nbit_l(u[0]); + u[1].e = y; + mask_nbit_l(u[1]); + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].bits.exp == 32767 && (u[0].bits.manh | u[0].bits.manl) != 0) + return (y); + if (u[1].bits.exp == 32767 && (u[1].bits.manh | u[1].bits.manl) != 0) + return (x); + + /* Handle comparisons of signed zeroes. */ + if (u[0].bits.sign != u[1].bits.sign) + return (u[0].bits.sign ? y : x); + + return (x > y ? x : y); +} diff --git a/openlibm/src/s_fmin.c b/openlibm/src/s_fmin.c new file mode 100644 index 0000000..9c52739 --- /dev/null +++ b/openlibm/src/s_fmin.c @@ -0,0 +1,54 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fmin.c,v 1.1 2004/06/30 07:04:01 das Exp $"); + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT double +fmin(double x, double y) +{ + union IEEEd2bits u[2]; + + u[0].d = x; + u[1].d = y; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].bits.exp == 2047 && (u[0].bits.manh | u[0].bits.manl) != 0) + return (y); + if (u[1].bits.exp == 2047 && (u[1].bits.manh | u[1].bits.manl) != 0) + return (x); + + /* Handle comparisons of signed zeroes. */ + if (u[0].bits.sign != u[1].bits.sign) + return (u[u[1].bits.sign].d); + + return (x < y ? x : y); +} diff --git a/openlibm/src/s_fminf.c b/openlibm/src/s_fminf.c new file mode 100644 index 0000000..cc4017f --- /dev/null +++ b/openlibm/src/s_fminf.c @@ -0,0 +1,54 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fminf.c,v 1.1 2004/06/30 07:04:01 das Exp $"); + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT float +fminf(float x, float y) +{ + union IEEEf2bits u[2]; + + u[0].f = x; + u[1].f = y; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].bits.exp == 255 && u[0].bits.man != 0) + return (y); + if (u[1].bits.exp == 255 && u[1].bits.man != 0) + return (x); + + /* Handle comparisons of signed zeroes. */ + if (u[0].bits.sign != u[1].bits.sign) + return (u[u[1].bits.sign].f); + + return (x < y ? x : y); +} diff --git a/openlibm/src/s_fminl.c b/openlibm/src/s_fminl.c new file mode 100644 index 0000000..043886d --- /dev/null +++ b/openlibm/src/s_fminl.c @@ -0,0 +1,56 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_fminl.c,v 1.1 2004/06/30 07:04:01 das Exp $"); + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT long double +fminl(long double x, long double y) +{ + union IEEEl2bits u[2]; + + u[0].e = x; + mask_nbit_l(u[0]); + u[1].e = y; + mask_nbit_l(u[1]); + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].bits.exp == 32767 && (u[0].bits.manh | u[0].bits.manl) != 0) + return (y); + if (u[1].bits.exp == 32767 && (u[1].bits.manh | u[1].bits.manl) != 0) + return (x); + + /* Handle comparisons of signed zeroes. */ + if (u[0].bits.sign != u[1].bits.sign) + return (u[1].bits.sign ? y : x); + + return (x < y ? x : y); +} diff --git a/openlibm/src/s_fpclassify.c b/openlibm/src/s_fpclassify.c new file mode 100644 index 0000000..2b552e1 --- /dev/null +++ b/openlibm/src/s_fpclassify.c @@ -0,0 +1,98 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + */ + +#include +#include "math_private.h" +#include "fpmath.h" + +OLM_DLLEXPORT int +__fpclassifyd(double d) +{ + union IEEEd2bits u; + + u.d = d; + if (u.bits.exp == 2047) { + if (u.bits.manl == 0 && u.bits.manh == 0) { + return FP_INFINITE; + } else { + return FP_NAN; + } + } else if (u.bits.exp != 0) { + return FP_NORMAL; + } else if (u.bits.manl == 0 && u.bits.manh == 0) { + return FP_ZERO; + } else { + return FP_SUBNORMAL; + } +} + + +OLM_DLLEXPORT int +__fpclassifyf(float f) +{ + union IEEEf2bits u; + + u.f = f; + if (u.bits.exp == 255) { + if (u.bits.man == 0) { + return FP_INFINITE; + } else { + return FP_NAN; + } + } else if (u.bits.exp != 0) { + return FP_NORMAL; + } else if (u.bits.man == 0) { + return FP_ZERO; + } else { + return FP_SUBNORMAL; + } +} + +#ifdef OLM_LONG_DOUBLE +OLM_DLLEXPORT int +__fpclassifyl(long double e) +{ + union IEEEl2bits u; + + u.e = e; + mask_nbit_l(u); + if (u.bits.exp == 32767) { + if (u.bits.manl == 0 && u.bits.manh == 0) { + return FP_INFINITE; + } else { + return FP_NAN; + } + } else if (u.bits.exp != 0) { + return FP_NORMAL; + } else if (u.bits.manl == 0 && u.bits.manh == 0) { + return FP_ZERO; + } else { + return FP_SUBNORMAL; + } +} +#endif + diff --git a/openlibm/src/s_frexp.c b/openlibm/src/s_frexp.c new file mode 100644 index 0000000..0385acf --- /dev/null +++ b/openlibm/src/s_frexp.c @@ -0,0 +1,56 @@ +/* @(#)s_frexp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_frexp.c,v 1.11 2008/02/22 02:30:35 das Exp $"); + +/* + * for non-zero x + * x = frexp(arg,&exp); + * return a double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. + */ + +#include +#include + +#include "math_private.h" + +static const double +two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */ + +OLM_DLLEXPORT double +frexp(double x, int *eptr) +{ + int32_t hx, ix, lx; + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */ + if (ix<0x00100000) { /* subnormal */ + x *= two54; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -54; + } + *eptr += (ix>>20)-1022; + hx = (hx&0x800fffff)|0x3fe00000; + SET_HIGH_WORD(x,hx); + return x; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(frexp, frexpl); +#endif diff --git a/openlibm/src/s_frexpf.c b/openlibm/src/s_frexpf.c new file mode 100644 index 0000000..fe63046 --- /dev/null +++ b/openlibm/src/s_frexpf.c @@ -0,0 +1,44 @@ +/* s_frexpf.c -- float version of s_frexp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_frexpf.c,v 1.10 2008/02/22 02:30:35 das Exp $"); + +#include + +#include "math_private.h" + +static const float +two25 = 3.3554432000e+07; /* 0x4c000000 */ + +OLM_DLLEXPORT float +frexpf(float x, int *eptr) +{ + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7f800000||(ix==0)) return x; /* 0,inf,nan */ + if (ix<0x00800000) { /* subnormal */ + x *= two25; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -25; + } + *eptr += (ix>>23)-126; + hx = (hx&0x807fffff)|0x3f000000; + SET_FLOAT_WORD(x,hx); + return x; +} diff --git a/openlibm/src/s_frexpl.c b/openlibm/src/s_frexpl.c new file mode 100644 index 0000000..ed2d28b --- /dev/null +++ b/openlibm/src/s_frexpl.c @@ -0,0 +1,63 @@ +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_frexpl.c,v 1.1 2005/03/07 04:54:51 das Exp $ + */ + +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#if LDBL_MAX_EXP != 0x4000 +#error "Unsupported long double format" +#endif + +OLM_DLLEXPORT long double +frexpl(long double x, int *ex) +{ + union IEEEl2bits u; + + u.e = x; + switch (u.bits.exp) { + case 0: /* 0 or subnormal */ + if ((u.bits.manl | u.bits.manh) == 0) { + *ex = 0; + } else { + u.e *= 0x1.0p514; + *ex = u.bits.exp - 0x4200; + u.bits.exp = 0x3ffe; + } + break; + case 0x7fff: /* infinity or NaN; value of *ex is unspecified */ + break; + default: /* normal */ + *ex = u.bits.exp - 0x3ffe; + u.bits.exp = 0x3ffe; + break; + } + return (u.e); +} diff --git a/openlibm/src/s_ilogb.c b/openlibm/src/s_ilogb.c new file mode 100644 index 0000000..897e6d6 --- /dev/null +++ b/openlibm/src/s_ilogb.c @@ -0,0 +1,49 @@ +/* @(#)s_ilogb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_ilogb.c,v 1.10 2008/02/22 02:30:35 das Exp $"); + +/* ilogb(double x) + * return the binary exponent of non-zero x + * ilogb(0) = FP_ILOGB0 + * ilogb(NaN) = FP_ILOGBNAN (no signal is raised) + * ilogb(inf) = INT_MAX (no signal is raised) + */ + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT int +ilogb(double x) +{ + int32_t hx,lx,ix; + + EXTRACT_WORDS(hx,lx,x); + hx &= 0x7fffffff; + if(hx<0x00100000) { + if((hx|lx)==0) + return FP_ILOGB0; + else /* subnormal x */ + if(hx==0) { + for (ix = -1043; lx>0; lx<<=1) ix -=1; + } else { + for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1; + } + return ix; + } + else if (hx<0x7ff00000) return (hx>>20)-1023; + else if (hx>0x7ff00000 || lx!=0) return FP_ILOGBNAN; + else return INT_MAX; +} diff --git a/openlibm/src/s_ilogbf.c b/openlibm/src/s_ilogbf.c new file mode 100644 index 0000000..79e359d --- /dev/null +++ b/openlibm/src/s_ilogbf.c @@ -0,0 +1,41 @@ +/* s_ilogbf.c -- float version of s_ilogb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_ilogbf.c,v 1.8 2008/02/22 02:30:35 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT int +ilogbf(float x) +{ + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + hx &= 0x7fffffff; + if(hx<0x00800000) { + if(hx==0) + return FP_ILOGB0; + else /* subnormal x */ + for (ix = -126,hx<<=8; hx>0; hx<<=1) ix -=1; + return ix; + } + else if (hx<0x7f800000) return (hx>>23)-127; + else if (hx>0x7f800000) return FP_ILOGBNAN; + else return INT_MAX; +} diff --git a/openlibm/src/s_ilogbl.c b/openlibm/src/s_ilogbl.c new file mode 100644 index 0000000..d67eea8 --- /dev/null +++ b/openlibm/src/s_ilogbl.c @@ -0,0 +1,54 @@ +/* + * From: @(#)s_ilogb.c 5.1 93/09/24 + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_ilogbl.c,v 1.2 2008/02/22 02:30:35 das Exp $"); + +#include +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT int +ilogbl(long double x) +{ + union IEEEl2bits u; + unsigned long m; + int b; + + u.e = x; + if (u.bits.exp == 0) { + if ((u.bits.manl | u.bits.manh) == 0) + return (FP_ILOGB0); + /* denormalized */ + if (u.bits.manh == 0) { + m = 1lu << (LDBL_MANL_SIZE - 1); + for (b = LDBL_MANH_SIZE; !(u.bits.manl & m); m >>= 1) + b++; + } else { + m = 1lu << (LDBL_MANH_SIZE - 1); + for (b = 0; !(u.bits.manh & m); m >>= 1) + b++; + } +#ifdef LDBL_IMPLICIT_NBIT + b++; +#endif + return (LDBL_MIN_EXP - b - 1); + } else if (u.bits.exp < (LDBL_MAX_EXP << 1) - 1) + return (u.bits.exp - LDBL_MAX_EXP + 1); + else if (u.bits.manl != 0 || u.bits.manh != 0) + return (FP_ILOGBNAN); + else + return (INT_MAX); +} diff --git a/openlibm/src/s_isfinite.c b/openlibm/src/s_isfinite.c new file mode 100644 index 0000000..7c11876 --- /dev/null +++ b/openlibm/src/s_isfinite.c @@ -0,0 +1,61 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_isfinite.c,v 1.1 2004/07/09 03:32:39 das Exp $ + */ + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT int +__isfinite(double d) +{ + union IEEEd2bits u; + + u.d = d; + return (u.bits.exp != 2047); +} + +OLM_DLLEXPORT int +__isfinitef(float f) +{ + union IEEEf2bits u; + + u.f = f; + return (u.bits.exp != 255); +} + +#ifdef OLM_LONG_DOUBLE +OLM_DLLEXPORT int +__isfinitel(long double e) +{ + union IEEEl2bits u; + + u.e = e; + return (u.bits.exp != 32767); +} +#endif diff --git a/openlibm/src/s_isinf.c b/openlibm/src/s_isinf.c new file mode 100644 index 0000000..02eaff3 --- /dev/null +++ b/openlibm/src/s_isinf.c @@ -0,0 +1,66 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + */ + +#include + +#include "fpmath.h" +#include "math_private.h" + +/* Provided by libc */ +#if 1 +OLM_DLLEXPORT int +(isinf) (double d) +{ + union IEEEd2bits u; + + u.d = d; + return (u.bits.exp == 2047 && u.bits.manl == 0 && u.bits.manh == 0); +} +#endif + +OLM_DLLEXPORT int +__isinff(float f) +{ + union IEEEf2bits u; + + u.f = f; + return (u.bits.exp == 255 && u.bits.man == 0); +} + +#ifdef OLM_LONG_DOUBLE +OLM_DLLEXPORT int +__isinfl(long double e) +{ + union IEEEl2bits u; + + u.e = e; + mask_nbit_l(u); + return (u.bits.exp == 32767 && u.bits.manl == 0 && u.bits.manh == 0); +} +#endif + +openlibm_weak_reference(__isinff, isinff); diff --git a/openlibm/src/s_isnan.c b/openlibm/src/s_isnan.c new file mode 100644 index 0000000..b9066aa --- /dev/null +++ b/openlibm/src/s_isnan.c @@ -0,0 +1,67 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_isnan.c,v 1.9 2010/06/12 17:32:05 das Exp $ + */ + +#include + +#include "fpmath.h" +#include "math_private.h" + +/* Provided by libc */ +#if 1 +OLM_DLLEXPORT int +(isnan) (double d) +{ + union IEEEd2bits u; + + u.d = d; + return (u.bits.exp == 2047 && (u.bits.manl != 0 || u.bits.manh != 0)); +} +#endif + +OLM_DLLEXPORT int +__isnanf(float f) +{ + union IEEEf2bits u; + + u.f = f; + return (u.bits.exp == 255 && u.bits.man != 0); +} + +#ifdef OLM_LONG_DOUBLE +OLM_DLLEXPORT int +__isnanl(long double e) +{ + union IEEEl2bits u; + + u.e = e; + mask_nbit_l(u); + return (u.bits.exp == 32767 && (u.bits.manl != 0 || u.bits.manh != 0)); +} +#endif + +openlibm_weak_reference(__isnanf, isnanf); diff --git a/openlibm/src/s_isnormal.c b/openlibm/src/s_isnormal.c new file mode 100644 index 0000000..3c721d7 --- /dev/null +++ b/openlibm/src/s_isnormal.c @@ -0,0 +1,61 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_isnormal.c,v 1.1 2004/07/09 03:32:39 das Exp $ + */ + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT int +__isnormal(double d) +{ + union IEEEd2bits u; + + u.d = d; + return (u.bits.exp != 0 && u.bits.exp != 2047); +} + +OLM_DLLEXPORT int +__isnormalf(float f) +{ + union IEEEf2bits u; + + u.f = f; + return (u.bits.exp != 0 && u.bits.exp != 255); +} + +#ifdef OLM_LONG_DOUBLE +OLM_DLLEXPORT int +__isnormall(long double e) +{ + union IEEEl2bits u; + + u.e = e; + return (u.bits.exp != 0 && u.bits.exp != 32767); +} +#endif diff --git a/openlibm/src/s_llrint.c b/openlibm/src/s_llrint.c new file mode 100644 index 0000000..dcd6aed --- /dev/null +++ b/openlibm/src/s_llrint.c @@ -0,0 +1,9 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_llrint.c,v 1.1 2005/01/11 23:12:55 das Exp $"); + +#define type double +#define roundit rint +#define dtype long long +#define fn llrint + +#include "s_lrint.c" diff --git a/openlibm/src/s_llrintf.c b/openlibm/src/s_llrintf.c new file mode 100644 index 0000000..81ae8f0 --- /dev/null +++ b/openlibm/src/s_llrintf.c @@ -0,0 +1,9 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_llrintf.c,v 1.1 2005/01/11 23:12:55 das Exp $"); + +#define type float +#define roundit rintf +#define dtype long long +#define fn llrintf + +#include "s_lrint.c" diff --git a/openlibm/src/s_llrintl.c b/openlibm/src/s_llrintl.c new file mode 100644 index 0000000..3b23238 --- /dev/null +++ b/openlibm/src/s_llrintl.c @@ -0,0 +1,9 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_llrintl.c,v 1.1 2008/01/14 02:12:06 das Exp $"); + +#define type long double +#define roundit rintl +#define dtype long long +#define fn llrintl + +#include "s_lrint.c" diff --git a/openlibm/src/s_llround.c b/openlibm/src/s_llround.c new file mode 100644 index 0000000..717ea96 --- /dev/null +++ b/openlibm/src/s_llround.c @@ -0,0 +1,11 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_llround.c,v 1.2 2005/04/08 00:52:27 das Exp $"); + +#define type double +#define roundit round +#define dtype long long +#define DTYPE_MIN LLONG_MIN +#define DTYPE_MAX LLONG_MAX +#define fn llround + +#include "s_lround.c" diff --git a/openlibm/src/s_llroundf.c b/openlibm/src/s_llroundf.c new file mode 100644 index 0000000..9b8b8b8 --- /dev/null +++ b/openlibm/src/s_llroundf.c @@ -0,0 +1,11 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_llroundf.c,v 1.2 2005/04/08 00:52:27 das Exp $"); + +#define type float +#define roundit roundf +#define dtype long long +#define DTYPE_MIN LLONG_MIN +#define DTYPE_MAX LLONG_MAX +#define fn llroundf + +#include "s_lround.c" diff --git a/openlibm/src/s_llroundl.c b/openlibm/src/s_llroundl.c new file mode 100644 index 0000000..7a00657 --- /dev/null +++ b/openlibm/src/s_llroundl.c @@ -0,0 +1,11 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_llroundl.c,v 1.1 2005/04/08 01:24:08 das Exp $"); + +#define type long double +#define roundit roundl +#define dtype long long +#define DTYPE_MIN LLONG_MIN +#define DTYPE_MAX LLONG_MAX +#define fn llroundl + +#include "s_lround.c" diff --git a/openlibm/src/s_log1p.c b/openlibm/src/s_log1p.c new file mode 100644 index 0000000..1921b6a --- /dev/null +++ b/openlibm/src/s_log1p.c @@ -0,0 +1,179 @@ +/* @(#)s_log1p.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_log1p.c,v 1.10 2008/03/29 16:37:59 das Exp $"); + +/* double log1p(double x) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f + * may not be representable exactly. In that case, a correction + * term is need. Let u=1+x rounded. Let c = (1+x)-u, then + * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), + * and add back the correction term c/u. + * (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log1p(f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s + * (the values of Lp1 to Lp7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log1p(f) = f - (hfsq - s*(hfsq+R)). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(+INF) is +INF; log1p(-1) is -INF with signal; + * log1p(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + * + * Note: Assuming log() return accurate answer, the following + * algorithm can be used to compute log1p(x) to within a few ULP: + * + * u = 1+x; + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + +#include +#include + +#include "math_private.h" + +static const double +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +OLM_DLLEXPORT double +log1p(double x) +{ + double hfsq,f,c,s,z,R,u; + int32_t k,hx,hu,ax; + + GET_HIGH_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3FDA827A) { /* 1+x < sqrt(2)+ */ + if(ax>=0x3ff00000) { /* x <= -1.0 */ + if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x3e200000) { /* |x| < 2**-29 */ + if(two54+x>zero /* raise inexact */ + &&ax<0x3c900000) /* |x| < 2**-54 */ + return x; + else + return x - x*x*0.5; + } + if(hx>0||hx<=((int32_t)0xbfd2bec4)) { + k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ + } + if (hx >= 0x7ff00000) return x+x; + if(k!=0) { + if(hx<0x43400000) { + STRICT_ASSIGN(double,u,1.0+x); + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ + c /= u; + } else { + u = x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = 0; + } + hu &= 0x000fffff; + /* + * The approximation to sqrt(2) used in thresholds is not + * critical. However, the ones used above must give less + * strict bounds than the one here so that the k==0 case is + * never reached from here, since here we have committed to + * using the correction term but don't use it if k==0. + */ + if(hu<0x6a09e) { /* u ~< sqrt(2) */ + SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ + } else { + k += 1; + SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ + hu = (0x00100000-hu)>>2; + } + f = u-1.0; + } + hfsq=0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { + if(k==0) { + return zero; + } else { + c += k*ln2_lo; + return k*ln2_hi+c; + } + } + R = hfsq*(1.0-0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/(2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(log1p, log1pl); +#endif diff --git a/openlibm/src/s_log1pf.c b/openlibm/src/s_log1pf.c new file mode 100644 index 0000000..53c8f49 --- /dev/null +++ b/openlibm/src/s_log1pf.c @@ -0,0 +1,114 @@ +/* s_log1pf.c -- float version of s_log1p.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_log1pf.c,v 1.12 2008/03/29 16:37:59 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const float +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lp3 = 2.8571429849e-01, /* 3E924925 */ +Lp4 = 2.2222198546e-01, /* 3E638E29 */ +Lp5 = 1.8183572590e-01, /* 3E3A3325 */ +Lp6 = 1.5313838422e-01, /* 3E1CD04F */ +Lp7 = 1.4798198640e-01; /* 3E178897 */ + +static const float zero = 0.0; + +OLM_DLLEXPORT float +log1pf(float x) +{ + float hfsq,f,c,s,z,R,u; + int32_t k,hx,hu,ax; + + GET_FLOAT_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */ + if(ax>=0x3f800000) { /* x <= -1.0 */ + if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x38000000) { /* |x| < 2**-15 */ + if(two25+x>zero /* raise inexact */ + &&ax<0x33800000) /* |x| < 2**-24 */ + return x; + else + return x - x*x*(float)0.5; + } + if(hx>0||hx<=((int32_t)0xbe95f619)) { + k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ + } + if (hx >= 0x7f800000) return x+x; + if(k!=0) { + if(hx<0x5a000000) { + STRICT_ASSIGN(float,u,(float)1.0+x); + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + /* correction term */ + c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); + c /= u; + } else { + u = x; + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + c = 0; + } + hu &= 0x007fffff; + /* + * The approximation to sqrt(2) used in thresholds is not + * critical. However, the ones used above must give less + * strict bounds than the one here so that the k==0 case is + * never reached from here, since here we have committed to + * using the correction term but don't use it if k==0. + */ + if(hu<0x3504f4) { /* u < sqrt(2) */ + SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ + } else { + k += 1; + SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ + hu = (0x00800000-hu)>>2; + } + f = u-(float)1.0; + } + hfsq=(float)0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { + if(k==0) { + return zero; + } else { + c += k*ln2_lo; + return k*ln2_hi+c; + } + } + R = hfsq*((float)1.0-(float)0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/((float)2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} diff --git a/openlibm/src/s_logb.c b/openlibm/src/s_logb.c new file mode 100644 index 0000000..116b696 --- /dev/null +++ b/openlibm/src/s_logb.c @@ -0,0 +1,49 @@ +/* @(#)s_logb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_logb.c,v 1.12 2008/02/08 01:22:13 bde Exp $"); + +/* + * double logb(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include +#include + +#include "math_private.h" + +static const double +two54 = 1.80143985094819840000e+16; /* 43500000 00000000 */ + +OLM_DLLEXPORT double +logb(double x) +{ + int32_t lx,ix; + EXTRACT_WORDS(ix,lx,x); + ix &= 0x7fffffff; /* high |x| */ + if((ix|lx)==0) return -1.0/fabs(x); + if(ix>=0x7ff00000) return x*x; + if(ix<0x00100000) { + x *= two54; /* convert subnormal x to normal */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + return (double) ((ix>>20)-1023-54); + } else + return (double) ((ix>>20)-1023); +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(logb, logbl); +#endif diff --git a/openlibm/src/s_logbf.c b/openlibm/src/s_logbf.c new file mode 100644 index 0000000..8b1d117 --- /dev/null +++ b/openlibm/src/s_logbf.c @@ -0,0 +1,41 @@ +/* s_logbf.c -- float version of s_logb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_logbf.c,v 1.9 2008/02/22 02:30:35 das Exp $"); + +#include + +#include "math_private.h" + +static const float +two25 = 3.355443200e+07; /* 0x4c000000 */ + +OLM_DLLEXPORT float +logbf(float x) +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high |x| */ + if(ix==0) return (float)-1.0/fabsf(x); + if(ix>=0x7f800000) return x*x; + if(ix<0x00800000) { + x *= two25; /* convert subnormal x to normal */ + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + return (float) ((ix>>23)-127-25); + } else + return (float) ((ix>>23)-127); +} diff --git a/openlibm/src/s_logbl.c b/openlibm/src/s_logbl.c new file mode 100644 index 0000000..3c1336b --- /dev/null +++ b/openlibm/src/s_logbl.c @@ -0,0 +1,52 @@ +/* + * From: @(#)s_ilogb.c 5.1 93/09/24 + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT long double +logbl(long double x) +{ + union IEEEl2bits u; + unsigned long m; + int b; + + u.e = x; + if (u.bits.exp == 0) { + if ((u.bits.manl | u.bits.manh) == 0) { /* x == 0 */ + u.bits.sign = 1; + return (1.0L / u.e); + } + /* denormalized */ + if (u.bits.manh == 0) { + m = 1lu << (LDBL_MANL_SIZE - 1); + for (b = LDBL_MANH_SIZE; !(u.bits.manl & m); m >>= 1) + b++; + } else { + m = 1lu << (LDBL_MANH_SIZE - 1); + for (b = 0; !(u.bits.manh & m); m >>= 1) + b++; + } +#ifdef LDBL_IMPLICIT_NBIT + b++; +#endif + return ((long double)(LDBL_MIN_EXP - b - 1)); + } + if (u.bits.exp < (LDBL_MAX_EXP << 1) - 1) /* normal */ + return ((long double)(u.bits.exp - LDBL_MAX_EXP + 1)); + else /* +/- inf or nan */ + return (x * x); +} diff --git a/openlibm/src/s_lrint.c b/openlibm/src/s_lrint.c new file mode 100644 index 0000000..e1c5546 --- /dev/null +++ b/openlibm/src/s_lrint.c @@ -0,0 +1,61 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" + +#include +#include + +#include "math_private.h" + +#ifndef type +//__FBSDID("$FreeBSD: src/lib/msun/src/s_lrint.c,v 1.1 2005/01/11 23:12:55 das Exp $"); +#define type double +#define roundit rint +#define dtype long +#define fn lrint +#endif + +/* + * C99 says we should not raise a spurious inexact exception when an + * invalid exception is raised. Unfortunately, the set of inputs + * that overflows depends on the rounding mode when 'dtype' has more + * significant bits than 'type'. Hence, we bend over backwards for the + * sake of correctness; an MD implementation could be more efficient. + */ +OLM_DLLEXPORT dtype +fn(type x) +{ + fenv_t env; + dtype d; + + feholdexcept(&env); + d = (dtype)roundit(x); + if (fetestexcept(FE_INVALID)) + feclearexcept(FE_INEXACT); + feupdateenv(&env); + return (d); +} diff --git a/openlibm/src/s_lrintf.c b/openlibm/src/s_lrintf.c new file mode 100644 index 0000000..f29ad52 --- /dev/null +++ b/openlibm/src/s_lrintf.c @@ -0,0 +1,9 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_lrintf.c,v 1.1 2005/01/11 23:12:55 das Exp $"); + +#define type float +#define roundit rintf +#define dtype long +#define fn lrintf + +#include "s_lrint.c" diff --git a/openlibm/src/s_lrintl.c b/openlibm/src/s_lrintl.c new file mode 100644 index 0000000..b57c27d --- /dev/null +++ b/openlibm/src/s_lrintl.c @@ -0,0 +1,9 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_lrintl.c,v 1.1 2008/01/14 02:12:06 das Exp $"); + +#define type long double +#define roundit rintl +#define dtype long +#define fn lrintl + +#include "s_lrint.c" diff --git a/openlibm/src/s_lround.c b/openlibm/src/s_lround.c new file mode 100644 index 0000000..76fa732 --- /dev/null +++ b/openlibm/src/s_lround.c @@ -0,0 +1,69 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" + +#include +#include +#include + +#include "math_private.h" + +#ifndef type +//__FBSDID("$FreeBSD: src/lib/msun/src/s_lround.c,v 1.2 2005/04/08 00:52:16 das Exp $"); +#define type double +#define roundit round +#define dtype long +#define DTYPE_MIN LONG_MIN +#define DTYPE_MAX LONG_MAX +#define fn lround +#endif + +/* + * If type has more precision than dtype, the endpoints dtype_(min|max) are + * of the form xxx.5; they are "out of range" because lround() rounds away + * from 0. On the other hand, if type has less precision than dtype, then + * all values that are out of range are integral, so we might as well assume + * that everything is in range. At compile time, INRANGE(x) should reduce to + * two floating-point comparisons in the former case, or TRUE otherwise. + */ +static const type dtype_min = DTYPE_MIN - 0.5; +static const type dtype_max = DTYPE_MAX + 0.5; +#define INRANGE(x) (dtype_max - DTYPE_MAX != 0.5 || \ + ((x) > dtype_min && (x) < dtype_max)) + +OLM_DLLEXPORT dtype +fn(type x) +{ + + if (INRANGE(x)) { + x = roundit(x); + return ((dtype)x); + } else { + feraiseexcept(FE_INVALID); + return (DTYPE_MAX); + } +} diff --git a/openlibm/src/s_lroundf.c b/openlibm/src/s_lroundf.c new file mode 100644 index 0000000..f526eef --- /dev/null +++ b/openlibm/src/s_lroundf.c @@ -0,0 +1,11 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_lroundf.c,v 1.2 2005/04/08 00:52:27 das Exp $"); + +#define type float +#define roundit roundf +#define dtype long +#define DTYPE_MIN LONG_MIN +#define DTYPE_MAX LONG_MAX +#define fn lroundf + +#include "s_lround.c" diff --git a/openlibm/src/s_lroundl.c b/openlibm/src/s_lroundl.c new file mode 100644 index 0000000..eb8997c --- /dev/null +++ b/openlibm/src/s_lroundl.c @@ -0,0 +1,11 @@ +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_lroundl.c,v 1.1 2005/04/08 01:24:08 das Exp $"); + +#define type long double +#define roundit roundl +#define dtype long +#define DTYPE_MIN LONG_MIN +#define DTYPE_MAX LONG_MAX +#define fn lroundl + +#include "s_lround.c" diff --git a/openlibm/src/s_modf.c b/openlibm/src/s_modf.c new file mode 100644 index 0000000..e3b517b --- /dev/null +++ b/openlibm/src/s_modf.c @@ -0,0 +1,76 @@ +/* @(#)s_modf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * modf(double x, double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include + +#include "math_private.h" + +static const double one = 1.0; + +OLM_DLLEXPORT double +modf(double x, double *iptr) +{ + int32_t i0,i1,j0; + u_int32_t i; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent of x */ + if(j0<20) { /* integer part in high x */ + if(j0<0) { /* |x|<1 */ + INSERT_WORDS(*iptr,i0&0x80000000,0); /* *iptr = +-0 */ + return x; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) { /* x is integral */ + u_int32_t high; + *iptr = x; + GET_HIGH_WORD(high,x); + INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */ + return x; + } else { + INSERT_WORDS(*iptr,i0&(~i),0); + return x - *iptr; + } + } + } else if (j0>51) { /* no fraction part */ + u_int32_t high; + if (j0 == 0x400) { /* inf/NaN */ + *iptr = x; + return 0.0 / x; + } + *iptr = x*one; + GET_HIGH_WORD(high,x); + INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */ + return x; + } else { /* fraction part in low x */ + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) { /* x is integral */ + u_int32_t high; + *iptr = x; + GET_HIGH_WORD(high,x); + INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */ + return x; + } else { + INSERT_WORDS(*iptr,i0,i1&(~i)); + return x - *iptr; + } + } +} diff --git a/openlibm/src/s_modff.c b/openlibm/src/s_modff.c new file mode 100644 index 0000000..0a0c840 --- /dev/null +++ b/openlibm/src/s_modff.c @@ -0,0 +1,58 @@ +/* s_modff.c -- float version of s_modf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_modff.c,v 1.9 2008/02/22 02:30:35 das Exp $"); + +#include + +#include "math_private.h" + +static const float one = 1.0; + +OLM_DLLEXPORT float +modff(float x, float *iptr) +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; /* exponent of x */ + if(j0<23) { /* integer part in x */ + if(j0<0) { /* |x|<1 */ + SET_FLOAT_WORD(*iptr,i0&0x80000000); /* *iptr = +-0 */ + return x; + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) { /* x is integral */ + u_int32_t ix; + *iptr = x; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x80000000); /* return +-0 */ + return x; + } else { + SET_FLOAT_WORD(*iptr,i0&(~i)); + return x - *iptr; + } + } + } else { /* no fraction part */ + u_int32_t ix; + *iptr = x*one; + if (x != x) /* NaN */ + return x; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x80000000); /* return +-0 */ + return x; + } +} diff --git a/openlibm/src/s_modfl.c b/openlibm/src/s_modfl.c new file mode 100644 index 0000000..44a9363 --- /dev/null +++ b/openlibm/src/s_modfl.c @@ -0,0 +1,101 @@ +/*- + * Copyright (c) 2007 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * Derived from s_modf.c, which has the following Copyright: + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * $FreeBSD: src/lib/msun/src/s_modfl.c,v 1.1 2007/01/07 07:54:21 das Exp $ + */ + +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#if LDBL_MANL_SIZE > 32 +#define MASK ((u_int64_t)-1) +#else +#define MASK ((u_int32_t)-1) +#endif +/* Return the last n bits of a word, representing the fractional part. */ +#define GETFRAC(bits, n) ((bits) & ~(MASK << (n))) +/* The number of fraction bits in manh, not counting the integer bit */ +#define HIBITS (LDBL_MANT_DIG - LDBL_MANL_SIZE) + +static const long double zero[] = { 0.0L, -0.0L }; + +OLM_DLLEXPORT long double +modfl(long double x, long double *iptr) +{ + union IEEEl2bits ux; + int e; + + ux.e = x; + e = ux.bits.exp - LDBL_MAX_EXP + 1; + if (e < HIBITS) { /* Integer part is in manh. */ + if (e < 0) { /* |x|<1 */ + *iptr = zero[ux.bits.sign]; + return (x); + } else { + if ((GETFRAC(ux.bits.manh, HIBITS - 1 - e) | + ux.bits.manl) == 0) { /* X is an integer. */ + *iptr = x; + return (zero[ux.bits.sign]); + } else { + /* Clear all but the top e+1 bits. */ + ux.bits.manh >>= HIBITS - 1 - e; + ux.bits.manh <<= HIBITS - 1 - e; + ux.bits.manl = 0; + *iptr = ux.e; + return (x - ux.e); + } + } + } else if (e >= LDBL_MANT_DIG - 1) { /* x has no fraction part. */ + *iptr = x; + if (x != x) /* Handle NaNs. */ + return (x); + return (zero[ux.bits.sign]); + } else { /* Fraction part is in manl. */ + if (GETFRAC(ux.bits.manl, LDBL_MANT_DIG - 1 - e) == 0) { + /* x is integral. */ + *iptr = x; + return (zero[ux.bits.sign]); + } else { + /* Clear all but the top e+1 bits. */ + ux.bits.manl >>= LDBL_MANT_DIG - 1 - e; + ux.bits.manl <<= LDBL_MANT_DIG - 1 - e; + *iptr = ux.e; + return (x - ux.e); + } + } +} diff --git a/openlibm/src/s_nan.c b/openlibm/src/s_nan.c new file mode 100644 index 0000000..dd1c5af --- /dev/null +++ b/openlibm/src/s_nan.c @@ -0,0 +1,124 @@ +/*- + * Copyright (c) 2007 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_nan.c,v 1.2 2007/12/18 23:46:32 das Exp $ + */ + +//VBS +//#include +#include +#include +#include +#include +#include //for memset + +#include "math_private.h" + +#if !defined(__APPLE__) && !defined(__FreeBSD__) && !defined(__DragonFly__) +static __inline int digittoint(int c) { + if ('0' <= c && c <= '9') + return (c - '0'); + else if ('A' <= c && c <= 'F') + return (c - 'A' + 10); + else if ('a' <= c && c <= 'f') + return (c - 'a' + 10); + return 0; +} +#endif + + +/* + * Scan a string of hexadecimal digits (the format nan(3) expects) and + * make a bit array (using the local endianness). We stop when we + * encounter an invalid character, NUL, etc. If we overflow, we do + * the same as gcc's __builtin_nan(), namely, discard the high order bits. + * + * The format this routine accepts needs to be compatible with what is used + * in contrib/gdtoa/hexnan.c (for strtod/scanf) and what is used in + * __builtin_nan(). In fact, we're only 100% compatible for strings we + * consider valid, so we might be violating the C standard. But it's + * impossible to use nan(3) portably anyway, so this seems good enough. + */ +OLM_DLLEXPORT void +__scan_nan(u_int32_t *words, int num_words, const char *s) +{ + int si; /* index into s */ + int bitpos; /* index into words (in bits) */ + + memset(words, 0, num_words * sizeof(u_int32_t)); + + /* Allow a leading '0x'. (It's expected, but redundant.) */ + if (s[0] == '0' && (s[1] == 'x' || s[1] == 'X')) + s += 2; + + /* Scan forwards in the string, looking for the end of the sequence. */ + for (si = 0; isxdigit(s[si]); si++) + ; + + /* Scan backwards, filling in the bits in words[] as we go. */ +#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ + for (bitpos = 0; bitpos < 32 * num_words; bitpos += 4) { +#else + for (bitpos = 32 * num_words - 4; bitpos >= 0; bitpos -= 4) { +#endif + if (--si < 0) + break; + words[bitpos / 32] |= digittoint(s[si]) << (bitpos % 32); + } +} + +OLM_DLLEXPORT double +nan(const char *s) +{ + union { + double d; + u_int32_t bits[2]; + } u; + + __scan_nan(u.bits, 2, s); +#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ + u.bits[1] |= 0x7ff80000; +#else + u.bits[0] |= 0x7ff80000; +#endif + return (u.d); +} + +OLM_DLLEXPORT float +nanf(const char *s) +{ + union { + float f; + u_int32_t bits[1]; + } u; + + __scan_nan(u.bits, 1, s); + u.bits[0] |= 0x7fc00000; + return (u.f); +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(nan, nanl); +#endif diff --git a/openlibm/src/s_nearbyint.c b/openlibm/src/s_nearbyint.c new file mode 100644 index 0000000..95162a5 --- /dev/null +++ b/openlibm/src/s_nearbyint.c @@ -0,0 +1,56 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_nearbyint.c,v 1.2 2008/01/14 02:12:06 das Exp $"); + +#include +#include + +#include "math_private.h" + +/* + * We save and restore the floating-point environment to avoid raising + * an inexact exception. We can get away with using fesetenv() + * instead of feclearexcept()/feupdateenv() to restore the environment + * because the only exception defined for rint() is overflow, and + * rounding can't overflow as long as emax >= p. + */ +#define DECL(type, fn, rint) \ +OLM_DLLEXPORT type \ +fn(type x) \ +{ \ + type ret; \ + fenv_t env; \ + \ + fegetenv(&env); \ + ret = rint(x); \ + fesetenv(&env); \ + return (ret); \ +} + +DECL(double, nearbyint, rint) +DECL(float, nearbyintf, rintf) diff --git a/openlibm/src/s_nextafter.c b/openlibm/src/s_nextafter.c new file mode 100644 index 0000000..8b2ea05 --- /dev/null +++ b/openlibm/src/s_nextafter.c @@ -0,0 +1,83 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_nextafter.c,v 1.12 2008/02/22 02:30:35 das Exp $"); + +/* IEEE functions + * nextafter(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +nextafter(double x, double y) +{ + volatile double t; + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */ + return x+y; + if(x==y) return y; /* x=y, return y */ + if((ix|lx)==0) { /* x == 0 */ + INSERT_WORDS(x,hy&0x80000000,1); /* return +-minsubnormal */ + t = x*x; + if(t==x) return t; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) return x+x; /* overflow */ + if(hy<0x00100000) { /* underflow */ + t = x*x; + if(t!=x) { /* raise underflow flag */ + INSERT_WORDS(y,hx,lx); + return y; + } + } + INSERT_WORDS(x,hx,lx); + return x; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(nextafter, nexttoward); +openlibm_weak_reference(nextafter, nexttowardl); +openlibm_weak_reference(nextafter, nextafterl); +#endif diff --git a/openlibm/src/s_nextafterf.c b/openlibm/src/s_nextafterf.c new file mode 100644 index 0000000..d4cd630 --- /dev/null +++ b/openlibm/src/s_nextafterf.c @@ -0,0 +1,67 @@ +/* s_nextafterf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_nextafterf.c,v 1.11 2008/02/22 02:30:35 das Exp $"); + +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +nextafterf(float x, float y) +{ + volatile float t; + int32_t hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>0x7f800000)) /* y is nan */ + return x+y; + if(x==y) return y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + SET_FLOAT_WORD(x,(hy&0x80000000)|1);/* return +-minsubnormal */ + t = x*x; + if(t==x) return t; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hx>hy) { /* x > y, x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy){ /* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) return x+x; /* overflow */ + if(hy<0x00800000) { /* underflow */ + t = x*x; + if(t!=x) { /* raise underflow flag */ + SET_FLOAT_WORD(y,hx); + return y; + } + } + SET_FLOAT_WORD(x,hx); + return x; +} diff --git a/openlibm/src/s_nextafterl.c b/openlibm/src/s_nextafterl.c new file mode 100644 index 0000000..bb73141 --- /dev/null +++ b/openlibm/src/s_nextafterl.c @@ -0,0 +1,80 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_nextafterl.c,v 1.2 2008/02/22 02:30:36 das Exp $"); + +/* IEEE functions + * nextafter(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#if LDBL_MAX_EXP != 0x4000 +#error "Unsupported long double format" +#endif + +OLM_DLLEXPORT long double +nextafterl(long double x, long double y) +{ + volatile long double t; + union IEEEl2bits ux, uy; + + ux.e = x; + uy.e = y; + + if ((ux.bits.exp == 0x7fff && + ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl) != 0) || + (uy.bits.exp == 0x7fff && + ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0)) + return x+y; /* x or y is nan */ + if(x==y) return y; /* x=y, return y */ + if(x==0.0) { + ux.bits.manh = 0; /* return +-minsubnormal */ + ux.bits.manl = 1; + ux.bits.sign = uy.bits.sign; + t = ux.e*ux.e; + if(t==ux.e) return t; else return ux.e; /* raise underflow flag */ + } + if((x>0.0) ^ (x +#include + +#include "fpmath.h" +#include "math_private.h" + +#if LDBL_MAX_EXP != 0x4000 +#error "Unsupported long double format" +#endif + +OLM_DLLEXPORT double +nexttoward(double x, long double y) +{ + union IEEEl2bits uy; + volatile double t; + int32_t hx,ix; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; /* |x| */ + uy.e = y; + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || + (uy.bits.exp == 0x7fff && + ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0)) + return x+y; /* x or y is nan */ + if(x==y) return (double)y; /* x=y, return y */ + if(x==0.0) { + INSERT_WORDS(x,uy.bits.sign<<31,1); /* return +-minsubnormal */ + t = x*x; + if(t==x) return t; else return x; /* raise underflow flag */ + } + if((hx>0.0) ^ (x < y)) { /* x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + ix = hx&0x7ff00000; + if(ix>=0x7ff00000) return x+x; /* overflow */ + if(ix<0x00100000) { /* underflow */ + t = x*x; + if(t!=x) { /* raise underflow flag */ + INSERT_WORDS(x,hx,lx); + return x; + } + } + INSERT_WORDS(x,hx,lx); + return x; +} diff --git a/openlibm/src/s_nexttowardf.c b/openlibm/src/s_nexttowardf.c new file mode 100644 index 0000000..bf50862 --- /dev/null +++ b/openlibm/src/s_nexttowardf.c @@ -0,0 +1,61 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_nexttowardf.c,v 1.3 2011/02/10 07:38:38 das Exp $"); + +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#define LDBL_INFNAN_EXP (LDBL_MAX_EXP * 2 - 1) + +#ifdef OLM_LONG_DOUBLE +OLM_DLLEXPORT float +nexttowardf(float x, long double y) +{ + union IEEEl2bits uy; + volatile float t; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; /* |x| */ + uy.e = y; + + if((ix>0x7f800000) || + (uy.bits.exp == LDBL_INFNAN_EXP && + ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl) != 0)) + return x+y; /* x or y is nan */ + if(x==y) return (float)y; /* x=y, return y */ + if(ix==0) { /* x == 0 */ + SET_FLOAT_WORD(x,(uy.bits.sign<<31)|1);/* return +-minsubnormal */ + t = x*x; + if(t==x) return t; else return x; /* raise underflow flag */ + } + if((hx>=0) ^ (x < y)) /* x -= ulp */ + hx -= 1; + else /* x += ulp */ + hx += 1; + ix = hx&0x7f800000; + if(ix>=0x7f800000) return x+x; /* overflow */ + if(ix<0x00800000) { /* underflow */ + t = x*x; + if(t!=x) { /* raise underflow flag */ + SET_FLOAT_WORD(x,hx); + return x; + } + } + SET_FLOAT_WORD(x,hx); + return x; +} +#endif diff --git a/openlibm/src/s_remquo.c b/openlibm/src/s_remquo.c new file mode 100644 index 0000000..5c566c7 --- /dev/null +++ b/openlibm/src/s_remquo.c @@ -0,0 +1,158 @@ +/* @(#)e_fmod.c 1.3 95/01/18 */ +/*- + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_remquo.c,v 1.2 2008/03/30 20:47:26 das Exp $"); + +#include +#include + +#include "math_private.h" + +static const double Zero[] = {0.0, -0.0,}; + +/* + * Return the IEEE remainder and set *quo to the last n bits of the + * quotient, rounded to the nearest integer. We choose n=31 because + * we wind up computing all the integer bits of the quotient anyway as + * a side-effect of computing the remainder by the shift and subtract + * method. In practice, this is far more bits than are needed to use + * remquo in reduction algorithms. + */ +OLM_DLLEXPORT double +remquo(double x, double y, int *quo) +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + u_int32_t lx,ly,lz,q,sxy; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + sxy = (hx ^ hy) & 0x80000000; + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ + ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<=hy) { + if((hx>31]; /* |x|=|y| return x*0*/ + } + } + + /* determine ix = ilogb(x) */ + if(hx<0x00100000) { /* subnormal x */ + if(hx==0) { + for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; + } else { + for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; + } + } else ix = (hx>>20)-1023; + + /* determine iy = ilogb(y) */ + if(hy<0x00100000) { /* subnormal y */ + if(hy==0) { + for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; + } else { + for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; + } + } else iy = (hy>>20)-1023; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -1022) + hx = 0x00100000|(0x000fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -1022-ix; + if(n<=31) { + hx = (hx<>(32-n)); + lx <<= n; + } else { + hx = lx<<(n-32); + lx = 0; + } + } + if(iy >= -1022) + hy = 0x00100000|(0x000fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -1022-iy; + if(n<=31) { + hy = (hy<>(32-n)); + ly <<= n; + } else { + hy = ly<<(n-32); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + q = 0; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx>31); lx = lx+lx;} + else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} + q <<= 1; + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;q++;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) { /* return sign(x)*0 */ + *quo = (sxy ? -q : q); + return Zero[(u_int32_t)sx>>31]; + } + while(hx<0x00100000) { /* normalize x */ + hx = hx+hx+(lx>>31); lx = lx+lx; + iy -= 1; + } + if(iy>= -1022) { /* normalize output */ + hx = ((hx-0x00100000)|((iy+1023)<<20)); + } else { /* subnormal output */ + n = -1022 - iy; + if(n<=20) { + lx = (lx>>n)|((u_int32_t)hx<<(32-n)); + hx >>= n; + } else if (n<=31) { + lx = (hx<<(32-n))|(lx>>n); hx = sx; + } else { + lx = hx>>(n-32); hx = sx; + } + } +fixup: + INSERT_WORDS(x,hx,lx); + y = fabs(y); + if (y < 0x1p-1021) { + if (x+x>y || (x+x==y && (q & 1))) { + q++; + x-=y; + } + } else if (x>0.5*y || (x==0.5*y && (q & 1))) { + q++; + x-=y; + } + GET_HIGH_WORD(hx,x); + SET_HIGH_WORD(x,hx^sx); + q &= 0x7fffffff; + *quo = (sxy ? -q : q); + return x; +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(remquo, remquol); +#endif diff --git a/openlibm/src/s_remquof.c b/openlibm/src/s_remquof.c new file mode 100644 index 0000000..7ef0f72 --- /dev/null +++ b/openlibm/src/s_remquof.c @@ -0,0 +1,122 @@ +/* @(#)e_fmod.c 1.3 95/01/18 */ +/*- + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_remquof.c,v 1.1 2005/03/25 04:40:44 das Exp $"); + +#include + +#include "math_private.h" + +static const float Zero[] = {0.0, -0.0,}; + +/* + * Return the IEEE remainder and set *quo to the last n bits of the + * quotient, rounded to the nearest integer. We choose n=31 because + * we wind up computing all the integer bits of the quotient anyway as + * a side-effect of computing the remainder by the shift and subtract + * method. In practice, this is far more bits than are needed to use + * remquo in reduction algorithms. + */ +OLM_DLLEXPORT float +remquof(float x, float y, int *quo) +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + u_int32_t q,sxy; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + sxy = (hx ^ hy) & 0x80000000; + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if(hy==0||hx>=0x7f800000||hy>0x7f800000) /* y=0,NaN;or x not finite */ + return (x*y)/(x*y); + if(hx>31]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(hx<0x00800000) { /* subnormal x */ + for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; + } else ix = (hx>>23)-127; + + /* determine iy = ilogb(y) */ + if(hy<0x00800000) { /* subnormal y */ + for (iy = -126,i=(hy<<8); i>0; i<<=1) iy -=1; + } else iy = (hy>>23)-127; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -126) + hx = 0x00800000|(0x007fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -126-ix; + hx <<= n; + } + if(iy >= -126) + hy = 0x00800000|(0x007fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -126-iy; + hy <<= n; + } + + /* fix point fmod */ + n = ix - iy; + q = 0; + while(n--) { + hz=hx-hy; + if(hz<0) hx = hx << 1; + else {hx = hz << 1; q++;} + q <<= 1; + } + hz=hx-hy; + if(hz>=0) {hx=hz;q++;} + + /* convert back to floating value and restore the sign */ + if(hx==0) { /* return sign(x)*0 */ + *quo = (sxy ? -q : q); + return Zero[(u_int32_t)sx>>31]; + } + while(hx<0x00800000) { /* normalize x */ + hx <<= 1; + iy -= 1; + } + if(iy>= -126) { /* normalize output */ + hx = ((hx-0x00800000)|((iy+127)<<23)); + } else { /* subnormal output */ + n = -126 - iy; + hx >>= n; + } +fixup: + SET_FLOAT_WORD(x,hx); + y = fabsf(y); + if (y < 0x1p-125f) { + if (x+x>y || (x+x==y && (q & 1))) { + q++; + x-=y; + } + } else if (x>0.5f*y || (x==0.5f*y && (q & 1))) { + q++; + x-=y; + } + GET_FLOAT_WORD(hx,x); + SET_FLOAT_WORD(x,hx^sx); + q &= 0x7fffffff; + *quo = (sxy ? -q : q); + return x; +} diff --git a/openlibm/src/s_remquol.c b/openlibm/src/s_remquol.c new file mode 100644 index 0000000..ebde999 --- /dev/null +++ b/openlibm/src/s_remquol.c @@ -0,0 +1,177 @@ +/* @(#)e_fmod.c 1.3 95/01/18 */ +/*- + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_remquol.c,v 1.2 2008/07/31 20:09:47 das Exp $"); + +#include +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#define BIAS (LDBL_MAX_EXP - 1) + +#if LDBL_MANL_SIZE > 32 +typedef u_int64_t manl_t; +#else +typedef u_int32_t manl_t; +#endif + +#if LDBL_MANH_SIZE > 32 +typedef u_int64_t manh_t; +#else +typedef u_int32_t manh_t; +#endif + +/* + * These macros add and remove an explicit integer bit in front of the + * fractional mantissa, if the architecture doesn't have such a bit by + * default already. + */ +#ifdef LDBL_IMPLICIT_NBIT +#define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) +#define HFRAC_BITS LDBL_MANH_SIZE +#else +#define SET_NBIT(hx) (hx) +#define HFRAC_BITS (LDBL_MANH_SIZE - 1) +#endif + +#define MANL_SHIFT (LDBL_MANL_SIZE - 1) + +static const long double Zero[] = {0.0L, -0.0L}; + +/* + * Return the IEEE remainder and set *quo to the last n bits of the + * quotient, rounded to the nearest integer. We choose n=31 because + * we wind up computing all the integer bits of the quotient anyway as + * a side-effect of computing the remainder by the shift and subtract + * method. In practice, this is far more bits than are needed to use + * remquo in reduction algorithms. + * + * Assumptions: + * - The low part of the mantissa fits in a manl_t exactly. + * - The high part of the mantissa fits in an int64_t with enough room + * for an explicit integer bit in front of the fractional bits. + */ +OLM_DLLEXPORT long double +remquol(long double x, long double y, int *quo) +{ + union IEEEl2bits ux, uy; + int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ + manh_t hy; + manl_t lx,ly,lz; + int ix,iy,n,q,sx,sxy; + + ux.e = x; + uy.e = y; + sx = ux.bits.sign; + sxy = sx ^ uy.bits.sign; + ux.bits.sign = 0; /* |x| */ + uy.bits.sign = 0; /* |y| */ + x = ux.e; + + /* purge off exception values */ + if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */ + (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ + (uy.bits.exp == BIAS + LDBL_MAX_EXP && + ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */ + return (x*y)/(x*y); + if(ux.bits.exp<=uy.bits.exp) { + if((ux.bits.exp>MANL_SHIFT); lx = lx+lx;} + else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;} + q <<= 1; + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;q++;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) { /* return sign(x)*0 */ + *quo = (sxy ? -q : q); + return Zero[sx]; + } + while(hx<(1ULL<>MANL_SHIFT); lx = lx+lx; + iy -= 1; + } + ux.bits.manh = hx; /* The integer bit is truncated here if needed. */ + ux.bits.manl = lx; + if (iy < LDBL_MIN_EXP) { + ux.bits.exp = iy + (BIAS + 512); + ux.e *= 0x1p-512; + } else { + ux.bits.exp = iy + BIAS; + } + ux.bits.sign = 0; + x = ux.e; +fixup: + y = fabsl(y); + if (y < LDBL_MIN * 2) { + if (x+x>y || (x+x==y && (q & 1))) { + q++; + x-=y; + } + } else if (x>0.5*y || (x==0.5*y && (q & 1))) { + q++; + x-=y; + } + + ux.e = x; + ux.bits.sign ^= sx; + x = ux.e; + + q &= 0x7fffffff; + *quo = (sxy ? -q : q); + return x; +} diff --git a/openlibm/src/s_rint.c b/openlibm/src/s_rint.c new file mode 100644 index 0000000..f81e692 --- /dev/null +++ b/openlibm/src/s_rint.c @@ -0,0 +1,92 @@ +/* @(#)s_rint.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_rint.c,v 1.16 2008/02/22 02:30:35 das Exp $"); + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include +#include + +#include "math_private.h" + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +OLM_DLLEXPORT double +rint(double x) +{ + int32_t i0,j0,sx; + u_int32_t i,i1; + double w,t; + EXTRACT_WORDS(i0,i1,x); + sx = (i0>>31)&1; + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { + if(((i0&0x7fffffff)|i1)==0) return x; + i1 |= (i0&0x0fffff); + i0 &= 0xfffe0000; + i0 |= ((i1|-i1)>>12)&0x80000; + SET_HIGH_WORD(x,i0); + STRICT_ASSIGN(double,w,TWO52[sx]+x); + t = w-TWO52[sx]; + GET_HIGH_WORD(i0,t); + SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + /* + * Some bit is set after the 0.5 bit. To avoid the + * possibility of errors from double rounding in + * w = TWO52[sx]+x, adjust the 0.25 bit to a lower + * guard bit. We do this for all j0<=51. The + * adjustment is trickiest for j0==18 and j0==19 + * since then it spans the word boundary. + */ + if(j0==19) i1 = 0x40000000; else + if(j0==18) i1 = 0x80000000; else + i0 = (i0&(~i))|((0x20000)>>j0); + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20)); + } + INSERT_WORDS(x,i0,i1); + STRICT_ASSIGN(double,w,TWO52[sx]+x); + return w-TWO52[sx]; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(rint, rintl); +#endif diff --git a/openlibm/src/s_rintf.c b/openlibm/src/s_rintf.c new file mode 100644 index 0000000..60cdb46 --- /dev/null +++ b/openlibm/src/s_rintf.c @@ -0,0 +1,53 @@ +/* s_rintf.c -- float version of s_rint.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_rintf.c,v 1.12 2008/02/22 02:30:35 das Exp $"); + +#include +#include +#include + +#include "math_private.h" + +static const float +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +OLM_DLLEXPORT float +rintf(float x) +{ + int32_t i0,j0,sx; + float w,t; + GET_FLOAT_WORD(i0,x); + sx = (i0>>31)&1; + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { + if((i0&0x7fffffff)==0) return x; + STRICT_ASSIGN(float,w,TWO23[sx]+x); + t = w-TWO23[sx]; + GET_FLOAT_WORD(i0,t); + SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } + STRICT_ASSIGN(float,w,TWO23[sx]+x); + return w-TWO23[sx]; + } + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ +} diff --git a/openlibm/src/s_rintl.c b/openlibm/src/s_rintl.c new file mode 100644 index 0000000..d20768e --- /dev/null +++ b/openlibm/src/s_rintl.c @@ -0,0 +1,116 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_rintl.c,v 1.5 2008/02/22 11:59:05 bde Exp $"); + +#include +#include +#include + +#include "fpmath.h" + +//VBS +#include "math_private.h" + + +#if LDBL_MAX_EXP != 0x4000 +/* We also require the usual bias, min exp and expsign packing. */ +#error "Unsupported long double format" +#endif + +#define BIAS (LDBL_MAX_EXP - 1) + +static const float +shift[2] = { +#if LDBL_MANT_DIG == 64 + 0x1.0p63, -0x1.0p63 +#elif LDBL_MANT_DIG == 113 + 0x1.0p112, -0x1.0p112 +#else +#error "Unsupported long double format" +#endif +}; +static const float zero[2] = { 0.0, -0.0 }; + +OLM_DLLEXPORT long double +rintl(long double x) +{ + union IEEEl2bits u; + u_int32_t expsign; + int ex, sign; + + u.e = x; + expsign = u.xbits.expsign; + ex = expsign & 0x7fff; + + if (ex >= BIAS + LDBL_MANT_DIG - 1) { + if (ex == BIAS + LDBL_MAX_EXP) + return (x + x); /* Inf, NaN, or unsupported format */ + return (x); /* finite and already an integer */ + } + sign = expsign >> 15; + + /* + * The following code assumes that intermediate results are + * evaluated in long double precision. If they are evaluated in + * greater precision, double rounding may occur, and if they are + * evaluated in less precision (as on i386), results will be + * wildly incorrect. + */ + x += shift[sign]; + x -= shift[sign]; + + /* + * If the result is +-0, then it must have the same sign as x, but + * the above calculation doesn't always give this. Fix up the sign. + */ + if (ex < BIAS && x == 0.0L) + return (zero[sign]); + + return (x); +} + +/* + * We save and restore the floating-point environment to avoid raising + * an inexact exception. We can get away with using fesetenv() + * instead of feclearexcept()/feupdateenv() to restore the environment + * because the only exception defined for rint() is overflow, and + * rounding can't overflow as long as emax >= p. + */ +#define DECL(type, fn, rint) \ +OLM_DLLEXPORT type \ +fn(type x) \ +{ \ + type ret; \ + fenv_t env; \ + \ + fegetenv(&env); \ + ret = rint(x); \ + fesetenv(&env); \ + return (ret); \ +} +DECL(long double, nearbyintl, rintl) diff --git a/openlibm/src/s_round.c b/openlibm/src/s_round.c new file mode 100644 index 0000000..a982ec3 --- /dev/null +++ b/openlibm/src/s_round.c @@ -0,0 +1,55 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_round.c,v 1.4 2005/12/02 13:45:06 bde Exp $"); + +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +round(double x) +{ + double t; + uint32_t hx; + + GET_HIGH_WORD(hx, x); + if ((hx & 0x7fffffff) == 0x7ff00000) + return (x + x); + + if (!(hx & 0x80000000)) { + t = floor(x); + if (t - x <= -0.5) + t += 1; + return (t); + } else { + t = floor(-x); + if (t + x <= -0.5) + t += 1; + return (-t); + } +} diff --git a/openlibm/src/s_roundf.c b/openlibm/src/s_roundf.c new file mode 100644 index 0000000..784a8a5 --- /dev/null +++ b/openlibm/src/s_roundf.c @@ -0,0 +1,53 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_roundf.c,v 1.4 2005/12/02 13:45:06 bde Exp $"); + +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +roundf(float x) +{ + float t; + + if (!isfinite(x)) + return (x); + + if (x >= 0.0) { + t = floorf(x); + if (t - x <= -0.5) + t += 1.0; + return (t); + } else { + t = floorf(-x); + if (t + x <= -0.5) + t += 1.0; + return (-t); + } +} diff --git a/openlibm/src/s_roundl.c b/openlibm/src/s_roundl.c new file mode 100644 index 0000000..dbcd651 --- /dev/null +++ b/openlibm/src/s_roundl.c @@ -0,0 +1,53 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_roundl.c,v 1.2 2005/12/02 13:45:06 bde Exp $"); + +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double +roundl(long double x) +{ + long double t; + + if (!isfinite(x)) + return (x); + + if (x >= 0.0) { + t = floorl(x); + if (t - x <= -0.5) + t += 1.0; + return (t); + } else { + t = floorl(-x); + if (t + x <= -0.5) + t += 1.0; + return (-t); + } +} diff --git a/openlibm/src/s_scalbln.c b/openlibm/src/s_scalbln.c new file mode 100644 index 0000000..8239db5 --- /dev/null +++ b/openlibm/src/s_scalbln.c @@ -0,0 +1,80 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_scalbln.c,v 1.2 2005/03/07 04:57:50 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +scalbln (double x, long n) +{ + int in; + + in = (int)n; + if (in != n) { + if (n > 0) + in = INT_MAX; + else + in = INT_MIN; + } + return (scalbn(x, in)); +} + +OLM_DLLEXPORT float +scalblnf (float x, long n) +{ + int in; + + in = (int)n; + if (in != n) { + if (n > 0) + in = INT_MAX; + else + in = INT_MIN; + } + return (scalbnf(x, in)); +} + +#ifdef OLM_LONG_DOUBLE +OLM_DLLEXPORT long double +scalblnl (long double x, long n) +{ + int in; + + in = (int)n; + if (in != n) { + if (n > 0) + in = INT_MAX; + else + in = INT_MIN; + } + return (scalbnl(x, (int)n)); +} +#endif diff --git a/openlibm/src/s_scalbn.c b/openlibm/src/s_scalbn.c new file mode 100644 index 0000000..dc3a0cf --- /dev/null +++ b/openlibm/src/s_scalbn.c @@ -0,0 +1,66 @@ +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "cdefs-compat.h" + +#include +#include + +#include "math_private.h" + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +OLM_DLLEXPORT double +scalbn (double x, int n) +{ + int32_t k,hx,lx; + EXTRACT_WORDS(hx,lx,x); + k = (hx&0x7ff00000)>>20; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD(hx,x); + k = ((hx&0x7ff00000)>>20) - 54; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0x7ff) return x+x; /* NaN or Inf */ + k = k+n; + if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;} + if (k <= -54) { + if (n > 50000) /* in case integer overflow in n+k */ + return huge*copysign(huge,x); /*overflow*/ + else return tiny*copysign(tiny,x); /*underflow*/ + } + k += 54; /* subnormal result */ + SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); + return x*twom54; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(scalbn, ldexpl); +openlibm_weak_reference(scalbn, scalbnl); +#endif + +openlibm_strong_reference(scalbn, ldexp); diff --git a/openlibm/src/s_scalbnf.c b/openlibm/src/s_scalbnf.c new file mode 100644 index 0000000..930ab8f --- /dev/null +++ b/openlibm/src/s_scalbnf.c @@ -0,0 +1,57 @@ +/* s_scalbnf.c -- float version of s_scalbn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + + +#include "cdefs-compat.h" + +#include + +#include "math_private.h" + +static const float +two25 = 3.355443200e+07, /* 0x4c000000 */ +twom25 = 2.9802322388e-08, /* 0x33000000 */ +huge = 1.0e+30, +tiny = 1.0e-30; + +OLM_DLLEXPORT float +scalbnf (float x, int n) +{ + int32_t k,ix; + GET_FLOAT_WORD(ix,x); + k = (ix&0x7f800000)>>23; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((ix&0x7fffffff)==0) return x; /* +-0 */ + x *= two25; + GET_FLOAT_WORD(ix,x); + k = ((ix&0x7f800000)>>23) - 25; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0xff) return x+x; /* NaN or Inf */ + k = k+n; + if (k > 0xfe) return huge*copysignf(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;} + if (k <= -25) { + if (n > 50000) /* in case integer overflow in n+k */ + return huge*copysignf(huge,x); /*overflow*/ + else return tiny*copysignf(tiny,x); /*underflow*/ + } + k += 25; /* subnormal result */ + SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); + return x*twom25; +} + +openlibm_strong_reference(scalbnf, ldexpf); diff --git a/openlibm/src/s_scalbnl.c b/openlibm/src/s_scalbnl.c new file mode 100644 index 0000000..7732944 --- /dev/null +++ b/openlibm/src/s_scalbnl.c @@ -0,0 +1,70 @@ +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbnl (long double x, int n) + * scalbnl(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +/* + * We assume that a long double has a 15-bit exponent. On systems + * where long double is the same as double, scalbnl() is an alias + * for scalbn(), so we don't use this routine. + */ + +#include "cdefs-compat.h" + +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#if LDBL_MAX_EXP != 0x4000 +#error "Unsupported long double format" +#endif + +static const long double +huge = 0x1p16000L, +tiny = 0x1p-16000L; + +OLM_DLLEXPORT long double +scalbnl (long double x, int n) +{ + union IEEEl2bits u; + int k; + u.e = x; + k = u.bits.exp; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((u.bits.manh|u.bits.manl)==0) return x; /* +-0 */ + u.e *= 0x1p+128; + k = u.bits.exp - 128; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0x7fff) return x+x; /* NaN or Inf */ + k = k+n; + if (k >= 0x7fff) return huge*copysignl(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {u.bits.exp = k; return u.e;} + if (k <= -128) { + if (n > 50000) /* in case integer overflow in n+k */ + return huge*copysign(huge,x); /*overflow*/ + else return tiny*copysign(tiny,x); /*underflow*/ + } + k += 128; /* subnormal result */ + u.bits.exp = k; + return u.e*0x1p-128; +} + +openlibm_strong_reference(scalbnl, ldexpl); diff --git a/openlibm/src/s_signbit.c b/openlibm/src/s_signbit.c new file mode 100644 index 0000000..87f40f2 --- /dev/null +++ b/openlibm/src/s_signbit.c @@ -0,0 +1,61 @@ +/*- + * Copyright (c) 2003 Mike Barcroft + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * $FreeBSD: src/lib/msun/src/s_signbit.c,v 1.1 2004/07/19 08:16:10 das Exp $ + */ + +#include + +#include "fpmath.h" +#include "math_private.h" + +OLM_DLLEXPORT int +__signbit(double d) +{ + union IEEEd2bits u; + + u.d = d; + return (u.bits.sign); +} + +OLM_DLLEXPORT int +__signbitf(float f) +{ + union IEEEf2bits u; + + u.f = f; + return (u.bits.sign); +} + +#ifdef OLM_LONG_DOUBLE +OLM_DLLEXPORT int +__signbitl(long double e) +{ + union IEEEl2bits u; + + u.e = e; + return (u.bits.sign); +} +#endif diff --git a/openlibm/src/s_signgam.c b/openlibm/src/s_signgam.c new file mode 100644 index 0000000..ad72a73 --- /dev/null +++ b/openlibm/src/s_signgam.c @@ -0,0 +1,7 @@ +#include + +#include "math_private.h" + +#ifndef OPENLIBM_ONLY_THREAD_SAFE +int signgam = 0; +#endif diff --git a/openlibm/src/s_sin.c b/openlibm/src/s_sin.c new file mode 100644 index 0000000..cc0a5c6 --- /dev/null +++ b/openlibm/src/s_sin.c @@ -0,0 +1,89 @@ +/* @(#)s_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_sin.c,v 1.13 2011/02/10 07:37:50 das Exp $"); + +/* sin(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include +#include + +//#define INLINE_REM_PIO2 +#include "math_private.h" +//#include "e_rem_pio2.c" + +OLM_DLLEXPORT double +sin(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) { + if(ix<0x3e500000) /* |x| < 2**-26 */ + {if((int)x==0) return x;} /* generate inexact */ + return __kernel_sin(x,z,0); + } + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_sin(y[0],y[1],1); + case 1: return __kernel_cos(y[0],y[1]); + case 2: return -__kernel_sin(y[0],y[1],1); + default: + return -__kernel_cos(y[0],y[1]); + } + } +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(sin, sinl); +#endif diff --git a/openlibm/src/s_sincos.c b/openlibm/src/s_sincos.c new file mode 100644 index 0000000..8628235 --- /dev/null +++ b/openlibm/src/s_sincos.c @@ -0,0 +1,159 @@ +/* @(#)s_sincos.c 5.1 13/07/15 */ +/* See openlibm LICENSE.md for full license details. + * + * ==================================================== + * This file is derived from fdlibm: + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * + * ==================================================== + * Copyright (C) 2013 Elliot Saba. All rights reserved. + * + * Developed at the University of Washington. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + #include "cdefs-compat.h" + +/* sincos(x, s, c) + * Several applications need sine and cosine of the same + * angle x. This function computes both at the same time, + * and stores the results in *sin and *cos. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Borrow liberally from s_sin.c and s_cos.c, merging + * efforts where applicable and returning their values in + * appropriate variables, thereby slightly reducing the + * amount of work relative to just calling sin/cos(x) + * separately + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * sincos(+-INF, s, c) is NaN, with signals; + * sincos(NaN, s, c) is that NaN; + */ + +#include +#include + +//#define INLINE_REM_PIO2 +#include "math_private.h" +//#include "e_rem_pio2.c" + +/* Constants used in polynomial approximation of sin/cos */ +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ +S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ +S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ +S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ +S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ +S6 = 1.58969099521155010221e-10, /* 0x3DE5D93A, 0x5ACFD57C */ +C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ +C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ +C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ +C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ +C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ + +static void +__kernel_sincos( double x, double y, int iy, double * k_s, double * k_c ) +{ + /* Inline calculation of sin/cos, as we can save + some work, and we will always need to calculate + both values, no matter the result of switch */ + double z, w, r, v, hz; + z = x*x; + w = z*z; + + /* cos-specific computation; equivalent to calling + __kernel_cos(x,y) and storing in k_c*/ + r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6)); + hz = 0.5*z; + v = one-hz; + + *k_c = v + (((one-v)-hz) + (z*r-x*y)); + + /* sin-specific computation; equivalent to calling + __kernel_sin(x,y,1) and storing in k_s*/ + r = S2+z*(S3+z*S4) + z*w*(S5+z*S6); + v = z*x; + if(iy == 0) + *k_s = x+v*(S1+z*r); + else + *k_s = x-((z*(half*y-v*r)-y)-v*S1); +} + +OLM_DLLEXPORT void +sincos(double x, double * s, double * c) +{ + double y[2]; + int32_t ix; + + /* Store high word of x in ix */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) { + /* Check for small x for sin and cos */ + if(ix<0x3e46a09e) { + /* Check for exact zero */ + if( (int)x==0 ) { + *s = x; + *c = 1.0; + return; + } + } + /* Call kernel function with 0 extra */ + __kernel_sincos(x,0.0,0, s, c); + } else if( ix >= 0x7ff00000 ) { + /* sincos(Inf or NaN) is NaN */ + *s = x-x; + *c = x-x; + } + + /*argument reduction needed*/ + else { + double k_c, k_s; + + /* Calculate remainer, then sub out to kernel */ + int32_t n = __ieee754_rem_pio2(x,y); + __kernel_sincos( y[0], y[1], 1, &k_s, &k_c ); + + /* Figure out permutation of sin/cos outputs to true outputs */ + switch(n&3) { + case 0: + *c = k_c; + *s = k_s; + break; + case 1: + *c = -k_s; + *s = k_c; + break; + case 2: + *c = -k_c; + *s = -k_s; + break; + default: + *c = k_s; + *s = -k_c; + break; + } + } +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(sincos, sincosl); +#endif diff --git a/openlibm/src/s_sincosf.c b/openlibm/src/s_sincosf.c new file mode 100644 index 0000000..62caaac --- /dev/null +++ b/openlibm/src/s_sincosf.c @@ -0,0 +1,172 @@ +/* s_sincosf.c -- float version of s_sincos.c + * + * ==================================================== + * This file is derived from fdlibm: + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * + * ==================================================== + * Copyright (C) 2013 Elliot Saba + * Developed at the University of Washington + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== +*/ + +#include "cdefs-compat.h" + +#include +#include + +//#define INLINE_KERNEL_COSDF +//#define INLINE_KERNEL_SINDF +//#define INLINE_REM_PIO2F +#include "math_private.h" +//#include "e_rem_pio2f.c" +//#include "k_cosf.c" +//#include "k_sinf.c" + + +/* Constants used in shortcircuits in sincosf */ +static const double +sc1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ +sc2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ +sc3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ +sc4pio2 = 4*M_PI_2, /* 0x401921FB, 0x54442D18 */ + +/* Constants used in polynomial approximation of sin/cos */ +one = 1.0, +S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */ +S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */ +S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */ +S4 = 0x16cd878c3b46a7.0p-71, /* 0.0000027183114939898219064 */ +C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */ +C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */ +C2 = -0x16c087e80f1e27.0p-62, /* -0.00138867637746099294692 */ +C3 = 0x199342e0ee5069.0p-68; /* 0.0000243904487962774090654 */ + +static void +__kernel_sincosdf( double x, float * s, float * c ) +{ + double r, w, z, v; + z = x*x; + w = z*z; + + /* cos-specific computation; equivalent to calling + __kernel_cos(x,y) and storing in k_c*/ + r = C2+z*C3; + double k_c = ((one+z*C0) + w*C1) + (w*z)*r; + + /* sin-specific computation; equivalent to calling + __kernel_sin(x,y,1) and storing in k_s*/ + r = S3+z*S4; + v = z*x; + double k_s = (x + v*(S1+z*S2)) + v*w*r; + + *c = k_c; + *s = k_s; +} + +OLM_DLLEXPORT void +sincosf(float x, float * s, float * c) { + // Worst approximation of sin and cos NA + *s = x; + *c = x; + + double y; + float k_c, k_s; + int32_t n, hx, ix; + + GET_FLOAT_WORD(hx,x); + ix = hx & 0x7fffffff; + + if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ + if(ix<0x39800000) { /* |x| < 2**-12 */ + /* Check if x is exactly zero */ + if(((int)x)==0) { + *s = x; + *c = 1.0f; + return; + } + } + __kernel_sincosdf(x, s, c); + return; + } + /* |x| ~<= 5*pi/4 */ + if (ix<=0x407b53d1) { + /* |x| ~<= 3pi/4 */ + if(ix<=0x4016cbe3) { + if(hx>0) { + __kernel_sincosdf( sc1pio2 - x, c, s ); + } + else { + __kernel_sincosdf( sc1pio2 + x, c, &k_s ); + *s = -k_s; + } + } else { + + if(hx>0) { + __kernel_sincosdf( sc2pio2 - x, s, &k_c ); + *c = -k_c; + } else { + __kernel_sincosdf( -sc2pio2 - x, s, &k_c ); + *c = -k_c; + } + } + return; + } + + /* |x| ~<= 9*pi/4 */ + if(ix<=0x40e231d5) { + /* |x| ~> 7*pi/4 */ + if(ix<=0x40afeddf) { + if(hx>0) { + __kernel_sincosdf( x - sc3pio2, c, &k_s ); + *s = -k_s; + } else { + __kernel_sincosdf( x + sc3pio2, &k_c, s ); + *c = -k_c; + } + } + else { + if( hx > 0 ) { + __kernel_sincosdf( x - sc4pio2, s, c ); + } else { + __kernel_sincosdf( x + sc4pio2, s, c ); + } + } + return; + } + + /* cos(Inf or NaN) is NaN */ + else if(ix>=0x7f800000) { + *c = *s = x-x; + } else { + /* general argument reduction needed */ + n = __ieee754_rem_pio2f(x,&y); + + switch(n&3) { + case 0: + __kernel_sincosdf( y, s, c ); + break; + case 1: + __kernel_sincosdf( -y, c, s ); + break; + case 2: + __kernel_sincosdf( -y, s, &k_c); + *c = -k_c; + break; + default: + __kernel_sincosdf( -y, &k_c, &k_s ); + *c = -k_c; + *s = -k_s; + break; + } + } + +} diff --git a/openlibm/src/s_sincosl.c b/openlibm/src/s_sincosl.c new file mode 100644 index 0000000..e2d3a34 --- /dev/null +++ b/openlibm/src/s_sincosl.c @@ -0,0 +1,31 @@ +/* s_sincosl.c -- long double version of s_sincos.c + * + * Copyright (C) 2013 Elliot Saba + * Developed at the University of Washington + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== +*/ + +#include "cdefs-compat.h" + +#include +#include + +#include "math_private.h" +#if LDBL_MANT_DIG == 64 +#include "../ld80/e_rem_pio2l.h" +#elif LDBL_MANT_DIG == 113 +#include "../ld128/e_rem_pio2l.h" +#else +#error "Unsupported long double format" +#endif + +OLM_DLLEXPORT void +sincosl( long double x, long double * s, long double * c ) +{ + *s = sinl( x ); + *c = cosl( x ); +} diff --git a/openlibm/src/s_sinf.c b/openlibm/src/s_sinf.c new file mode 100644 index 0000000..d987369 --- /dev/null +++ b/openlibm/src/s_sinf.c @@ -0,0 +1,85 @@ +/* s_sinf.c -- float version of s_sin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_sinf.c,v 1.17 2008/02/25 22:19:17 bde Exp $"); + +#include +#include + +//#define INLINE_KERNEL_COSDF +//#define INLINE_KERNEL_SINDF +//#define INLINE_REM_PIO2F +#include "math_private.h" +//#include "e_rem_pio2f.c" +//#include "k_cosf.c" +//#include "k_sinf.c" + +/* Small multiples of pi/2 rounded to double precision. */ +static const double +s1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ +s2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ +s3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ +s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ + +OLM_DLLEXPORT float +sinf(float x) +{ + double y; + int32_t n, hx, ix; + + GET_FLOAT_WORD(hx,x); + ix = hx & 0x7fffffff; + + if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ + if(ix<0x39800000) /* |x| < 2**-12 */ + if(((int)x)==0) return x; /* x with inexact if x != 0 */ + return __kernel_sindf(x); + } + if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */ + if(ix<=0x4016cbe3) { /* |x| ~<= 3pi/4 */ + if(hx>0) + return __kernel_cosdf(x - s1pio2); + else + return -__kernel_cosdf(x + s1pio2); + } else + return __kernel_sindf((hx > 0 ? s2pio2 : -s2pio2) - x); + } + if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4 */ + if(ix<=0x40afeddf) { /* |x| ~<= 7*pi/4 */ + if(hx>0) + return -__kernel_cosdf(x - s3pio2); + else + return __kernel_cosdf(x + s3pio2); + } else + return __kernel_sindf(x + (hx > 0 ? -s4pio2 : s4pio2)); + } + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* general argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,&y); + switch(n&3) { + case 0: return __kernel_sindf(y); + case 1: return __kernel_cosdf(y); + case 2: return __kernel_sindf(-y); + default: + return -__kernel_cosdf(y); + } + } +} diff --git a/openlibm/src/s_sinl.c b/openlibm/src/s_sinl.c new file mode 100644 index 0000000..7304fc7 --- /dev/null +++ b/openlibm/src/s_sinl.c @@ -0,0 +1,88 @@ +/*- + * Copyright (c) 2007 Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_sinl.c,v 1.3 2011/05/30 19:41:28 kargl Exp $"); + +#include +#include + +#include "math_private.h" +#if LDBL_MANT_DIG == 64 +#include "../ld80/e_rem_pio2l.h" +#elif LDBL_MANT_DIG == 113 +#include "../ld128/e_rem_pio2l.h" +#else +#error "Unsupported long double format" +#endif + +OLM_DLLEXPORT long double +sinl(long double x) +{ + union IEEEl2bits z; + int e0, s; + long double y[2]; + long double hi, lo; + + z.e = x; + s = z.bits.sign; + z.bits.sign = 0; + + /* If x = +-0 or x is a subnormal number, then sin(x) = x */ + if (z.bits.exp == 0) + return (x); + + /* If x = NaN or Inf, then sin(x) = NaN. */ + if (z.bits.exp == 32767) + return ((x - x) / (x - x)); + + /* Optimize the case where x is already within range. */ + if (z.e < M_PI_4) { + hi = __kernel_sinl(z.e, 0, 0); + return (s ? -hi : hi); + } + + e0 = __ieee754_rem_pio2l(x, y); + hi = y[0]; + lo = y[1]; + + switch (e0 & 3) { + case 0: + hi = __kernel_sinl(hi, lo, 1); + break; + case 1: + hi = __kernel_cosl(hi, lo); + break; + case 2: + hi = - __kernel_sinl(hi, lo, 1); + break; + case 3: + hi = - __kernel_cosl(hi, lo); + break; + } + + return (hi); +} diff --git a/openlibm/src/s_tan.c b/openlibm/src/s_tan.c new file mode 100644 index 0000000..2b234a2 --- /dev/null +++ b/openlibm/src/s_tan.c @@ -0,0 +1,83 @@ +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_tan.c,v 1.13 2011/02/10 07:37:50 das Exp $"); + +/* tan(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tan ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include +#include + +//#define INLINE_REM_PIO2 +#include "math_private.h" +//#include "e_rem_pio2.c" + +OLM_DLLEXPORT double +tan(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) { + if(ix<0x3e400000) /* x < 2**-27 */ + if((int)x==0) return x; /* generate inexact */ + return __kernel_tan(x,z,1); + } + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(tan, tanl); +#endif diff --git a/openlibm/src/s_tanf.c b/openlibm/src/s_tanf.c new file mode 100644 index 0000000..7ffe193 --- /dev/null +++ b/openlibm/src/s_tanf.c @@ -0,0 +1,72 @@ +/* s_tanf.c -- float version of s_tan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + * Optimized by Bruce D. Evans. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_tanf.c,v 1.17 2008/02/25 22:19:17 bde Exp $"); + +#include +#include + +//#define INLINE_KERNEL_TANDF +//#define INLINE_REM_PIO2F +#include "math_private.h" +//#include "e_rem_pio2f.c" +//#include "k_tanf.c" + +/* Small multiples of pi/2 rounded to double precision. */ +static const double +t1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ +t2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ +t3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ +t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ + +OLM_DLLEXPORT float +tanf(float x) +{ + double y; + int32_t n, hx, ix; + + GET_FLOAT_WORD(hx,x); + ix = hx & 0x7fffffff; + + if(ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ + if(ix<0x39800000) /* |x| < 2**-12 */ + if(((int)x)==0) return x; /* x with inexact if x != 0 */ + return __kernel_tandf(x,1); + } + if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */ + if(ix<=0x4016cbe3) /* |x| ~<= 3pi/4 */ + return __kernel_tandf(x + (hx>0 ? -t1pio2 : t1pio2), -1); + else + return __kernel_tandf(x + (hx>0 ? -t2pio2 : t2pio2), 1); + } + if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4 */ + if(ix<=0x40afeddf) /* |x| ~<= 7*pi/4 */ + return __kernel_tandf(x + (hx>0 ? -t3pio2 : t3pio2), -1); + else + return __kernel_tandf(x + (hx>0 ? -t4pio2 : t4pio2), 1); + } + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* general argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,&y); + /* integer parameter: 1 -- n even; -1 -- n odd */ + return __kernel_tandf(y,1-((n&1)<<1)); + } +} diff --git a/openlibm/src/s_tanh.c b/openlibm/src/s_tanh.c new file mode 100644 index 0000000..1fa734d --- /dev/null +++ b/openlibm/src/s_tanh.c @@ -0,0 +1,83 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_tanh.c,v 1.9 2008/02/22 02:30:36 das Exp $"); + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0 + * -t + * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x) + * t + 2 + * 22 <= x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include +#include + +#include "math_private.h" + +static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300; + +OLM_DLLEXPORT double +tanh(double x) +{ + double t,z; + int32_t jx,ix; + + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */ + } + if (ix>=0x3ff00000) { /* |x|>=1 */ + t = expm1(two*fabs(x)); + z = one - two/(t+two); + } else { + t = expm1(-two*fabs(x)); + z= -t/(t+two); + } + /* |x| >= 22, return +-1 */ + } else { + z = one - tiny; /* raise inexact flag */ + } + return (jx>=0)? z: -z; +} + +#if (LDBL_MANT_DIG == 53) +openlibm_weak_reference(tanh, tanhl); +#endif diff --git a/openlibm/src/s_tanhf.c b/openlibm/src/s_tanhf.c new file mode 100644 index 0000000..cd77e4e --- /dev/null +++ b/openlibm/src/s_tanhf.c @@ -0,0 +1,56 @@ +/* s_tanhf.c -- float version of s_tanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_tanhf.c,v 1.9 2008/02/22 02:30:36 das Exp $"); + +#include + +#include "math_private.h" + +static const float one=1.0, two=2.0, tiny = 1.0e-30, huge = 1.0e30; +OLM_DLLEXPORT float +tanhf(float x) +{ + float t,z; + int32_t jx,ix; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 9 */ + if (ix < 0x41100000) { /* |x|<9 */ + if (ix<0x39800000) { /* |x|<2**-12 */ + if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */ + } + if (ix>=0x3f800000) { /* |x|>=1 */ + t = expm1f(two*fabsf(x)); + z = one - two/(t+two); + } else { + t = expm1f(-two*fabsf(x)); + z= -t/(t+two); + } + /* |x| >= 9, return +-1 */ + } else { + z = one - tiny; /* raise inexact flag */ + } + return (jx>=0)? z: -z; +} diff --git a/openlibm/src/s_tanl.c b/openlibm/src/s_tanl.c new file mode 100644 index 0000000..0370e6b --- /dev/null +++ b/openlibm/src/s_tanl.c @@ -0,0 +1,90 @@ +/*- + * Copyright (c) 2007 Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_tanl.c,v 1.3 2011/05/30 19:41:28 kargl Exp $"); + +/* + * Limited testing on pseudorandom numbers drawn within [0:4e8] shows + * an accuracy of <= 1.5 ULP where 247024 values of x out of 40 million + * possibles resulted in tan(x) that exceeded 0.5 ULP (ie., 0.6%). + */ + +#include +#include + +#include "math_private.h" +#if LDBL_MANT_DIG == 64 +#include "../ld80/e_rem_pio2l.h" +#elif LDBL_MANT_DIG == 113 +#include "../ld128/e_rem_pio2l.h" +#else +#error "Unsupported long double format" +#endif + +OLM_DLLEXPORT long double +tanl(long double x) +{ + union IEEEl2bits z; + int e0, s; + long double y[2]; + long double hi, lo; + + z.e = x; + s = z.bits.sign; + z.bits.sign = 0; + + /* If x = +-0 or x is subnormal, then tan(x) = x. */ + if (z.bits.exp == 0) + return (x); + + /* If x = NaN or Inf, then tan(x) = NaN. */ + if (z.bits.exp == 32767) + return ((x - x) / (x - x)); + + /* Optimize the case where x is already within range. */ + if (z.e < M_PI_4) { + hi = __kernel_tanl(z.e, 0, 0); + return (s ? -hi : hi); + } + + e0 = __ieee754_rem_pio2l(x, y); + hi = y[0]; + lo = y[1]; + + switch (e0 & 3) { + case 0: + case 2: + hi = __kernel_tanl(hi, lo, 0); + break; + case 1: + case 3: + hi = __kernel_tanl(hi, lo, 1); + break; + } + + return (hi); +} diff --git a/openlibm/src/s_tgammaf.c b/openlibm/src/s_tgammaf.c new file mode 100644 index 0000000..fbfa3fe --- /dev/null +++ b/openlibm/src/s_tgammaf.c @@ -0,0 +1,45 @@ +/*- + * Copyright (c) 2008 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_tgammaf.c,v 1.1 2008/02/18 17:27:10 das Exp $"); + +#include + +#include "math_private.h" + +/* + * We simply call tgamma() rather than bloating the math library with + * a float-optimized version of it. The reason is that tgammaf() is + * essentially useless, since the function is superexponential and + * floats have very limited range. + */ +OLM_DLLEXPORT float +tgammaf(float x) +{ + + return (tgamma(x)); +} diff --git a/openlibm/src/s_trunc.c b/openlibm/src/s_trunc.c new file mode 100644 index 0000000..c460cc9 --- /dev/null +++ b/openlibm/src/s_trunc.c @@ -0,0 +1,67 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_trunc.c,v 1.4 2008/02/22 02:27:34 das Exp $"); + +/* + * trunc(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to trunc(x). + */ + +#include +#include + +#include "math_private.h" + +static const double huge = 1.0e300; + +OLM_DLLEXPORT double +trunc(double x) +{ + int32_t i0,i1,j0; + u_int32_t i; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* |x|<1, so return 0*sign(x) */ + i0 &= 0x80000000U; + i1 = 0; + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) /* raise inexact flag */ + i1 &= (~i); + } + INSERT_WORDS(x,i0,i1); + return x; +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(trunc, truncl); +#endif diff --git a/openlibm/src/s_truncf.c b/openlibm/src/s_truncf.c new file mode 100644 index 0000000..d9fc62e --- /dev/null +++ b/openlibm/src/s_truncf.c @@ -0,0 +1,54 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_truncf.c,v 1.1 2004/06/20 09:25:43 das Exp $"); + +/* + * truncf(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to truncf(x). + */ + +#include + +#include "math_private.h" + +static const float huge = 1.0e30F; + +OLM_DLLEXPORT float +truncf(float x) +{ + int32_t i0,j0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0F) /* |x|<1, so return 0*sign(x) */ + i0 &= 0x80000000; + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>0.0F) /* raise inexact flag */ + i0 &= (~i); + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/openlibm/src/s_truncl.c b/openlibm/src/s_truncl.c new file mode 100644 index 0000000..34d7b65 --- /dev/null +++ b/openlibm/src/s_truncl.c @@ -0,0 +1,69 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * From: @(#)s_floor.c 5.1 93/09/24 + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/s_truncl.c,v 1.9 2008/02/14 15:10:34 bde Exp $"); + +/* + * truncl(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to truncl(x). + */ + +#include +#include +#include + +#include "fpmath.h" +#include "math_private.h" + +#ifdef LDBL_IMPLICIT_NBIT +#define MANH_SIZE (LDBL_MANH_SIZE + 1) +#else +#define MANH_SIZE LDBL_MANH_SIZE +#endif + +static const long double huge = 1.0e300; +static const float zero[] = { 0.0, -0.0 }; + +OLM_DLLEXPORT long double +truncl(long double x) +{ + union IEEEl2bits u = { .e = x }; + int e = u.bits.exp - LDBL_MAX_EXP + 1; + + if (e < MANH_SIZE - 1) { + if (e < 0) { /* raise inexact if x != 0 */ + if (huge + x > 0.0) + u.e = zero[u.bits.sign]; + } else { + uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1); + if (((u.bits.manh & m) | u.bits.manl) == 0) + return (x); /* x is integral */ + if (huge + x > 0.0) { /* raise inexact flag */ + u.bits.manh &= ~m; + u.bits.manl = 0; + } + } + } else if (e < LDBL_MANT_DIG - 1) { + uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1); + if ((u.bits.manl & m) == 0) + return (x); /* x is integral */ + if (huge + x > 0.0) /* raise inexact flag */ + u.bits.manl &= ~m; + } + return (u.e); +} diff --git a/openlibm/src/types-compat.h b/openlibm/src/types-compat.h new file mode 100644 index 0000000..b20b5ae --- /dev/null +++ b/openlibm/src/types-compat.h @@ -0,0 +1,13 @@ +#ifndef _TYPES_COMPAT_H_ +#define _TYPES_COMPAT_H_ + +#include +#include + +typedef uint8_t u_int8_t; +typedef uint16_t u_int16_t; +typedef uint32_t u_int32_t; +typedef uint64_t u_int64_t; + + +#endif diff --git a/openlibm/src/w_cabs.c b/openlibm/src/w_cabs.c new file mode 100644 index 0000000..6dc9bde --- /dev/null +++ b/openlibm/src/w_cabs.c @@ -0,0 +1,25 @@ +/* + * cabs() wrapper for hypot(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/w_cabs.c,v 1.7 2008/03/30 20:03:06 das Exp $"); + +#include +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT double +cabs(double complex z) +{ + return hypot(creal(z), cimag(z)); +} + +#if LDBL_MANT_DIG == 53 +openlibm_weak_reference(cabs, cabsl); +#endif diff --git a/openlibm/src/w_cabsf.c b/openlibm/src/w_cabsf.c new file mode 100644 index 0000000..f14c71a --- /dev/null +++ b/openlibm/src/w_cabsf.c @@ -0,0 +1,19 @@ +/* + * cabsf() wrapper for hypotf(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + */ + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT float +cabsf(z) + float complex z; +{ + + return hypotf(crealf(z), cimagf(z)); +} diff --git a/openlibm/src/w_cabsl.c b/openlibm/src/w_cabsl.c new file mode 100644 index 0000000..c10f1d4 --- /dev/null +++ b/openlibm/src/w_cabsl.c @@ -0,0 +1,22 @@ +/* + * cabs() wrapper for hypot(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + * + * Modified by Steven G. Kargl for the long double type. + */ + +#include "cdefs-compat.h" +//__FBSDID("$FreeBSD: src/lib/msun/src/w_cabsl.c,v 1.1 2008/03/30 20:02:03 das Exp $"); + +#include +#include + +#include "math_private.h" + +OLM_DLLEXPORT long double +cabsl(long double complex z) +{ + return hypotl(creall(z), cimagl(z)); +} diff --git a/openlibm/test/.gitignore b/openlibm/test/.gitignore new file mode 100644 index 0000000..2d85b23 --- /dev/null +++ b/openlibm/test/.gitignore @@ -0,0 +1,9 @@ +/test-float +/test-float-system +/test-float.dSYM +/test-double +/test-double-system +/test-double.dSYM +/bench-openlibm +/bench-syslibm +/*.exe diff --git a/openlibm/test/Makefile b/openlibm/test/Makefile new file mode 100644 index 0000000..a61ce5a --- /dev/null +++ b/openlibm/test/Makefile @@ -0,0 +1,37 @@ +OPENLIBM_HOME=$(abspath ..) +include ../Make.inc + +# Set rpath of tests to builddir for loading shared library +OPENLIBM_LIB = -L.. -lopenlibm +ifneq ($(OS),WINNT) +ifneq ($(OS),Darwin) +OPENLIBM_LIB += -Wl,-rpath=$(OPENLIBM_HOME) +endif +else # WINNT +CFLAGS_add += -DIMPORT_EXPORTS +endif + +all: test-double test-float # test-double-system test-float-system + +bench: bench-syslibm bench-openlibm + +test-double: test-double.c libm-test.c libm-test-ulps.h + $(CC) $(CPPFLAGS) $(CFLAGS) $(CFLAGS_add) $(LDFLAGS) $(LDFLAGS_arch) $@.c -D__BSD_VISIBLE -I ../include -I../src $(OPENLIBM_LIB) -o $@ + +test-float: test-float.c libm-test.c libm-test-ulps.h + $(CC) $(CPPFLAGS) $(CFLAGS) $(CFLAGS_add) $(LDFLAGS) $(LDFLAGS_arch) $@.c -D__BSD_VISIBLE -I ../include -I../src $(OPENLIBM_LIB) -o $@ + +test-double-system: test-double.c libm-test.c libm-test-ulps.h + $(CC) $(CPPFLAGS) $(CFLAGS) $(CFLAGS_add) $(LDFLAGS) $(LDFLAGS_arch) $< -DSYS_MATH_H -lm -o $@ + +test-float-system: test-float.c libm-test.c libm-test-ulps.h + $(CC) $(CPPFLAGS) $(CFLAGS) $(CFLAGS_add) $(LDFLAGS) $(LDFLAGS_arch) $< -DSYS_MATH_H -lm -o $@ + +bench-openlibm: libm-bench.cpp + $(CC) $(CPPFLAGS) $(CFLAGS) $(CFLAGS_add) $(LDFLAGS) $(LDFLAGS_arch) $< $(OPENLIBM_LIB) -o $@ + +bench-syslibm: libm-bench.cpp + $(CC) $(CPPFLAGS) $(CFLAGS) $(CFLAGS_add) $(LDFLAGS) $(LDFLAGS_arch) $< -lm -o $@ + +clean: + rm -fr test-double test-float test-double-system test-float-system bench-openlibm bench-syslibm *.dSYM diff --git a/openlibm/test/inf_torture.c b/openlibm/test/inf_torture.c new file mode 100644 index 0000000..f2b0124 --- /dev/null +++ b/openlibm/test/inf_torture.c @@ -0,0 +1,76 @@ +#include +#include + +int main(); +int main2(); +int main3(); +int main4(); + +int main() { + printf("+inf:\n"); + float fx = (float)INFINITY; unsigned int *fxi = (unsigned int*)&fx; + double dx = (double)INFINITY; long unsigned long int *dxi = (long unsigned long int*)&dx; + long double ldx = (long double)INFINITY; long unsigned long int *ldxi1 = (long unsigned long int*)&ldx; long unsigned long int *ldxi2 = &(ldxi1[1]); + printf("\t\tf d ld\n"); + printf("correct:\t%x %x %x\n", isinf(fx), isinf(dx), isinf(ldx)); + printf("as floats:\t%x %x %x\n", isinf(*(float*)fxi), isinf(*(float*)dxi), isinf(*(float*)ldxi1)); + printf("as double:\t%x %x %x\n", isinf(*(double*)fxi), isinf(*(double*)dxi), isinf(*(double*)ldxi1)); + printf("as long double:\t%x %x %x\n", isinf(*(long double*)fxi), isinf(*(long double*)dxi), isinf(*(long double*)ldxi1)); + printf("sizes ?4 8 12?:\t%d %d %d\n", (int)sizeof(fx), (int)sizeof(dx), (int)sizeof(ldx)); + printf("sizes:\t%d %d %d\n", (int)sizeof(*fxi), (int)sizeof(*dxi), (int)sizeof(*ldxi1)*2); + printf("bit repr:\n f: %x\n d: %llx\n ld: %llx%llx\n", *fxi, *dxi, (0xFFFF)&*ldxi2, *ldxi1); + printf("\n"); + main2(); + return 0; +} + +int main2() { + printf("-inf:\n"); + float fx = (float)-INFINITY; unsigned int *fxi = (unsigned int*)&fx; + double dx = (double)-INFINITY; long unsigned long int *dxi = (long unsigned long int*)&dx; + long double ldx = (long double)-INFINITY; long unsigned long int *ldxi1 = (long unsigned long int*)&ldx; long unsigned long int *ldxi2 = &(ldxi1[1]); + printf("\t\tf d ld\n"); + printf("correct:\t%x %x %x\n", isinf(fx), isinf(dx), isinf(ldx)); + printf("as floats:\t%x %x %x\n", isinf(*(float*)fxi), isinf(*(float*)dxi), isinf(*(float*)ldxi1)); + printf("as double:\t%x %x %x\n", isinf(*(double*)fxi), isinf(*(double*)dxi), isinf(*(double*)ldxi1)); + printf("as long double:\t%x %x %x\n", isinf(*(long double*)fxi), isinf(*(long double*)dxi), isinf(*(long double*)ldxi1)); + printf("sizes ?4 8 12?:\t%d %d %d\n", (int)sizeof(fx), (int)sizeof(dx), (int)sizeof(ldx)); + printf("bit repr:\n f: %x\n d: %llx\n ld: %llx%llx\n", *fxi, *dxi, (0xFFFF)&*ldxi2, *ldxi1); + printf("\n"); + main3(); + return 0; +} + +int main3() { + printf("+NaN:\n"); + float fx = (float)NAN; unsigned int *fxi = (unsigned int*)&fx; + double dx = (double)NAN; long unsigned long int *dxi = (long unsigned long int*)&dx; + long double ldx = (long double)NAN; long unsigned long int *ldxi1 = (long unsigned long int*)&ldx; long unsigned long int *ldxi2 = &(ldxi1[1]); + printf("\t\tf d ld\n"); + printf("correct:\t%x %x %x\n", isnan(fx), isnan(dx), isnan(ldx)); + printf("as floats:\t%x %x %x\n", isnan(*(float*)fxi), isnan(*(float*)dxi), isnan(*(float*)ldxi1)); + printf("as double:\t%x %x %x\n", isnan(*(double*)fxi), isnan(*(double*)dxi), isnan(*(double*)ldxi1)); + printf("as long double:\t%x %x %x\n", isnan(*(long double*)fxi), isnan(*(long double*)dxi), isnan(*(long double*)ldxi1)); + printf("sizes ?4 8 12?:\t%d %d %d\n", (int)sizeof(fx), (int)sizeof(dx), (int)sizeof(ldx)); + printf("sizes:\t%d %d %d\n", (int)sizeof(*fxi), (int)sizeof(*dxi), (int)sizeof(*ldxi1)*2); + printf("bit repr:\n f: %x\n d: %llx\n ld: %llx%llx\n", *fxi, *dxi, (0xFFFF)&*ldxi2, *ldxi1); + printf("\n"); + main4(); + return 0; +} + +int main4() { + printf("-NaN:\n"); + float fx = (float)-NAN; unsigned int *fxi = (unsigned int*)&fx; + double dx = (double)-NAN; long unsigned long int *dxi = (long unsigned long int*)&dx; + long double ldx = (long double)-NAN; long unsigned long int *ldxi1 = (long unsigned long int*)&ldx; long unsigned long int *ldxi2 = &(ldxi1[1]); + printf("\t\tf d ld\n"); + printf("correct:\t%x %x %x\n", isnan(fx), isnan(dx), isnan(ldx)); + printf("as floats:\t%x %x %x\n", isnan(*(float*)fxi), isnan(*(float*)dxi), isnan(*(float*)ldxi1)); + printf("as double:\t%x %x %x\n", isnan(*(double*)fxi), isnan(*(double*)dxi), isnan(*(double*)ldxi1)); + printf("as long double:\t%x %x %x\n", isnan(*(long double*)fxi), isnan(*(long double*)dxi), isnan(*(long double*)ldxi1)); + printf("sizes ?4 8 12?:\t%d %d %d\n", (int)sizeof(fx), (int)sizeof(dx), (int)sizeof(ldx)); + printf("bit repr:\n f: %x\n d: %llx\n ld: %llx%llx\n", *fxi, *dxi, (0xFFFF)&*ldxi2, *ldxi1); + printf("\n"); + return 0; +} diff --git a/openlibm/test/libm-bench.cpp b/openlibm/test/libm-bench.cpp new file mode 100644 index 0000000..04876de --- /dev/null +++ b/openlibm/test/libm-bench.cpp @@ -0,0 +1,144 @@ +// Copyright (C) Dahua Lin, 2014. Provided under the MIT license. + +// Benchmark on libm functions + +#include +#include +#include +#include + + +// Timing facilities + +#ifdef __MACH__ + +#include + +class stimer +{ +public: + typedef uint64_t time_type; + + stimer() + { + ::mach_timebase_info(&m_baseinfo); + } + + time_type current() const + { + return ::mach_absolute_time(); + } + + double span(const time_type& t0, const time_type& t1) const + { + uint64_t d = (m_baseinfo.numer * (t1 - t0)) / m_baseinfo.denom; + return static_cast(d) / 1.0e9; + } + +private: + mach_timebase_info_data_t m_baseinfo; +}; + +#else + +class stimer +{ +public: + typedef timespec time_type; + + time_type current() const + { + time_type t; + ::clock_gettime(CLOCK_REALTIME, &t); + return t; + } + + double span(const time_type& t0, const time_type& t1) const + { + return double(t1.tv_sec - t0.tv_sec) + + double(t1.tv_nsec - t0.tv_nsec) * 1.0e-9; + } +}; + +#endif + + +inline double sec2mps(double s, long n) +{ + return n / (s * 1e6); +} + + +const long ARR_LEN = 1024; + +double a[ARR_LEN]; +double b[ARR_LEN]; +double r[ARR_LEN]; + +#define TFUN1(FNAME) \ + void test_##FNAME(long n) { \ + for (int j = 0; j < ARR_LEN; ++j) r[j] = FNAME(a[j]); \ + stimer tm; \ + stimer::time_type t0 = tm.current(); \ + for(int i = 0; i < n; ++i) { \ + for (int j = 0; j < ARR_LEN; ++j) r[j] = FNAME(a[j]); \ + } \ + double s = tm.span(t0, tm.current()); \ + double mps = sec2mps(s, n * ARR_LEN); \ + printf(" %-8s: %7.4f MPS\n", #FNAME, mps); } + +#define TFUN2(FNAME) \ + void test_##FNAME(long n) { \ + for (int j = 0; j < ARR_LEN; ++j) r[j] = FNAME(a[j], b[j]); \ + stimer tm; \ + stimer::time_type t0 = tm.current(); \ + for(int i = 0; i < n; ++i) { \ + for (int j = 0; j < ARR_LEN; ++j) r[j] = FNAME(a[j], b[j]); \ + } \ + double s = tm.span(t0, tm.current()); \ + double mps = sec2mps(s, n * ARR_LEN); \ + printf(" %-8s: %7.4f MPS\n", #FNAME, mps); } + + +#define TCALL(FNAME) test_##FNAME(20000) + +// define benchmark functions + +TFUN2(pow) +TFUN2(hypot) + +TFUN1(exp) +TFUN1(log) +TFUN1(log10) +TFUN1(sin) +TFUN1(cos) +TFUN1(tan) +TFUN1(asin) +TFUN1(acos) +TFUN1(atan) +TFUN2(atan2) + +int main(int argc, char *argv[]) +{ + // initialize array contents + for (int i = 0; i < ARR_LEN; ++i) + { + a[i] = rand() / (double) RAND_MAX; + b[i] = rand() / (double) RAND_MAX; + } + + TCALL(pow); + TCALL(hypot); + TCALL(exp); + TCALL(log); + TCALL(log10); + TCALL(sin); + TCALL(cos); + TCALL(tan); + TCALL(asin); + TCALL(acos); + TCALL(atan); + TCALL(atan2); + + return 0; +} diff --git a/openlibm/test/libm-test-ulps.h b/openlibm/test/libm-test-ulps.h new file mode 100644 index 0000000..67a415c --- /dev/null +++ b/openlibm/test/libm-test-ulps.h @@ -0,0 +1,254 @@ +/* This file is automatically generated + from libm-test-ulps with gen-libm-test.pl. + Don't change it - change instead the master files. */ + + +/* Maximal error of functions. */ +#define DELTAacos CHOOSE(1150, 1, 1, 1150, 0, 0) /* acos */ +#define DELTAacosh CHOOSE(1, 0, 0, 1, 0, 0) /* acosh */ +#define DELTAasin CHOOSE(1, 1, 0, 1, 0, 0) /* asin */ +#define DELTAasinh CHOOSE(656, 0, 0, 656, 0, 0) /* asinh */ +#define DELTAatan CHOOSE(549, 0, 0, 549, 0, 0) /* atan */ +#define DELTAatanh CHOOSE(1605, 1, 0, 1605, 1, 0) /* atanh */ +#define DELTAatan2 CHOOSE(549, 0, 0, 549, 0, 0) /* atan2 */ +#define DELTAcabs CHOOSE(560, 1, 1, 560, 1, 1) /* cabs */ +#define DELTAcacos CHOOSE(BUILD_COMPLEX (151, 329), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1, 2), BUILD_COMPLEX (151, 329), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1, 2)) /* cacos */ +#define DELTAcacosh CHOOSE(BUILD_COMPLEX (328, 151), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (4, 4), BUILD_COMPLEX (328, 151), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (4, 4)) /* cacosh */ +#define DELTAcasin CHOOSE(BUILD_COMPLEX (603, 329), BUILD_COMPLEX (3, 0), BUILD_COMPLEX (2, 2), BUILD_COMPLEX (603, 329), BUILD_COMPLEX (3, 0), BUILD_COMPLEX (2, 2)) /* casin */ +#define DELTAcasinh CHOOSE(BUILD_COMPLEX (892, 12), BUILD_COMPLEX (5, 3), BUILD_COMPLEX (1, 6), BUILD_COMPLEX (892, 12), BUILD_COMPLEX (5, 3), BUILD_COMPLEX (1, 6)) /* casinh */ +#define DELTAcatan CHOOSE(BUILD_COMPLEX (251, 474), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (251, 474), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* catan */ +#define DELTAcatanh CHOOSE(BUILD_COMPLEX (66, 447), BUILD_COMPLEX (2, 0), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (66, 447), BUILD_COMPLEX (2, 0), BUILD_COMPLEX (1, 0)) /* catanh */ +#define DELTAcbrt CHOOSE(716, 1, 0, 716, 1, 0) /* cbrt */ +#define DELTAccos CHOOSE(BUILD_COMPLEX (5, 1901), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (5, 1901), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 1)) /* ccos */ +#define DELTAccosh CHOOSE(BUILD_COMPLEX (1467, 1183), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1467, 1183), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 1)) /* ccosh */ +#define DELTAcexp CHOOSE(BUILD_COMPLEX (940, 1067), 0, BUILD_COMPLEX (1, 0), BUILD_COMPLEX (940, 1067), 0, BUILD_COMPLEX (1, 0)) /* cexp */ +#define DELTAclog CHOOSE(BUILD_COMPLEX (0, 1), 0, 0, BUILD_COMPLEX (0, 1), 0, 0) /* clog */ +#define DELTAclog10 CHOOSE(BUILD_COMPLEX (1403, 186), BUILD_COMPLEX (2, 1), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1403, 186), BUILD_COMPLEX (2, 1), BUILD_COMPLEX (1, 1)) /* clog10 */ +#define DELTAcos CHOOSE(529, 2, 1, 529, 2, 1) /* cos */ +#define DELTAcosh CHOOSE(309, 0, 0, 309, 0, 0) /* cosh */ +#define DELTAcpow CHOOSE(BUILD_COMPLEX (2, 9), BUILD_COMPLEX (1, 1.104), BUILD_COMPLEX (4, 2.5333), BUILD_COMPLEX (2, 9), BUILD_COMPLEX (1, 1.104), BUILD_COMPLEX (4, 2.5333)) /* cpow */ +#define DELTAcsin CHOOSE(BUILD_COMPLEX (966, 168), 0, 0, BUILD_COMPLEX (966, 168), 0, 0) /* csin */ +#define DELTAcsinh CHOOSE(BUILD_COMPLEX (413, 477), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (413, 477), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 1)) /* csinh */ +#define DELTAcsqrt CHOOSE(BUILD_COMPLEX (237, 128), BUILD_COMPLEX (1, 0), 0, BUILD_COMPLEX (237, 128), BUILD_COMPLEX (1, 0), 0) /* csqrt */ +#define DELTActan CHOOSE(BUILD_COMPLEX (690, 367), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (690, 367), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 1)) /* ctan */ +#define DELTActanh CHOOSE(BUILD_COMPLEX (286, 3074), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (286, 3074), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (1, 1)) /* ctanh */ +#define DELTAerfc CHOOSE(36, 24, 12, 36, 24, 12) /* erfc */ +#define DELTAexp CHOOSE(754, 0, 0, 754, 0, 0) /* exp */ +#define DELTAexp10 CHOOSE(1182, 1, 0, 1182, 1, 0) /* exp10 */ +#define DELTAexp2 CHOOSE(462, 0, 0, 462, 0, 0) /* exp2 */ +#define DELTAexpm1 CHOOSE(825, 1, 1, 825, 0, 0) /* expm1 */ +#define DELTAfmod CHOOSE(4096, 2, 1, 4096, 2, 1) /* fmod */ +#define DELTAgamma CHOOSE(1, 1, 0, 1, 1, 0) /* gamma */ +#define DELTAhypot CHOOSE(560, 1, 1, 560, 0, 0) /* hypot */ +#define DELTAj0 CHOOSE(0, 2, 2, 0, 2, 1) /* j0 */ +#define DELTAj1 CHOOSE(2, 2, 2, 2, 2, 1) /* j1 */ +#define DELTAjn CHOOSE(2, 6, 4, 2, 5, 2) /* jn */ +#define DELTAlgamma CHOOSE(1, 1, 2, 1, 1, 2) /* lgamma */ +#define DELTAlog CHOOSE(2341, 1, 1, 2341, 1, 1) /* log */ +#define DELTAlog10 CHOOSE(2033, 1, 1, 2033, 1, 1) /* log10 */ +#define DELTAlog1p CHOOSE(585, 1, 1, 585, 1, 1) /* log1p */ +#define DELTAlog2 CHOOSE(1688, 1, 1, 1688, 1, 1) /* log2 */ +#define DELTApow CHOOSE(725, 0, 0, 725, 0, 0) /* pow */ +#define DELTAsin CHOOSE(627, 0, 0, 627, 0, 0) /* sin */ +#define DELTAsincos CHOOSE(627, 1, 1, 627, 1, 1) /* sincos */ +#define DELTAsinh CHOOSE(1029, 1, 1, 1028, 0, 1) /* sinh */ +#define DELTAsqrt CHOOSE(489, 0, 0, 489, 0, 0) /* sqrt */ +#define DELTAtan CHOOSE(1401, 1, 1, 1401, 0.5, 0) /* tan */ +#define DELTAtanh CHOOSE(521, 1, 1, 521, 0, 0) /* tanh */ +#define DELTAtgamma CHOOSE(2, 2, 1, 2, 2, 1) /* tgamma */ +#define DELTAy0 CHOOSE(2, 3, 1, 2, 3, 1) /* y0 */ +#define DELTAy1 CHOOSE(2, 3, 2, 2, 3, 2) /* y1 */ +#define DELTAyn CHOOSE(7, 6, 3, 7, 6, 3) /* yn */ + +/* Error of single function calls. */ +#define DELTA16 CHOOSE(1, 0, 0, 1, 0, 0) /* acosh (7) == 2.633915793849633417250092694615937 */ +#define DELTA24 CHOOSE(1, 1, 0, 1, 0, 0) /* asin (0.5) == pi/6 */ +#define DELTA25 CHOOSE(1, 1, 0, 1, 0, 0) /* asin (-0.5) == -pi/6 */ +#define DELTA26 CHOOSE(1, 0, 0, 1, 0, 0) /* asin (1.0) == pi/2 */ +#define DELTA27 CHOOSE(1, 0, 0, 1, 0, 0) /* asin (-1.0) == -pi/2 */ +#define DELTA28 CHOOSE(1, 1, 0, 1, 0, 0) /* asin (0.7) == 0.77539749661075306374035335271498708 */ +#define DELTA34 CHOOSE(656, 1, 0, 656, 0, 0) /* asinh (0.7) == 0.652666566082355786 */ +#define DELTA42 CHOOSE(549, 0, 0, 549, 0, 0) /* atan (0.7) == 0.61072596438920861654375887649023613 */ +#define DELTA50 CHOOSE(1605, 1, 0, 1605, 1, 0) /* atanh (0.7) == 0.8673005276940531944 */ +#define DELTA74 CHOOSE(549, 0, 0, 549, 0, 0) /* atan2 (0.7, 1) == 0.61072596438920861654375887649023613 */ +#define DELTA78 CHOOSE(1, 0, 0, 1, 0, 0) /* atan2 (0.4, 0.0003) == 1.5700463269355215717704032607580829 */ +#define DELTA85 CHOOSE(0, 0, 1, 0, 0, 1) /* cabs (0.7 + 12.4 i) == 12.419742348374220601176836866763271 */ +#define DELTA86 CHOOSE(0, 0, 1, 0, 0, 1) /* cabs (-12.4 + 0.7 i) == 12.419742348374220601176836866763271 */ +#define DELTA87 CHOOSE(0, 0, 1, 0, 0, 1) /* cabs (-0.7 + 12.4 i) == 12.419742348374220601176836866763271 */ +#define DELTA88 CHOOSE(0, 0, 1, 0, 0, 1) /* cabs (-12.4 - 0.7 i) == 12.419742348374220601176836866763271 */ +#define DELTA89 CHOOSE(0, 0, 1, 0, 0, 1) /* cabs (-0.7 - 12.4 i) == 12.419742348374220601176836866763271 */ +#define DELTA96 CHOOSE(560, 1, 0, 560, 1, 0) /* cabs (0.7 + 1.2 i) == 1.3892443989449804508432547041028554 */ +#define DELTA130 CHOOSE(BUILD_COMPLEX (151, 329), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1, 2), BUILD_COMPLEX (151, 329), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1, 2)) /* cacos (0.7 + 1.2 i) == 1.1351827477151551088992008271819053 - 1.0927647857577371459105272080819308 i */ +#define DELTA131 CHOOSE(BUILD_COMPLEX (0, 1), 0, 0, BUILD_COMPLEX (0, 1), 0, 0) /* cacos (-2 - 3 i) == 2.1414491111159960199416055713254211 + 1.9833870299165354323470769028940395 i */ +#define DELTA165 CHOOSE(BUILD_COMPLEX (328, 151), BUILD_COMPLEX (1, 0), 0, BUILD_COMPLEX (328, 151), BUILD_COMPLEX (1, 0), 0) /* cacosh (0.7 + 1.2 i) == 1.0927647857577371459105272080819308 + 1.1351827477151551088992008271819053 i */ +#define DELTA166 CHOOSE(BUILD_COMPLEX (6, 1), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (4, 4), BUILD_COMPLEX (6, 1), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (4, 4)) /* cacosh (-2 - 3 i) == -1.9833870299165354323470769028940395 + 2.1414491111159960199416055713254211 i */ +#define DELTA225 CHOOSE(BUILD_COMPLEX (603, 329), BUILD_COMPLEX (3, 0), BUILD_COMPLEX (2, 2), BUILD_COMPLEX (603, 329), BUILD_COMPLEX (3, 0), BUILD_COMPLEX (2, 2)) /* casin (0.7 + 1.2 i) == 0.4356135790797415103321208644578462 + 1.0927647857577371459105272080819308 i */ +#define DELTA226 CHOOSE(BUILD_COMPLEX (0, 1), 0, 0, BUILD_COMPLEX (0, 1), 0, 0) /* casin (-2 - 3 i) == -0.57065278432109940071028387968566963 - 1.9833870299165354323470769028940395 i */ +#define DELTA262 CHOOSE(BUILD_COMPLEX (892, 12), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (892, 12), 0, BUILD_COMPLEX (0, 1)) /* casinh (0.7 + 1.2 i) == 0.97865459559367387689317593222160964 + 0.91135418953156011567903546856170941 i */ +#define DELTA263 CHOOSE(BUILD_COMPLEX (6, 6), BUILD_COMPLEX (5, 3), BUILD_COMPLEX (1, 6), BUILD_COMPLEX (6, 6), BUILD_COMPLEX (5, 3), BUILD_COMPLEX (1, 6)) /* casinh (-2 - 3 i) == -1.9686379257930962917886650952454982 - 0.96465850440760279204541105949953237 i */ +#define DELTA301 CHOOSE(BUILD_COMPLEX (251, 474), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (251, 474), 0, BUILD_COMPLEX (0, 1)) /* catan (0.7 + 1.2 i) == 1.0785743834118921877443707996386368 + 0.57705737765343067644394541889341712 i */ +#define DELTA302 CHOOSE(BUILD_COMPLEX (0, 7), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 7), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i */ +#define DELTA340 CHOOSE(BUILD_COMPLEX (66, 447), BUILD_COMPLEX (1, 0), 0, BUILD_COMPLEX (66, 447), BUILD_COMPLEX (1, 0), 0) /* catanh (0.7 + 1.2 i) == 0.2600749516525135959200648705635915 + 0.97024030779509898497385130162655963 i */ +#define DELTA341 CHOOSE(BUILD_COMPLEX (6, 0), BUILD_COMPLEX (2, 0), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (6, 0), BUILD_COMPLEX (2, 0), BUILD_COMPLEX (1, 0)) /* catanh (-2 - 3 i) == -0.14694666622552975204743278515471595 - 1.3389725222944935611241935759091443 i */ +#define DELTA347 CHOOSE(716, 0, 0, 716, 0, 0) /* cbrt (-0.001) == -0.1 */ +#define DELTA349 CHOOSE(1, 0, 0, 1, 0, 0) /* cbrt (-27.0) == -3.0 */ +#define DELTA350 CHOOSE(306, 0, 0, 306, 0, 0) /* cbrt (0.970299) == 0.99 */ +#define DELTA351 CHOOSE(346, 1, 0, 346, 1, 0) /* cbrt (0.7) == 0.8879040017426007084 */ +#define DELTA389 CHOOSE(BUILD_COMPLEX (5, 1901), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (5, 1901), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 0)) /* ccos (0.7 + 1.2 i) == 1.3848657645312111080 - 0.97242170335830028619 i */ +#define DELTA390 CHOOSE(BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1)) /* ccos (-2 - 3 i) == -4.1896256909688072301 - 9.1092278937553365979 i */ +#define DELTA428 CHOOSE(BUILD_COMPLEX (1467, 1183), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1467, 1183), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1, 0)) /* ccosh (0.7 + 1.2 i) == 0.4548202223691477654 + 0.7070296600921537682 i */ +#define DELTA429 CHOOSE(BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* ccosh (-2 - 3 i) == -3.7245455049153225654 + 0.5118225699873846088 i */ +#define DELTA469 CHOOSE(BUILD_COMPLEX (940, 0), 0, BUILD_COMPLEX (1, 0), BUILD_COMPLEX (940, 0), 0, BUILD_COMPLEX (1, 0)) /* cexp (0.7 + 1.2 i) == 0.72969890915032360123451688642930727 + 1.8768962328348102821139467908203072 i */ +#define DELTA470 CHOOSE(BUILD_COMPLEX (4, 18), 0, 0, BUILD_COMPLEX (4, 18), 0, 0) /* cexp (-2.0 - 3.0 i) == -0.13398091492954261346140525546115575 - 0.019098516261135196432576240858800925 i */ +#define DELTA515 CHOOSE(BUILD_COMPLEX (0, 1), 0, 0, BUILD_COMPLEX (0, 1), 0, 0) /* clog (-2 - 3 i) == 1.2824746787307683680267437207826593 - 2.1587989303424641704769327722648368 i */ +#define DELTA520 CHOOSE(0, BUILD_COMPLEX (0, 1), 0, 0, BUILD_COMPLEX (0, 1), 0) /* clog10 (-inf + inf i) == inf + 3/4 pi*log10(e) i */ +#define DELTA521 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (inf + inf i) == inf + pi/4*log10(e) i */ +#define DELTA522 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (inf - inf i) == inf - pi/4*log10(e) i */ +#define DELTA523 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (0 + inf i) == inf + pi/2*log10(e) i */ +#define DELTA524 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (3 + inf i) == inf + pi/2*log10(e) i */ +#define DELTA525 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (-0 + inf i) == inf + pi/2*log10(e) i */ +#define DELTA526 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (-3 + inf i) == inf + pi/2*log10(e) i */ +#define DELTA527 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (0 - inf i) == inf - pi/2*log10(e) i */ +#define DELTA528 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (3 - inf i) == inf - pi/2*log10(e) i */ +#define DELTA529 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (-0 - inf i) == inf - pi/2*log10(e) i */ +#define DELTA530 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (-3 - inf i) == inf - pi/2*log10(e) i */ +#define DELTA531 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (-inf + 0 i) == inf + pi*log10(e) i */ +#define DELTA532 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (-inf + 1 i) == inf + pi*log10(e) i */ +#define DELTA533 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (-inf - 0 i) == inf - pi*log10(e) i */ +#define DELTA534 CHOOSE(0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1)) /* clog10 (-inf - 1 i) == inf - pi*log10(e) i */ +#define DELTA552 CHOOSE(BUILD_COMPLEX (1403, 186), BUILD_COMPLEX (2, 1), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1403, 186), BUILD_COMPLEX (2, 1), BUILD_COMPLEX (1, 0)) /* clog10 (0.7 + 1.2 i) == 0.1427786545038868803 + 0.4528483579352493248 i */ +#define DELTA553 CHOOSE(BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 1), 0) /* clog10 (-2 - 3 i) == 0.5569716761534183846 - 0.9375544629863747085 i */ +#define DELTA582 CHOOSE(0, 1, 0.5, 0, 1, 0.5) /* cos (M_PI_6l * 2.0) == 0.5 */ +#define DELTA583 CHOOSE(0.5, 2, 1, 0.5, 2, 1) /* cos (M_PI_6l * 4.0) == -0.5 */ +#define DELTA584 CHOOSE(0.25, 0.2758, 0.3667, 0.25, 0.2758, 0.3667) /* cos (pi/2) == 0 */ +#define DELTA585 CHOOSE(529, 1, 0, 529, 1, 0) /* cos (0.7) == 0.76484218728448842625585999019186495 */ +#define DELTA591 CHOOSE(309, 0, 0, 309, 0, 0) /* cosh (0.7) == 1.255169005630943018 */ +#define DELTA594 CHOOSE(BUILD_COMPLEX (0, 9), BUILD_COMPLEX (0, 1.104), BUILD_COMPLEX (0, 2.5333), BUILD_COMPLEX (0, 9), BUILD_COMPLEX (0, 1.104), BUILD_COMPLEX (0, 2.5333)) /* cpow (e + 0 i, 0 + 2 * M_PIl i) == 1.0 + 0.0 i */ +#define DELTA595 CHOOSE(BUILD_COMPLEX (2, 5), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (4, 1), BUILD_COMPLEX (2, 5), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (4, 1)) /* cpow (2 + 3 i, 4 + 0 i) == -119.0 - 120.0 i */ +#define DELTA652 CHOOSE(BUILD_COMPLEX (966, 168), 0, 0, BUILD_COMPLEX (966, 168), 0, 0) /* csin (0.7 + 1.2 i) == 1.1664563419657581376 + 1.1544997246948547371 i */ +#define DELTA691 CHOOSE(BUILD_COMPLEX (413, 477), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (413, 477), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (1, 0)) /* csinh (0.7 + 1.2 i) == 0.27487868678117583582 + 1.1698665727426565139 i */ +#define DELTA692 CHOOSE(BUILD_COMPLEX (0, 2), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (0, 2), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (0, 1)) /* csinh (-2 - 3 i) == 3.5905645899857799520 - 0.5309210862485198052 i */ +#define DELTA732 CHOOSE(BUILD_COMPLEX (237, 128), BUILD_COMPLEX (1, 0), 0, BUILD_COMPLEX (237, 128), BUILD_COMPLEX (1, 0), 0) /* csqrt (0.7 + 1.2 i) == 1.022067610030026450706487883081139 + 0.58704531296356521154977678719838035 i */ +#define DELTA733 CHOOSE(BUILD_COMPLEX (1, 0), 0, 0, BUILD_COMPLEX (1, 0), 0, 0) /* csqrt (-2 - 3 i) == 0.89597747612983812471573375529004348 - 1.6741492280355400404480393008490519 i */ +#define DELTA734 CHOOSE(BUILD_COMPLEX (1, 0), 0, 0, BUILD_COMPLEX (1, 0), 0, 0) /* csqrt (-2 + 3 i) == 0.89597747612983812471573375529004348 + 1.6741492280355400404480393008490519 i */ +#define DELTA766 CHOOSE(BUILD_COMPLEX (690, 367), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (690, 367), BUILD_COMPLEX (1, 1), BUILD_COMPLEX (1, 0)) /* ctan (0.7 + 1.2 i) == 0.1720734197630349001 + 0.9544807059989405538 i */ +#define DELTA767 CHOOSE(BUILD_COMPLEX (439, 2), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (439, 2), 0, BUILD_COMPLEX (0, 1)) /* ctan (-2 - 3 i) == 0.0037640256415042482 - 1.0032386273536098014 i */ +#define DELTA799 CHOOSE(0, BUILD_COMPLEX (0, 0.5), BUILD_COMPLEX (0, 1), 0, BUILD_COMPLEX (0, 0.5), BUILD_COMPLEX (0, 1)) /* ctanh (0 + pi/4 i) == 0.0 + 1.0 i */ +#define DELTA800 CHOOSE(BUILD_COMPLEX (286, 3074), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (1, 0), BUILD_COMPLEX (286, 3074), BUILD_COMPLEX (0, 1), BUILD_COMPLEX (1, 0)) /* ctanh (0.7 + 1.2 i) == 1.3472197399061191630 + 0.4778641038326365540 i */ +#define DELTA801 CHOOSE(BUILD_COMPLEX (5, 25), 0, BUILD_COMPLEX (0, 1), BUILD_COMPLEX (5, 25), 0, BUILD_COMPLEX (0, 1)) /* ctanh (-2 - 3 i) == -0.9653858790221331242 + 0.0098843750383224937 i */ +#define DELTA817 CHOOSE(1, 1, 0, 1, 1, 0) /* erfc (0.7) == 0.32219880616258152702 */ +#define DELTA818 CHOOSE(3, 1, 2, 3, 1, 2) /* erfc (1.2) == 0.089686021770364619762 */ +#define DELTA819 CHOOSE(0, 1, 1, 0, 1, 0) /* erfc (2.0) == 0.0046777349810472658379 */ +#define DELTA820 CHOOSE(12, 24, 12, 12, 24, 12) /* erfc (4.1) == 0.67000276540848983727e-8 */ +#define DELTA821 CHOOSE(36, 0, 0, 36, 0, 0) /* erfc (9) == 0.41370317465138102381e-36 */ +#define DELTA830 CHOOSE(412, 0, 0, 412, 0, 0) /* exp (0.7) == 2.0137527074704765216 */ +#define DELTA831 CHOOSE(16, 0, 0, 16, 0, 0) /* exp (50.0) == 5184705528587072464087.45332293348538 */ +#define DELTA832 CHOOSE(754, 0, 0, 754, 0, 0) /* exp (1000.0) == 0.197007111401704699388887935224332313e435 */ +#define DELTA838 CHOOSE(8, 0, 0, 8, 0, 0) /* exp10 (3) == 1000 */ +#define DELTA839 CHOOSE(818, 0, 0, 818, 0, 0) /* exp10 (-1) == 0.1 */ +#define DELTA842 CHOOSE(1182, 1, 0, 1182, 1, 0) /* exp10 (0.7) == 5.0118723362727228500155418688494574 */ +#define DELTA852 CHOOSE(462, 0, 0, 462, 0, 0) /* exp2 (0.7) == 1.6245047927124710452 */ +#define DELTA859 CHOOSE(825, 0, 0, 825, 0, 0) /* expm1 (0.7) == 1.0137527074704765216 */ +#define DELTA972 CHOOSE(4096, 2, 1, 4096, 2, 1) /* fmod (6.5, 2.3) == 1.9 */ +#define DELTA973 CHOOSE(4096, 2, 1, 4096, 2, 1) /* fmod (-6.5, 2.3) == -1.9 */ +#define DELTA974 CHOOSE(4096, 2, 1, 4096, 2, 1) /* fmod (6.5, -2.3) == 1.9 */ +#define DELTA975 CHOOSE(4096, 2, 1, 4096, 2, 1) /* fmod (-6.5, -2.3) == -1.9 */ +#define DELTA1004 CHOOSE(1, 1, 0, 1, 1, 0) /* gamma (-0.5) == log(2*sqrt(pi)) */ +#define DELTA1013 CHOOSE(406, 0, 1, 406, 0, 0) /* hypot (0.7, 12.4) == 12.419742348374220601176836866763271 */ +#define DELTA1014 CHOOSE(406, 0, 1, 406, 0, 0) /* hypot (-0.7, 12.4) == 12.419742348374220601176836866763271 */ +#define DELTA1015 CHOOSE(406, 0, 1, 406, 0, 0) /* hypot (0.7, -12.4) == 12.419742348374220601176836866763271 */ +#define DELTA1016 CHOOSE(406, 0, 1, 406, 0, 0) /* hypot (-0.7, -12.4) == 12.419742348374220601176836866763271 */ +#define DELTA1017 CHOOSE(406, 0, 1, 406, 0, 0) /* hypot (12.4, 0.7) == 12.419742348374220601176836866763271 */ +#define DELTA1018 CHOOSE(406, 0, 1, 406, 0, 0) /* hypot (-12.4, 0.7) == 12.419742348374220601176836866763271 */ +#define DELTA1019 CHOOSE(406, 0, 1, 406, 0, 0) /* hypot (12.4, -0.7) == 12.419742348374220601176836866763271 */ +#define DELTA1020 CHOOSE(406, 0, 1, 406, 0, 0) /* hypot (-12.4, -0.7) == 12.419742348374220601176836866763271 */ +#define DELTA1024 CHOOSE(560, 1, 0, 560, 0, 0) /* hypot (0.7, 1.2) == 1.3892443989449804508432547041028554 */ +#define DELTA1053 CHOOSE(0, 2, 2, 0, 1, 1) /* j0 (2.0) == 0.22389077914123566805 */ +#define DELTA1054 CHOOSE(0, 0, 1, 0, 0, 1) /* j0 (8.0) == 0.17165080713755390609 */ +#define DELTA1055 CHOOSE(0, 2, 2, 0, 2, 1) /* j0 (10.0) == -0.24593576445134833520 */ +#define DELTA1064 CHOOSE(0, 1, 0, 0, 1, 0) /* j1 (2.0) == 0.57672480775687338720 */ +#define DELTA1065 CHOOSE(1, 1, 1, 1, 0, 1) /* j1 (8.0) == 0.23463634685391462438 */ +#define DELTA1066 CHOOSE(2, 2, 2, 2, 2, 1) /* j1 (10.0) == 0.043472746168861436670 */ +#define DELTA1075 CHOOSE(0, 2, 2, 0, 1, 1) /* jn (0, 2.0) == 0.22389077914123566805 */ +#define DELTA1076 CHOOSE(1, 0, 1, 1, 0, 1) /* jn (0, 8.0) == 0.17165080713755390609 */ +#define DELTA1077 CHOOSE(2, 2, 1, 2, 2, 1) /* jn (0, 10.0) == -0.24593576445134833520 */ +#define DELTA1086 CHOOSE(0, 1, 0, 0, 1, 0) /* jn (1, 2.0) == 0.57672480775687338720 */ +#define DELTA1087 CHOOSE(1, 1, 1, 1, 0, 1) /* jn (1, 8.0) == 0.23463634685391462438 */ +#define DELTA1088 CHOOSE(2, 2, 2, 2, 2, 1) /* jn (1, 10.0) == 0.043472746168861436670 */ +#define DELTA1091 CHOOSE(1, 0, 0, 1, 0, 0) /* jn (3, -1.0) == -0.019563353982668405919 */ +#define DELTA1093 CHOOSE(1, 1, 0, 1, 1, 0) /* jn (3, 0.1) == 0.000020820315754756261429 */ +#define DELTA1094 CHOOSE(0, 2, 1, 0, 2, 0) /* jn (3, 0.7) == 0.0069296548267508408077 */ +#define DELTA1095 CHOOSE(1, 0, 0, 1, 0, 0) /* jn (3, 1.0) == 0.019563353982668405919 */ +#define DELTA1096 CHOOSE(0, 1, 1, 0, 1, 1) /* jn (3, 2.0) == 0.12894324947440205110 */ +#define DELTA1097 CHOOSE(1, 3, 1, 1, 3, 1) /* jn (3, 10.0) == 0.058379379305186812343 */ +#define DELTA1100 CHOOSE(1, 1, 1, 1, 1, 1) /* jn (10, -1.0) == 0.26306151236874532070e-9 */ +#define DELTA1102 CHOOSE(1, 6, 4, 1, 5, 2) /* jn (10, 0.1) == 0.26905328954342155795e-19 */ +#define DELTA1103 CHOOSE(2, 4, 1, 2, 4, 1) /* jn (10, 0.7) == 0.75175911502153953928e-11 */ +#define DELTA1104 CHOOSE(1, 1, 1, 1, 1, 1) /* jn (10, 1.0) == 0.26306151236874532070e-9 */ +#define DELTA1105 CHOOSE(1, 2, 2, 1, 2, 1) /* jn (10, 2.0) == 0.25153862827167367096e-6 */ +#define DELTA1106 CHOOSE(2, 4, 3, 2, 4, 2) /* jn (10, 10.0) == 0.20748610663335885770 */ +#define DELTA1126 CHOOSE(1, 1, 0, 1, 1, 0) /* lgamma (-0.5) == log(2*sqrt(pi)) */ +#define DELTA1128 CHOOSE(0, 1, 1, 0, 1, 1) /* lgamma (0.7) == 0.26086724653166651439 */ +#define DELTA1130 CHOOSE(1, 1, 2, 1, 1, 2) /* lgamma (1.2) == -0.853740900033158497197e-1 */ +#define DELTA1163 CHOOSE(1, 0, 0.5, 1, 0, 0.5) /* log (e) == 1 */ +#define DELTA1164 CHOOSE(1, 0, 0, 1, 0, 0) /* log (1.0 / M_El) == -1 */ +#define DELTA1167 CHOOSE(2341, 1, 1, 2341, 1, 1) /* log (0.7) == -0.35667494393873237891263871124118447 */ +#define DELTA1178 CHOOSE(1, 0, 1, 1, 0, 1) /* log10 (e) == log10(e) */ +#define DELTA1179 CHOOSE(2033, 1, 0, 2033, 1, 0) /* log10 (0.7) == -0.15490195998574316929 */ +#define DELTA1186 CHOOSE(1, 0, 0, 1, 0, 0) /* log1p (M_El - 1.0) == 1 */ +#define DELTA1187 CHOOSE(585, 1, 1, 585, 1, 1) /* log1p (-0.3) == -0.35667494393873237891263871124118447 */ +#define DELTA1198 CHOOSE(1688, 1, 1, 1688, 1, 1) /* log2 (0.7) == -0.51457317282975824043 */ +#define DELTA1398 CHOOSE(725, 0, 0, 725, 0, 0) /* pow (0.7, 1.2) == 0.65180494056638638188 */ +#define DELTA1524 CHOOSE(627, 0, 0, 627, 0, 0) /* sin (0.7) == 0.64421768723769105367261435139872014 */ +#define DELTA1536 CHOOSE(0.25, 0.2758, 0.3667, 0.25, 0.2758, 0.3667) /* sincos (pi/2, &sin_res, &cos_res) puts 0 in cos_res */ +#define DELTA1539 CHOOSE(1, 1, 1, 1, 1, 1) /* sincos (M_PI_6l*2.0, &sin_res, &cos_res) puts 0.86602540378443864676372317075293616 in sin_res */ +#define DELTA1540 CHOOSE(0, 1, 0.5, 0, 1, 0.5) /* sincos (M_PI_6l*2.0, &sin_res, &cos_res) puts 0.5 in cos_res */ +#define DELTA1541 CHOOSE(627, 0, 0, 627, 0, 0) /* sincos (0.7, &sin_res, &cos_res) puts 0.64421768723769105367261435139872014 in sin_res */ +#define DELTA1542 CHOOSE(528, 1, 0, 528, 1, 0) /* sincos (0.7, &sin_res, &cos_res) puts 0.76484218728448842625585999019186495 in cos_res */ +#define DELTA1548 CHOOSE(1029, 1, 1, 1028, 0, 1) /* sinh (0.7) == 0.75858370183953350346 */ +#define DELTA1562 CHOOSE(325, 0, 0, 325, 0, 0) /* sqrt (15239.9025) == 123.45 */ +#define DELTA1569 CHOOSE(0, 0.5, 0, 0, 0.5, 0) /* tan (pi/4) == 1 */ +#define DELTA1570 CHOOSE(1401, 1, 1, 1401, 0, 0) /* tan (0.7) == 0.84228838046307944812813500221293775 */ +#define DELTA1576 CHOOSE(521, 1, 1, 521, 0, 0) /* tanh (0.7) == 0.60436777711716349631 */ +#define DELTA1577 CHOOSE(1, 1, 1, 1, 0, 0) /* tanh (-0.7) == -0.60436777711716349631 */ +#define DELTA1587 CHOOSE(0, 0, 1, 0, 0, 1) /* tgamma (0.5) == sqrt (pi) */ +#define DELTA1588 CHOOSE(2, 2, 1, 2, 2, 1) /* tgamma (-0.5) == -2 sqrt (pi) */ +#define DELTA1590 CHOOSE(2, 0, 0, 2, 0, 0) /* tgamma (4) == 6 */ +#define DELTA1591 CHOOSE(0, 1, 1, 0, 1, 1) /* tgamma (0.7) == 1.29805533264755778568 */ +#define DELTA1614 CHOOSE(0, 1, 1, 0, 1, 1) /* y0 (0.1) == -1.5342386513503668441 */ +#define DELTA1615 CHOOSE(2, 3, 1, 2, 3, 1) /* y0 (0.7) == -0.19066492933739506743 */ +#define DELTA1616 CHOOSE(0, 2, 1, 0, 2, 1) /* y0 (1.0) == 0.088256964215676957983 */ +#define DELTA1617 CHOOSE(0, 1, 1, 0, 1, 1) /* y0 (1.5) == 0.38244892379775884396 */ +#define DELTA1618 CHOOSE(0, 1, 0, 0, 1, 0) /* y0 (2.0) == 0.51037567264974511960 */ +#define DELTA1619 CHOOSE(1, 1, 1, 1, 1, 1) /* y0 (8.0) == 0.22352148938756622053 */ +#define DELTA1620 CHOOSE(1, 2, 1, 2, 2, 1) /* y0 (10.0) == 0.055671167283599391424 */ +#define DELTA1625 CHOOSE(1, 1, 1, 1, 1, 1) /* y1 (0.1) == -6.4589510947020269877 */ +#define DELTA1626 CHOOSE(0, 1, 1, 0, 1, 0) /* y1 (0.7) == -1.1032498719076333697 */ +#define DELTA1627 CHOOSE(0, 1, 0, 0, 1, 0) /* y1 (1.0) == -0.78121282130028871655 */ +#define DELTA1628 CHOOSE(0, 0, 1, 0, 0, 1) /* y1 (1.5) == -0.41230862697391129595 */ +#define DELTA1629 CHOOSE(1, 1, 2, 1, 1, 2) /* y1 (2.0) == -0.10703243154093754689 */ +#define DELTA1630 CHOOSE(2, 1, 2, 2, 0, 2) /* y1 (8.0) == -0.15806046173124749426 */ +#define DELTA1631 CHOOSE(0, 3, 2, 0, 3, 2) /* y1 (10.0) == 0.24901542420695388392 */ +#define DELTA1636 CHOOSE(0, 1, 1, 0, 1, 1) /* yn (0, 0.1) == -1.5342386513503668441 */ +#define DELTA1637 CHOOSE(2, 3, 1, 2, 3, 1) /* yn (0, 0.7) == -0.19066492933739506743 */ +#define DELTA1638 CHOOSE(0, 2, 1, 0, 2, 1) /* yn (0, 1.0) == 0.088256964215676957983 */ +#define DELTA1639 CHOOSE(0, 1, 1, 0, 1, 1) /* yn (0, 1.5) == 0.38244892379775884396 */ +#define DELTA1640 CHOOSE(0, 1, 0, 0, 1, 0) /* yn (0, 2.0) == 0.51037567264974511960 */ +#define DELTA1641 CHOOSE(1, 1, 1, 1, 1, 1) /* yn (0, 8.0) == 0.22352148938756622053 */ +#define DELTA1642 CHOOSE(1, 2, 1, 1, 2, 1) /* yn (0, 10.0) == 0.055671167283599391424 */ +#define DELTA1647 CHOOSE(1, 1, 1, 1, 1, 1) /* yn (1, 0.1) == -6.4589510947020269877 */ +#define DELTA1648 CHOOSE(0, 1, 1, 0, 1, 0) /* yn (1, 0.7) == -1.1032498719076333697 */ +#define DELTA1649 CHOOSE(0, 1, 0, 0, 1, 0) /* yn (1, 1.0) == -0.78121282130028871655 */ +#define DELTA1650 CHOOSE(0, 0, 1, 0, 0, 1) /* yn (1, 1.5) == -0.41230862697391129595 */ +#define DELTA1651 CHOOSE(1, 1, 2, 1, 1, 2) /* yn (1, 2.0) == -0.10703243154093754689 */ +#define DELTA1652 CHOOSE(2, 1, 2, 2, 0, 2) /* yn (1, 8.0) == -0.15806046173124749426 */ +#define DELTA1653 CHOOSE(0, 3, 2, 0, 3, 2) /* yn (1, 10.0) == 0.24901542420695388392 */ +#define DELTA1656 CHOOSE(2, 1, 2, 2, 1, 1) /* yn (3, 0.1) == -5099.3323786129048894 */ +#define DELTA1657 CHOOSE(2, 3, 1, 2, 3, 1) /* yn (3, 0.7) == -15.819479052819633505 */ +#define DELTA1659 CHOOSE(0, 1, 1, 0, 1, 1) /* yn (3, 2.0) == -1.1277837768404277861 */ +#define DELTA1660 CHOOSE(0, 1, 1, 0, 1, 1) /* yn (3, 10.0) == -0.25136265718383732978 */ +#define DELTA1663 CHOOSE(2, 2, 2, 2, 2, 1) /* yn (10, 0.1) == -0.11831335132045197885e19 */ +#define DELTA1664 CHOOSE(7, 6, 3, 7, 6, 3) /* yn (10, 0.7) == -0.42447194260703866924e10 */ +#define DELTA1665 CHOOSE(0, 1, 2, 0, 1, 1) /* yn (10, 1.0) == -0.12161801427868918929e9 */ +#define DELTA1666 CHOOSE(1, 3, 3, 1, 2, 1) /* yn (10, 2.0) == -129184.54220803928264 */ +#define DELTA1667 CHOOSE(0, 2, 1, 0, 2, 1) /* yn (10, 10.0) == -0.35981415218340272205 */ diff --git a/openlibm/test/libm-test.c b/openlibm/test/libm-test.c new file mode 100644 index 0000000..0cef025 --- /dev/null +++ b/openlibm/test/libm-test.c @@ -0,0 +1,4537 @@ +/* Copyright (C) 1997, 1998, 1999, 2000, 2001 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Andreas Jaeger , 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, write to the Free + Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA + 02111-1307 USA. */ + +/* Part of testsuite for libm. + + This file is processed by a perl script. The resulting file has to + be included by a master file that defines: + + Makros: + FUNC(function): converts general function name (like cos) to + name with correct suffix (e.g. cosl or cosf) + MATHCONST(x): like FUNC but for constants (e.g convert 0.0 to 0.0L) + FLOAT: floating point type to test + - TEST_MSG: informal message to be displayed + CHOOSE(Clongdouble,Cdouble,Cfloat,Cinlinelongdouble,Cinlinedouble,Cinlinefloat): + chooses one of the parameters as delta for testing + equality + PRINTF_EXPR Floating point conversion specification to print a variable + of type FLOAT with printf. PRINTF_EXPR just contains + the specifier, not the percent and width arguments, + e.g. "f". + PRINTF_XEXPR Like PRINTF_EXPR, but print in hexadecimal format. + PRINTF_NEXPR Like PRINTF_EXPR, but print nice. */ + +/* This testsuite has currently tests for: + acos, acosh, asin, asinh, atan, atan2, atanh, + cbrt, ceil, copysign, cos, cosh, erf, erfc, exp, exp10, exp2, expm1, + fabs, fdim, floor, fma, fmax, fmin, fmod, fpclassify, + frexp, gamma, hypot, + ilogb, isfinite, isinf, isnan, isnormal, + isless, islessequal, isgreater, isgreaterequal, islessgreater, isunordered, + j0, j1, jn, + ldexp, lgamma, log, log10, log1p, log2, logb, + modf, nearbyint, nextafter, + pow, remainder, remquo, rint, lrint, llrint, + round, lround, llround, + scalb, scalbn, scalbln, signbit, sin, sincos, sinh, sqrt, tan, tanh, tgamma, trunc, + y0, y1, yn + + and for the following complex math functions: + cabs, cacos, cacosh, carg, casin, casinh, catan, catanh, + ccos, ccosh, cexp, clog, cpow, cproj, csin, csinh, csqrt, ctan, ctanh. + + At the moment the following functions aren't tested: + drem, significand, nan + + Parameter handling is primitive in the moment: + --verbose=[0..3] for different levels of output: + 0: only error count + 1: basic report on failed tests (default) + 2: full report on all tests + -v for full output (equals --verbose=3) + -u for generation of an ULPs file + */ + +/* "Philosophy": + + This suite tests some aspects of the correct implementation of + mathematical functions in libm. Some simple, specific parameters + are tested for correctness but there's no exhaustive + testing. Handling of specific inputs (e.g. infinity, not-a-number) + is also tested. Correct handling of exceptions is checked + against. These implemented tests should check all cases that are + specified in ISO C99. + + Exception testing: At the moment only divide-by-zero and invalid + exceptions are tested. Overflow/underflow and inexact exceptions + aren't checked at the moment. + + NaN values: There exist signalling and quiet NaNs. This implementation + only uses signalling NaN as parameter but does not differenciate + between the two kinds of NaNs as result. + + Inline functions: Inlining functions should give an improvement in + speed - but not in precission. The inlined functions return + reasonable values for a reasonable range of input values. The + result is not necessarily correct for all values and exceptions are + not correctly raised in all cases. Problematic input and return + values are infinity, not-a-number and minus zero. This suite + therefore does not check these specific inputs and the exception + handling for inlined mathematical functions - just the "reasonable" + values are checked. + + Beware: The tests might fail for any of the following reasons: + - Tests are wrong + - Functions are wrong + - Floating Point Unit not working properly + - Compiler has errors + + With e.g. gcc 2.7.2.2 the test for cexp fails because of a compiler error. + + + To Do: All parameter should be numbers that can be represented as + exact floating point values. Currently some values cannot be represented + exactly and therefore the result is not the expected result. +*/ + +#ifndef _GNU_SOURCE +# define _GNU_SOURCE +#endif + +#include "libm-test-ulps.h" +#include +#ifdef SYS_MATH_H +#include +#include +#else +#include +#endif + +#if 0 /* XXX scp XXX */ +#define FE_INEXACT FE_INEXACT +#define FE_DIVBYZERO FE_DIVBYZERO +#define FE_UNDERFLOW FE_UNDERFLOW +#define FE_OVERFLOW FE_OVERFLOW +#define FE_INVALID FE_INVALID +#endif + +#include + +#include +#include +#include +#include +#if 0 /* XXX scp XXX */ +#include +#endif + +// Some native libm implementations don't have sincos defined, so we have to do it ourselves +void FUNC(sincos) (FLOAT x, FLOAT * s, FLOAT * c); + +#ifdef __APPLE__ +#ifdef SYS_MATH_H +void sincos(FLOAT x, FLOAT * s, FLOAT * c) +{ + *s = sin(x); + *c = cos(x); +} +#endif +#endif + +/* Possible exceptions */ +#define NO_EXCEPTION 0x0 +#define INVALID_EXCEPTION 0x1 +#define DIVIDE_BY_ZERO_EXCEPTION 0x2 +/* The next flags signals that those exceptions are allowed but not required. */ +#define INVALID_EXCEPTION_OK 0x4 +#define DIVIDE_BY_ZERO_EXCEPTION_OK 0x8 +#define EXCEPTIONS_OK INVALID_EXCEPTION_OK+DIVIDE_BY_ZERO_EXCEPTION_OK +/* Some special test flags, passed togther with exceptions. */ +#define IGNORE_ZERO_INF_SIGN 0x10 + +/* Various constants (we must supply them precalculated for accuracy). */ +#define M_PI_6l .52359877559829887307710723054658383L +#define M_E2l 7.389056098930650227230427460575008L +#define M_E3l 20.085536923187667740928529654581719L +#define M_2_SQRT_PIl 3.5449077018110320545963349666822903L /* 2 sqrt (M_PIl) */ +#define M_SQRT_PIl 1.7724538509055160272981674833411451L /* sqrt (M_PIl) */ +#define M_LOG_SQRT_PIl 0.57236494292470008707171367567652933L /* log(sqrt(M_PIl)) */ +#define M_LOG_2_SQRT_PIl 1.265512123484645396488945797134706L /* log(2*sqrt(M_PIl)) */ +#define M_PI_34l (M_PIl - M_PI_4l) /* 3*pi/4 */ +#define M_PI_34_LOG10El (M_PIl - M_PI_4l) * M_LOG10El +#define M_PI2_LOG10El M_PI_2l * M_LOG10El +#define M_PI4_LOG10El M_PI_4l * M_LOG10El +#define M_PI_LOG10El M_PIl * M_LOG10El + +#if 1 /* XXX scp XXX */ +# define M_El 2.7182818284590452353602874713526625L /* e */ +# define M_LOG2El 1.4426950408889634073599246810018922L /* log_2 e */ +# define M_LOG10El 0.4342944819032518276511289189166051L /* log_10 e */ +# define M_LN2l 0.6931471805599453094172321214581766L /* log_e 2 */ +# define M_LN10l 2.3025850929940456840179914546843642L /* log_e 10 */ +# define M_PIl 3.1415926535897932384626433832795029L /* pi */ +# define M_PI_2l 1.5707963267948966192313216916397514L /* pi/2 */ +# define M_PI_4l 0.7853981633974483096156608458198757L /* pi/4 */ +# define M_1_PIl 0.3183098861837906715377675267450287L /* 1/pi */ +# define M_2_PIl 0.6366197723675813430755350534900574L /* 2/pi */ +# define M_2_SQRTPIl 1.1283791670955125738961589031215452L /* 2/sqrt(pi) */ +# define M_SQRT2l 1.4142135623730950488016887242096981L /* sqrt(2) */ +# define M_SQRT1_2l 0.7071067811865475244008443621048490L /* 1/sqrt(2) */ +#endif + +static FILE *ulps_file; /* File to document difference. */ +static int output_ulps; /* Should ulps printed? */ + +static int noErrors; /* number of errors */ +static int noTests; /* number of tests (without testing exceptions) */ +static int noExcTests; /* number of tests for exception flags */ +static int noXFails; /* number of expected failures. */ +static int noXPasses; /* number of unexpected passes. */ + +static int verbose; +static int output_max_error; /* Should the maximal errors printed? */ +static int output_points; /* Should the single function results printed? */ +static int ignore_max_ulp; /* Should we ignore max_ulp? */ + +static FLOAT minus_zero, plus_zero; +static FLOAT plus_infty, minus_infty, nan_value; + +static FLOAT max_error, real_max_error, imag_max_error; + + +#if 0 /* XXX scp XXX */ +#define BUILD_COMPLEX(real, imag) \ + ({ __complex__ FLOAT __retval; \ + __real__ __retval = (real); \ + __imag__ __retval = (imag); \ + __retval; }) + +#define BUILD_COMPLEX_INT(real, imag) \ + ({ __complex__ int __retval; \ + __real__ __retval = (real); \ + __imag__ __retval = (imag); \ + __retval; }) +#endif + + +#define MANT_DIG CHOOSE ((LDBL_MANT_DIG-1), (DBL_MANT_DIG-1), (FLT_MANT_DIG-1), \ + (LDBL_MANT_DIG-1), (DBL_MANT_DIG-1), (FLT_MANT_DIG-1)) + + +static void +init_max_error (void) +{ + max_error = 0; + real_max_error = 0; + imag_max_error = 0; + feclearexcept (FE_ALL_EXCEPT); +} + +static void +set_max_error (FLOAT current, FLOAT *curr_max_error) +{ + if (current > *curr_max_error) + *curr_max_error = current; +} + + +/* Should the message print to screen? This depends on the verbose flag, + and the test status. */ +static int +print_screen (int ok, int xfail) +{ + if (output_points + && (verbose > 1 + || (verbose == 1 && ok == xfail))) + return 1; + return 0; +} + + +/* Should the message print to screen? This depends on the verbose flag, + and the test status. */ +static int +print_screen_max_error (int ok, int xfail) +{ + if (output_max_error + && (verbose > 1 + || ((verbose == 1) && (ok == xfail)))) + return 1; + return 0; +} + +/* Update statistic counters. */ +static void +update_stats (int ok, int xfail) +{ + ++noTests; + if (ok && xfail) + ++noXPasses; + else if (!ok && xfail) + ++noXFails; + else if (!ok && !xfail) + ++noErrors; +} + +static void +print_ulps (const char *test_name, FLOAT ulp) +{ + if (output_ulps) + { + fprintf (ulps_file, "Test \"%s\":\n", test_name); + fprintf (ulps_file, "%s: % .4" PRINTF_NEXPR "\n", + CHOOSE("ldouble", "double", "float", + "ildouble", "idouble", "ifloat"), ulp); + } +} + +static void +print_function_ulps (const char *function_name, FLOAT ulp) +{ + if (output_ulps) + { + fprintf (ulps_file, "Function: \"%s\":\n", function_name); + fprintf (ulps_file, "%s: % .4" PRINTF_NEXPR "\n", + CHOOSE("ldouble", "double", "float", + "ildouble", "idouble", "ifloat"), ulp); + } +} + + +#if 0 /* XXX scp XXX */ +static void +print_complex_function_ulps (const char *function_name, FLOAT real_ulp, + FLOAT imag_ulp) +{ + if (output_ulps) + { + if (real_ulp != 0.0) + { + fprintf (ulps_file, "Function: Real part of \"%s\":\n", function_name); + fprintf (ulps_file, "%s: % .4" PRINTF_NEXPR "\n", + CHOOSE("ldouble", "double", "float", + "ildouble", "idouble", "ifloat"), real_ulp); + } + if (imag_ulp != 0.0) + { + fprintf (ulps_file, "Function: Imaginary part of \"%s\":\n", function_name); + fprintf (ulps_file, "%s: % .4" PRINTF_NEXPR "\n", + CHOOSE("ldouble", "double", "float", + "ildouble", "idouble", "ifloat"), imag_ulp); + } + + + } +} +#endif + + +static void +print_max_error (const char *func_name, FLOAT allowed, int xfail) +{ + int ok = 0; + + if (max_error == 0.0 || (max_error <= allowed && !ignore_max_ulp)) + { + ok = 1; + } + + if (!ok) + print_function_ulps (func_name, max_error); + + + if (print_screen_max_error (ok, xfail)) + { + printf ("Maximal error of `%s'\n", func_name); + printf (" is : % .4" PRINTF_NEXPR " ulp\n", max_error); + printf (" accepted: % .4" PRINTF_NEXPR " ulp\n", allowed); + } + + update_stats (ok, xfail); +} + + +#if 0 /* XXX scp XXX */ +static void +print_complex_max_error (const char *func_name, __complex__ FLOAT allowed, + __complex__ int xfail) +{ + int ok = 0; + + if ((real_max_error <= __real__ allowed) + && (imag_max_error <= __imag__ allowed)) + { + ok = 1; + } + + if (!ok) + print_complex_function_ulps (func_name, real_max_error, imag_max_error); + + + if (print_screen_max_error (ok, xfail)) + { + printf ("Maximal error of real part of: %s\n", func_name); + printf (" is : % .4" PRINTF_NEXPR " ulp\n", real_max_error); + printf (" accepted: % .4" PRINTF_NEXPR " ulp\n", __real__ allowed); + printf ("Maximal error of imaginary part of: %s\n", func_name); + printf (" is : % .4" PRINTF_NEXPR " ulp\n", imag_max_error); + printf (" accepted: % .4" PRINTF_NEXPR " ulp\n", __imag__ allowed); + } + + update_stats (ok, xfail); +} +#endif + + +/* Test whether a given exception was raised. */ +static void +test_single_exception (const char *test_name, + int exception, + int exc_flag, + int fe_flag, + const char *flag_name) +{ +/* Don't perform these checks if we're compiling with clang, because clang + doesn't bother to set floating-point exceptions properly */ +#ifndef __clang__ +#ifndef TEST_INLINE + int ok = 1; + if (exception & exc_flag) + { + if (fetestexcept (fe_flag)) + { + if (print_screen (1, 0)) + printf ("Pass: %s: Exception \"%s\" set\n", test_name, flag_name); + } + else + { + ok = 0; + if (print_screen (0, 0)) + printf ("Failure: %s: Exception \"%s\" not set\n", + test_name, flag_name); + } + } + else + { + if (fetestexcept (fe_flag)) + { + ok = 0; + if (print_screen (0, 0)) + printf ("Failure: %s: Exception \"%s\" set\n", + test_name, flag_name); + } + else + { + if (print_screen (1, 0)) + printf ("%s: Exception \"%s\" not set\n", test_name, + flag_name); + } + } + if (!ok) + ++noErrors; + +#endif +#endif // __clang__ +} + + +/* Test whether exceptions given by EXCEPTION are raised. Ignore thereby + allowed but not required exceptions. +*/ +static void +test_exceptions (const char *test_name, int exception) +{ + ++noExcTests; +#ifdef FE_DIVBYZERO + if ((exception & DIVIDE_BY_ZERO_EXCEPTION_OK) == 0) + test_single_exception (test_name, exception, + DIVIDE_BY_ZERO_EXCEPTION, FE_DIVBYZERO, + "Divide by zero"); +#endif +#ifdef FE_INVALID + if ((exception & INVALID_EXCEPTION_OK) == 0) + test_single_exception (test_name, exception, INVALID_EXCEPTION, FE_INVALID, + "Invalid operation"); +#endif + feclearexcept (FE_ALL_EXCEPT); +} + + +static void +check_float_internal (const char *test_name, FLOAT computed, FLOAT expected, + FLOAT max_ulp, int xfail, int exceptions, + FLOAT *curr_max_error) +{ + int ok = 0; + int print_diff = 0; + FLOAT diff = 0; + FLOAT ulp = 0; + + test_exceptions (test_name, exceptions); + if (isnan (computed) && isnan (expected)) + ok = 1; + else if (isinf (computed) && isinf (expected)) + { + /* Test for sign of infinities. */ + if ((exceptions & IGNORE_ZERO_INF_SIGN) == 0 + && signbit (computed) != signbit (expected)) + { + ok = 0; + printf ("infinity has wrong sign.\n"); + } + else + ok = 1; + } + /* Don't calc ulp for NaNs or infinities. */ + else if (isinf (computed) || isnan (computed) || isinf (expected) || isnan (expected)) + ok = 0; + else + { + diff = FUNC(fabs) (computed - expected); + /* ilogb (0) isn't allowed. */ + if (expected == 0.0) + ulp = diff / FUNC(ldexp) (1.0, - MANT_DIG); + else + ulp = diff / FUNC(ldexp) (1.0, FUNC(ilogb) (expected) - MANT_DIG); + set_max_error (ulp, curr_max_error); + print_diff = 1; + if ((exceptions & IGNORE_ZERO_INF_SIGN) == 0 + && computed == 0.0 && expected == 0.0 + && signbit(computed) != signbit (expected)) + ok = 0; + else if (ulp == 0.0 || (ulp <= max_ulp && !ignore_max_ulp)) + ok = 1; + else + { + ok = 0; + print_ulps (test_name, ulp); + } + + } + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure: "); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: % .20" PRINTF_EXPR " % .20" PRINTF_XEXPR "\n", + computed, computed); + printf (" should be: % .20" PRINTF_EXPR " % .20" PRINTF_XEXPR "\n", + expected, expected); + if (print_diff) + { + printf (" difference: % .20" PRINTF_EXPR " % .20" PRINTF_XEXPR + "\n", diff, diff); + printf (" ulp : % .4" PRINTF_NEXPR "\n", ulp); + printf (" max.ulp : % .4" PRINTF_NEXPR "\n", max_ulp); + } + } + update_stats (ok, xfail); +} + + +static void +check_float (const char *test_name, FLOAT computed, FLOAT expected, + FLOAT max_ulp, int xfail, int exceptions) +{ + check_float_internal (test_name, computed, expected, max_ulp, xfail, + exceptions, &max_error); +} + +#if 0 /* XXX scp XXX */ +static void +check_complex (const char *test_name, __complex__ FLOAT computed, + __complex__ FLOAT expected, + __complex__ FLOAT max_ulp, __complex__ int xfail, + int exception) +{ + FLOAT part_comp, part_exp, part_max_ulp; + int part_xfail; + char str[200]; + + sprintf (str, "Real part of: %s", test_name); + part_comp = __real__ computed; + part_exp = __real__ expected; + part_max_ulp = __real__ max_ulp; + part_xfail = __real__ xfail; + + check_float_internal (str, part_comp, part_exp, part_max_ulp, part_xfail, + exception, &real_max_error); + + sprintf (str, "Imaginary part of: %s", test_name); + part_comp = __imag__ computed; + part_exp = __imag__ expected; + part_max_ulp = __imag__ max_ulp; + part_xfail = __imag__ xfail; + + /* Don't check again for exceptions, just pass through the + zero/inf sign test. */ + check_float_internal (str, part_comp, part_exp, part_max_ulp, part_xfail, + exception & IGNORE_ZERO_INF_SIGN, + &imag_max_error); +} +#endif + +/* Check that computed and expected values are equal (int values). */ +static void +check_int (const char *test_name, int computed, int expected, int max_ulp, + int xfail, int exceptions) +{ + int diff = computed - expected; + int ok = 0; + + test_exceptions (test_name, exceptions); + noTests++; + if (abs (diff) <= max_ulp) + ok = 1; + + if (!ok) + print_ulps (test_name, diff); + + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure: "); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: %d\n", computed); + printf (" should be: %d\n", expected); + } + + update_stats (ok, xfail); +} + + +/* Check that computed and expected values are equal (long int values). */ +static void +check_long (const char *test_name, long int computed, long int expected, + long int max_ulp, int xfail, int exceptions) +{ + long int diff = computed - expected; + int ok = 0; + + test_exceptions (test_name, exceptions); + noTests++; + if (labs (diff) <= max_ulp) + ok = 1; + + if (!ok) + print_ulps (test_name, diff); + + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure: "); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: %ld\n", computed); + printf (" should be: %ld\n", expected); + } + + update_stats (ok, xfail); +} + + +/* Check that computed value is true/false. */ +static void +check_bool (const char *test_name, int computed, int expected, + long int max_ulp, int xfail, int exceptions) +{ + int ok = 0; + + test_exceptions (test_name, exceptions); + noTests++; + if ((computed == 0) == (expected == 0)) + ok = 1; + + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure: "); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: %d\n", computed); + printf (" should be: %d\n", expected); + } + + update_stats (ok, xfail); +} + + +/* check that computed and expected values are equal (long int values) */ +static void +check_longlong (const char *test_name, long long int computed, + long long int expected, + long long int max_ulp, int xfail, + int exceptions) +{ + long long int diff = computed - expected; + int ok = 0; + + test_exceptions (test_name, exceptions); + noTests++; + if (llabs (diff) <= max_ulp) + ok = 1; + + if (!ok) + print_ulps (test_name, diff); + + if (print_screen (ok, xfail)) + { + if (!ok) + printf ("Failure:"); + printf ("Test: %s\n", test_name); + printf ("Result:\n"); + printf (" is: %lld\n", computed); + printf (" should be: %lld\n", expected); + } + + update_stats (ok, xfail); +} + + +#if 0 /* XXX scp XXX */ +/* This is to prevent messages from the SVID libm emulation. */ +int +matherr (struct exception *x __attribute__ ((unused))) +{ + return 1; +} +#endif + +/**************************************************************************** + Tests for single functions of libm. + Please keep them alphabetically sorted! +****************************************************************************/ + +static void +acos_test (void) +{ + errno = 0; + FUNC(acos) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("acos (inf) == NaN plus invalid exception", FUNC(acos) (plus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("acos (-inf) == NaN plus invalid exception", FUNC(acos) (minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("acos (NaN) == NaN", FUNC(acos) (nan_value), nan_value, 0, 0, 0); + + /* |x| > 1: */ + check_float ("acos (1.1) == NaN plus invalid exception", FUNC(acos) (1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("acos (-1.1) == NaN plus invalid exception", FUNC(acos) (-1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + + check_float ("acos (0) == pi/2", FUNC(acos) (0), M_PI_2l, 0, 0, 0); + check_float ("acos (-0) == pi/2", FUNC(acos) (minus_zero), M_PI_2l, 0, 0, 0); + check_float ("acos (1) == 0", FUNC(acos) (1), 0, 0, 0, 0); + check_float ("acos (-1) == pi", FUNC(acos) (-1), M_PIl, 0, 0, 0); + check_float ("acos (0.5) == M_PI_6l*2.0", FUNC(acos) (0.5), M_PI_6l*2.0, 1, 0, 0); + check_float ("acos (-0.5) == M_PI_6l*4.0", FUNC(acos) (-0.5), M_PI_6l*4.0, 0, 0, 0); + check_float ("acos (0.7) == 0.79539883018414355549096833892476432", FUNC(acos) (0.7L), 0.79539883018414355549096833892476432L, 0, 0, 0); + + print_max_error ("acos", DELTAacos, 0); +} + +static void +acosh_test (void) +{ + errno = 0; + FUNC(acosh) (7); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("acosh (inf) == inf", FUNC(acosh) (plus_infty), plus_infty, 0, 0, 0); + check_float ("acosh (-inf) == NaN plus invalid exception", FUNC(acosh) (minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + + /* x < 1: */ + check_float ("acosh (-1.1) == NaN plus invalid exception", FUNC(acosh) (-1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + + check_float ("acosh (1) == 0", FUNC(acosh) (1), 0, 0, 0, 0); + check_float ("acosh (7) == 2.633915793849633417250092694615937", FUNC(acosh) (7), 2.633915793849633417250092694615937L, DELTA16, 0, 0); + + print_max_error ("acosh", DELTAacosh, 0); +} + +static void +asin_test (void) +{ + errno = 0; + FUNC(asin) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("asin (inf) == NaN plus invalid exception", FUNC(asin) (plus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("asin (-inf) == NaN plus invalid exception", FUNC(asin) (minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("asin (NaN) == NaN", FUNC(asin) (nan_value), nan_value, 0, 0, 0); + + /* asin x == NaN plus invalid exception for |x| > 1. */ + check_float ("asin (1.1) == NaN plus invalid exception", FUNC(asin) (1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("asin (-1.1) == NaN plus invalid exception", FUNC(asin) (-1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + + check_float ("asin (0) == 0", FUNC(asin) (0), 0, 0, 0, 0); + check_float ("asin (-0) == -0", FUNC(asin) (minus_zero), minus_zero, 0, 0, 0); + check_float ("asin (0.5) == pi/6", FUNC(asin) (0.5), M_PI_6l, DELTA24, 0, 0); + check_float ("asin (-0.5) == -pi/6", FUNC(asin) (-0.5), -M_PI_6l, DELTA25, 0, 0); + check_float ("asin (1.0) == pi/2", FUNC(asin) (1.0), M_PI_2l, DELTA26, 0, 0); + check_float ("asin (-1.0) == -pi/2", FUNC(asin) (-1.0), -M_PI_2l, DELTA27, 0, 0); + check_float ("asin (0.7) == 0.77539749661075306374035335271498708", FUNC(asin) (0.7L), 0.77539749661075306374035335271498708L, DELTA28, 0, 0); + + print_max_error ("asin", DELTAasin, 0); +} + +static void +asinh_test (void) +{ + errno = 0; + FUNC(asinh) (0.7L); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("asinh (0) == 0", FUNC(asinh) (0), 0, 0, 0, 0); + check_float ("asinh (-0) == -0", FUNC(asinh) (minus_zero), minus_zero, 0, 0, 0); +#ifndef TEST_INLINE + check_float ("asinh (inf) == inf", FUNC(asinh) (plus_infty), plus_infty, 0, 0, 0); + check_float ("asinh (-inf) == -inf", FUNC(asinh) (minus_infty), minus_infty, 0, 0, 0); +#endif + check_float ("asinh (NaN) == NaN", FUNC(asinh) (nan_value), nan_value, 0, 0, 0); + check_float ("asinh (0.7) == 0.652666566082355786", FUNC(asinh) (0.7L), 0.652666566082355786L, DELTA34, 0, 0); + + print_max_error ("asinh", DELTAasinh, 0); +} + +static void +atan_test (void) +{ + errno = 0; + FUNC(atan) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("atan (0) == 0", FUNC(atan) (0), 0, 0, 0, 0); + check_float ("atan (-0) == -0", FUNC(atan) (minus_zero), minus_zero, 0, 0, 0); + + check_float ("atan (inf) == pi/2", FUNC(atan) (plus_infty), M_PI_2l, 0, 0, 0); + check_float ("atan (-inf) == -pi/2", FUNC(atan) (minus_infty), -M_PI_2l, 0, 0, 0); + check_float ("atan (NaN) == NaN", FUNC(atan) (nan_value), nan_value, 0, 0, 0); + + check_float ("atan (1) == pi/4", FUNC(atan) (1), M_PI_4l, 0, 0, 0); + check_float ("atan (-1) == -pi/4", FUNC(atan) (-1), -M_PI_4l, 0, 0, 0); + + check_float ("atan (0.7) == 0.61072596438920861654375887649023613", FUNC(atan) (0.7L), 0.61072596438920861654375887649023613L, DELTA42, 0, 0); + + print_max_error ("atan", DELTAatan, 0); +} + + + +static void +atanh_test (void) +{ + errno = 0; + FUNC(atanh) (0.7L); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + + check_float ("atanh (0) == 0", FUNC(atanh) (0), 0, 0, 0, 0); + check_float ("atanh (-0) == -0", FUNC(atanh) (minus_zero), minus_zero, 0, 0, 0); + + check_float ("atanh (1) == inf plus division by zero exception", FUNC(atanh) (1), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("atanh (-1) == -inf plus division by zero exception", FUNC(atanh) (-1), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("atanh (NaN) == NaN", FUNC(atanh) (nan_value), nan_value, 0, 0, 0); + + /* atanh (x) == NaN plus invalid exception if |x| > 1. */ + check_float ("atanh (1.1) == NaN plus invalid exception", FUNC(atanh) (1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("atanh (-1.1) == NaN plus invalid exception", FUNC(atanh) (-1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + + check_float ("atanh (0.7) == 0.8673005276940531944", FUNC(atanh) (0.7L), 0.8673005276940531944L, DELTA50, 0, 0); + + print_max_error ("atanh", DELTAatanh, 0); +} + +static void +atan2_test (void) +{ + errno = 0; + FUNC(atan2) (-0, 1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + /* atan2 (0,x) == 0 for x > 0. */ + check_float ("atan2 (0, 1) == 0", FUNC(atan2) (0, 1), 0, 0, 0, 0); + + /* atan2 (-0,x) == -0 for x > 0. */ + check_float ("atan2 (-0, 1) == -0", FUNC(atan2) (minus_zero, 1), minus_zero, 0, 0, 0); + + check_float ("atan2 (0, 0) == 0", FUNC(atan2) (0, 0), 0, 0, 0, 0); + check_float ("atan2 (-0, 0) == -0", FUNC(atan2) (minus_zero, 0), minus_zero, 0, 0, 0); + + /* atan2 (+0,x) == +pi for x < 0. */ + check_float ("atan2 (0, -1) == pi", FUNC(atan2) (0, -1), M_PIl, 0, 0, 0); + + /* atan2 (-0,x) == -pi for x < 0. */ + check_float ("atan2 (-0, -1) == -pi", FUNC(atan2) (minus_zero, -1), -M_PIl, 0, 0, 0); + + check_float ("atan2 (0, -0) == pi", FUNC(atan2) (0, minus_zero), M_PIl, 0, 0, 0); + check_float ("atan2 (-0, -0) == -pi", FUNC(atan2) (minus_zero, minus_zero), -M_PIl, 0, 0, 0); + + /* atan2 (y,+0) == pi/2 for y > 0. */ + check_float ("atan2 (1, 0) == pi/2", FUNC(atan2) (1, 0), M_PI_2l, 0, 0, 0); + + /* atan2 (y,-0) == pi/2 for y > 0. */ + check_float ("atan2 (1, -0) == pi/2", FUNC(atan2) (1, minus_zero), M_PI_2l, 0, 0, 0); + + /* atan2 (y,+0) == -pi/2 for y < 0. */ + check_float ("atan2 (-1, 0) == -pi/2", FUNC(atan2) (-1, 0), -M_PI_2l, 0, 0, 0); + + /* atan2 (y,-0) == -pi/2 for y < 0. */ + check_float ("atan2 (-1, -0) == -pi/2", FUNC(atan2) (-1, minus_zero), -M_PI_2l, 0, 0, 0); + + /* atan2 (y,inf) == +0 for finite y > 0. */ + check_float ("atan2 (1, inf) == 0", FUNC(atan2) (1, plus_infty), 0, 0, 0, 0); + + /* atan2 (y,inf) == -0 for finite y < 0. */ + check_float ("atan2 (-1, inf) == -0", FUNC(atan2) (-1, plus_infty), minus_zero, 0, 0, 0); + + /* atan2(+inf, x) == pi/2 for finite x. */ + check_float ("atan2 (inf, -1) == pi/2", FUNC(atan2) (plus_infty, -1), M_PI_2l, 0, 0, 0); + + /* atan2(-inf, x) == -pi/2 for finite x. */ + check_float ("atan2 (-inf, 1) == -pi/2", FUNC(atan2) (minus_infty, 1), -M_PI_2l, 0, 0, 0); + + /* atan2 (y,-inf) == +pi for finite y > 0. */ + check_float ("atan2 (1, -inf) == pi", FUNC(atan2) (1, minus_infty), M_PIl, 0, 0, 0); + + /* atan2 (y,-inf) == -pi for finite y < 0. */ + check_float ("atan2 (-1, -inf) == -pi", FUNC(atan2) (-1, minus_infty), -M_PIl, 0, 0, 0); + + check_float ("atan2 (inf, inf) == pi/4", FUNC(atan2) (plus_infty, plus_infty), M_PI_4l, 0, 0, 0); + check_float ("atan2 (-inf, inf) == -pi/4", FUNC(atan2) (minus_infty, plus_infty), -M_PI_4l, 0, 0, 0); + check_float ("atan2 (inf, -inf) == 3/4 pi", FUNC(atan2) (plus_infty, minus_infty), M_PI_34l, 0, 0, 0); + check_float ("atan2 (-inf, -inf) == -3/4 pi", FUNC(atan2) (minus_infty, minus_infty), -M_PI_34l, 0, 0, 0); + check_float ("atan2 (NaN, NaN) == NaN", FUNC(atan2) (nan_value, nan_value), nan_value, 0, 0, 0); + + check_float ("atan2 (0.7, 1) == 0.61072596438920861654375887649023613", FUNC(atan2) (0.7L, 1), 0.61072596438920861654375887649023613L, DELTA74, 0, 0); + check_float ("atan2 (-0.7, 1.0) == -0.61072596438920861654375887649023613", FUNC(atan2) (-0.7L, 1.0L), -0.61072596438920861654375887649023613L, 0, 0, 0); + check_float ("atan2 (0.7, -1.0) == 2.530866689200584621918884506789267", FUNC(atan2) (0.7L, -1.0L), 2.530866689200584621918884506789267L, 0, 0, 0); + check_float ("atan2 (-0.7, -1.0) == -2.530866689200584621918884506789267", FUNC(atan2) (-0.7L, -1.0L), -2.530866689200584621918884506789267L, 0, 0, 0); + check_float ("atan2 (0.4, 0.0003) == 1.5700463269355215717704032607580829", FUNC(atan2) (0.4L, 0.0003L), 1.5700463269355215717704032607580829L, DELTA78, 0, 0); + check_float ("atan2 (1.4, -0.93) == 2.1571487668237843754887415992772736", FUNC(atan2) (1.4L, -0.93L), 2.1571487668237843754887415992772736L, 0, 0, 0); + + print_max_error ("atan2", DELTAatan2, 0); +} + + +#if 0 /* XXX scp XXX */ +static void +cabs_test (void) +{ + errno = 0; + FUNC(cabs) (BUILD_COMPLEX (0.7L, 12.4L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + /* cabs (x + iy) is specified as hypot (x,y) */ + + /* cabs (+inf + i x) == +inf. */ + check_float ("cabs (inf + 1.0 i) == inf", FUNC(cabs) (BUILD_COMPLEX (plus_infty, 1.0)), plus_infty, 0, 0, 0); + /* cabs (-inf + i x) == +inf. */ + check_float ("cabs (-inf + 1.0 i) == inf", FUNC(cabs) (BUILD_COMPLEX (minus_infty, 1.0)), plus_infty, 0, 0, 0); + + check_float ("cabs (-inf + NaN i) == inf", FUNC(cabs) (BUILD_COMPLEX (minus_infty, nan_value)), plus_infty, 0, 0, 0); + check_float ("cabs (-inf + NaN i) == inf", FUNC(cabs) (BUILD_COMPLEX (minus_infty, nan_value)), plus_infty, 0, 0, 0); + + check_float ("cabs (NaN + NaN i) == NaN", FUNC(cabs) (BUILD_COMPLEX (nan_value, nan_value)), nan_value, 0, 0, 0); + + /* cabs (x,y) == cabs (y,x). */ + check_float ("cabs (0.7 + 12.4 i) == 12.419742348374220601176836866763271", FUNC(cabs) (BUILD_COMPLEX (0.7L, 12.4L)), 12.419742348374220601176836866763271L, DELTA85, 0, 0); + /* cabs (x,y) == cabs (-x,y). */ + check_float ("cabs (-12.4 + 0.7 i) == 12.419742348374220601176836866763271", FUNC(cabs) (BUILD_COMPLEX (-12.4L, 0.7L)), 12.419742348374220601176836866763271L, DELTA86, 0, 0); + /* cabs (x,y) == cabs (-y,x). */ + check_float ("cabs (-0.7 + 12.4 i) == 12.419742348374220601176836866763271", FUNC(cabs) (BUILD_COMPLEX (-0.7L, 12.4L)), 12.419742348374220601176836866763271L, DELTA87, 0, 0); + /* cabs (x,y) == cabs (-x,-y). */ + check_float ("cabs (-12.4 - 0.7 i) == 12.419742348374220601176836866763271", FUNC(cabs) (BUILD_COMPLEX (-12.4L, -0.7L)), 12.419742348374220601176836866763271L, DELTA88, 0, 0); + /* cabs (x,y) == cabs (-y,-x). */ + check_float ("cabs (-0.7 - 12.4 i) == 12.419742348374220601176836866763271", FUNC(cabs) (BUILD_COMPLEX (-0.7L, -12.4L)), 12.419742348374220601176836866763271L, DELTA89, 0, 0); + /* cabs (x,0) == fabs (x). */ + check_float ("cabs (-0.7 + 0 i) == 0.7", FUNC(cabs) (BUILD_COMPLEX (-0.7L, 0)), 0.7L, 0, 0, 0); + check_float ("cabs (0.7 + 0 i) == 0.7", FUNC(cabs) (BUILD_COMPLEX (0.7L, 0)), 0.7L, 0, 0, 0); + check_float ("cabs (-1.0 + 0 i) == 1.0", FUNC(cabs) (BUILD_COMPLEX (-1.0L, 0)), 1.0L, 0, 0, 0); + check_float ("cabs (1.0 + 0 i) == 1.0", FUNC(cabs) (BUILD_COMPLEX (1.0L, 0)), 1.0L, 0, 0, 0); + check_float ("cabs (-5.7e7 + 0 i) == 5.7e7", FUNC(cabs) (BUILD_COMPLEX (-5.7e7L, 0)), 5.7e7L, 0, 0, 0); + check_float ("cabs (5.7e7 + 0 i) == 5.7e7", FUNC(cabs) (BUILD_COMPLEX (5.7e7L, 0)), 5.7e7L, 0, 0, 0); + + check_float ("cabs (0.7 + 1.2 i) == 1.3892443989449804508432547041028554", FUNC(cabs) (BUILD_COMPLEX (0.7L, 1.2L)), 1.3892443989449804508432547041028554L, DELTA96, 0, 0); + + print_max_error ("cabs", DELTAcabs, 0); +} + +static void +cacos_test (void) +{ + errno = 0; + FUNC(cacos) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + + check_complex ("cacos (0 + 0 i) == pi/2 - 0 i", FUNC(cacos) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("cacos (-0 + 0 i) == pi/2 - 0 i", FUNC(cacos) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("cacos (-0 - 0 i) == pi/2 + 0.0 i", FUNC(cacos) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (M_PI_2l, 0.0), 0, 0, 0); + check_complex ("cacos (0 - 0 i) == pi/2 + 0.0 i", FUNC(cacos) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (M_PI_2l, 0.0), 0, 0, 0); + + check_complex ("cacos (-inf + inf i) == 3/4 pi - inf i", FUNC(cacos) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (M_PI_34l, minus_infty), 0, 0, 0); + check_complex ("cacos (-inf - inf i) == 3/4 pi + inf i", FUNC(cacos) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (M_PI_34l, plus_infty), 0, 0, 0); + + check_complex ("cacos (inf + inf i) == pi/4 - inf i", FUNC(cacos) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (M_PI_4l, minus_infty), 0, 0, 0); + check_complex ("cacos (inf - inf i) == pi/4 + inf i", FUNC(cacos) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (M_PI_4l, plus_infty), 0, 0, 0); + + check_complex ("cacos (-10.0 + inf i) == pi/2 - inf i", FUNC(cacos) (BUILD_COMPLEX (-10.0, plus_infty)), BUILD_COMPLEX (M_PI_2l, minus_infty), 0, 0, 0); + check_complex ("cacos (-10.0 - inf i) == pi/2 + inf i", FUNC(cacos) (BUILD_COMPLEX (-10.0, minus_infty)), BUILD_COMPLEX (M_PI_2l, plus_infty), 0, 0, 0); + check_complex ("cacos (0 + inf i) == pi/2 - inf i", FUNC(cacos) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (M_PI_2l, minus_infty), 0, 0, 0); + check_complex ("cacos (0 - inf i) == pi/2 + inf i", FUNC(cacos) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (M_PI_2l, plus_infty), 0, 0, 0); + check_complex ("cacos (0.1 + inf i) == pi/2 - inf i", FUNC(cacos) (BUILD_COMPLEX (0.1L, plus_infty)), BUILD_COMPLEX (M_PI_2l, minus_infty), 0, 0, 0); + check_complex ("cacos (0.1 - inf i) == pi/2 + inf i", FUNC(cacos) (BUILD_COMPLEX (0.1L, minus_infty)), BUILD_COMPLEX (M_PI_2l, plus_infty), 0, 0, 0); + + check_complex ("cacos (-inf + 0 i) == pi - inf i", FUNC(cacos) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (M_PIl, minus_infty), 0, 0, 0); + check_complex ("cacos (-inf - 0 i) == pi + inf i", FUNC(cacos) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (M_PIl, plus_infty), 0, 0, 0); + check_complex ("cacos (-inf + 100 i) == pi - inf i", FUNC(cacos) (BUILD_COMPLEX (minus_infty, 100)), BUILD_COMPLEX (M_PIl, minus_infty), 0, 0, 0); + check_complex ("cacos (-inf - 100 i) == pi + inf i", FUNC(cacos) (BUILD_COMPLEX (minus_infty, -100)), BUILD_COMPLEX (M_PIl, plus_infty), 0, 0, 0); + + check_complex ("cacos (inf + 0 i) == 0.0 - inf i", FUNC(cacos) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (0.0, minus_infty), 0, 0, 0); + check_complex ("cacos (inf - 0 i) == 0.0 + inf i", FUNC(cacos) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (0.0, plus_infty), 0, 0, 0); + check_complex ("cacos (inf + 0.5 i) == 0.0 - inf i", FUNC(cacos) (BUILD_COMPLEX (plus_infty, 0.5)), BUILD_COMPLEX (0.0, minus_infty), 0, 0, 0); + check_complex ("cacos (inf - 0.5 i) == 0.0 + inf i", FUNC(cacos) (BUILD_COMPLEX (plus_infty, -0.5)), BUILD_COMPLEX (0.0, plus_infty), 0, 0, 0); + + check_complex ("cacos (inf + NaN i) == NaN + inf i plus sign of zero/inf not specified", FUNC(cacos) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("cacos (-inf + NaN i) == NaN + inf i plus sign of zero/inf not specified", FUNC(cacos) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("cacos (0 + NaN i) == pi/2 + NaN i", FUNC(cacos) (BUILD_COMPLEX (0, nan_value)), BUILD_COMPLEX (M_PI_2l, nan_value), 0, 0, 0); + check_complex ("cacos (-0 + NaN i) == pi/2 + NaN i", FUNC(cacos) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (M_PI_2l, nan_value), 0, 0, 0); + + check_complex ("cacos (NaN + inf i) == NaN - inf i", FUNC(cacos) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (nan_value, minus_infty), 0, 0, 0); + check_complex ("cacos (NaN - inf i) == NaN + inf i", FUNC(cacos) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, 0); + + check_complex ("cacos (10.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(cacos) (BUILD_COMPLEX (10.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("cacos (-10.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(cacos) (BUILD_COMPLEX (-10.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("cacos (NaN + 0.75 i) == NaN + NaN i plus invalid exception allowed", FUNC(cacos) (BUILD_COMPLEX (nan_value, 0.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("cacos (NaN - 0.75 i) == NaN + NaN i plus invalid exception allowed", FUNC(cacos) (BUILD_COMPLEX (nan_value, -0.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("cacos (NaN + NaN i) == NaN + NaN i", FUNC(cacos) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("cacos (0.7 + 1.2 i) == 1.1351827477151551088992008271819053 - 1.0927647857577371459105272080819308 i", FUNC(cacos) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (1.1351827477151551088992008271819053L, -1.0927647857577371459105272080819308L), DELTA130, 0, 0); + check_complex ("cacos (-2 - 3 i) == 2.1414491111159960199416055713254211 + 1.9833870299165354323470769028940395 i", FUNC(cacos) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (2.1414491111159960199416055713254211L, 1.9833870299165354323470769028940395L), DELTA131, 0, 0); + + print_complex_max_error ("cacos", DELTAcacos, 0); +} + + +static void +cacosh_test (void) +{ + errno = 0; + FUNC(cacosh) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + + check_complex ("cacosh (0 + 0 i) == 0.0 + pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (0.0, M_PI_2l), 0, 0, 0); + check_complex ("cacosh (-0 + 0 i) == 0.0 + pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (0.0, M_PI_2l), 0, 0, 0); + check_complex ("cacosh (0 - 0 i) == 0.0 - pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (0.0, -M_PI_2l), 0, 0, 0); + check_complex ("cacosh (-0 - 0 i) == 0.0 - pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (0.0, -M_PI_2l), 0, 0, 0); + check_complex ("cacosh (-inf + inf i) == inf + 3/4 pi i", FUNC(cacosh) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_34l), 0, 0, 0); + check_complex ("cacosh (-inf - inf i) == inf - 3/4 pi i", FUNC(cacosh) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_34l), 0, 0, 0); + + check_complex ("cacosh (inf + inf i) == inf + pi/4 i", FUNC(cacosh) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_4l), 0, 0, 0); + check_complex ("cacosh (inf - inf i) == inf - pi/4 i", FUNC(cacosh) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_4l), 0, 0, 0); + + check_complex ("cacosh (-10.0 + inf i) == inf + pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (-10.0, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_2l), 0, 0, 0); + check_complex ("cacosh (-10.0 - inf i) == inf - pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (-10.0, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_2l), 0, 0, 0); + check_complex ("cacosh (0 + inf i) == inf + pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_2l), 0, 0, 0); + check_complex ("cacosh (0 - inf i) == inf - pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_2l), 0, 0, 0); + check_complex ("cacosh (0.1 + inf i) == inf + pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (0.1L, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_2l), 0, 0, 0); + check_complex ("cacosh (0.1 - inf i) == inf - pi/2 i", FUNC(cacosh) (BUILD_COMPLEX (0.1L, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_2l), 0, 0, 0); + + check_complex ("cacosh (-inf + 0 i) == inf + pi i", FUNC(cacosh) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (plus_infty, M_PIl), 0, 0, 0); + check_complex ("cacosh (-inf - 0 i) == inf - pi i", FUNC(cacosh) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, -M_PIl), 0, 0, 0); + check_complex ("cacosh (-inf + 100 i) == inf + pi i", FUNC(cacosh) (BUILD_COMPLEX (minus_infty, 100)), BUILD_COMPLEX (plus_infty, M_PIl), 0, 0, 0); + check_complex ("cacosh (-inf - 100 i) == inf - pi i", FUNC(cacosh) (BUILD_COMPLEX (minus_infty, -100)), BUILD_COMPLEX (plus_infty, -M_PIl), 0, 0, 0); + + check_complex ("cacosh (inf + 0 i) == inf + 0.0 i", FUNC(cacosh) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("cacosh (inf - 0 i) == inf - 0 i", FUNC(cacosh) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("cacosh (inf + 0.5 i) == inf + 0.0 i", FUNC(cacosh) (BUILD_COMPLEX (plus_infty, 0.5)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("cacosh (inf - 0.5 i) == inf - 0 i", FUNC(cacosh) (BUILD_COMPLEX (plus_infty, -0.5)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + + check_complex ("cacosh (inf + NaN i) == inf + NaN i", FUNC(cacosh) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + check_complex ("cacosh (-inf + NaN i) == inf + NaN i", FUNC(cacosh) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("cacosh (0 + NaN i) == NaN + NaN i", FUNC(cacosh) (BUILD_COMPLEX (0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + check_complex ("cacosh (-0 + NaN i) == NaN + NaN i", FUNC(cacosh) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("cacosh (NaN + inf i) == inf + NaN i", FUNC(cacosh) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + check_complex ("cacosh (NaN - inf i) == inf + NaN i", FUNC(cacosh) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("cacosh (10.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(cacosh) (BUILD_COMPLEX (10.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("cacosh (-10.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(cacosh) (BUILD_COMPLEX (-10.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("cacosh (NaN + 0.75 i) == NaN + NaN i plus invalid exception allowed", FUNC(cacosh) (BUILD_COMPLEX (nan_value, 0.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("cacosh (NaN - 0.75 i) == NaN + NaN i plus invalid exception allowed", FUNC(cacosh) (BUILD_COMPLEX (nan_value, -0.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("cacosh (NaN + NaN i) == NaN + NaN i", FUNC(cacosh) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("cacosh (0.7 + 1.2 i) == 1.0927647857577371459105272080819308 + 1.1351827477151551088992008271819053 i", FUNC(cacosh) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (1.0927647857577371459105272080819308L, 1.1351827477151551088992008271819053L), DELTA165, 0, 0); + check_complex ("cacosh (-2 - 3 i) == -1.9833870299165354323470769028940395 + 2.1414491111159960199416055713254211 i", FUNC(cacosh) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (-1.9833870299165354323470769028940395L, 2.1414491111159960199416055713254211L), DELTA166, 0, 0); + + print_complex_max_error ("cacosh", DELTAcacosh, 0); +} + +static void +carg_test (void) +{ + init_max_error (); + + /* carg (x + iy) is specified as atan2 (y, x) */ + + /* carg (x + i 0) == 0 for x > 0. */ + check_float ("carg (2.0 + 0 i) == 0", FUNC(carg) (BUILD_COMPLEX (2.0, 0)), 0, 0, 0, 0); + /* carg (x - i 0) == -0 for x > 0. */ + check_float ("carg (2.0 - 0 i) == -0", FUNC(carg) (BUILD_COMPLEX (2.0, minus_zero)), minus_zero, 0, 0, 0); + + check_float ("carg (0 + 0 i) == 0", FUNC(carg) (BUILD_COMPLEX (0, 0)), 0, 0, 0, 0); + check_float ("carg (0 - 0 i) == -0", FUNC(carg) (BUILD_COMPLEX (0, minus_zero)), minus_zero, 0, 0, 0); + + /* carg (x + i 0) == +pi for x < 0. */ + check_float ("carg (-2.0 + 0 i) == pi", FUNC(carg) (BUILD_COMPLEX (-2.0, 0)), M_PIl, 0, 0, 0); + + /* carg (x - i 0) == -pi for x < 0. */ + check_float ("carg (-2.0 - 0 i) == -pi", FUNC(carg) (BUILD_COMPLEX (-2.0, minus_zero)), -M_PIl, 0, 0, 0); + + check_float ("carg (-0 + 0 i) == pi", FUNC(carg) (BUILD_COMPLEX (minus_zero, 0)), M_PIl, 0, 0, 0); + check_float ("carg (-0 - 0 i) == -pi", FUNC(carg) (BUILD_COMPLEX (minus_zero, minus_zero)), -M_PIl, 0, 0, 0); + + /* carg (+0 + i y) == pi/2 for y > 0. */ + check_float ("carg (0 + 2.0 i) == pi/2", FUNC(carg) (BUILD_COMPLEX (0, 2.0)), M_PI_2l, 0, 0, 0); + + /* carg (-0 + i y) == pi/2 for y > 0. */ + check_float ("carg (-0 + 2.0 i) == pi/2", FUNC(carg) (BUILD_COMPLEX (minus_zero, 2.0)), M_PI_2l, 0, 0, 0); + + /* carg (+0 + i y) == -pi/2 for y < 0. */ + check_float ("carg (0 - 2.0 i) == -pi/2", FUNC(carg) (BUILD_COMPLEX (0, -2.0)), -M_PI_2l, 0, 0, 0); + + /* carg (-0 + i y) == -pi/2 for y < 0. */ + check_float ("carg (-0 - 2.0 i) == -pi/2", FUNC(carg) (BUILD_COMPLEX (minus_zero, -2.0)), -M_PI_2l, 0, 0, 0); + + /* carg (inf + i y) == +0 for finite y > 0. */ + check_float ("carg (inf + 2.0 i) == 0", FUNC(carg) (BUILD_COMPLEX (plus_infty, 2.0)), 0, 0, 0, 0); + + /* carg (inf + i y) == -0 for finite y < 0. */ + check_float ("carg (inf - 2.0 i) == -0", FUNC(carg) (BUILD_COMPLEX (plus_infty, -2.0)), minus_zero, 0, 0, 0); + + /* carg(x + i inf) == pi/2 for finite x. */ + check_float ("carg (10.0 + inf i) == pi/2", FUNC(carg) (BUILD_COMPLEX (10.0, plus_infty)), M_PI_2l, 0, 0, 0); + + /* carg(x - i inf) == -pi/2 for finite x. */ + check_float ("carg (10.0 - inf i) == -pi/2", FUNC(carg) (BUILD_COMPLEX (10.0, minus_infty)), -M_PI_2l, 0, 0, 0); + + /* carg (-inf + i y) == +pi for finite y > 0. */ + check_float ("carg (-inf + 10.0 i) == pi", FUNC(carg) (BUILD_COMPLEX (minus_infty, 10.0)), M_PIl, 0, 0, 0); + + /* carg (-inf + i y) == -pi for finite y < 0. */ + check_float ("carg (-inf - 10.0 i) == -pi", FUNC(carg) (BUILD_COMPLEX (minus_infty, -10.0)), -M_PIl, 0, 0, 0); + + check_float ("carg (inf + inf i) == pi/4", FUNC(carg) (BUILD_COMPLEX (plus_infty, plus_infty)), M_PI_4l, 0, 0, 0); + + check_float ("carg (inf - inf i) == -pi/4", FUNC(carg) (BUILD_COMPLEX (plus_infty, minus_infty)), -M_PI_4l, 0, 0, 0); + + check_float ("carg (-inf + inf i) == 3 * M_PI_4l", FUNC(carg) (BUILD_COMPLEX (minus_infty, plus_infty)), 3 * M_PI_4l, 0, 0, 0); + + check_float ("carg (-inf - inf i) == -3 * M_PI_4l", FUNC(carg) (BUILD_COMPLEX (minus_infty, minus_infty)), -3 * M_PI_4l, 0, 0, 0); + + check_float ("carg (NaN + NaN i) == NaN", FUNC(carg) (BUILD_COMPLEX (nan_value, nan_value)), nan_value, 0, 0, 0); + + print_max_error ("carg", 0, 0); +} + +static void +casin_test (void) +{ + errno = 0; + FUNC(casin) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("casin (0 + 0 i) == 0.0 + 0.0 i", FUNC(casin) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("casin (-0 + 0 i) == -0 + 0.0 i", FUNC(casin) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (minus_zero, 0.0), 0, 0, 0); + check_complex ("casin (0 - 0 i) == 0.0 - 0 i", FUNC(casin) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + check_complex ("casin (-0 - 0 i) == -0 - 0 i", FUNC(casin) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + + check_complex ("casin (inf + inf i) == pi/4 + inf i", FUNC(casin) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (M_PI_4l, plus_infty), 0, 0, 0); + check_complex ("casin (inf - inf i) == pi/4 - inf i", FUNC(casin) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (M_PI_4l, minus_infty), 0, 0, 0); + check_complex ("casin (-inf + inf i) == -pi/4 + inf i", FUNC(casin) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (-M_PI_4l, plus_infty), 0, 0, 0); + check_complex ("casin (-inf - inf i) == -pi/4 - inf i", FUNC(casin) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (-M_PI_4l, minus_infty), 0, 0, 0); + + check_complex ("casin (-10.0 + inf i) == -0 + inf i", FUNC(casin) (BUILD_COMPLEX (-10.0, plus_infty)), BUILD_COMPLEX (minus_zero, plus_infty), 0, 0, 0); + check_complex ("casin (-10.0 - inf i) == -0 - inf i", FUNC(casin) (BUILD_COMPLEX (-10.0, minus_infty)), BUILD_COMPLEX (minus_zero, minus_infty), 0, 0, 0); + check_complex ("casin (0 + inf i) == 0.0 + inf i", FUNC(casin) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (0.0, plus_infty), 0, 0, 0); + check_complex ("casin (0 - inf i) == 0.0 - inf i", FUNC(casin) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (0.0, minus_infty), 0, 0, 0); + check_complex ("casin (-0 + inf i) == -0 + inf i", FUNC(casin) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (minus_zero, plus_infty), 0, 0, 0); + check_complex ("casin (-0 - inf i) == -0 - inf i", FUNC(casin) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (minus_zero, minus_infty), 0, 0, 0); + check_complex ("casin (0.1 + inf i) == 0.0 + inf i", FUNC(casin) (BUILD_COMPLEX (0.1L, plus_infty)), BUILD_COMPLEX (0.0, plus_infty), 0, 0, 0); + check_complex ("casin (0.1 - inf i) == 0.0 - inf i", FUNC(casin) (BUILD_COMPLEX (0.1L, minus_infty)), BUILD_COMPLEX (0.0, minus_infty), 0, 0, 0); + + check_complex ("casin (-inf + 0 i) == -pi/2 + inf i", FUNC(casin) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (-M_PI_2l, plus_infty), 0, 0, 0); + check_complex ("casin (-inf - 0 i) == -pi/2 - inf i", FUNC(casin) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (-M_PI_2l, minus_infty), 0, 0, 0); + check_complex ("casin (-inf + 100 i) == -pi/2 + inf i", FUNC(casin) (BUILD_COMPLEX (minus_infty, 100)), BUILD_COMPLEX (-M_PI_2l, plus_infty), 0, 0, 0); + check_complex ("casin (-inf - 100 i) == -pi/2 - inf i", FUNC(casin) (BUILD_COMPLEX (minus_infty, -100)), BUILD_COMPLEX (-M_PI_2l, minus_infty), 0, 0, 0); + + check_complex ("casin (inf + 0 i) == pi/2 + inf i", FUNC(casin) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (M_PI_2l, plus_infty), 0, 0, 0); + check_complex ("casin (inf - 0 i) == pi/2 - inf i", FUNC(casin) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (M_PI_2l, minus_infty), 0, 0, 0); + check_complex ("casin (inf + 0.5 i) == pi/2 + inf i", FUNC(casin) (BUILD_COMPLEX (plus_infty, 0.5)), BUILD_COMPLEX (M_PI_2l, plus_infty), 0, 0, 0); + check_complex ("casin (inf - 0.5 i) == pi/2 - inf i", FUNC(casin) (BUILD_COMPLEX (plus_infty, -0.5)), BUILD_COMPLEX (M_PI_2l, minus_infty), 0, 0, 0); + + check_complex ("casin (NaN + inf i) == NaN + inf i", FUNC(casin) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, 0); + check_complex ("casin (NaN - inf i) == NaN - inf i", FUNC(casin) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (nan_value, minus_infty), 0, 0, 0); + + check_complex ("casin (0.0 + NaN i) == 0.0 + NaN i", FUNC(casin) (BUILD_COMPLEX (0.0, nan_value)), BUILD_COMPLEX (0.0, nan_value), 0, 0, 0); + check_complex ("casin (-0 + NaN i) == -0 + NaN i", FUNC(casin) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (minus_zero, nan_value), 0, 0, 0); + + check_complex ("casin (inf + NaN i) == NaN + inf i plus sign of zero/inf not specified", FUNC(casin) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("casin (-inf + NaN i) == NaN + inf i plus sign of zero/inf not specified", FUNC(casin) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("casin (NaN + 10.5 i) == NaN + NaN i plus invalid exception allowed", FUNC(casin) (BUILD_COMPLEX (nan_value, 10.5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("casin (NaN - 10.5 i) == NaN + NaN i plus invalid exception allowed", FUNC(casin) (BUILD_COMPLEX (nan_value, -10.5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("casin (0.75 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(casin) (BUILD_COMPLEX (0.75, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("casin (-0.75 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(casin) (BUILD_COMPLEX (-0.75, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("casin (NaN + NaN i) == NaN + NaN i", FUNC(casin) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("casin (0.7 + 1.2 i) == 0.4356135790797415103321208644578462 + 1.0927647857577371459105272080819308 i", FUNC(casin) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (0.4356135790797415103321208644578462L, 1.0927647857577371459105272080819308L), DELTA225, 0, 0); + check_complex ("casin (-2 - 3 i) == -0.57065278432109940071028387968566963 - 1.9833870299165354323470769028940395 i", FUNC(casin) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (-0.57065278432109940071028387968566963L, -1.9833870299165354323470769028940395L), DELTA226, 0, 0); + + print_complex_max_error ("casin", DELTAcasin, 0); +} + + +static void +casinh_test (void) +{ + errno = 0; + FUNC(casinh) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("casinh (0 + 0 i) == 0.0 + 0.0 i", FUNC(casinh) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("casinh (-0 + 0 i) == -0 + 0 i", FUNC(casinh) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (minus_zero, 0), 0, 0, 0); + check_complex ("casinh (0 - 0 i) == 0.0 - 0 i", FUNC(casinh) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + check_complex ("casinh (-0 - 0 i) == -0 - 0 i", FUNC(casinh) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + + check_complex ("casinh (inf + inf i) == inf + pi/4 i", FUNC(casinh) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_4l), 0, 0, 0); + check_complex ("casinh (inf - inf i) == inf - pi/4 i", FUNC(casinh) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_4l), 0, 0, 0); + check_complex ("casinh (-inf + inf i) == -inf + pi/4 i", FUNC(casinh) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (minus_infty, M_PI_4l), 0, 0, 0); + check_complex ("casinh (-inf - inf i) == -inf - pi/4 i", FUNC(casinh) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (minus_infty, -M_PI_4l), 0, 0, 0); + + check_complex ("casinh (-10.0 + inf i) == -inf + pi/2 i", FUNC(casinh) (BUILD_COMPLEX (-10.0, plus_infty)), BUILD_COMPLEX (minus_infty, M_PI_2l), 0, 0, 0); + check_complex ("casinh (-10.0 - inf i) == -inf - pi/2 i", FUNC(casinh) (BUILD_COMPLEX (-10.0, minus_infty)), BUILD_COMPLEX (minus_infty, -M_PI_2l), 0, 0, 0); + check_complex ("casinh (0 + inf i) == inf + pi/2 i", FUNC(casinh) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_2l), 0, 0, 0); + check_complex ("casinh (0 - inf i) == inf - pi/2 i", FUNC(casinh) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_2l), 0, 0, 0); + check_complex ("casinh (-0 + inf i) == -inf + pi/2 i", FUNC(casinh) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (minus_infty, M_PI_2l), 0, 0, 0); + check_complex ("casinh (-0 - inf i) == -inf - pi/2 i", FUNC(casinh) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (minus_infty, -M_PI_2l), 0, 0, 0); + check_complex ("casinh (0.1 + inf i) == inf + pi/2 i", FUNC(casinh) (BUILD_COMPLEX (0.1L, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_2l), 0, 0, 0); + check_complex ("casinh (0.1 - inf i) == inf - pi/2 i", FUNC(casinh) (BUILD_COMPLEX (0.1L, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_2l), 0, 0, 0); + + check_complex ("casinh (-inf + 0 i) == -inf + 0.0 i", FUNC(casinh) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (minus_infty, 0.0), 0, 0, 0); + check_complex ("casinh (-inf - 0 i) == -inf - 0 i", FUNC(casinh) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (minus_infty, minus_zero), 0, 0, 0); + check_complex ("casinh (-inf + 100 i) == -inf + 0.0 i", FUNC(casinh) (BUILD_COMPLEX (minus_infty, 100)), BUILD_COMPLEX (minus_infty, 0.0), 0, 0, 0); + check_complex ("casinh (-inf - 100 i) == -inf - 0 i", FUNC(casinh) (BUILD_COMPLEX (minus_infty, -100)), BUILD_COMPLEX (minus_infty, minus_zero), 0, 0, 0); + + check_complex ("casinh (inf + 0 i) == inf + 0.0 i", FUNC(casinh) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("casinh (inf - 0 i) == inf - 0 i", FUNC(casinh) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("casinh (inf + 0.5 i) == inf + 0.0 i", FUNC(casinh) (BUILD_COMPLEX (plus_infty, 0.5)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("casinh (inf - 0.5 i) == inf - 0 i", FUNC(casinh) (BUILD_COMPLEX (plus_infty, -0.5)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + + check_complex ("casinh (inf + NaN i) == inf + NaN i", FUNC(casinh) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + check_complex ("casinh (-inf + NaN i) == -inf + NaN i", FUNC(casinh) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (minus_infty, nan_value), 0, 0, 0); + + check_complex ("casinh (NaN + 0 i) == NaN + 0.0 i", FUNC(casinh) (BUILD_COMPLEX (nan_value, 0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, 0); + check_complex ("casinh (NaN - 0 i) == NaN - 0 i", FUNC(casinh) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, minus_zero), 0, 0, 0); + + check_complex ("casinh (NaN + inf i) == inf + NaN i plus sign of zero/inf not specified", FUNC(casinh) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("casinh (NaN - inf i) == inf + NaN i plus sign of zero/inf not specified", FUNC(casinh) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("casinh (10.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(casinh) (BUILD_COMPLEX (10.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("casinh (-10.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(casinh) (BUILD_COMPLEX (-10.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("casinh (NaN + 0.75 i) == NaN + NaN i plus invalid exception allowed", FUNC(casinh) (BUILD_COMPLEX (nan_value, 0.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("casinh (-0.75 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(casinh) (BUILD_COMPLEX (-0.75, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("casinh (NaN + NaN i) == NaN + NaN i", FUNC(casinh) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("casinh (0.7 + 1.2 i) == 0.97865459559367387689317593222160964 + 0.91135418953156011567903546856170941 i", FUNC(casinh) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (0.97865459559367387689317593222160964L, 0.91135418953156011567903546856170941L), DELTA262, 0, 0); + check_complex ("casinh (-2 - 3 i) == -1.9686379257930962917886650952454982 - 0.96465850440760279204541105949953237 i", FUNC(casinh) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (-1.9686379257930962917886650952454982L, -0.96465850440760279204541105949953237L), DELTA263, 0, 0); + + print_complex_max_error ("casinh", DELTAcasinh, 0); +} + + +static void +catan_test (void) +{ + errno = 0; + FUNC(catan) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("catan (0 + 0 i) == 0 + 0 i", FUNC(catan) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (0, 0), 0, 0, 0); + check_complex ("catan (-0 + 0 i) == -0 + 0 i", FUNC(catan) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (minus_zero, 0), 0, 0, 0); + check_complex ("catan (0 - 0 i) == 0 - 0 i", FUNC(catan) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (0, minus_zero), 0, 0, 0); + check_complex ("catan (-0 - 0 i) == -0 - 0 i", FUNC(catan) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + + check_complex ("catan (inf + inf i) == pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (M_PI_2l, 0), 0, 0, 0); + check_complex ("catan (inf - inf i) == pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("catan (-inf + inf i) == -pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (-M_PI_2l, 0), 0, 0, 0); + check_complex ("catan (-inf - inf i) == -pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (-M_PI_2l, minus_zero), 0, 0, 0); + + + check_complex ("catan (inf - 10.0 i) == pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (plus_infty, -10.0)), BUILD_COMPLEX (M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("catan (-inf - 10.0 i) == -pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (minus_infty, -10.0)), BUILD_COMPLEX (-M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("catan (inf - 0 i) == pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("catan (-inf - 0 i) == -pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (-M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("catan (inf + 0.0 i) == pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (plus_infty, 0.0)), BUILD_COMPLEX (M_PI_2l, 0), 0, 0, 0); + check_complex ("catan (-inf + 0.0 i) == -pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (minus_infty, 0.0)), BUILD_COMPLEX (-M_PI_2l, 0), 0, 0, 0); + check_complex ("catan (inf + 0.1 i) == pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (plus_infty, 0.1L)), BUILD_COMPLEX (M_PI_2l, 0), 0, 0, 0); + check_complex ("catan (-inf + 0.1 i) == -pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (minus_infty, 0.1L)), BUILD_COMPLEX (-M_PI_2l, 0), 0, 0, 0); + + check_complex ("catan (0.0 - inf i) == pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (0.0, minus_infty)), BUILD_COMPLEX (M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("catan (-0 - inf i) == -pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (-M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("catan (100.0 - inf i) == pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (100.0, minus_infty)), BUILD_COMPLEX (M_PI_2l, minus_zero), 0, 0, 0); + check_complex ("catan (-100.0 - inf i) == -pi/2 - 0 i", FUNC(catan) (BUILD_COMPLEX (-100.0, minus_infty)), BUILD_COMPLEX (-M_PI_2l, minus_zero), 0, 0, 0); + + check_complex ("catan (0.0 + inf i) == pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (0.0, plus_infty)), BUILD_COMPLEX (M_PI_2l, 0), 0, 0, 0); + check_complex ("catan (-0 + inf i) == -pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (-M_PI_2l, 0), 0, 0, 0); + check_complex ("catan (0.5 + inf i) == pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (0.5, plus_infty)), BUILD_COMPLEX (M_PI_2l, 0), 0, 0, 0); + check_complex ("catan (-0.5 + inf i) == -pi/2 + 0 i", FUNC(catan) (BUILD_COMPLEX (-0.5, plus_infty)), BUILD_COMPLEX (-M_PI_2l, 0), 0, 0, 0); + + check_complex ("catan (NaN + 0.0 i) == NaN + 0 i", FUNC(catan) (BUILD_COMPLEX (nan_value, 0.0)), BUILD_COMPLEX (nan_value, 0), 0, 0, 0); + check_complex ("catan (NaN - 0 i) == NaN - 0 i", FUNC(catan) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, minus_zero), 0, 0, 0); + + check_complex ("catan (NaN + inf i) == NaN + 0 i", FUNC(catan) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (nan_value, 0), 0, 0, 0); + check_complex ("catan (NaN - inf i) == NaN - 0 i", FUNC(catan) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (nan_value, minus_zero), 0, 0, 0); + + check_complex ("catan (0.0 + NaN i) == NaN + NaN i", FUNC(catan) (BUILD_COMPLEX (0.0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + check_complex ("catan (-0 + NaN i) == NaN + NaN i", FUNC(catan) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("catan (inf + NaN i) == pi/2 + 0 i plus sign of zero/inf not specified", FUNC(catan) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (M_PI_2l, 0), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("catan (-inf + NaN i) == -pi/2 + 0 i plus sign of zero/inf not specified", FUNC(catan) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (-M_PI_2l, 0), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("catan (NaN + 10.5 i) == NaN + NaN i plus invalid exception allowed", FUNC(catan) (BUILD_COMPLEX (nan_value, 10.5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("catan (NaN - 10.5 i) == NaN + NaN i plus invalid exception allowed", FUNC(catan) (BUILD_COMPLEX (nan_value, -10.5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("catan (0.75 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(catan) (BUILD_COMPLEX (0.75, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("catan (-0.75 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(catan) (BUILD_COMPLEX (-0.75, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("catan (NaN + NaN i) == NaN + NaN i", FUNC(catan) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("catan (0.7 + 1.2 i) == 1.0785743834118921877443707996386368 + 0.57705737765343067644394541889341712 i", FUNC(catan) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (1.0785743834118921877443707996386368L, 0.57705737765343067644394541889341712L), DELTA301, 0, 0); + + check_complex ("catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i", FUNC(catan) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (-1.4099210495965755225306193844604208L, -0.22907268296853876629588180294200276L), DELTA302, 0, 0); + + print_complex_max_error ("catan", DELTAcatan, 0); +} + +static void +catanh_test (void) +{ + errno = 0; + FUNC(catanh) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("catanh (0 + 0 i) == 0.0 + 0.0 i", FUNC(catanh) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("catanh (-0 + 0 i) == -0 + 0.0 i", FUNC(catanh) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (minus_zero, 0.0), 0, 0, 0); + check_complex ("catanh (0 - 0 i) == 0.0 - 0 i", FUNC(catanh) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + check_complex ("catanh (-0 - 0 i) == -0 - 0 i", FUNC(catanh) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + + check_complex ("catanh (inf + inf i) == 0.0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (0.0, M_PI_2l), 0, 0, 0); + check_complex ("catanh (inf - inf i) == 0.0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (0.0, -M_PI_2l), 0, 0, 0); + check_complex ("catanh (-inf + inf i) == -0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (minus_zero, M_PI_2l), 0, 0, 0); + check_complex ("catanh (-inf - inf i) == -0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (minus_zero, -M_PI_2l), 0, 0, 0); + + check_complex ("catanh (-10.0 + inf i) == -0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (-10.0, plus_infty)), BUILD_COMPLEX (minus_zero, M_PI_2l), 0, 0, 0); + check_complex ("catanh (-10.0 - inf i) == -0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (-10.0, minus_infty)), BUILD_COMPLEX (minus_zero, -M_PI_2l), 0, 0, 0); + check_complex ("catanh (-0 + inf i) == -0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (minus_zero, M_PI_2l), 0, 0, 0); + check_complex ("catanh (-0 - inf i) == -0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (minus_zero, -M_PI_2l), 0, 0, 0); + check_complex ("catanh (0 + inf i) == 0.0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (0.0, M_PI_2l), 0, 0, 0); + check_complex ("catanh (0 - inf i) == 0.0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (0.0, -M_PI_2l), 0, 0, 0); + check_complex ("catanh (0.1 + inf i) == 0.0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (0.1L, plus_infty)), BUILD_COMPLEX (0.0, M_PI_2l), 0, 0, 0); + check_complex ("catanh (0.1 - inf i) == 0.0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (0.1L, minus_infty)), BUILD_COMPLEX (0.0, -M_PI_2l), 0, 0, 0); + + check_complex ("catanh (-inf + 0 i) == -0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (minus_zero, M_PI_2l), 0, 0, 0); + check_complex ("catanh (-inf - 0 i) == -0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (minus_zero, -M_PI_2l), 0, 0, 0); + check_complex ("catanh (-inf + 100 i) == -0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (minus_infty, 100)), BUILD_COMPLEX (minus_zero, M_PI_2l), 0, 0, 0); + check_complex ("catanh (-inf - 100 i) == -0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (minus_infty, -100)), BUILD_COMPLEX (minus_zero, -M_PI_2l), 0, 0, 0); + + check_complex ("catanh (inf + 0 i) == 0.0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (0.0, M_PI_2l), 0, 0, 0); + check_complex ("catanh (inf - 0 i) == 0.0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (0.0, -M_PI_2l), 0, 0, 0); + check_complex ("catanh (inf + 0.5 i) == 0.0 + pi/2 i", FUNC(catanh) (BUILD_COMPLEX (plus_infty, 0.5)), BUILD_COMPLEX (0.0, M_PI_2l), 0, 0, 0); + check_complex ("catanh (inf - 0.5 i) == 0.0 - pi/2 i", FUNC(catanh) (BUILD_COMPLEX (plus_infty, -0.5)), BUILD_COMPLEX (0.0, -M_PI_2l), 0, 0, 0); + + check_complex ("catanh (0 + NaN i) == 0.0 + NaN i", FUNC(catanh) (BUILD_COMPLEX (0, nan_value)), BUILD_COMPLEX (0.0, nan_value), 0, 0, 0); + check_complex ("catanh (-0 + NaN i) == -0 + NaN i", FUNC(catanh) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (minus_zero, nan_value), 0, 0, 0); + + check_complex ("catanh (inf + NaN i) == 0.0 + NaN i", FUNC(catanh) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (0.0, nan_value), 0, 0, 0); + check_complex ("catanh (-inf + NaN i) == -0 + NaN i", FUNC(catanh) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (minus_zero, nan_value), 0, 0, 0); + + check_complex ("catanh (NaN + 0 i) == NaN + NaN i", FUNC(catanh) (BUILD_COMPLEX (nan_value, 0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + check_complex ("catanh (NaN - 0 i) == NaN + NaN i", FUNC(catanh) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("catanh (NaN + inf i) == 0.0 + pi/2 i plus sign of zero/inf not specified", FUNC(catanh) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (0.0, M_PI_2l), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("catanh (NaN - inf i) == 0.0 - pi/2 i plus sign of zero/inf not specified", FUNC(catanh) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (0.0, -M_PI_2l), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("catanh (10.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(catanh) (BUILD_COMPLEX (10.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("catanh (-10.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(catanh) (BUILD_COMPLEX (-10.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("catanh (NaN + 0.75 i) == NaN + NaN i plus invalid exception allowed", FUNC(catanh) (BUILD_COMPLEX (nan_value, 0.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("catanh (NaN - 0.75 i) == NaN + NaN i plus invalid exception allowed", FUNC(catanh) (BUILD_COMPLEX (nan_value, -0.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("catanh (NaN + NaN i) == NaN + NaN i", FUNC(catanh) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("catanh (0.7 + 1.2 i) == 0.2600749516525135959200648705635915 + 0.97024030779509898497385130162655963 i", FUNC(catanh) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (0.2600749516525135959200648705635915L, 0.97024030779509898497385130162655963L), DELTA340, 0, 0); + check_complex ("catanh (-2 - 3 i) == -0.14694666622552975204743278515471595 - 1.3389725222944935611241935759091443 i", FUNC(catanh) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (-0.14694666622552975204743278515471595L, -1.3389725222944935611241935759091443L), DELTA341, 0, 0); + + print_complex_max_error ("catanh", DELTAcatanh, 0); +} +#endif + +static void +cbrt_test (void) +{ + errno = 0; + FUNC(cbrt) (8); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("cbrt (0.0) == 0.0", FUNC(cbrt) (0.0), 0.0, 0, 0, 0); + check_float ("cbrt (-0) == -0", FUNC(cbrt) (minus_zero), minus_zero, 0, 0, 0); + + check_float ("cbrt (inf) == inf", FUNC(cbrt) (plus_infty), plus_infty, 0, 0, 0); + check_float ("cbrt (-inf) == -inf", FUNC(cbrt) (minus_infty), minus_infty, 0, 0, 0); + check_float ("cbrt (NaN) == NaN", FUNC(cbrt) (nan_value), nan_value, 0, 0, 0); + + check_float ("cbrt (-0.001) == -0.1", FUNC(cbrt) (-0.001L), -0.1L, DELTA347, 0, 0); + check_float ("cbrt (8) == 2", FUNC(cbrt) (8), 2, 0, 0, 0); + check_float ("cbrt (-27.0) == -3.0", FUNC(cbrt) (-27.0), -3.0, DELTA349, 0, 0); + check_float ("cbrt (0.970299) == 0.99", FUNC(cbrt) (0.970299L), 0.99L, DELTA350, 0, 0); + check_float ("cbrt (0.7) == 0.8879040017426007084", FUNC(cbrt) (0.7L), 0.8879040017426007084L, DELTA351, 0, 0); + + print_max_error ("cbrt", DELTAcbrt, 0); +} + +#if 0 /* XXX scp XXX */ +static void +ccos_test (void) +{ + errno = 0; + FUNC(ccos) (BUILD_COMPLEX (0, 0)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("ccos (0.0 + 0.0 i) == 1.0 - 0 i", FUNC(ccos) (BUILD_COMPLEX (0.0, 0.0)), BUILD_COMPLEX (1.0, minus_zero), 0, 0, 0); + check_complex ("ccos (-0 + 0.0 i) == 1.0 + 0.0 i", FUNC(ccos) (BUILD_COMPLEX (minus_zero, 0.0)), BUILD_COMPLEX (1.0, 0.0), 0, 0, 0); + check_complex ("ccos (0.0 - 0 i) == 1.0 + 0.0 i", FUNC(ccos) (BUILD_COMPLEX (0.0, minus_zero)), BUILD_COMPLEX (1.0, 0.0), 0, 0, 0); + check_complex ("ccos (-0 - 0 i) == 1.0 - 0 i", FUNC(ccos) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (1.0, minus_zero), 0, 0, 0); + + check_complex ("ccos (inf + 0.0 i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(ccos) (BUILD_COMPLEX (plus_infty, 0.0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("ccos (inf - 0 i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(ccos) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("ccos (-inf + 0.0 i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(ccos) (BUILD_COMPLEX (minus_infty, 0.0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("ccos (-inf - 0 i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(ccos) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + + check_complex ("ccos (0.0 + inf i) == inf - 0 i", FUNC(ccos) (BUILD_COMPLEX (0.0, plus_infty)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("ccos (0.0 - inf i) == inf + 0.0 i", FUNC(ccos) (BUILD_COMPLEX (0.0, minus_infty)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("ccos (-0 + inf i) == inf + 0.0 i", FUNC(ccos) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("ccos (-0 - inf i) == inf - 0 i", FUNC(ccos) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + + check_complex ("ccos (inf + inf i) == inf + NaN i plus invalid exception", FUNC(ccos) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccos (-inf + inf i) == inf + NaN i plus invalid exception", FUNC(ccos) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccos (inf - inf i) == inf + NaN i plus invalid exception", FUNC(ccos) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccos (-inf - inf i) == inf + NaN i plus invalid exception", FUNC(ccos) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("ccos (4.625 + inf i) == -inf + inf i", FUNC(ccos) (BUILD_COMPLEX (4.625, plus_infty)), BUILD_COMPLEX (minus_infty, plus_infty), 0, 0, 0); + check_complex ("ccos (4.625 - inf i) == -inf - inf i", FUNC(ccos) (BUILD_COMPLEX (4.625, minus_infty)), BUILD_COMPLEX (minus_infty, minus_infty), 0, 0, 0); + check_complex ("ccos (-4.625 + inf i) == -inf - inf i", FUNC(ccos) (BUILD_COMPLEX (-4.625, plus_infty)), BUILD_COMPLEX (minus_infty, minus_infty), 0, 0, 0); + check_complex ("ccos (-4.625 - inf i) == -inf + inf i", FUNC(ccos) (BUILD_COMPLEX (-4.625, minus_infty)), BUILD_COMPLEX (minus_infty, plus_infty), 0, 0, 0); + + check_complex ("ccos (inf + 6.75 i) == NaN + NaN i plus invalid exception", FUNC(ccos) (BUILD_COMPLEX (plus_infty, 6.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccos (inf - 6.75 i) == NaN + NaN i plus invalid exception", FUNC(ccos) (BUILD_COMPLEX (plus_infty, -6.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccos (-inf + 6.75 i) == NaN + NaN i plus invalid exception", FUNC(ccos) (BUILD_COMPLEX (minus_infty, 6.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccos (-inf - 6.75 i) == NaN + NaN i plus invalid exception", FUNC(ccos) (BUILD_COMPLEX (minus_infty, -6.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("ccos (NaN + 0.0 i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(ccos) (BUILD_COMPLEX (nan_value, 0.0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("ccos (NaN - 0 i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(ccos) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("ccos (NaN + inf i) == inf + NaN i", FUNC(ccos) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + check_complex ("ccos (NaN - inf i) == inf + NaN i", FUNC(ccos) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("ccos (NaN + 9.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(ccos) (BUILD_COMPLEX (nan_value, 9.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ccos (NaN - 9.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(ccos) (BUILD_COMPLEX (nan_value, -9.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ccos (0.0 + NaN i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(ccos) (BUILD_COMPLEX (0.0, nan_value)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("ccos (-0 + NaN i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(ccos) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("ccos (10.0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ccos) (BUILD_COMPLEX (10.0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ccos (-10.0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ccos) (BUILD_COMPLEX (-10.0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ccos (inf + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ccos) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ccos (-inf + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ccos) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ccos (NaN + NaN i) == NaN + NaN i", FUNC(ccos) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("ccos (0.7 + 1.2 i) == 1.3848657645312111080 - 0.97242170335830028619 i", FUNC(ccos) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (1.3848657645312111080L, -0.97242170335830028619L), DELTA389, 0, 0); + + check_complex ("ccos (-2 - 3 i) == -4.1896256909688072301 - 9.1092278937553365979 i", FUNC(ccos) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (-4.1896256909688072301L, -9.1092278937553365979L), DELTA390, 0, 0); + + print_complex_max_error ("ccos", DELTAccos, 0); +} + + +static void +ccosh_test (void) +{ + errno = 0; + FUNC(ccosh) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("ccosh (0.0 + 0.0 i) == 1.0 + 0.0 i", FUNC(ccosh) (BUILD_COMPLEX (0.0, 0.0)), BUILD_COMPLEX (1.0, 0.0), 0, 0, 0); + check_complex ("ccosh (-0 + 0.0 i) == 1.0 - 0 i", FUNC(ccosh) (BUILD_COMPLEX (minus_zero, 0.0)), BUILD_COMPLEX (1.0, minus_zero), 0, 0, 0); + check_complex ("ccosh (0.0 - 0 i) == 1.0 - 0 i", FUNC(ccosh) (BUILD_COMPLEX (0.0, minus_zero)), BUILD_COMPLEX (1.0, minus_zero), 0, 0, 0); + check_complex ("ccosh (-0 - 0 i) == 1.0 + 0.0 i", FUNC(ccosh) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (1.0, 0.0), 0, 0, 0); + + check_complex ("ccosh (0.0 + inf i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(ccosh) (BUILD_COMPLEX (0.0, plus_infty)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("ccosh (-0 + inf i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(ccosh) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("ccosh (0.0 - inf i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(ccosh) (BUILD_COMPLEX (0.0, minus_infty)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("ccosh (-0 - inf i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(ccosh) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + + check_complex ("ccosh (inf + 0.0 i) == inf + 0.0 i", FUNC(ccosh) (BUILD_COMPLEX (plus_infty, 0.0)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("ccosh (-inf + 0.0 i) == inf - 0 i", FUNC(ccosh) (BUILD_COMPLEX (minus_infty, 0.0)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("ccosh (inf - 0 i) == inf - 0 i", FUNC(ccosh) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("ccosh (-inf - 0 i) == inf + 0.0 i", FUNC(ccosh) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + + check_complex ("ccosh (inf + inf i) == inf + NaN i plus invalid exception", FUNC(ccosh) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccosh (-inf + inf i) == inf + NaN i plus invalid exception", FUNC(ccosh) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccosh (inf - inf i) == inf + NaN i plus invalid exception", FUNC(ccosh) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccosh (-inf - inf i) == inf + NaN i plus invalid exception", FUNC(ccosh) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("ccosh (inf + 4.625 i) == -inf - inf i", FUNC(ccosh) (BUILD_COMPLEX (plus_infty, 4.625)), BUILD_COMPLEX (minus_infty, minus_infty), 0, 0, 0); + check_complex ("ccosh (-inf + 4.625 i) == -inf + inf i", FUNC(ccosh) (BUILD_COMPLEX (minus_infty, 4.625)), BUILD_COMPLEX (minus_infty, plus_infty), 0, 0, 0); + check_complex ("ccosh (inf - 4.625 i) == -inf + inf i", FUNC(ccosh) (BUILD_COMPLEX (plus_infty, -4.625)), BUILD_COMPLEX (minus_infty, plus_infty), 0, 0, 0); + check_complex ("ccosh (-inf - 4.625 i) == -inf - inf i", FUNC(ccosh) (BUILD_COMPLEX (minus_infty, -4.625)), BUILD_COMPLEX (minus_infty, minus_infty), 0, 0, 0); + + check_complex ("ccosh (6.75 + inf i) == NaN + NaN i plus invalid exception", FUNC(ccosh) (BUILD_COMPLEX (6.75, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccosh (-6.75 + inf i) == NaN + NaN i plus invalid exception", FUNC(ccosh) (BUILD_COMPLEX (-6.75, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccosh (6.75 - inf i) == NaN + NaN i plus invalid exception", FUNC(ccosh) (BUILD_COMPLEX (6.75, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ccosh (-6.75 - inf i) == NaN + NaN i plus invalid exception", FUNC(ccosh) (BUILD_COMPLEX (-6.75, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("ccosh (0.0 + NaN i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(ccosh) (BUILD_COMPLEX (0.0, nan_value)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("ccosh (-0 + NaN i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(ccosh) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("ccosh (inf + NaN i) == inf + NaN i", FUNC(ccosh) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + check_complex ("ccosh (-inf + NaN i) == inf + NaN i", FUNC(ccosh) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("ccosh (9.0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ccosh) (BUILD_COMPLEX (9.0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ccosh (-9.0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ccosh) (BUILD_COMPLEX (-9.0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ccosh (NaN + 0.0 i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(ccosh) (BUILD_COMPLEX (nan_value, 0.0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("ccosh (NaN - 0 i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(ccosh) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("ccosh (NaN + 10.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(ccosh) (BUILD_COMPLEX (nan_value, 10.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ccosh (NaN - 10.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(ccosh) (BUILD_COMPLEX (nan_value, -10.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ccosh (NaN + inf i) == NaN + NaN i plus invalid exception allowed", FUNC(ccosh) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ccosh (NaN - inf i) == NaN + NaN i plus invalid exception allowed", FUNC(ccosh) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ccosh (NaN + NaN i) == NaN + NaN i", FUNC(ccosh) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("ccosh (0.7 + 1.2 i) == 0.4548202223691477654 + 0.7070296600921537682 i", FUNC(ccosh) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (0.4548202223691477654L, 0.7070296600921537682L), DELTA428, 0, 0); + + check_complex ("ccosh (-2 - 3 i) == -3.7245455049153225654 + 0.5118225699873846088 i", FUNC(ccosh) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (-3.7245455049153225654L, 0.5118225699873846088L), DELTA429, 0, 0); + + print_complex_max_error ("ccosh", DELTAccosh, 0); +} +#endif + + +static void +ceil_test (void) +{ + init_max_error (); + + check_float ("ceil (0.0) == 0.0", FUNC(ceil) (0.0), 0.0, 0, 0, 0); + check_float ("ceil (-0) == -0", FUNC(ceil) (minus_zero), minus_zero, 0, 0, 0); + check_float ("ceil (inf) == inf", FUNC(ceil) (plus_infty), plus_infty, 0, 0, 0); + check_float ("ceil (-inf) == -inf", FUNC(ceil) (minus_infty), minus_infty, 0, 0, 0); + check_float ("ceil (NaN) == NaN", FUNC(ceil) (nan_value), nan_value, 0, 0, 0); + + check_float ("ceil (pi) == 4.0", FUNC(ceil) (M_PIl), 4.0, 0, 0, 0); + check_float ("ceil (-pi) == -3.0", FUNC(ceil) (-M_PIl), -3.0, 0, 0, 0); + + print_max_error ("ceil", 0, 0); +} + + +#if 0 /* XXX scp XXX */ +static void +cexp_test (void) +{ + errno = 0; + FUNC(cexp) (BUILD_COMPLEX (0, 0)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("cexp (+0 + +0 i) == 1 + 0.0 i", FUNC(cexp) (BUILD_COMPLEX (plus_zero, plus_zero)), BUILD_COMPLEX (1, 0.0), 0, 0, 0); + check_complex ("cexp (-0 + +0 i) == 1 + 0.0 i", FUNC(cexp) (BUILD_COMPLEX (minus_zero, plus_zero)), BUILD_COMPLEX (1, 0.0), 0, 0, 0); + check_complex ("cexp (+0 - 0 i) == 1 - 0 i", FUNC(cexp) (BUILD_COMPLEX (plus_zero, minus_zero)), BUILD_COMPLEX (1, minus_zero), 0, 0, 0); + check_complex ("cexp (-0 - 0 i) == 1 - 0 i", FUNC(cexp) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (1, minus_zero), 0, 0, 0); + + check_complex ("cexp (inf + +0 i) == inf + 0.0 i", FUNC(cexp) (BUILD_COMPLEX (plus_infty, plus_zero)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("cexp (inf - 0 i) == inf - 0 i", FUNC(cexp) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + + check_complex ("cexp (-inf + +0 i) == 0.0 + 0.0 i", FUNC(cexp) (BUILD_COMPLEX (minus_infty, plus_zero)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("cexp (-inf - 0 i) == 0.0 - 0 i", FUNC(cexp) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + + check_complex ("cexp (0.0 + inf i) == NaN + NaN i plus invalid exception", FUNC(cexp) (BUILD_COMPLEX (0.0, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("cexp (-0 + inf i) == NaN + NaN i plus invalid exception", FUNC(cexp) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("cexp (0.0 - inf i) == NaN + NaN i plus invalid exception", FUNC(cexp) (BUILD_COMPLEX (0.0, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("cexp (-0 - inf i) == NaN + NaN i plus invalid exception", FUNC(cexp) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("cexp (100.0 + inf i) == NaN + NaN i plus invalid exception", FUNC(cexp) (BUILD_COMPLEX (100.0, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("cexp (-100.0 + inf i) == NaN + NaN i plus invalid exception", FUNC(cexp) (BUILD_COMPLEX (-100.0, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("cexp (100.0 - inf i) == NaN + NaN i plus invalid exception", FUNC(cexp) (BUILD_COMPLEX (100.0, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("cexp (-100.0 - inf i) == NaN + NaN i plus invalid exception", FUNC(cexp) (BUILD_COMPLEX (-100.0, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("cexp (-inf + 2.0 i) == -0 + 0.0 i", FUNC(cexp) (BUILD_COMPLEX (minus_infty, 2.0)), BUILD_COMPLEX (minus_zero, 0.0), 0, 0, 0); + check_complex ("cexp (-inf + 4.0 i) == -0 - 0 i", FUNC(cexp) (BUILD_COMPLEX (minus_infty, 4.0)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + check_complex ("cexp (inf + 2.0 i) == -inf + inf i", FUNC(cexp) (BUILD_COMPLEX (plus_infty, 2.0)), BUILD_COMPLEX (minus_infty, plus_infty), 0, 0, 0); + check_complex ("cexp (inf + 4.0 i) == -inf - inf i", FUNC(cexp) (BUILD_COMPLEX (plus_infty, 4.0)), BUILD_COMPLEX (minus_infty, minus_infty), 0, 0, 0); + + check_complex ("cexp (inf + inf i) == inf + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(cexp) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("cexp (inf - inf i) == inf + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(cexp) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + + check_complex ("cexp (-inf + inf i) == 0.0 + 0.0 i plus sign of zero/inf not specified", FUNC(cexp) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (0.0, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("cexp (-inf - inf i) == 0.0 - 0 i plus sign of zero/inf not specified", FUNC(cexp) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("cexp (-inf + NaN i) == 0 + 0 i plus sign of zero/inf not specified", FUNC(cexp) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (0, 0), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("cexp (inf + NaN i) == inf + NaN i", FUNC(cexp) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("cexp (NaN + 0.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(cexp) (BUILD_COMPLEX (nan_value, 0.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("cexp (NaN + 1.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(cexp) (BUILD_COMPLEX (nan_value, 1.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("cexp (NaN + inf i) == NaN + NaN i plus invalid exception allowed", FUNC(cexp) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("cexp (0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(cexp) (BUILD_COMPLEX (0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("cexp (1 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(cexp) (BUILD_COMPLEX (1, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("cexp (NaN + NaN i) == NaN + NaN i", FUNC(cexp) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("cexp (0.7 + 1.2 i) == 0.72969890915032360123451688642930727 + 1.8768962328348102821139467908203072 i", FUNC(cexp) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (0.72969890915032360123451688642930727L, 1.8768962328348102821139467908203072L), DELTA469, 0, 0); + check_complex ("cexp (-2.0 - 3.0 i) == -0.13398091492954261346140525546115575 - 0.019098516261135196432576240858800925 i", FUNC(cexp) (BUILD_COMPLEX (-2.0, -3.0)), BUILD_COMPLEX (-0.13398091492954261346140525546115575L, -0.019098516261135196432576240858800925L), DELTA470, 0, 0); + + print_complex_max_error ("cexp", DELTAcexp, 0); +} + +static void +cimag_test (void) +{ + init_max_error (); + check_float ("cimag (1.0 + 0.0 i) == 0.0", FUNC(cimag) (BUILD_COMPLEX (1.0, 0.0)), 0.0, 0, 0, 0); + check_float ("cimag (1.0 - 0 i) == -0", FUNC(cimag) (BUILD_COMPLEX (1.0, minus_zero)), minus_zero, 0, 0, 0); + check_float ("cimag (1.0 + NaN i) == NaN", FUNC(cimag) (BUILD_COMPLEX (1.0, nan_value)), nan_value, 0, 0, 0); + check_float ("cimag (NaN + NaN i) == NaN", FUNC(cimag) (BUILD_COMPLEX (nan_value, nan_value)), nan_value, 0, 0, 0); + check_float ("cimag (1.0 + inf i) == inf", FUNC(cimag) (BUILD_COMPLEX (1.0, plus_infty)), plus_infty, 0, 0, 0); + check_float ("cimag (1.0 - inf i) == -inf", FUNC(cimag) (BUILD_COMPLEX (1.0, minus_infty)), minus_infty, 0, 0, 0); + check_float ("cimag (2.0 + 3.0 i) == 3.0", FUNC(cimag) (BUILD_COMPLEX (2.0, 3.0)), 3.0, 0, 0, 0); + + print_max_error ("cimag", 0, 0); +} + +static void +clog_test (void) +{ + errno = 0; + FUNC(clog) (BUILD_COMPLEX (-2, -3)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("clog (-0 + 0 i) == -inf + pi i plus division by zero exception", FUNC(clog) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (minus_infty, M_PIl), 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_complex ("clog (-0 - 0 i) == -inf - pi i plus division by zero exception", FUNC(clog) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_infty, -M_PIl), 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + check_complex ("clog (0 + 0 i) == -inf + 0.0 i plus division by zero exception", FUNC(clog) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (minus_infty, 0.0), 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_complex ("clog (0 - 0 i) == -inf - 0 i plus division by zero exception", FUNC(clog) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (minus_infty, minus_zero), 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + check_complex ("clog (-inf + inf i) == inf + 3/4 pi i", FUNC(clog) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_34l), 0, 0, 0); + check_complex ("clog (-inf - inf i) == inf - 3/4 pi i", FUNC(clog) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_34l), 0, 0, 0); + + check_complex ("clog (inf + inf i) == inf + pi/4 i", FUNC(clog) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_4l), 0, 0, 0); + check_complex ("clog (inf - inf i) == inf - pi/4 i", FUNC(clog) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_4l), 0, 0, 0); + + check_complex ("clog (0 + inf i) == inf + pi/2 i", FUNC(clog) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_2l), 0, 0, 0); + check_complex ("clog (3 + inf i) == inf + pi/2 i", FUNC(clog) (BUILD_COMPLEX (3, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_2l), 0, 0, 0); + check_complex ("clog (-0 + inf i) == inf + pi/2 i", FUNC(clog) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_2l), 0, 0, 0); + check_complex ("clog (-3 + inf i) == inf + pi/2 i", FUNC(clog) (BUILD_COMPLEX (-3, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_2l), 0, 0, 0); + check_complex ("clog (0 - inf i) == inf - pi/2 i", FUNC(clog) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_2l), 0, 0, 0); + check_complex ("clog (3 - inf i) == inf - pi/2 i", FUNC(clog) (BUILD_COMPLEX (3, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_2l), 0, 0, 0); + check_complex ("clog (-0 - inf i) == inf - pi/2 i", FUNC(clog) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_2l), 0, 0, 0); + check_complex ("clog (-3 - inf i) == inf - pi/2 i", FUNC(clog) (BUILD_COMPLEX (-3, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI_2l), 0, 0, 0); + + check_complex ("clog (-inf + 0 i) == inf + pi i", FUNC(clog) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (plus_infty, M_PIl), 0, 0, 0); + check_complex ("clog (-inf + 1 i) == inf + pi i", FUNC(clog) (BUILD_COMPLEX (minus_infty, 1)), BUILD_COMPLEX (plus_infty, M_PIl), 0, 0, 0); + check_complex ("clog (-inf - 0 i) == inf - pi i", FUNC(clog) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, -M_PIl), 0, 0, 0); + check_complex ("clog (-inf - 1 i) == inf - pi i", FUNC(clog) (BUILD_COMPLEX (minus_infty, -1)), BUILD_COMPLEX (plus_infty, -M_PIl), 0, 0, 0); + + check_complex ("clog (inf + 0 i) == inf + 0.0 i", FUNC(clog) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("clog (inf + 1 i) == inf + 0.0 i", FUNC(clog) (BUILD_COMPLEX (plus_infty, 1)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("clog (inf - 0 i) == inf - 0 i", FUNC(clog) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("clog (inf - 1 i) == inf - 0 i", FUNC(clog) (BUILD_COMPLEX (plus_infty, -1)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + + check_complex ("clog (inf + NaN i) == inf + NaN i", FUNC(clog) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + check_complex ("clog (-inf + NaN i) == inf + NaN i", FUNC(clog) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("clog (NaN + inf i) == inf + NaN i", FUNC(clog) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + check_complex ("clog (NaN - inf i) == inf + NaN i", FUNC(clog) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("clog (0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(clog) (BUILD_COMPLEX (0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog (3 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(clog) (BUILD_COMPLEX (3, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog (-0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(clog) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog (-3 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(clog) (BUILD_COMPLEX (-3, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("clog (NaN + 0 i) == NaN + NaN i plus invalid exception allowed", FUNC(clog) (BUILD_COMPLEX (nan_value, 0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog (NaN + 5 i) == NaN + NaN i plus invalid exception allowed", FUNC(clog) (BUILD_COMPLEX (nan_value, 5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog (NaN - 0 i) == NaN + NaN i plus invalid exception allowed", FUNC(clog) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog (NaN - 5 i) == NaN + NaN i plus invalid exception allowed", FUNC(clog) (BUILD_COMPLEX (nan_value, -5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("clog (NaN + NaN i) == NaN + NaN i", FUNC(clog) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + check_complex ("clog (-2 - 3 i) == 1.2824746787307683680267437207826593 - 2.1587989303424641704769327722648368 i", FUNC(clog) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (1.2824746787307683680267437207826593L, -2.1587989303424641704769327722648368L), DELTA515, 0, 0); + + print_complex_max_error ("clog", DELTAclog, 0); +} + + +static void +clog10_test (void) +{ + errno = 0; + FUNC(clog10) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("clog10 (-0 + 0 i) == -inf + pi i plus division by zero exception", FUNC(clog10) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (minus_infty, M_PIl), 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_complex ("clog10 (-0 - 0 i) == -inf - pi i plus division by zero exception", FUNC(clog10) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_infty, -M_PIl), 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + check_complex ("clog10 (0 + 0 i) == -inf + 0.0 i plus division by zero exception", FUNC(clog10) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (minus_infty, 0.0), 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_complex ("clog10 (0 - 0 i) == -inf - 0 i plus division by zero exception", FUNC(clog10) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (minus_infty, minus_zero), 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + check_complex ("clog10 (-inf + inf i) == inf + 3/4 pi*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI_34_LOG10El), DELTA520, 0, 0); + + check_complex ("clog10 (inf + inf i) == inf + pi/4*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI4_LOG10El), DELTA521, 0, 0); + check_complex ("clog10 (inf - inf i) == inf - pi/4*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI4_LOG10El), DELTA522, 0, 0); + + check_complex ("clog10 (0 + inf i) == inf + pi/2*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI2_LOG10El), DELTA523, 0, 0); + check_complex ("clog10 (3 + inf i) == inf + pi/2*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (3, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI2_LOG10El), DELTA524, 0, 0); + check_complex ("clog10 (-0 + inf i) == inf + pi/2*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI2_LOG10El), DELTA525, 0, 0); + check_complex ("clog10 (-3 + inf i) == inf + pi/2*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (-3, plus_infty)), BUILD_COMPLEX (plus_infty, M_PI2_LOG10El), DELTA526, 0, 0); + check_complex ("clog10 (0 - inf i) == inf - pi/2*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI2_LOG10El), DELTA527, 0, 0); + check_complex ("clog10 (3 - inf i) == inf - pi/2*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (3, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI2_LOG10El), DELTA528, 0, 0); + check_complex ("clog10 (-0 - inf i) == inf - pi/2*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI2_LOG10El), DELTA529, 0, 0); + check_complex ("clog10 (-3 - inf i) == inf - pi/2*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (-3, minus_infty)), BUILD_COMPLEX (plus_infty, -M_PI2_LOG10El), DELTA530, 0, 0); + + check_complex ("clog10 (-inf + 0 i) == inf + pi*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (plus_infty, M_PI_LOG10El), DELTA531, 0, 0); + check_complex ("clog10 (-inf + 1 i) == inf + pi*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (minus_infty, 1)), BUILD_COMPLEX (plus_infty, M_PI_LOG10El), DELTA532, 0, 0); + check_complex ("clog10 (-inf - 0 i) == inf - pi*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, -M_PI_LOG10El), DELTA533, 0, 0); + check_complex ("clog10 (-inf - 1 i) == inf - pi*log10(e) i", FUNC(clog10) (BUILD_COMPLEX (minus_infty, -1)), BUILD_COMPLEX (plus_infty, -M_PI_LOG10El), DELTA534, 0, 0); + + check_complex ("clog10 (inf + 0 i) == inf + 0.0 i", FUNC(clog10) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("clog10 (inf + 1 i) == inf + 0.0 i", FUNC(clog10) (BUILD_COMPLEX (plus_infty, 1)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("clog10 (inf - 0 i) == inf - 0 i", FUNC(clog10) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("clog10 (inf - 1 i) == inf - 0 i", FUNC(clog10) (BUILD_COMPLEX (plus_infty, -1)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + + check_complex ("clog10 (inf + NaN i) == inf + NaN i", FUNC(clog10) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + check_complex ("clog10 (-inf + NaN i) == inf + NaN i", FUNC(clog10) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("clog10 (NaN + inf i) == inf + NaN i", FUNC(clog10) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + check_complex ("clog10 (NaN - inf i) == inf + NaN i", FUNC(clog10) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("clog10 (0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(clog10) (BUILD_COMPLEX (0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog10 (3 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(clog10) (BUILD_COMPLEX (3, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog10 (-0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(clog10) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog10 (-3 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(clog10) (BUILD_COMPLEX (-3, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("clog10 (NaN + 0 i) == NaN + NaN i plus invalid exception allowed", FUNC(clog10) (BUILD_COMPLEX (nan_value, 0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog10 (NaN + 5 i) == NaN + NaN i plus invalid exception allowed", FUNC(clog10) (BUILD_COMPLEX (nan_value, 5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog10 (NaN - 0 i) == NaN + NaN i plus invalid exception allowed", FUNC(clog10) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("clog10 (NaN - 5 i) == NaN + NaN i plus invalid exception allowed", FUNC(clog10) (BUILD_COMPLEX (nan_value, -5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("clog10 (NaN + NaN i) == NaN + NaN i", FUNC(clog10) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("clog10 (0.7 + 1.2 i) == 0.1427786545038868803 + 0.4528483579352493248 i", FUNC(clog10) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (0.1427786545038868803L, 0.4528483579352493248L), DELTA552, 0, 0); + check_complex ("clog10 (-2 - 3 i) == 0.5569716761534183846 - 0.9375544629863747085 i", FUNC(clog10) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (0.5569716761534183846L, -0.9375544629863747085L), DELTA553, 0, 0); + + print_complex_max_error ("clog10", DELTAclog10, 0); +} + +static void +conj_test (void) +{ + init_max_error (); + check_complex ("conj (0.0 + 0.0 i) == 0.0 - 0 i", FUNC(conj) (BUILD_COMPLEX (0.0, 0.0)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + check_complex ("conj (0.0 - 0 i) == 0.0 + 0.0 i", FUNC(conj) (BUILD_COMPLEX (0.0, minus_zero)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("conj (NaN + NaN i) == NaN + NaN i", FUNC(conj) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + check_complex ("conj (inf - inf i) == inf + inf i", FUNC(conj) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, plus_infty), 0, 0, 0); + check_complex ("conj (inf + inf i) == inf - inf i", FUNC(conj) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, minus_infty), 0, 0, 0); + check_complex ("conj (1.0 + 2.0 i) == 1.0 - 2.0 i", FUNC(conj) (BUILD_COMPLEX (1.0, 2.0)), BUILD_COMPLEX (1.0, -2.0), 0, 0, 0); + check_complex ("conj (3.0 - 4.0 i) == 3.0 + 4.0 i", FUNC(conj) (BUILD_COMPLEX (3.0, -4.0)), BUILD_COMPLEX (3.0, 4.0), 0, 0, 0); + + print_complex_max_error ("conj", 0, 0); +} +#endif + + +static void +copysign_test (void) +{ + init_max_error (); + + check_float ("copysign (0, 4) == 0", FUNC(copysign) (0, 4), 0, 0, 0, 0); + check_float ("copysign (0, -4) == -0", FUNC(copysign) (0, -4), minus_zero, 0, 0, 0); + check_float ("copysign (-0, 4) == 0", FUNC(copysign) (minus_zero, 4), 0, 0, 0, 0); + check_float ("copysign (-0, -4) == -0", FUNC(copysign) (minus_zero, -4), minus_zero, 0, 0, 0); + + check_float ("copysign (inf, 0) == inf", FUNC(copysign) (plus_infty, 0), plus_infty, 0, 0, 0); + check_float ("copysign (inf, -0) == -inf", FUNC(copysign) (plus_infty, minus_zero), minus_infty, 0, 0, 0); + check_float ("copysign (-inf, 0) == inf", FUNC(copysign) (minus_infty, 0), plus_infty, 0, 0, 0); + check_float ("copysign (-inf, -0) == -inf", FUNC(copysign) (minus_infty, minus_zero), minus_infty, 0, 0, 0); + + check_float ("copysign (0, inf) == 0", FUNC(copysign) (0, plus_infty), 0, 0, 0, 0); + check_float ("copysign (0, -0) == -0", FUNC(copysign) (0, minus_zero), minus_zero, 0, 0, 0); + check_float ("copysign (-0, inf) == 0", FUNC(copysign) (minus_zero, plus_infty), 0, 0, 0, 0); + check_float ("copysign (-0, -0) == -0", FUNC(copysign) (minus_zero, minus_zero), minus_zero, 0, 0, 0); + + /* XXX More correctly we would have to check the sign of the NaN. */ + check_float ("copysign (NaN, 0) == NaN", FUNC(copysign) (nan_value, 0), nan_value, 0, 0, 0); + check_float ("copysign (NaN, -0) == NaN", FUNC(copysign) (nan_value, minus_zero), nan_value, 0, 0, 0); + check_float ("copysign (-NaN, 0) == NaN", FUNC(copysign) (-nan_value, 0), nan_value, 0, 0, 0); + check_float ("copysign (-NaN, -0) == NaN", FUNC(copysign) (-nan_value, minus_zero), nan_value, 0, 0, 0); + + print_max_error ("copysign", 0, 0); +} + +static void +cos_test (void) +{ + errno = 0; + FUNC(cos) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("cos (0) == 1", FUNC(cos) (0), 1, 0, 0, 0); + check_float ("cos (-0) == 1", FUNC(cos) (minus_zero), 1, 0, 0, 0); + check_float ("cos (inf) == NaN plus invalid exception", FUNC(cos) (plus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("cos (-inf) == NaN plus invalid exception", FUNC(cos) (minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("cos (NaN) == NaN", FUNC(cos) (nan_value), nan_value, 0, 0, 0); + + check_float ("cos (M_PI_6l * 2.0) == 0.5", FUNC(cos) (M_PI_6l * 2.0), 0.5, DELTA582, 0, 0); + check_float ("cos (M_PI_6l * 4.0) == -0.5", FUNC(cos) (M_PI_6l * 4.0), -0.5, DELTA583, 0, 0); + check_float ("cos (pi/2) == 0", FUNC(cos) (M_PI_2l), 0, DELTA584, 0, 0); + + check_float ("cos (0.7) == 0.76484218728448842625585999019186495", FUNC(cos) (0.7L), 0.76484218728448842625585999019186495L, DELTA585, 0, 0); + + print_max_error ("cos", DELTAcos, 0); +} + +static void +cosh_test (void) +{ + errno = 0; + FUNC(cosh) (0.7L); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + check_float ("cosh (0) == 1", FUNC(cosh) (0), 1, 0, 0, 0); + check_float ("cosh (-0) == 1", FUNC(cosh) (minus_zero), 1, 0, 0, 0); + +#ifndef TEST_INLINE + check_float ("cosh (inf) == inf", FUNC(cosh) (plus_infty), plus_infty, 0, 0, 0); + check_float ("cosh (-inf) == inf", FUNC(cosh) (minus_infty), plus_infty, 0, 0, 0); +#endif + check_float ("cosh (NaN) == NaN", FUNC(cosh) (nan_value), nan_value, 0, 0, 0); + + check_float ("cosh (0.7) == 1.255169005630943018", FUNC(cosh) (0.7L), 1.255169005630943018L, DELTA591, 0, 0); + print_max_error ("cosh", DELTAcosh, 0); +} + + +#if 0 /* XXX scp XXX */ +static void +cpow_test (void) +{ + errno = 0; + FUNC(cpow) (BUILD_COMPLEX (1, 0), BUILD_COMPLEX (0, 0)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("cpow (1 + 0 i, 0 + 0 i) == 1.0 + 0.0 i", FUNC(cpow) (BUILD_COMPLEX (1, 0), BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (1.0, 0.0), 0, 0, 0); + check_complex ("cpow (2 + 0 i, 10 + 0 i) == 1024.0 + 0.0 i", FUNC(cpow) (BUILD_COMPLEX (2, 0), BUILD_COMPLEX (10, 0)), BUILD_COMPLEX (1024.0, 0.0), 0, 0, 0); + + check_complex ("cpow (e + 0 i, 0 + 2 * M_PIl i) == 1.0 + 0.0 i", FUNC(cpow) (BUILD_COMPLEX (M_El, 0), BUILD_COMPLEX (0, 2 * M_PIl)), BUILD_COMPLEX (1.0, 0.0), DELTA594, 0, 0); + check_complex ("cpow (2 + 3 i, 4 + 0 i) == -119.0 - 120.0 i", FUNC(cpow) (BUILD_COMPLEX (2, 3), BUILD_COMPLEX (4, 0)), BUILD_COMPLEX (-119.0, -120.0), DELTA595, 0, 0); + + check_complex ("cpow (NaN + NaN i, NaN + NaN i) == NaN + NaN i", FUNC(cpow) (BUILD_COMPLEX (nan_value, nan_value), BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + print_complex_max_error ("cpow", DELTAcpow, 0); +} + +static void +cproj_test (void) +{ + init_max_error (); + check_complex ("cproj (0.0 + 0.0 i) == 0.0 + 0.0 i", FUNC(cproj) (BUILD_COMPLEX (0.0, 0.0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("cproj (-0 - 0 i) == -0 - 0 i", FUNC(cproj) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + check_complex ("cproj (0.0 - 0 i) == 0.0 - 0 i", FUNC(cproj) (BUILD_COMPLEX (0.0, minus_zero)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + check_complex ("cproj (-0 + 0.0 i) == -0 + 0.0 i", FUNC(cproj) (BUILD_COMPLEX (minus_zero, 0.0)), BUILD_COMPLEX (minus_zero, 0.0), 0, 0, 0); + + check_complex ("cproj (NaN + NaN i) == NaN + NaN i", FUNC(cproj) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("cproj (inf + inf i) == inf + 0.0 i", FUNC(cproj) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("cproj (inf - inf i) == inf - 0 i", FUNC(cproj) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("cproj (-inf + inf i) == inf + 0.0 i", FUNC(cproj) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("cproj (-inf - inf i) == inf - 0 i", FUNC(cproj) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + + check_complex ("cproj (1.0 + 0.0 i) == 1.0 + 0.0 i", FUNC(cproj) (BUILD_COMPLEX (1.0, 0.0)), BUILD_COMPLEX (1.0, 0.0), 0, 0, 0); + check_complex ("cproj (2.0 + 3.0 i) == 0.2857142857142857142857142857142857 + 0.42857142857142857142857142857142855 i", FUNC(cproj) (BUILD_COMPLEX (2.0, 3.0)), BUILD_COMPLEX (0.2857142857142857142857142857142857L, 0.42857142857142857142857142857142855L), 0, 0, 0); + + print_complex_max_error ("cproj", 0, 0); +} + +static void +creal_test (void) +{ + init_max_error (); + check_float ("creal (0.0 + 1.0 i) == 0.0", FUNC(creal) (BUILD_COMPLEX (0.0, 1.0)), 0.0, 0, 0, 0); + check_float ("creal (-0 + 1.0 i) == -0", FUNC(creal) (BUILD_COMPLEX (minus_zero, 1.0)), minus_zero, 0, 0, 0); + check_float ("creal (NaN + 1.0 i) == NaN", FUNC(creal) (BUILD_COMPLEX (nan_value, 1.0)), nan_value, 0, 0, 0); + check_float ("creal (NaN + NaN i) == NaN", FUNC(creal) (BUILD_COMPLEX (nan_value, nan_value)), nan_value, 0, 0, 0); + check_float ("creal (inf + 1.0 i) == inf", FUNC(creal) (BUILD_COMPLEX (plus_infty, 1.0)), plus_infty, 0, 0, 0); + check_float ("creal (-inf + 1.0 i) == -inf", FUNC(creal) (BUILD_COMPLEX (minus_infty, 1.0)), minus_infty, 0, 0, 0); + check_float ("creal (2.0 + 3.0 i) == 2.0", FUNC(creal) (BUILD_COMPLEX (2.0, 3.0)), 2.0, 0, 0, 0); + + print_max_error ("creal", 0, 0); +} + +static void +csin_test (void) +{ + errno = 0; + FUNC(csin) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("csin (0.0 + 0.0 i) == 0.0 + 0.0 i", FUNC(csin) (BUILD_COMPLEX (0.0, 0.0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("csin (-0 + 0.0 i) == -0 + 0.0 i", FUNC(csin) (BUILD_COMPLEX (minus_zero, 0.0)), BUILD_COMPLEX (minus_zero, 0.0), 0, 0, 0); + check_complex ("csin (0.0 - 0 i) == 0 - 0 i", FUNC(csin) (BUILD_COMPLEX (0.0, minus_zero)), BUILD_COMPLEX (0, minus_zero), 0, 0, 0); + check_complex ("csin (-0 - 0 i) == -0 - 0 i", FUNC(csin) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + + check_complex ("csin (0.0 + inf i) == 0.0 + inf i", FUNC(csin) (BUILD_COMPLEX (0.0, plus_infty)), BUILD_COMPLEX (0.0, plus_infty), 0, 0, 0); + check_complex ("csin (-0 + inf i) == -0 + inf i", FUNC(csin) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (minus_zero, plus_infty), 0, 0, 0); + check_complex ("csin (0.0 - inf i) == 0.0 - inf i", FUNC(csin) (BUILD_COMPLEX (0.0, minus_infty)), BUILD_COMPLEX (0.0, minus_infty), 0, 0, 0); + check_complex ("csin (-0 - inf i) == -0 - inf i", FUNC(csin) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (minus_zero, minus_infty), 0, 0, 0); + + check_complex ("csin (inf + 0.0 i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (plus_infty, 0.0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csin (-inf + 0.0 i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (minus_infty, 0.0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csin (inf - 0 i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csin (-inf - 0 i) == NaN + 0.0 i plus invalid exception and sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + + check_complex ("csin (inf + inf i) == NaN + inf i plus invalid exception and sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csin (-inf + inf i) == NaN + inf i plus invalid exception and sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csin (inf - inf i) == NaN + inf i plus invalid exception and sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csin (-inf - inf i) == NaN + inf i plus invalid exception and sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + + check_complex ("csin (inf + 6.75 i) == NaN + NaN i plus invalid exception", FUNC(csin) (BUILD_COMPLEX (plus_infty, 6.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("csin (inf - 6.75 i) == NaN + NaN i plus invalid exception", FUNC(csin) (BUILD_COMPLEX (plus_infty, -6.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("csin (-inf + 6.75 i) == NaN + NaN i plus invalid exception", FUNC(csin) (BUILD_COMPLEX (minus_infty, 6.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("csin (-inf - 6.75 i) == NaN + NaN i plus invalid exception", FUNC(csin) (BUILD_COMPLEX (minus_infty, -6.75)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("csin (4.625 + inf i) == -inf - inf i", FUNC(csin) (BUILD_COMPLEX (4.625, plus_infty)), BUILD_COMPLEX (minus_infty, minus_infty), 0, 0, 0); + check_complex ("csin (4.625 - inf i) == -inf + inf i", FUNC(csin) (BUILD_COMPLEX (4.625, minus_infty)), BUILD_COMPLEX (minus_infty, plus_infty), 0, 0, 0); + check_complex ("csin (-4.625 + inf i) == inf - inf i", FUNC(csin) (BUILD_COMPLEX (-4.625, plus_infty)), BUILD_COMPLEX (plus_infty, minus_infty), 0, 0, 0); + check_complex ("csin (-4.625 - inf i) == inf + inf i", FUNC(csin) (BUILD_COMPLEX (-4.625, minus_infty)), BUILD_COMPLEX (plus_infty, plus_infty), 0, 0, 0); + + check_complex ("csin (NaN + 0.0 i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (nan_value, 0.0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("csin (NaN - 0 i) == NaN + 0.0 i plus sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("csin (NaN + inf i) == NaN + inf i plus sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("csin (NaN - inf i) == NaN + inf i plus sign of zero/inf not specified", FUNC(csin) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("csin (NaN + 9.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(csin) (BUILD_COMPLEX (nan_value, 9.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csin (NaN - 9.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(csin) (BUILD_COMPLEX (nan_value, -9.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("csin (0.0 + NaN i) == 0.0 + NaN i", FUNC(csin) (BUILD_COMPLEX (0.0, nan_value)), BUILD_COMPLEX (0.0, nan_value), 0, 0, 0); + check_complex ("csin (-0 + NaN i) == -0 + NaN i", FUNC(csin) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (minus_zero, nan_value), 0, 0, 0); + + check_complex ("csin (10.0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(csin) (BUILD_COMPLEX (10.0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csin (NaN - 10.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(csin) (BUILD_COMPLEX (nan_value, -10.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("csin (inf + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(csin) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csin (-inf + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(csin) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("csin (NaN + NaN i) == NaN + NaN i", FUNC(csin) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("csin (0.7 + 1.2 i) == 1.1664563419657581376 + 1.1544997246948547371 i", FUNC(csin) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (1.1664563419657581376L, 1.1544997246948547371L), DELTA652, 0, 0); + + check_complex ("csin (-2 - 3 i) == -9.1544991469114295734 + 4.1689069599665643507 i", FUNC(csin) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (-9.1544991469114295734L, 4.1689069599665643507L), 0, 0, 0); + + print_complex_max_error ("csin", DELTAcsin, 0); +} + + +static void +csinh_test (void) +{ + errno = 0; + FUNC(csinh) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("csinh (0.0 + 0.0 i) == 0.0 + 0.0 i", FUNC(csinh) (BUILD_COMPLEX (0.0, 0.0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("csinh (-0 + 0.0 i) == -0 + 0.0 i", FUNC(csinh) (BUILD_COMPLEX (minus_zero, 0.0)), BUILD_COMPLEX (minus_zero, 0.0), 0, 0, 0); + check_complex ("csinh (0.0 - 0 i) == 0.0 - 0 i", FUNC(csinh) (BUILD_COMPLEX (0.0, minus_zero)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + check_complex ("csinh (-0 - 0 i) == -0 - 0 i", FUNC(csinh) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + + check_complex ("csinh (0.0 + inf i) == 0.0 + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (0.0, plus_infty)), BUILD_COMPLEX (0.0, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csinh (-0 + inf i) == 0.0 + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (0.0, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csinh (0.0 - inf i) == 0.0 + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (0.0, minus_infty)), BUILD_COMPLEX (0.0, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csinh (-0 - inf i) == 0.0 + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (0.0, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + + check_complex ("csinh (inf + 0.0 i) == inf + 0.0 i", FUNC(csinh) (BUILD_COMPLEX (plus_infty, 0.0)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("csinh (-inf + 0.0 i) == -inf + 0.0 i", FUNC(csinh) (BUILD_COMPLEX (minus_infty, 0.0)), BUILD_COMPLEX (minus_infty, 0.0), 0, 0, 0); + check_complex ("csinh (inf - 0 i) == inf - 0 i", FUNC(csinh) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("csinh (-inf - 0 i) == -inf - 0 i", FUNC(csinh) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (minus_infty, minus_zero), 0, 0, 0); + + check_complex ("csinh (inf + inf i) == inf + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csinh (-inf + inf i) == inf + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csinh (inf - inf i) == inf + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + check_complex ("csinh (-inf - inf i) == inf + NaN i plus invalid exception and sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, INVALID_EXCEPTION|IGNORE_ZERO_INF_SIGN); + + check_complex ("csinh (inf + 4.625 i) == -inf - inf i", FUNC(csinh) (BUILD_COMPLEX (plus_infty, 4.625)), BUILD_COMPLEX (minus_infty, minus_infty), 0, 0, 0); + check_complex ("csinh (-inf + 4.625 i) == inf - inf i", FUNC(csinh) (BUILD_COMPLEX (minus_infty, 4.625)), BUILD_COMPLEX (plus_infty, minus_infty), 0, 0, 0); + check_complex ("csinh (inf - 4.625 i) == -inf + inf i", FUNC(csinh) (BUILD_COMPLEX (plus_infty, -4.625)), BUILD_COMPLEX (minus_infty, plus_infty), 0, 0, 0); + check_complex ("csinh (-inf - 4.625 i) == inf + inf i", FUNC(csinh) (BUILD_COMPLEX (minus_infty, -4.625)), BUILD_COMPLEX (plus_infty, plus_infty), 0, 0, 0); + + check_complex ("csinh (6.75 + inf i) == NaN + NaN i plus invalid exception", FUNC(csinh) (BUILD_COMPLEX (6.75, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("csinh (-6.75 + inf i) == NaN + NaN i plus invalid exception", FUNC(csinh) (BUILD_COMPLEX (-6.75, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("csinh (6.75 - inf i) == NaN + NaN i plus invalid exception", FUNC(csinh) (BUILD_COMPLEX (6.75, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("csinh (-6.75 - inf i) == NaN + NaN i plus invalid exception", FUNC(csinh) (BUILD_COMPLEX (-6.75, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("csinh (0.0 + NaN i) == 0.0 + NaN i plus sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (0.0, nan_value)), BUILD_COMPLEX (0.0, nan_value), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("csinh (-0 + NaN i) == 0.0 + NaN i plus sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (0.0, nan_value), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("csinh (inf + NaN i) == inf + NaN i plus sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("csinh (-inf + NaN i) == inf + NaN i plus sign of zero/inf not specified", FUNC(csinh) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("csinh (9.0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(csinh) (BUILD_COMPLEX (9.0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csinh (-9.0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(csinh) (BUILD_COMPLEX (-9.0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("csinh (NaN + 0.0 i) == NaN + 0.0 i", FUNC(csinh) (BUILD_COMPLEX (nan_value, 0.0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, 0); + check_complex ("csinh (NaN - 0 i) == NaN - 0 i", FUNC(csinh) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, minus_zero), 0, 0, 0); + + check_complex ("csinh (NaN + 10.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(csinh) (BUILD_COMPLEX (nan_value, 10.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csinh (NaN - 10.0 i) == NaN + NaN i plus invalid exception allowed", FUNC(csinh) (BUILD_COMPLEX (nan_value, -10.0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("csinh (NaN + inf i) == NaN + NaN i plus invalid exception allowed", FUNC(csinh) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csinh (NaN - inf i) == NaN + NaN i plus invalid exception allowed", FUNC(csinh) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("csinh (NaN + NaN i) == NaN + NaN i", FUNC(csinh) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("csinh (0.7 + 1.2 i) == 0.27487868678117583582 + 1.1698665727426565139 i", FUNC(csinh) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (0.27487868678117583582L, 1.1698665727426565139L), DELTA691, 0, 0); + check_complex ("csinh (-2 - 3 i) == 3.5905645899857799520 - 0.5309210862485198052 i", FUNC(csinh) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (3.5905645899857799520L, -0.5309210862485198052L), DELTA692, 0, 0); + + print_complex_max_error ("csinh", DELTAcsinh, 0); +} + +static void +csqrt_test (void) +{ + errno = 0; + FUNC(csqrt) (BUILD_COMPLEX (-1, 0)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("csqrt (0 + 0 i) == 0.0 + 0.0 i", FUNC(csqrt) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("csqrt (0 - 0 i) == 0 - 0 i", FUNC(csqrt) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (0, minus_zero), 0, 0, 0); + check_complex ("csqrt (-0 + 0 i) == 0.0 + 0.0 i", FUNC(csqrt) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("csqrt (-0 - 0 i) == 0.0 - 0 i", FUNC(csqrt) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + + check_complex ("csqrt (-inf + 0 i) == 0.0 + inf i", FUNC(csqrt) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (0.0, plus_infty), 0, 0, 0); + check_complex ("csqrt (-inf + 6 i) == 0.0 + inf i", FUNC(csqrt) (BUILD_COMPLEX (minus_infty, 6)), BUILD_COMPLEX (0.0, plus_infty), 0, 0, 0); + check_complex ("csqrt (-inf - 0 i) == 0.0 - inf i", FUNC(csqrt) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (0.0, minus_infty), 0, 0, 0); + check_complex ("csqrt (-inf - 6 i) == 0.0 - inf i", FUNC(csqrt) (BUILD_COMPLEX (minus_infty, -6)), BUILD_COMPLEX (0.0, minus_infty), 0, 0, 0); + + check_complex ("csqrt (inf + 0 i) == inf + 0.0 i", FUNC(csqrt) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("csqrt (inf + 6 i) == inf + 0.0 i", FUNC(csqrt) (BUILD_COMPLEX (plus_infty, 6)), BUILD_COMPLEX (plus_infty, 0.0), 0, 0, 0); + check_complex ("csqrt (inf - 0 i) == inf - 0 i", FUNC(csqrt) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + check_complex ("csqrt (inf - 6 i) == inf - 0 i", FUNC(csqrt) (BUILD_COMPLEX (plus_infty, -6)), BUILD_COMPLEX (plus_infty, minus_zero), 0, 0, 0); + + check_complex ("csqrt (0 + inf i) == inf + inf i", FUNC(csqrt) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (plus_infty, plus_infty), 0, 0, 0); + check_complex ("csqrt (4 + inf i) == inf + inf i", FUNC(csqrt) (BUILD_COMPLEX (4, plus_infty)), BUILD_COMPLEX (plus_infty, plus_infty), 0, 0, 0); + check_complex ("csqrt (inf + inf i) == inf + inf i", FUNC(csqrt) (BUILD_COMPLEX (plus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, plus_infty), 0, 0, 0); + check_complex ("csqrt (-0 + inf i) == inf + inf i", FUNC(csqrt) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (plus_infty, plus_infty), 0, 0, 0); + check_complex ("csqrt (-4 + inf i) == inf + inf i", FUNC(csqrt) (BUILD_COMPLEX (-4, plus_infty)), BUILD_COMPLEX (plus_infty, plus_infty), 0, 0, 0); + check_complex ("csqrt (-inf + inf i) == inf + inf i", FUNC(csqrt) (BUILD_COMPLEX (minus_infty, plus_infty)), BUILD_COMPLEX (plus_infty, plus_infty), 0, 0, 0); + check_complex ("csqrt (0 - inf i) == inf - inf i", FUNC(csqrt) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (plus_infty, minus_infty), 0, 0, 0); + check_complex ("csqrt (4 - inf i) == inf - inf i", FUNC(csqrt) (BUILD_COMPLEX (4, minus_infty)), BUILD_COMPLEX (plus_infty, minus_infty), 0, 0, 0); + check_complex ("csqrt (inf - inf i) == inf - inf i", FUNC(csqrt) (BUILD_COMPLEX (plus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, minus_infty), 0, 0, 0); + check_complex ("csqrt (-0 - inf i) == inf - inf i", FUNC(csqrt) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (plus_infty, minus_infty), 0, 0, 0); + check_complex ("csqrt (-4 - inf i) == inf - inf i", FUNC(csqrt) (BUILD_COMPLEX (-4, minus_infty)), BUILD_COMPLEX (plus_infty, minus_infty), 0, 0, 0); + check_complex ("csqrt (-inf - inf i) == inf - inf i", FUNC(csqrt) (BUILD_COMPLEX (minus_infty, minus_infty)), BUILD_COMPLEX (plus_infty, minus_infty), 0, 0, 0); + + check_complex ("csqrt (-inf + NaN i) == NaN + inf i plus sign of zero/inf not specified", FUNC(csqrt) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (nan_value, plus_infty), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("csqrt (inf + NaN i) == inf + NaN i", FUNC(csqrt) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (plus_infty, nan_value), 0, 0, 0); + + check_complex ("csqrt (0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(csqrt) (BUILD_COMPLEX (0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csqrt (1 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(csqrt) (BUILD_COMPLEX (1, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csqrt (-0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(csqrt) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csqrt (-1 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(csqrt) (BUILD_COMPLEX (-1, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("csqrt (NaN + 0 i) == NaN + NaN i plus invalid exception allowed", FUNC(csqrt) (BUILD_COMPLEX (nan_value, 0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csqrt (NaN + 8 i) == NaN + NaN i plus invalid exception allowed", FUNC(csqrt) (BUILD_COMPLEX (nan_value, 8)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csqrt (NaN - 0 i) == NaN + NaN i plus invalid exception allowed", FUNC(csqrt) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("csqrt (NaN - 8 i) == NaN + NaN i plus invalid exception allowed", FUNC(csqrt) (BUILD_COMPLEX (nan_value, -8)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("csqrt (NaN + NaN i) == NaN + NaN i", FUNC(csqrt) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("csqrt (16.0 - 30.0 i) == 5.0 - 3.0 i", FUNC(csqrt) (BUILD_COMPLEX (16.0, -30.0)), BUILD_COMPLEX (5.0, -3.0), 0, 0, 0); + check_complex ("csqrt (-1 + 0 i) == 0.0 + 1.0 i", FUNC(csqrt) (BUILD_COMPLEX (-1, 0)), BUILD_COMPLEX (0.0, 1.0), 0, 0, 0); + check_complex ("csqrt (0 + 2 i) == 1.0 + 1.0 i", FUNC(csqrt) (BUILD_COMPLEX (0, 2)), BUILD_COMPLEX (1.0, 1.0), 0, 0, 0); + check_complex ("csqrt (119 + 120 i) == 12.0 + 5.0 i", FUNC(csqrt) (BUILD_COMPLEX (119, 120)), BUILD_COMPLEX (12.0, 5.0), 0, 0, 0); + check_complex ("csqrt (0.7 + 1.2 i) == 1.022067610030026450706487883081139 + 0.58704531296356521154977678719838035 i", FUNC(csqrt) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (1.022067610030026450706487883081139L, 0.58704531296356521154977678719838035L), DELTA732, 0, 0); + check_complex ("csqrt (-2 - 3 i) == 0.89597747612983812471573375529004348 - 1.6741492280355400404480393008490519 i", FUNC(csqrt) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (0.89597747612983812471573375529004348L, -1.6741492280355400404480393008490519L), DELTA733, 0, 0); + check_complex ("csqrt (-2 + 3 i) == 0.89597747612983812471573375529004348 + 1.6741492280355400404480393008490519 i", FUNC(csqrt) (BUILD_COMPLEX (-2, 3)), BUILD_COMPLEX (0.89597747612983812471573375529004348L, 1.6741492280355400404480393008490519L), DELTA734, 0, 0); + + print_complex_max_error ("csqrt", DELTAcsqrt, 0); +} + +static void +ctan_test (void) +{ + errno = 0; + FUNC(ctan) (BUILD_COMPLEX (0.7L, 1.2L)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("ctan (0 + 0 i) == 0.0 + 0.0 i", FUNC(ctan) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("ctan (0 - 0 i) == 0.0 - 0 i", FUNC(ctan) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + check_complex ("ctan (-0 + 0 i) == -0 + 0.0 i", FUNC(ctan) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (minus_zero, 0.0), 0, 0, 0); + check_complex ("ctan (-0 - 0 i) == -0 - 0 i", FUNC(ctan) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + + check_complex ("ctan (0 + inf i) == 0.0 + 1.0 i", FUNC(ctan) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (0.0, 1.0), 0, 0, 0); + check_complex ("ctan (1 + inf i) == 0.0 + 1.0 i", FUNC(ctan) (BUILD_COMPLEX (1, plus_infty)), BUILD_COMPLEX (0.0, 1.0), 0, 0, 0); + check_complex ("ctan (-0 + inf i) == -0 + 1.0 i", FUNC(ctan) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (minus_zero, 1.0), 0, 0, 0); + check_complex ("ctan (-1 + inf i) == -0 + 1.0 i", FUNC(ctan) (BUILD_COMPLEX (-1, plus_infty)), BUILD_COMPLEX (minus_zero, 1.0), 0, 0, 0); + + check_complex ("ctan (0 - inf i) == 0.0 - 1.0 i", FUNC(ctan) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (0.0, -1.0), 0, 0, 0); + check_complex ("ctan (1 - inf i) == 0.0 - 1.0 i", FUNC(ctan) (BUILD_COMPLEX (1, minus_infty)), BUILD_COMPLEX (0.0, -1.0), 0, 0, 0); + check_complex ("ctan (-0 - inf i) == -0 - 1.0 i", FUNC(ctan) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (minus_zero, -1.0), 0, 0, 0); + check_complex ("ctan (-1 - inf i) == -0 - 1.0 i", FUNC(ctan) (BUILD_COMPLEX (-1, minus_infty)), BUILD_COMPLEX (minus_zero, -1.0), 0, 0, 0); + + check_complex ("ctan (inf + 0 i) == NaN + NaN i plus invalid exception", FUNC(ctan) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctan (inf + 2 i) == NaN + NaN i plus invalid exception", FUNC(ctan) (BUILD_COMPLEX (plus_infty, 2)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctan (-inf + 0 i) == NaN + NaN i plus invalid exception", FUNC(ctan) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctan (-inf + 2 i) == NaN + NaN i plus invalid exception", FUNC(ctan) (BUILD_COMPLEX (minus_infty, 2)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctan (inf - 0 i) == NaN + NaN i plus invalid exception", FUNC(ctan) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctan (inf - 2 i) == NaN + NaN i plus invalid exception", FUNC(ctan) (BUILD_COMPLEX (plus_infty, -2)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctan (-inf - 0 i) == NaN + NaN i plus invalid exception", FUNC(ctan) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctan (-inf - 2 i) == NaN + NaN i plus invalid exception", FUNC(ctan) (BUILD_COMPLEX (minus_infty, -2)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("ctan (NaN + inf i) == 0.0 + 1.0 i plus sign of zero/inf not specified", FUNC(ctan) (BUILD_COMPLEX (nan_value, plus_infty)), BUILD_COMPLEX (0.0, 1.0), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("ctan (NaN - inf i) == 0.0 - 1.0 i plus sign of zero/inf not specified", FUNC(ctan) (BUILD_COMPLEX (nan_value, minus_infty)), BUILD_COMPLEX (0.0, -1.0), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("ctan (0 + NaN i) == 0.0 + NaN i", FUNC(ctan) (BUILD_COMPLEX (0, nan_value)), BUILD_COMPLEX (0.0, nan_value), 0, 0, 0); + check_complex ("ctan (-0 + NaN i) == -0 + NaN i", FUNC(ctan) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (minus_zero, nan_value), 0, 0, 0); + + check_complex ("ctan (0.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ctan) (BUILD_COMPLEX (0.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ctan (-4.5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ctan) (BUILD_COMPLEX (-4.5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ctan (NaN + 0 i) == NaN + NaN i plus invalid exception allowed", FUNC(ctan) (BUILD_COMPLEX (nan_value, 0)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ctan (NaN + 5 i) == NaN + NaN i plus invalid exception allowed", FUNC(ctan) (BUILD_COMPLEX (nan_value, 5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ctan (NaN - 0 i) == NaN + NaN i plus invalid exception allowed", FUNC(ctan) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ctan (NaN - 0.25 i) == NaN + NaN i plus invalid exception allowed", FUNC(ctan) (BUILD_COMPLEX (nan_value, -0.25)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ctan (NaN + NaN i) == NaN + NaN i", FUNC(ctan) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("ctan (0.7 + 1.2 i) == 0.1720734197630349001 + 0.9544807059989405538 i", FUNC(ctan) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (0.1720734197630349001L, 0.9544807059989405538L), DELTA766, 0, 0); + check_complex ("ctan (-2 - 3 i) == 0.0037640256415042482 - 1.0032386273536098014 i", FUNC(ctan) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (0.0037640256415042482L, -1.0032386273536098014L), DELTA767, 0, 0); + + print_complex_max_error ("ctan", DELTActan, 0); +} + + +static void +ctanh_test (void) +{ + errno = 0; + FUNC(ctanh) (BUILD_COMPLEX (0, 0)); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_complex ("ctanh (0 + 0 i) == 0.0 + 0.0 i", FUNC(ctanh) (BUILD_COMPLEX (0, 0)), BUILD_COMPLEX (0.0, 0.0), 0, 0, 0); + check_complex ("ctanh (0 - 0 i) == 0.0 - 0 i", FUNC(ctanh) (BUILD_COMPLEX (0, minus_zero)), BUILD_COMPLEX (0.0, minus_zero), 0, 0, 0); + check_complex ("ctanh (-0 + 0 i) == -0 + 0.0 i", FUNC(ctanh) (BUILD_COMPLEX (minus_zero, 0)), BUILD_COMPLEX (minus_zero, 0.0), 0, 0, 0); + check_complex ("ctanh (-0 - 0 i) == -0 - 0 i", FUNC(ctanh) (BUILD_COMPLEX (minus_zero, minus_zero)), BUILD_COMPLEX (minus_zero, minus_zero), 0, 0, 0); + + check_complex ("ctanh (inf + 0 i) == 1.0 + 0.0 i", FUNC(ctanh) (BUILD_COMPLEX (plus_infty, 0)), BUILD_COMPLEX (1.0, 0.0), 0, 0, 0); + check_complex ("ctanh (inf + 1 i) == 1.0 + 0.0 i", FUNC(ctanh) (BUILD_COMPLEX (plus_infty, 1)), BUILD_COMPLEX (1.0, 0.0), 0, 0, 0); + check_complex ("ctanh (inf - 0 i) == 1.0 - 0 i", FUNC(ctanh) (BUILD_COMPLEX (plus_infty, minus_zero)), BUILD_COMPLEX (1.0, minus_zero), 0, 0, 0); + check_complex ("ctanh (inf - 1 i) == 1.0 - 0 i", FUNC(ctanh) (BUILD_COMPLEX (plus_infty, -1)), BUILD_COMPLEX (1.0, minus_zero), 0, 0, 0); + check_complex ("ctanh (-inf + 0 i) == -1.0 + 0.0 i", FUNC(ctanh) (BUILD_COMPLEX (minus_infty, 0)), BUILD_COMPLEX (-1.0, 0.0), 0, 0, 0); + check_complex ("ctanh (-inf + 1 i) == -1.0 + 0.0 i", FUNC(ctanh) (BUILD_COMPLEX (minus_infty, 1)), BUILD_COMPLEX (-1.0, 0.0), 0, 0, 0); + check_complex ("ctanh (-inf - 0 i) == -1.0 - 0 i", FUNC(ctanh) (BUILD_COMPLEX (minus_infty, minus_zero)), BUILD_COMPLEX (-1.0, minus_zero), 0, 0, 0); + check_complex ("ctanh (-inf - 1 i) == -1.0 - 0 i", FUNC(ctanh) (BUILD_COMPLEX (minus_infty, -1)), BUILD_COMPLEX (-1.0, minus_zero), 0, 0, 0); + + check_complex ("ctanh (0 + inf i) == NaN + NaN i plus invalid exception", FUNC(ctanh) (BUILD_COMPLEX (0, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctanh (2 + inf i) == NaN + NaN i plus invalid exception", FUNC(ctanh) (BUILD_COMPLEX (2, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctanh (0 - inf i) == NaN + NaN i plus invalid exception", FUNC(ctanh) (BUILD_COMPLEX (0, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctanh (2 - inf i) == NaN + NaN i plus invalid exception", FUNC(ctanh) (BUILD_COMPLEX (2, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctanh (-0 + inf i) == NaN + NaN i plus invalid exception", FUNC(ctanh) (BUILD_COMPLEX (minus_zero, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctanh (-2 + inf i) == NaN + NaN i plus invalid exception", FUNC(ctanh) (BUILD_COMPLEX (-2, plus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctanh (-0 - inf i) == NaN + NaN i plus invalid exception", FUNC(ctanh) (BUILD_COMPLEX (minus_zero, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + check_complex ("ctanh (-2 - inf i) == NaN + NaN i plus invalid exception", FUNC(ctanh) (BUILD_COMPLEX (-2, minus_infty)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION); + + check_complex ("ctanh (inf + NaN i) == 1.0 + 0.0 i plus sign of zero/inf not specified", FUNC(ctanh) (BUILD_COMPLEX (plus_infty, nan_value)), BUILD_COMPLEX (1.0, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + check_complex ("ctanh (-inf + NaN i) == -1.0 + 0.0 i plus sign of zero/inf not specified", FUNC(ctanh) (BUILD_COMPLEX (minus_infty, nan_value)), BUILD_COMPLEX (-1.0, 0.0), 0, 0, IGNORE_ZERO_INF_SIGN); + + check_complex ("ctanh (NaN + 0 i) == NaN + 0.0 i", FUNC(ctanh) (BUILD_COMPLEX (nan_value, 0)), BUILD_COMPLEX (nan_value, 0.0), 0, 0, 0); + check_complex ("ctanh (NaN - 0 i) == NaN - 0 i", FUNC(ctanh) (BUILD_COMPLEX (nan_value, minus_zero)), BUILD_COMPLEX (nan_value, minus_zero), 0, 0, 0); + + check_complex ("ctanh (NaN + 0.5 i) == NaN + NaN i plus invalid exception allowed", FUNC(ctanh) (BUILD_COMPLEX (nan_value, 0.5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ctanh (NaN - 4.5 i) == NaN + NaN i plus invalid exception allowed", FUNC(ctanh) (BUILD_COMPLEX (nan_value, -4.5)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ctanh (0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ctanh) (BUILD_COMPLEX (0, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ctanh (5 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ctanh) (BUILD_COMPLEX (5, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ctanh (-0 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ctanh) (BUILD_COMPLEX (minus_zero, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + check_complex ("ctanh (-0.25 + NaN i) == NaN + NaN i plus invalid exception allowed", FUNC(ctanh) (BUILD_COMPLEX (-0.25, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, INVALID_EXCEPTION_OK); + + check_complex ("ctanh (NaN + NaN i) == NaN + NaN i", FUNC(ctanh) (BUILD_COMPLEX (nan_value, nan_value)), BUILD_COMPLEX (nan_value, nan_value), 0, 0, 0); + + check_complex ("ctanh (0 + pi/4 i) == 0.0 + 1.0 i", FUNC(ctanh) (BUILD_COMPLEX (0, M_PI_4l)), BUILD_COMPLEX (0.0, 1.0), DELTA799, 0, 0); + + check_complex ("ctanh (0.7 + 1.2 i) == 1.3472197399061191630 + 0.4778641038326365540 i", FUNC(ctanh) (BUILD_COMPLEX (0.7L, 1.2L)), BUILD_COMPLEX (1.3472197399061191630L, 0.4778641038326365540L), DELTA800, 0, 0); + check_complex ("ctanh (-2 - 3 i) == -0.9653858790221331242 + 0.0098843750383224937 i", FUNC(ctanh) (BUILD_COMPLEX (-2, -3)), BUILD_COMPLEX (-0.9653858790221331242L, 0.0098843750383224937L), DELTA801, 0, 0); + + print_complex_max_error ("ctanh", DELTActanh, 0); +} +#endif + +static void +erf_test (void) +{ + errno = 0; + FUNC(erf) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("erf (0) == 0", FUNC(erf) (0), 0, 0, 0, 0); + check_float ("erf (-0) == -0", FUNC(erf) (minus_zero), minus_zero, 0, 0, 0); + check_float ("erf (inf) == 1", FUNC(erf) (plus_infty), 1, 0, 0, 0); + check_float ("erf (-inf) == -1", FUNC(erf) (minus_infty), -1, 0, 0, 0); + check_float ("erf (NaN) == NaN", FUNC(erf) (nan_value), nan_value, 0, 0, 0); + + check_float ("erf (0.7) == 0.67780119383741847297", FUNC(erf) (0.7L), 0.67780119383741847297L, 0, 0, 0); + + check_float ("erf (1.2) == 0.91031397822963538024", FUNC(erf) (1.2L), 0.91031397822963538024L, 0, 0, 0); + check_float ("erf (2.0) == 0.99532226501895273416", FUNC(erf) (2.0), 0.99532226501895273416L, 0, 0, 0); + check_float ("erf (4.1) == 0.99999999329997234592", FUNC(erf) (4.1L), 0.99999999329997234592L, 0, 0, 0); + check_float ("erf (27) == 1.0", FUNC(erf) (27), 1.0L, 0, 0, 0); + + print_max_error ("erf", 0, 0); +} + + +static void +erfc_test (void) +{ + errno = 0; + FUNC(erfc) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("erfc (inf) == 0.0", FUNC(erfc) (plus_infty), 0.0, 0, 0, 0); + check_float ("erfc (-inf) == 2.0", FUNC(erfc) (minus_infty), 2.0, 0, 0, 0); + check_float ("erfc (0.0) == 1.0", FUNC(erfc) (0.0), 1.0, 0, 0, 0); + check_float ("erfc (-0) == 1.0", FUNC(erfc) (minus_zero), 1.0, 0, 0, 0); + check_float ("erfc (NaN) == NaN", FUNC(erfc) (nan_value), nan_value, 0, 0, 0); + + check_float ("erfc (0.7) == 0.32219880616258152702", FUNC(erfc) (0.7L), 0.32219880616258152702L, DELTA817, 0, 0); + + check_float ("erfc (1.2) == 0.089686021770364619762", FUNC(erfc) (1.2L), 0.089686021770364619762L, DELTA818, 0, 0); + check_float ("erfc (2.0) == 0.0046777349810472658379", FUNC(erfc) (2.0), 0.0046777349810472658379L, DELTA819, 0, 0); + check_float ("erfc (4.1) == 0.67000276540848983727e-8", FUNC(erfc) (4.1L), 0.67000276540848983727e-8L, DELTA820, 0, 0); + check_float ("erfc (9) == 0.41370317465138102381e-36", FUNC(erfc) (9), 0.41370317465138102381e-36L, DELTA821, 0, 0); + + print_max_error ("erfc", DELTAerfc, 0); +} + +static void +exp_test (void) +{ + errno = 0; + FUNC(exp) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("exp (0) == 1", FUNC(exp) (0), 1, 0, 0, 0); + check_float ("exp (-0) == 1", FUNC(exp) (minus_zero), 1, 0, 0, 0); + +#ifndef TEST_INLINE + check_float ("exp (inf) == inf", FUNC(exp) (plus_infty), plus_infty, 0, 0, 0); + check_float ("exp (-inf) == 0", FUNC(exp) (minus_infty), 0, 0, 0, 0); +#endif + check_float ("exp (NaN) == NaN", FUNC(exp) (nan_value), nan_value, 0, 0, 0); + check_float ("exp (1) == e", FUNC(exp) (1), M_El, 0, 0, 0); + + check_float ("exp (2) == e^2", FUNC(exp) (2), M_E2l, 0, 0, 0); + check_float ("exp (3) == e^3", FUNC(exp) (3), M_E3l, 0, 0, 0); + check_float ("exp (0.7) == 2.0137527074704765216", FUNC(exp) (0.7L), 2.0137527074704765216L, DELTA830, 0, 0); + check_float ("exp (50.0) == 5184705528587072464087.45332293348538", FUNC(exp) (50.0L), 5184705528587072464087.45332293348538L, DELTA831, 0, 0); +#ifdef TEST_LDOUBLE + /* The result can only be represented in long double. */ + check_float ("exp (1000.0) == 0.197007111401704699388887935224332313e435", FUNC(exp) (1000.0L), 0.197007111401704699388887935224332313e435L, DELTA832, 0, 0); +#endif + print_max_error ("exp", DELTAexp, 0); +} + + +#if 0 /* XXX scp XXX */ +static void +exp10_test (void) +{ + errno = 0; + FUNC(exp10) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("exp10 (0) == 1", FUNC(exp10) (0), 1, 0, 0, 0); + check_float ("exp10 (-0) == 1", FUNC(exp10) (minus_zero), 1, 0, 0, 0); + + check_float ("exp10 (inf) == inf", FUNC(exp10) (plus_infty), plus_infty, 0, 0, 0); + check_float ("exp10 (-inf) == 0", FUNC(exp10) (minus_infty), 0, 0, 0, 0); + check_float ("exp10 (NaN) == NaN", FUNC(exp10) (nan_value), nan_value, 0, 0, 0); + check_float ("exp10 (3) == 1000", FUNC(exp10) (3), 1000, DELTA838, 0, 0); + check_float ("exp10 (-1) == 0.1", FUNC(exp10) (-1), 0.1L, DELTA839, 0, 0); + check_float ("exp10 (1e6) == inf", FUNC(exp10) (1e6), plus_infty, 0, 0, 0); + check_float ("exp10 (-1e6) == 0", FUNC(exp10) (-1e6), 0, 0, 0, 0); + check_float ("exp10 (0.7) == 5.0118723362727228500155418688494574", FUNC(exp10) (0.7L), 5.0118723362727228500155418688494574L, DELTA842, 0, 0); + + print_max_error ("exp10", DELTAexp10, 0); +} +#endif + +static void +exp2_test (void) +{ + errno = 0; + FUNC(exp2) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("exp2 (0) == 1", FUNC(exp2) (0), 1, 0, 0, 0); + check_float ("exp2 (-0) == 1", FUNC(exp2) (minus_zero), 1, 0, 0, 0); + check_float ("exp2 (inf) == inf", FUNC(exp2) (plus_infty), plus_infty, 0, 0, 0); + check_float ("exp2 (-inf) == 0", FUNC(exp2) (minus_infty), 0, 0, 0, 0); + check_float ("exp2 (NaN) == NaN", FUNC(exp2) (nan_value), nan_value, 0, 0, 0); + + check_float ("exp2 (10) == 1024", FUNC(exp2) (10), 1024, 0, 0, 0); + check_float ("exp2 (-1) == 0.5", FUNC(exp2) (-1), 0.5, 0, 0, 0); + check_float ("exp2 (1e6) == inf", FUNC(exp2) (1e6), plus_infty, 0, 0, 0); + check_float ("exp2 (-1e6) == 0", FUNC(exp2) (-1e6), 0, 0, 0, 0); + check_float ("exp2 (0.7) == 1.6245047927124710452", FUNC(exp2) (0.7L), 1.6245047927124710452L, DELTA852, 0, 0); + + print_max_error ("exp2", DELTAexp2, 0); +} + +static void +expm1_test (void) +{ + errno = 0; + FUNC(expm1) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("expm1 (0) == 0", FUNC(expm1) (0), 0, 0, 0, 0); + check_float ("expm1 (-0) == -0", FUNC(expm1) (minus_zero), minus_zero, 0, 0, 0); + +#ifndef TEST_INLINE + check_float ("expm1 (inf) == inf", FUNC(expm1) (plus_infty), plus_infty, 0, 0, 0); + check_float ("expm1 (-inf) == -1", FUNC(expm1) (minus_infty), -1, 0, 0, 0); +#endif + check_float ("expm1 (NaN) == NaN", FUNC(expm1) (nan_value), nan_value, 0, 0, 0); + + check_float ("expm1 (1) == M_El - 1.0", FUNC(expm1) (1), M_El - 1.0, 1, 0, 0); + check_float ("expm1 (0.7) == 1.0137527074704765216", FUNC(expm1) (0.7L), 1.0137527074704765216L, DELTA859, 0, 0); + + print_max_error ("expm1", DELTAexpm1, 0); +} + +static void +fabs_test (void) +{ + init_max_error (); + + check_float ("fabs (0) == 0", FUNC(fabs) ((FLOAT)0.0), 0, 0, 0, 0); + check_float ("fabs (-0) == 0", FUNC(fabs) (minus_zero), 0, 0, 0, 0); + + check_float ("fabs (inf) == inf", FUNC(fabs) (plus_infty), plus_infty, 0, 0, 0); + check_float ("fabs (-inf) == inf", FUNC(fabs) (minus_infty), plus_infty, 0, 0, 0); + check_float ("fabs (NaN) == NaN", FUNC(fabs) (nan_value), nan_value, 0, 0, 0); + + check_float ("fabs (38.0) == 38.0", FUNC(fabs) ((FLOAT)38.0), 38.0, 0, 0, 0); + check_float ("fabs (-e) == e", FUNC(fabs) ((FLOAT)-M_El), M_El, 0, 0, 0); + + print_max_error ("fabs", 0, 0); +} + +static void +fdim_test (void) +{ + init_max_error (); + + check_float ("fdim (0, 0) == 0", FUNC(fdim) (0, 0), 0, 0, 0, 0); + check_float ("fdim (9, 0) == 9", FUNC(fdim) (9, 0), 9, 0, 0, 0); + check_float ("fdim (0, 9) == 0", FUNC(fdim) (0, 9), 0, 0, 0, 0); + check_float ("fdim (-9, 0) == 0", FUNC(fdim) (-9, 0), 0, 0, 0, 0); + check_float ("fdim (0, -9) == 9", FUNC(fdim) (0, -9), 9, 0, 0, 0); + + check_float ("fdim (inf, 9) == inf", FUNC(fdim) (plus_infty, 9), plus_infty, 0, 0, 0); + check_float ("fdim (inf, -9) == inf", FUNC(fdim) (plus_infty, -9), plus_infty, 0, 0, 0); + check_float ("fdim (-inf, 9) == 0", FUNC(fdim) (minus_infty, 9), 0, 0, 0, 0); + check_float ("fdim (-inf, -9) == 0", FUNC(fdim) (minus_infty, -9), 0, 0, 0, 0); + check_float ("fdim (9, -inf) == inf", FUNC(fdim) (9, minus_infty), plus_infty, 0, 0, 0); + check_float ("fdim (-9, -inf) == inf", FUNC(fdim) (-9, minus_infty), plus_infty, 0, 0, 0); + check_float ("fdim (9, inf) == 0", FUNC(fdim) (9, plus_infty), 0, 0, 0, 0); + check_float ("fdim (-9, inf) == 0", FUNC(fdim) (-9, plus_infty), 0, 0, 0, 0); + + check_float ("fdim (0, NaN) == NaN", FUNC(fdim) (0, nan_value), nan_value, 0, 0, 0); + check_float ("fdim (9, NaN) == NaN", FUNC(fdim) (9, nan_value), nan_value, 0, 0, 0); + check_float ("fdim (-9, NaN) == NaN", FUNC(fdim) (-9, nan_value), nan_value, 0, 0, 0); + check_float ("fdim (NaN, 9) == NaN", FUNC(fdim) (nan_value, 9), nan_value, 0, 0, 0); + check_float ("fdim (NaN, -9) == NaN", FUNC(fdim) (nan_value, -9), nan_value, 0, 0, 0); + check_float ("fdim (inf, NaN) == NaN", FUNC(fdim) (plus_infty, nan_value), nan_value, 0, 0, 0); + check_float ("fdim (-inf, NaN) == NaN", FUNC(fdim) (minus_infty, nan_value), nan_value, 0, 0, 0); + check_float ("fdim (NaN, inf) == NaN", FUNC(fdim) (nan_value, plus_infty), nan_value, 0, 0, 0); + check_float ("fdim (NaN, -inf) == NaN", FUNC(fdim) (nan_value, minus_infty), nan_value, 0, 0, 0); + check_float ("fdim (NaN, NaN) == NaN", FUNC(fdim) (nan_value, nan_value), nan_value, 0, 0, 0); + + print_max_error ("fdim", 0, 0); +} + +static void +floor_test (void) +{ + init_max_error (); + + check_float ("floor (0.0) == 0.0", FUNC(floor) (0.0), 0.0, 0, 0, 0); + check_float ("floor (-0) == -0", FUNC(floor) (minus_zero), minus_zero, 0, 0, 0); + check_float ("floor (inf) == inf", FUNC(floor) (plus_infty), plus_infty, 0, 0, 0); + check_float ("floor (-inf) == -inf", FUNC(floor) (minus_infty), minus_infty, 0, 0, 0); + check_float ("floor (NaN) == NaN", FUNC(floor) (nan_value), nan_value, 0, 0, 0); + + check_float ("floor (pi) == 3.0", FUNC(floor) (M_PIl), 3.0, 0, 0, 0); + check_float ("floor (-pi) == -4.0", FUNC(floor) (-M_PIl), -4.0, 0, 0, 0); + + print_max_error ("floor", 0, 0); +} + +static void +fma_test (void) +{ + init_max_error (); + + check_float ("fma (1.0, 2.0, 3.0) == 5.0", FUNC(fma) (1.0, 2.0, 3.0), 5.0, 0, 0, 0); + check_float ("fma (NaN, 2.0, 3.0) == NaN", FUNC(fma) (nan_value, 2.0, 3.0), nan_value, 0, 0, 0); + check_float ("fma (1.0, NaN, 3.0) == NaN", FUNC(fma) (1.0, nan_value, 3.0), nan_value, 0, 0, 0); + check_float ("fma (1.0, 2.0, NaN) == NaN plus invalid exception allowed", FUNC(fma) (1.0, 2.0, nan_value), nan_value, 0, 0, INVALID_EXCEPTION_OK); + check_float ("fma (inf, 0.0, NaN) == NaN plus invalid exception allowed", FUNC(fma) (plus_infty, 0.0, nan_value), nan_value, 0, 0, INVALID_EXCEPTION_OK); + check_float ("fma (-inf, 0.0, NaN) == NaN plus invalid exception allowed", FUNC(fma) (minus_infty, 0.0, nan_value), nan_value, 0, 0, INVALID_EXCEPTION_OK); + check_float ("fma (0.0, inf, NaN) == NaN plus invalid exception allowed", FUNC(fma) (0.0, plus_infty, nan_value), nan_value, 0, 0, INVALID_EXCEPTION_OK); + check_float ("fma (0.0, -inf, NaN) == NaN plus invalid exception allowed", FUNC(fma) (0.0, minus_infty, nan_value), nan_value, 0, 0, INVALID_EXCEPTION_OK); + check_float ("fma (inf, 0.0, 1.0) == NaN plus invalid exception", FUNC(fma) (plus_infty, 0.0, 1.0), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("fma (-inf, 0.0, 1.0) == NaN plus invalid exception", FUNC(fma) (minus_infty, 0.0, 1.0), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("fma (0.0, inf, 1.0) == NaN plus invalid exception", FUNC(fma) (0.0, plus_infty, 1.0), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("fma (0.0, -inf, 1.0) == NaN plus invalid exception", FUNC(fma) (0.0, minus_infty, 1.0), nan_value, 0, 0, INVALID_EXCEPTION); + + check_float ("fma (inf, inf, -inf) == NaN plus invalid exception", FUNC(fma) (plus_infty, plus_infty, minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("fma (-inf, inf, inf) == NaN plus invalid exception", FUNC(fma) (minus_infty, plus_infty, plus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("fma (inf, -inf, inf) == NaN plus invalid exception", FUNC(fma) (plus_infty, minus_infty, plus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("fma (-inf, -inf, -inf) == NaN plus invalid exception", FUNC(fma) (minus_infty, minus_infty, minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + + print_max_error ("fma", 0, 0); +} + + +static void +fmax_test (void) +{ + init_max_error (); + + check_float ("fmax (0, 0) == 0", FUNC(fmax) (0, 0), 0, 0, 0, 0); + check_float ("fmax (-0, -0) == -0", FUNC(fmax) (minus_zero, minus_zero), minus_zero, 0, 0, 0); + check_float ("fmax (9, 0) == 9", FUNC(fmax) (9, 0), 9, 0, 0, 0); + check_float ("fmax (0, 9) == 9", FUNC(fmax) (0, 9), 9, 0, 0, 0); + check_float ("fmax (-9, 0) == 0", FUNC(fmax) (-9, 0), 0, 0, 0, 0); + check_float ("fmax (0, -9) == 0", FUNC(fmax) (0, -9), 0, 0, 0, 0); + + check_float ("fmax (inf, 9) == inf", FUNC(fmax) (plus_infty, 9), plus_infty, 0, 0, 0); + check_float ("fmax (0, inf) == inf", FUNC(fmax) (0, plus_infty), plus_infty, 0, 0, 0); + check_float ("fmax (-9, inf) == inf", FUNC(fmax) (-9, plus_infty), plus_infty, 0, 0, 0); + check_float ("fmax (inf, -9) == inf", FUNC(fmax) (plus_infty, -9), plus_infty, 0, 0, 0); + + check_float ("fmax (-inf, 9) == 9", FUNC(fmax) (minus_infty, 9), 9, 0, 0, 0); + check_float ("fmax (-inf, -9) == -9", FUNC(fmax) (minus_infty, -9), -9, 0, 0, 0); + check_float ("fmax (9, -inf) == 9", FUNC(fmax) (9, minus_infty), 9, 0, 0, 0); + check_float ("fmax (-9, -inf) == -9", FUNC(fmax) (-9, minus_infty), -9, 0, 0, 0); + + check_float ("fmax (0, NaN) == 0", FUNC(fmax) (0, nan_value), 0, 0, 0, 0); + check_float ("fmax (9, NaN) == 9", FUNC(fmax) (9, nan_value), 9, 0, 0, 0); + check_float ("fmax (-9, NaN) == -9", FUNC(fmax) (-9, nan_value), -9, 0, 0, 0); + check_float ("fmax (NaN, 0) == 0", FUNC(fmax) (nan_value, 0), 0, 0, 0, 0); + check_float ("fmax (NaN, 9) == 9", FUNC(fmax) (nan_value, 9), 9, 0, 0, 0); + check_float ("fmax (NaN, -9) == -9", FUNC(fmax) (nan_value, -9), -9, 0, 0, 0); + check_float ("fmax (inf, NaN) == inf", FUNC(fmax) (plus_infty, nan_value), plus_infty, 0, 0, 0); + check_float ("fmax (-inf, NaN) == -inf", FUNC(fmax) (minus_infty, nan_value), minus_infty, 0, 0, 0); + check_float ("fmax (NaN, inf) == inf", FUNC(fmax) (nan_value, plus_infty), plus_infty, 0, 0, 0); + check_float ("fmax (NaN, -inf) == -inf", FUNC(fmax) (nan_value, minus_infty), minus_infty, 0, 0, 0); + check_float ("fmax (NaN, NaN) == NaN", FUNC(fmax) (nan_value, nan_value), nan_value, 0, 0, 0); + + print_max_error ("fmax", 0, 0); +} + + +static void +fmin_test (void) +{ + init_max_error (); + + check_float ("fmin (0, 0) == 0", FUNC(fmin) (0, 0), 0, 0, 0, 0); + check_float ("fmin (-0, -0) == -0", FUNC(fmin) (minus_zero, minus_zero), minus_zero, 0, 0, 0); + check_float ("fmin (9, 0) == 0", FUNC(fmin) (9, 0), 0, 0, 0, 0); + check_float ("fmin (0, 9) == 0", FUNC(fmin) (0, 9), 0, 0, 0, 0); + check_float ("fmin (-9, 0) == -9", FUNC(fmin) (-9, 0), -9, 0, 0, 0); + check_float ("fmin (0, -9) == -9", FUNC(fmin) (0, -9), -9, 0, 0, 0); + + check_float ("fmin (inf, 9) == 9", FUNC(fmin) (plus_infty, 9), 9, 0, 0, 0); + check_float ("fmin (9, inf) == 9", FUNC(fmin) (9, plus_infty), 9, 0, 0, 0); + check_float ("fmin (inf, -9) == -9", FUNC(fmin) (plus_infty, -9), -9, 0, 0, 0); + check_float ("fmin (-9, inf) == -9", FUNC(fmin) (-9, plus_infty), -9, 0, 0, 0); + check_float ("fmin (-inf, 9) == -inf", FUNC(fmin) (minus_infty, 9), minus_infty, 0, 0, 0); + check_float ("fmin (-inf, -9) == -inf", FUNC(fmin) (minus_infty, -9), minus_infty, 0, 0, 0); + check_float ("fmin (9, -inf) == -inf", FUNC(fmin) (9, minus_infty), minus_infty, 0, 0, 0); + check_float ("fmin (-9, -inf) == -inf", FUNC(fmin) (-9, minus_infty), minus_infty, 0, 0, 0); + + check_float ("fmin (0, NaN) == 0", FUNC(fmin) (0, nan_value), 0, 0, 0, 0); + check_float ("fmin (9, NaN) == 9", FUNC(fmin) (9, nan_value), 9, 0, 0, 0); + check_float ("fmin (-9, NaN) == -9", FUNC(fmin) (-9, nan_value), -9, 0, 0, 0); + check_float ("fmin (NaN, 0) == 0", FUNC(fmin) (nan_value, 0), 0, 0, 0, 0); + check_float ("fmin (NaN, 9) == 9", FUNC(fmin) (nan_value, 9), 9, 0, 0, 0); + check_float ("fmin (NaN, -9) == -9", FUNC(fmin) (nan_value, -9), -9, 0, 0, 0); + check_float ("fmin (inf, NaN) == inf", FUNC(fmin) (plus_infty, nan_value), plus_infty, 0, 0, 0); + check_float ("fmin (-inf, NaN) == -inf", FUNC(fmin) (minus_infty, nan_value), minus_infty, 0, 0, 0); + check_float ("fmin (NaN, inf) == inf", FUNC(fmin) (nan_value, plus_infty), plus_infty, 0, 0, 0); + check_float ("fmin (NaN, -inf) == -inf", FUNC(fmin) (nan_value, minus_infty), minus_infty, 0, 0, 0); + check_float ("fmin (NaN, NaN) == NaN", FUNC(fmin) (nan_value, nan_value), nan_value, 0, 0, 0); + + print_max_error ("fmin", 0, 0); +} + + +static void +fmod_test (void) +{ + errno = 0; + FUNC(fmod) (6.5, 2.3L); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + /* fmod (+0, y) == +0 for y != 0. */ + check_float ("fmod (0, 3) == 0", FUNC(fmod) (0, 3), 0, 0, 0, 0); + + /* fmod (-0, y) == -0 for y != 0. */ + check_float ("fmod (-0, 3) == -0", FUNC(fmod) (minus_zero, 3), minus_zero, 0, 0, 0); + + /* fmod (+inf, y) == NaN plus invalid exception. */ + check_float ("fmod (inf, 3) == NaN plus invalid exception", FUNC(fmod) (plus_infty, 3), nan_value, 0, 0, INVALID_EXCEPTION); + /* fmod (-inf, y) == NaN plus invalid exception. */ + check_float ("fmod (-inf, 3) == NaN plus invalid exception", FUNC(fmod) (minus_infty, 3), nan_value, 0, 0, INVALID_EXCEPTION); + /* fmod (x, +0) == NaN plus invalid exception. */ + check_float ("fmod (3, 0) == NaN plus invalid exception", FUNC(fmod) (3, 0), nan_value, 0, 0, INVALID_EXCEPTION); + /* fmod (x, -0) == NaN plus invalid exception. */ + check_float ("fmod (3, -0) == NaN plus invalid exception", FUNC(fmod) (3, minus_zero), nan_value, 0, 0, INVALID_EXCEPTION); + + /* fmod (x, +inf) == x for x not infinite. */ + check_float ("fmod (3.0, inf) == 3.0", FUNC(fmod) (3.0, plus_infty), 3.0, 0, 0, 0); + /* fmod (x, -inf) == x for x not infinite. */ + check_float ("fmod (3.0, -inf) == 3.0", FUNC(fmod) (3.0, minus_infty), 3.0, 0, 0, 0); + + check_float ("fmod (NaN, NaN) == NaN", FUNC(fmod) (nan_value, nan_value), nan_value, 0, 0, 0); + + check_float ("fmod (6.5, 2.3) == 1.9", FUNC(fmod) (6.5, 2.3L), 1.9L, DELTA972, 0, 0); + check_float ("fmod (-6.5, 2.3) == -1.9", FUNC(fmod) (-6.5, 2.3L), -1.9L, DELTA973, 0, 0); + check_float ("fmod (6.5, -2.3) == 1.9", FUNC(fmod) (6.5, -2.3L), 1.9L, DELTA974, 0, 0); + check_float ("fmod (-6.5, -2.3) == -1.9", FUNC(fmod) (-6.5, -2.3L), -1.9L, DELTA975, 0, 0); + + print_max_error ("fmod", DELTAfmod, 0); +} + +static void +fpclassify_test (void) +{ + init_max_error (); + + check_int ("fpclassify (NaN) == FP_NAN", fpclassify (nan_value), FP_NAN, 0, 0, 0); + check_int ("fpclassify (inf) == FP_INFINITE", fpclassify (plus_infty), FP_INFINITE, 0, 0, 0); + check_int ("fpclassify (-inf) == FP_INFINITE", fpclassify (minus_infty), FP_INFINITE, 0, 0, 0); + check_int ("fpclassify (+0) == FP_ZERO", fpclassify (plus_zero), FP_ZERO, 0, 0, 0); + check_int ("fpclassify (-0) == FP_ZERO", fpclassify (minus_zero), FP_ZERO, 0, 0, 0); + check_int ("fpclassify (1000) == FP_NORMAL", fpclassify (1000.0), FP_NORMAL, 0, 0, 0); + + print_max_error ("fpclassify", 0, 0); +} + + +static void +frexp_test (void) +{ + int x; + + init_max_error (); + + check_float ("frexp (inf, &x) == inf", FUNC(frexp) (plus_infty, &x), plus_infty, 0, 0, 0); + check_float ("frexp (-inf, &x) == -inf", FUNC(frexp) (minus_infty, &x), minus_infty, 0, 0, 0); + check_float ("frexp (NaN, &x) == NaN", FUNC(frexp) (nan_value, &x), nan_value, 0, 0, 0); + + check_float ("frexp (0.0, &x) == 0.0", FUNC(frexp) (0.0, &x), 0.0, 0, 0, 0); + check_int ("frexp (0.0, &x) sets x to 0.0", x, 0.0, 0, 0, 0); + check_float ("frexp (-0, &x) == -0", FUNC(frexp) (minus_zero, &x), minus_zero, 0, 0, 0); + check_int ("frexp (-0, &x) sets x to 0.0", x, 0.0, 0, 0, 0); + + check_float ("frexp (12.8, &x) == 0.8", FUNC(frexp) (12.8L, &x), 0.8L, 0, 0, 0); + check_int ("frexp (12.8, &x) sets x to 4", x, 4, 0, 0, 0); + check_float ("frexp (-27.34, &x) == -0.854375", FUNC(frexp) (-27.34L, &x), -0.854375L, 0, 0, 0); + check_int ("frexp (-27.34, &x) sets x to 5", x, 5, 0, 0, 0); + + print_max_error ("frexp", 0, 0); +} + +#define gamma lgamma /* XXX scp XXX */ +#define gammaf lgammaf /* XXX scp XXX */ +static void +gamma_test (void) +{ + errno = 0; + FUNC(gamma) (1); + + if (errno == ENOSYS) + /* Function not implemented. */ + return; + feclearexcept (FE_ALL_EXCEPT); + + init_max_error (); + + signgam = 0; + check_float ("gamma (inf) == inf", FUNC(gamma) (plus_infty), plus_infty, 0, 0, 0); + signgam = 0; + check_float ("gamma (0) == inf plus division by zero exception", FUNC(gamma) (0), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + signgam = 0; + check_float ("gamma (-3) == inf plus division by zero exception", FUNC(gamma) (-3), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + signgam = 0; + check_float ("gamma (-inf) == inf", FUNC(gamma) (minus_infty), plus_infty, 0, 0, 0); + signgam = 0; + check_float ("gamma (NaN) == NaN", FUNC(gamma) (nan_value), nan_value, 0, 0, 0); + + signgam = 0; + check_float ("gamma (1) == 0", FUNC(gamma) (1), 0, 0, 0, 0); + check_int ("gamma (1) sets signgam to 1", signgam, 1, 0, 0, 0); + signgam = 0; + check_float ("gamma (3) == M_LN2l", FUNC(gamma) (3), M_LN2l, 0, 0, 0); + check_int ("gamma (3) sets signgam to 1", signgam, 1, 0, 0, 0); + + signgam = 0; + check_float ("gamma (0.5) == log(sqrt(pi))", FUNC(gamma) (0.5), M_LOG_SQRT_PIl, 0, 0, 0); + check_int ("gamma (0.5) sets signgam to 1", signgam, 1, 0, 0, 0); + signgam = 0; + check_float ("gamma (-0.5) == log(2*sqrt(pi))", FUNC(gamma) (-0.5), M_LOG_2_SQRT_PIl, DELTA1004, 0, 0); + check_int ("gamma (-0.5) sets signgam to -1", signgam, -1, 0, 0, 0); + + print_max_error ("gamma", DELTAgamma, 0); +} +#undef gamma /* XXX scp XXX */ +#undef gammaf /* XXX scp XXX */ + +static void +hypot_test (void) +{ + errno = 0; + FUNC(hypot) (0.7L, 12.4L); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("hypot (inf, 1) == inf plus sign of zero/inf not specified", FUNC(hypot) (plus_infty, 1), plus_infty, 0, 0, IGNORE_ZERO_INF_SIGN); + check_float ("hypot (-inf, 1) == inf plus sign of zero/inf not specified", FUNC(hypot) (minus_infty, 1), plus_infty, 0, 0, IGNORE_ZERO_INF_SIGN); + +#ifndef TEST_INLINE + check_float ("hypot (inf, NaN) == inf", FUNC(hypot) (plus_infty, nan_value), plus_infty, 0, 0, 0); + check_float ("hypot (-inf, NaN) == inf", FUNC(hypot) (minus_infty, nan_value), plus_infty, 0, 0, 0); + check_float ("hypot (NaN, inf) == inf", FUNC(hypot) (nan_value, plus_infty), plus_infty, 0, 0, 0); + check_float ("hypot (NaN, -inf) == inf", FUNC(hypot) (nan_value, minus_infty), plus_infty, 0, 0, 0); +#endif + + check_float ("hypot (NaN, NaN) == NaN", FUNC(hypot) (nan_value, nan_value), nan_value, 0, 0, 0); + + /* hypot (x,y) == hypot (+-x, +-y) */ + check_float ("hypot (0.7, 12.4) == 12.419742348374220601176836866763271", FUNC(hypot) (0.7L, 12.4L), 12.419742348374220601176836866763271L, DELTA1013, 0, 0); + check_float ("hypot (-0.7, 12.4) == 12.419742348374220601176836866763271", FUNC(hypot) (-0.7L, 12.4L), 12.419742348374220601176836866763271L, DELTA1014, 0, 0); + check_float ("hypot (0.7, -12.4) == 12.419742348374220601176836866763271", FUNC(hypot) (0.7L, -12.4L), 12.419742348374220601176836866763271L, DELTA1015, 0, 0); + check_float ("hypot (-0.7, -12.4) == 12.419742348374220601176836866763271", FUNC(hypot) (-0.7L, -12.4L), 12.419742348374220601176836866763271L, DELTA1016, 0, 0); + check_float ("hypot (12.4, 0.7) == 12.419742348374220601176836866763271", FUNC(hypot) (12.4L, 0.7L), 12.419742348374220601176836866763271L, DELTA1017, 0, 0); + check_float ("hypot (-12.4, 0.7) == 12.419742348374220601176836866763271", FUNC(hypot) (-12.4L, 0.7L), 12.419742348374220601176836866763271L, DELTA1018, 0, 0); + check_float ("hypot (12.4, -0.7) == 12.419742348374220601176836866763271", FUNC(hypot) (12.4L, -0.7L), 12.419742348374220601176836866763271L, DELTA1019, 0, 0); + check_float ("hypot (-12.4, -0.7) == 12.419742348374220601176836866763271", FUNC(hypot) (-12.4L, -0.7L), 12.419742348374220601176836866763271L, DELTA1020, 0, 0); + + /* hypot (x,0) == fabs (x) */ + check_float ("hypot (0.7, 0) == 0.7", FUNC(hypot) (0.7L, 0), 0.7L, 0, 0, 0); + check_float ("hypot (-0.7, 0) == 0.7", FUNC(hypot) (-0.7L, 0), 0.7L, 0, 0, 0); + check_float ("hypot (-5.7e7, 0) == 5.7e7", FUNC(hypot) (-5.7e7, 0), 5.7e7L, 0, 0, 0); + + check_float ("hypot (0.7, 1.2) == 1.3892443989449804508432547041028554", FUNC(hypot) (0.7L, 1.2L), 1.3892443989449804508432547041028554L, DELTA1024, 0, 0); + + print_max_error ("hypot", DELTAhypot, 0); +} + + +static void +ilogb_test (void) +{ + init_max_error (); + + check_int ("ilogb (1) == 0", FUNC(ilogb) (1), 0, 0, 0, 0); + check_int ("ilogb (e) == 1", FUNC(ilogb) (M_El), 1, 0, 0, 0); + check_int ("ilogb (1024) == 10", FUNC(ilogb) (1024), 10, 0, 0, 0); + check_int ("ilogb (-2000) == 10", FUNC(ilogb) (-2000), 10, 0, 0, 0); + + /* XXX We have a problem here: the standard does not tell us whether + exceptions are allowed/required. ignore them for now. */ + + check_int ("ilogb (0.0) == FP_ILOGB0 plus exceptions allowed", FUNC(ilogb) (0.0), FP_ILOGB0, 0, 0, EXCEPTIONS_OK); + check_int ("ilogb (NaN) == FP_ILOGBNAN plus exceptions allowed", FUNC(ilogb) (nan_value), FP_ILOGBNAN, 0, 0, EXCEPTIONS_OK); + check_int ("ilogb (inf) == INT_MAX plus exceptions allowed", FUNC(ilogb) (plus_infty), INT_MAX, 0, 0, EXCEPTIONS_OK); + check_int ("ilogb (-inf) == INT_MAX plus exceptions allowed", FUNC(ilogb) (minus_infty), INT_MAX, 0, 0, EXCEPTIONS_OK); + + print_max_error ("ilogb", 0, 0); +} + +static void +isfinite_test (void) +{ + init_max_error (); + + check_bool ("isfinite (0) == true", isfinite (0.0), 1, 0, 0, 0); + check_bool ("isfinite (-0) == true", isfinite (minus_zero), 1, 0, 0, 0); + check_bool ("isfinite (10) == true", isfinite (10.0), 1, 0, 0, 0); + check_bool ("isfinite (inf) == false", isfinite (plus_infty), 0, 0, 0, 0); + check_bool ("isfinite (-inf) == false", isfinite (minus_infty), 0, 0, 0, 0); + check_bool ("isfinite (NaN) == false", isfinite (nan_value), 0, 0, 0, 0); + + print_max_error ("isfinite", 0, 0); +} + +static void +isnormal_test (void) +{ + init_max_error (); + + check_bool ("isnormal (0) == false", isnormal (0.0), 0, 0, 0, 0); + check_bool ("isnormal (-0) == false", isnormal (minus_zero), 0, 0, 0, 0); + check_bool ("isnormal (10) == true", isnormal (10.0), 1, 0, 0, 0); + check_bool ("isnormal (inf) == false", isnormal (plus_infty), 0, 0, 0, 0); + check_bool ("isnormal (-inf) == false", isnormal (minus_infty), 0, 0, 0, 0); + check_bool ("isnormal (NaN) == false", isnormal (nan_value), 0, 0, 0, 0); + + print_max_error ("isnormal", 0, 0); +} + +static void +j0_test (void) +{ + FLOAT s, c; + errno = 0; + FUNC (sincos) (0, &s, &c); + if (errno == ENOSYS) + /* Required function not implemented. */ + return; + FUNC(j0) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + /* j0 is the Bessel function of the first kind of order 0 */ + check_float ("j0 (NaN) == NaN", FUNC(j0) (nan_value), nan_value, 0, 0, 0); + check_float ("j0 (inf) == 0", FUNC(j0) (plus_infty), 0, 0, 0, 0); + check_float ("j0 (-1.0) == 0.76519768655796655145", FUNC(j0) (-1.0), 0.76519768655796655145L, 0, 0, 0); + check_float ("j0 (0.0) == 1.0", FUNC(j0) (0.0), 1.0, 0, 0, 0); + check_float ("j0 (0.1) == 0.99750156206604003228", FUNC(j0) (0.1L), 0.99750156206604003228L, 0, 0, 0); + check_float ("j0 (0.7) == 0.88120088860740528084", FUNC(j0) (0.7L), 0.88120088860740528084L, 0, 0, 0); + check_float ("j0 (1.0) == 0.76519768655796655145", FUNC(j0) (1.0), 0.76519768655796655145L, 0, 0, 0); + check_float ("j0 (1.5) == 0.51182767173591812875", FUNC(j0) (1.5), 0.51182767173591812875L, 0, 0, 0); + check_float ("j0 (2.0) == 0.22389077914123566805", FUNC(j0) (2.0), 0.22389077914123566805L, DELTA1053, 0, 0); + check_float ("j0 (8.0) == 0.17165080713755390609", FUNC(j0) (8.0), 0.17165080713755390609L, DELTA1054, 0, 0); + check_float ("j0 (10.0) == -0.24593576445134833520", FUNC(j0) (10.0), -0.24593576445134833520L, DELTA1055, 0, 0); + + print_max_error ("j0", DELTAj0, 0); +} + + +static void +j1_test (void) +{ + FLOAT s, c; + errno = 0; + FUNC (sincos) (0, &s, &c); + if (errno == ENOSYS) + /* Required function not implemented. */ + return; + FUNC(j1) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + /* j1 is the Bessel function of the first kind of order 1 */ + + init_max_error (); + + check_float ("j1 (NaN) == NaN", FUNC(j1) (nan_value), nan_value, 0, 0, 0); + check_float ("j1 (inf) == 0", FUNC(j1) (plus_infty), 0, 0, 0, 0); + + check_float ("j1 (-1.0) == -0.44005058574493351596", FUNC(j1) (-1.0), -0.44005058574493351596L, 0, 0, 0); + check_float ("j1 (0.0) == 0.0", FUNC(j1) (0.0), 0.0, 0, 0, 0); + check_float ("j1 (0.1) == 0.049937526036241997556", FUNC(j1) (0.1L), 0.049937526036241997556L, 0, 0, 0); + check_float ("j1 (0.7) == 0.32899574154005894785", FUNC(j1) (0.7L), 0.32899574154005894785L, 0, 0, 0); + check_float ("j1 (1.0) == 0.44005058574493351596", FUNC(j1) (1.0), 0.44005058574493351596L, 0, 0, 0); + check_float ("j1 (1.5) == 0.55793650791009964199", FUNC(j1) (1.5), 0.55793650791009964199L, 0, 0, 0); + check_float ("j1 (2.0) == 0.57672480775687338720", FUNC(j1) (2.0), 0.57672480775687338720L, DELTA1064, 0, 0); + check_float ("j1 (8.0) == 0.23463634685391462438", FUNC(j1) (8.0), 0.23463634685391462438L, DELTA1065, 0, 0); + check_float ("j1 (10.0) == 0.043472746168861436670", FUNC(j1) (10.0), 0.043472746168861436670L, DELTA1066, 0, 0); + + print_max_error ("j1", DELTAj1, 0); +} + +static void +jn_test (void) +{ + FLOAT s, c; + errno = 0; + FUNC (sincos) (0, &s, &c); + if (errno == ENOSYS) + /* Required function not implemented. */ + return; + FUNC(jn) (1, 1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + /* jn is the Bessel function of the first kind of order n. */ + init_max_error (); + + /* jn (0, x) == j0 (x) */ + check_float ("jn (0, NaN) == NaN", FUNC(jn) (0, nan_value), nan_value, 0, 0, 0); + check_float ("jn (0, inf) == 0", FUNC(jn) (0, plus_infty), 0, 0, 0, 0); + check_float ("jn (0, -1.0) == 0.76519768655796655145", FUNC(jn) (0, -1.0), 0.76519768655796655145L, 0, 0, 0); + check_float ("jn (0, 0.0) == 1.0", FUNC(jn) (0, 0.0), 1.0, 0, 0, 0); + check_float ("jn (0, 0.1) == 0.99750156206604003228", FUNC(jn) (0, 0.1L), 0.99750156206604003228L, 0, 0, 0); + check_float ("jn (0, 0.7) == 0.88120088860740528084", FUNC(jn) (0, 0.7L), 0.88120088860740528084L, 0, 0, 0); + check_float ("jn (0, 1.0) == 0.76519768655796655145", FUNC(jn) (0, 1.0), 0.76519768655796655145L, 0, 0, 0); + check_float ("jn (0, 1.5) == 0.51182767173591812875", FUNC(jn) (0, 1.5), 0.51182767173591812875L, 0, 0, 0); + check_float ("jn (0, 2.0) == 0.22389077914123566805", FUNC(jn) (0, 2.0), 0.22389077914123566805L, DELTA1075, 0, 0); + check_float ("jn (0, 8.0) == 0.17165080713755390609", FUNC(jn) (0, 8.0), 0.17165080713755390609L, DELTA1076, 0, 0); + check_float ("jn (0, 10.0) == -0.24593576445134833520", FUNC(jn) (0, 10.0), -0.24593576445134833520L, DELTA1077, 0, 0); + + /* jn (1, x) == j1 (x) */ + check_float ("jn (1, NaN) == NaN", FUNC(jn) (1, nan_value), nan_value, 0, 0, 0); + check_float ("jn (1, inf) == 0", FUNC(jn) (1, plus_infty), 0, 0, 0, 0); + + check_float ("jn (1, -1.0) == -0.44005058574493351596", FUNC(jn) (1, -1.0), -0.44005058574493351596L, 0, 0, 0); + check_float ("jn (1, 0.0) == 0.0", FUNC(jn) (1, 0.0), 0.0, 0, 0, 0); + check_float ("jn (1, 0.1) == 0.049937526036241997556", FUNC(jn) (1, 0.1L), 0.049937526036241997556L, 0, 0, 0); + check_float ("jn (1, 0.7) == 0.32899574154005894785", FUNC(jn) (1, 0.7L), 0.32899574154005894785L, 0, 0, 0); + check_float ("jn (1, 1.0) == 0.44005058574493351596", FUNC(jn) (1, 1.0), 0.44005058574493351596L, 0, 0, 0); + check_float ("jn (1, 1.5) == 0.55793650791009964199", FUNC(jn) (1, 1.5), 0.55793650791009964199L, 0, 0, 0); + check_float ("jn (1, 2.0) == 0.57672480775687338720", FUNC(jn) (1, 2.0), 0.57672480775687338720L, DELTA1086, 0, 0); + check_float ("jn (1, 8.0) == 0.23463634685391462438", FUNC(jn) (1, 8.0), 0.23463634685391462438L, DELTA1087, 0, 0); + check_float ("jn (1, 10.0) == 0.043472746168861436670", FUNC(jn) (1, 10.0), 0.043472746168861436670L, DELTA1088, 0, 0); + + /* jn (3, x) */ + check_float ("jn (3, NaN) == NaN", FUNC(jn) (3, nan_value), nan_value, 0, 0, 0); + check_float ("jn (3, inf) == 0", FUNC(jn) (3, plus_infty), 0, 0, 0, 0); + + check_float ("jn (3, -1.0) == -0.019563353982668405919", FUNC(jn) (3, -1.0), -0.019563353982668405919L, DELTA1091, 0, 0); + check_float ("jn (3, 0.0) == 0.0", FUNC(jn) (3, 0.0), 0.0, 0, 0, 0); + check_float ("jn (3, 0.1) == 0.000020820315754756261429", FUNC(jn) (3, 0.1L), 0.000020820315754756261429L, DELTA1093, 0, 0); + check_float ("jn (3, 0.7) == 0.0069296548267508408077", FUNC(jn) (3, 0.7L), 0.0069296548267508408077L, DELTA1094, 0, 0); + check_float ("jn (3, 1.0) == 0.019563353982668405919", FUNC(jn) (3, 1.0), 0.019563353982668405919L, DELTA1095, 0, 0); + check_float ("jn (3, 2.0) == 0.12894324947440205110", FUNC(jn) (3, 2.0), 0.12894324947440205110L, DELTA1096, 0, 0); + check_float ("jn (3, 10.0) == 0.058379379305186812343", FUNC(jn) (3, 10.0), 0.058379379305186812343L, DELTA1097, 0, 0); + + /* jn (10, x) */ + check_float ("jn (10, NaN) == NaN", FUNC(jn) (10, nan_value), nan_value, 0, 0, 0); + check_float ("jn (10, inf) == 0", FUNC(jn) (10, plus_infty), 0, 0, 0, 0); + + check_float ("jn (10, -1.0) == 0.26306151236874532070e-9", FUNC(jn) (10, -1.0), 0.26306151236874532070e-9L, DELTA1100, 0, 0); + check_float ("jn (10, 0.0) == 0.0", FUNC(jn) (10, 0.0), 0.0, 0, 0, 0); + check_float ("jn (10, 0.1) == 0.26905328954342155795e-19", FUNC(jn) (10, 0.1L), 0.26905328954342155795e-19L, DELTA1102, 0, 0); + check_float ("jn (10, 0.7) == 0.75175911502153953928e-11", FUNC(jn) (10, 0.7L), 0.75175911502153953928e-11L, DELTA1103, 0, 0); + check_float ("jn (10, 1.0) == 0.26306151236874532070e-9", FUNC(jn) (10, 1.0), 0.26306151236874532070e-9L, DELTA1104, 0, 0); + check_float ("jn (10, 2.0) == 0.25153862827167367096e-6", FUNC(jn) (10, 2.0), 0.25153862827167367096e-6L, DELTA1105, 0, 0); + check_float ("jn (10, 10.0) == 0.20748610663335885770", FUNC(jn) (10, 10.0), 0.20748610663335885770L, DELTA1106, 0, 0); + + print_max_error ("jn", DELTAjn, 0); +} + + +static void +ldexp_test (void) +{ + check_float ("ldexp (0, 0) == 0", FUNC(ldexp) (0, 0), 0, 0, 0, 0); + check_float ("ldexp (-0, 0) == -0", FUNC(ldexp) (minus_zero, 0), minus_zero, 0, 0, 0); + + check_float ("ldexp (inf, 1) == inf", FUNC(ldexp) (plus_infty, 1), plus_infty, 0, 0, 0); + check_float ("ldexp (-inf, 1) == -inf", FUNC(ldexp) (minus_infty, 1), minus_infty, 0, 0, 0); + check_float ("ldexp (NaN, 1) == NaN", FUNC(ldexp) (nan_value, 1), nan_value, 0, 0, 0); + + check_float ("ldexp (0.8, 4) == 12.8", FUNC(ldexp) (0.8L, 4), 12.8L, 0, 0, 0); + check_float ("ldexp (-0.854375, 5) == -27.34", FUNC(ldexp) (-0.854375L, 5), -27.34L, 0, 0, 0); + + /* ldexp (x, 0) == x. */ + check_float ("ldexp (1.0, 0) == 1.0", FUNC(ldexp) (1.0L, 0L), 1.0L, 0, 0, 0); +} + +static void +lgamma_test (void) +{ + errno = 0; + FUNC(lgamma) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + feclearexcept (FE_ALL_EXCEPT); + + init_max_error (); + + signgam = 0; + check_float ("lgamma (inf) == inf", FUNC(lgamma) (plus_infty), plus_infty, 0, 0, 0); + signgam = 0; + check_float ("lgamma (0) == inf plus division by zero exception", FUNC(lgamma) (0), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + signgam = 0; + check_float ("lgamma (NaN) == NaN", FUNC(lgamma) (nan_value), nan_value, 0, 0, 0); + + /* lgamma (x) == +inf plus divide by zero exception for integer x <= 0. */ + signgam = 0; + check_float ("lgamma (-3) == inf plus division by zero exception", FUNC(lgamma) (-3), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + signgam = 0; + check_float ("lgamma (-inf) == inf", FUNC(lgamma) (minus_infty), plus_infty, 0, 0, 0); + + signgam = 0; + check_float ("lgamma (1) == 0", FUNC(lgamma) (1), 0, 0, 0, 0); + check_int ("lgamma (1) sets signgam to 1", signgam, 1, 0, 0, 0); + + signgam = 0; + check_float ("lgamma (3) == M_LN2l", FUNC(lgamma) (3), M_LN2l, 0, 0, 0); + check_int ("lgamma (3) sets signgam to 1", signgam, 1, 0, 0, 0); + + signgam = 0; + check_float ("lgamma (0.5) == log(sqrt(pi))", FUNC(lgamma) (0.5), M_LOG_SQRT_PIl, 0, 0, 0); + check_int ("lgamma (0.5) sets signgam to 1", signgam, 1, 0, 0, 0); + signgam = 0; + check_float ("lgamma (-0.5) == log(2*sqrt(pi))", FUNC(lgamma) (-0.5), M_LOG_2_SQRT_PIl, DELTA1126, 0, 0); + check_int ("lgamma (-0.5) sets signgam to -1", signgam, -1, 0, 0, 0); + signgam = 0; + check_float ("lgamma (0.7) == 0.26086724653166651439", FUNC(lgamma) (0.7L), 0.26086724653166651439L, DELTA1128, 0, 0); + check_int ("lgamma (0.7) sets signgam to 1", signgam, 1, 0, 0, 0); + signgam = 0; + check_float ("lgamma (1.2) == -0.853740900033158497197e-1", FUNC(lgamma) (1.2L), -0.853740900033158497197e-1L, DELTA1130, 0, 0); + check_int ("lgamma (1.2) sets signgam to 1", signgam, 1, 0, 0, 0); + + print_max_error ("lgamma", DELTAlgamma, 0); +} + +static void +lrint_test (void) +{ + /* XXX this test is incomplete. We need to have a way to specifiy + the rounding method and test the critical cases. So far, only + unproblematic numbers are tested. */ + + init_max_error (); + + check_long ("lrint (0.0) == 0", FUNC(lrint) (0.0), 0, 0, 0, 0); + check_long ("lrint (-0) == 0", FUNC(lrint) (minus_zero), 0, 0, 0, 0); + check_long ("lrint (0.2) == 0", FUNC(lrint) (0.2L), 0, 0, 0, 0); + check_long ("lrint (-0.2) == 0", FUNC(lrint) (-0.2L), 0, 0, 0, 0); + + check_long ("lrint (1.4) == 1", FUNC(lrint) (1.4L), 1, 0, 0, 0); + check_long ("lrint (-1.4) == -1", FUNC(lrint) (-1.4L), -1, 0, 0, 0); + + check_long ("lrint (8388600.3) == 8388600", FUNC(lrint) (8388600.3L), 8388600, 0, 0, 0); + check_long ("lrint (-8388600.3) == -8388600", FUNC(lrint) (-8388600.3L), -8388600, 0, 0, 0); + + print_max_error ("lrint", 0, 0); +} + +static void +llrint_test (void) +{ + /* XXX this test is incomplete. We need to have a way to specifiy + the rounding method and test the critical cases. So far, only + unproblematic numbers are tested. */ + + init_max_error (); + + check_longlong ("llrint (0.0) == 0", FUNC(llrint) (0.0), 0, 0, 0, 0); + check_longlong ("llrint (-0) == 0", FUNC(llrint) (minus_zero), 0, 0, 0, 0); + check_longlong ("llrint (0.2) == 0", FUNC(llrint) (0.2L), 0, 0, 0, 0); + check_longlong ("llrint (-0.2) == 0", FUNC(llrint) (-0.2L), 0, 0, 0, 0); + + check_longlong ("llrint (1.4) == 1", FUNC(llrint) (1.4L), 1, 0, 0, 0); + check_longlong ("llrint (-1.4) == -1", FUNC(llrint) (-1.4L), -1, 0, 0, 0); + + check_longlong ("llrint (8388600.3) == 8388600", FUNC(llrint) (8388600.3L), 8388600, 0, 0, 0); + check_longlong ("llrint (-8388600.3) == -8388600", FUNC(llrint) (-8388600.3L), -8388600, 0, 0, 0); + + /* Test boundary conditions. */ + /* 0x1FFFFF */ + check_longlong ("llrint (2097151.0) == 2097151LL", FUNC(llrint) (2097151.0), 2097151LL, 0, 0, 0); + /* 0x800000 */ + check_longlong ("llrint (8388608.0) == 8388608LL", FUNC(llrint) (8388608.0), 8388608LL, 0, 0, 0); + /* 0x1000000 */ + check_longlong ("llrint (16777216.0) == 16777216LL", FUNC(llrint) (16777216.0), 16777216LL, 0, 0, 0); + /* 0x20000000000 */ + check_longlong ("llrint (2199023255552.0) == 2199023255552LL", FUNC(llrint) (2199023255552.0), 2199023255552LL, 0, 0, 0); + /* 0x40000000000 */ + check_longlong ("llrint (4398046511104.0) == 4398046511104LL", FUNC(llrint) (4398046511104.0), 4398046511104LL, 0, 0, 0); + /* 0x10000000000000 */ + check_longlong ("llrint (4503599627370496.0) == 4503599627370496LL", FUNC(llrint) (4503599627370496.0), 4503599627370496LL, 0, 0, 0); + /* 0x10000080000000 */ + check_longlong ("llrint (4503601774854144.0) == 4503601774854144LL", FUNC(llrint) (4503601774854144.0), 4503601774854144LL, 0, 0, 0); + /* 0x20000000000000 */ + check_longlong ("llrint (9007199254740992.0) == 9007199254740992LL", FUNC(llrint) (9007199254740992.0), 9007199254740992LL, 0, 0, 0); + /* 0x80000000000000 */ + check_longlong ("llrint (36028797018963968.0) == 36028797018963968LL", FUNC(llrint) (36028797018963968.0), 36028797018963968LL, 0, 0, 0); + /* 0x100000000000000 */ + check_longlong ("llrint (72057594037927936.0) == 72057594037927936LL", FUNC(llrint) (72057594037927936.0), 72057594037927936LL, 0, 0, 0); + + print_max_error ("llrint", 0, 0); +} + +static void +log_test (void) +{ + errno = 0; + FUNC(log) (1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + init_max_error (); + + check_float ("log (0) == -inf plus division by zero exception", FUNC(log) (0), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("log (-0) == -inf plus division by zero exception", FUNC(log) (minus_zero), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + check_float ("log (1) == 0", FUNC(log) (1), 0, 0, 0, 0); + + check_float ("log (-1) == NaN plus invalid exception", FUNC(log) (-1), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("log (inf) == inf", FUNC(log) (plus_infty), plus_infty, 0, 0, 0); + + check_float ("log (e) == 1", FUNC(log) (M_El), 1, DELTA1163, 0, 0); + check_float ("log (1.0 / M_El) == -1", FUNC(log) (1.0 / M_El), -1, DELTA1164, 0, 0); + check_float ("log (2) == M_LN2l", FUNC(log) (2), M_LN2l, 0, 0, 0); + check_float ("log (10) == M_LN10l", FUNC(log) (10), M_LN10l, 0, 0, 0); + check_float ("log (0.7) == -0.35667494393873237891263871124118447", FUNC(log) (0.7L), -0.35667494393873237891263871124118447L, DELTA1167, 0, 0); + + print_max_error ("log", DELTAlog, 0); +} + + +static void +log10_test (void) +{ + errno = 0; + FUNC(log10) (1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("log10 (0) == -inf plus division by zero exception", FUNC(log10) (0), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("log10 (-0) == -inf plus division by zero exception", FUNC(log10) (minus_zero), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + check_float ("log10 (1) == 0", FUNC(log10) (1), 0, 0, 0, 0); + + /* log10 (x) == NaN plus invalid exception if x < 0. */ + check_float ("log10 (-1) == NaN plus invalid exception", FUNC(log10) (-1), nan_value, 0, 0, INVALID_EXCEPTION); + + check_float ("log10 (inf) == inf", FUNC(log10) (plus_infty), plus_infty, 0, 0, 0); + check_float ("log10 (NaN) == NaN", FUNC(log10) (nan_value), nan_value, 0, 0, 0); + + check_float ("log10 (0.1) == -1", FUNC(log10) (0.1L), -1, 0, 0, 0); + check_float ("log10 (10.0) == 1", FUNC(log10) (10.0), 1, 0, 0, 0); + check_float ("log10 (100.0) == 2", FUNC(log10) (100.0), 2, 0, 0, 0); + check_float ("log10 (10000.0) == 4", FUNC(log10) (10000.0), 4, 0, 0, 0); + check_float ("log10 (e) == log10(e)", FUNC(log10) (M_El), M_LOG10El, DELTA1178, 0, 0); + check_float ("log10 (0.7) == -0.15490195998574316929", FUNC(log10) (0.7L), -0.15490195998574316929L, DELTA1179, 0, 0); + + print_max_error ("log10", DELTAlog10, 0); +} + + +static void +log1p_test (void) +{ + errno = 0; + FUNC(log1p) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("log1p (0) == 0", FUNC(log1p) (0), 0, 0, 0, 0); + check_float ("log1p (-0) == -0", FUNC(log1p) (minus_zero), minus_zero, 0, 0, 0); + + check_float ("log1p (-1) == -inf plus division by zero exception", FUNC(log1p) (-1), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("log1p (-2) == NaN plus invalid exception", FUNC(log1p) (-2), nan_value, 0, 0, INVALID_EXCEPTION); + + check_float ("log1p (inf) == inf", FUNC(log1p) (plus_infty), plus_infty, 0, 0, 0); + check_float ("log1p (NaN) == NaN", FUNC(log1p) (nan_value), nan_value, 0, 0, 0); + + check_float ("log1p (M_El - 1.0) == 1", FUNC(log1p) (M_El - 1.0), 1, DELTA1186, 0, 0); + + check_float ("log1p (-0.3) == -0.35667494393873237891263871124118447", FUNC(log1p) (-0.3L), -0.35667494393873237891263871124118447L, DELTA1187, 0, 0); + + print_max_error ("log1p", DELTAlog1p, 0); +} + + +static void +log2_test (void) +{ + errno = 0; + FUNC(log2) (1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("log2 (0) == -inf plus division by zero exception", FUNC(log2) (0), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("log2 (-0) == -inf plus division by zero exception", FUNC(log2) (minus_zero), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + check_float ("log2 (1) == 0", FUNC(log2) (1), 0, 0, 0, 0); + + check_float ("log2 (-1) == NaN plus invalid exception", FUNC(log2) (-1), nan_value, 0, 0, INVALID_EXCEPTION); + + check_float ("log2 (inf) == inf", FUNC(log2) (plus_infty), plus_infty, 0, 0, 0); + check_float ("log2 (NaN) == NaN", FUNC(log2) (nan_value), nan_value, 0, 0, 0); + + check_float ("log2 (e) == M_LOG2El", FUNC(log2) (M_El), M_LOG2El, 0, 0, 0); + check_float ("log2 (2.0) == 1", FUNC(log2) (2.0), 1, 0, 0, 0); + check_float ("log2 (16.0) == 4", FUNC(log2) (16.0), 4, 0, 0, 0); + check_float ("log2 (256.0) == 8", FUNC(log2) (256.0), 8, 0, 0, 0); + check_float ("log2 (0.7) == -0.51457317282975824043", FUNC(log2) (0.7L), -0.51457317282975824043L, DELTA1198, 0, 0); + + print_max_error ("log2", DELTAlog2, 0); +} + + +static void +logb_test (void) +{ + init_max_error (); + + check_float ("logb (inf) == inf", FUNC(logb) (plus_infty), plus_infty, 0, 0, 0); + check_float ("logb (-inf) == inf", FUNC(logb) (minus_infty), plus_infty, 0, 0, 0); + + check_float ("logb (0) == -inf plus division by zero exception", FUNC(logb) (0), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + check_float ("logb (-0) == -inf plus division by zero exception", FUNC(logb) (minus_zero), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("logb (NaN) == NaN", FUNC(logb) (nan_value), nan_value, 0, 0, 0); + + check_float ("logb (1) == 0", FUNC(logb) (1), 0, 0, 0, 0); + check_float ("logb (e) == 1", FUNC(logb) (M_El), 1, 0, 0, 0); + check_float ("logb (1024) == 10", FUNC(logb) (1024), 10, 0, 0, 0); + check_float ("logb (-2000) == 10", FUNC(logb) (-2000), 10, 0, 0, 0); + + print_max_error ("logb", 0, 0); +} + +static void +lround_test (void) +{ + init_max_error (); + + check_long ("lround (0) == 0", FUNC(lround) (0), 0, 0, 0, 0); + check_long ("lround (-0) == 0", FUNC(lround) (minus_zero), 0, 0, 0, 0); + check_long ("lround (0.2) == 0.0", FUNC(lround) (0.2L), 0.0, 0, 0, 0); + check_long ("lround (-0.2) == 0", FUNC(lround) (-0.2L), 0, 0, 0, 0); + check_long ("lround (0.5) == 1", FUNC(lround) (0.5), 1, 0, 0, 0); + check_long ("lround (-0.5) == -1", FUNC(lround) (-0.5), -1, 0, 0, 0); + check_long ("lround (0.8) == 1", FUNC(lround) (0.8L), 1, 0, 0, 0); + check_long ("lround (-0.8) == -1", FUNC(lround) (-0.8L), -1, 0, 0, 0); + check_long ("lround (1.5) == 2", FUNC(lround) (1.5), 2, 0, 0, 0); + check_long ("lround (-1.5) == -2", FUNC(lround) (-1.5), -2, 0, 0, 0); + check_long ("lround (22514.5) == 22515", FUNC(lround) (22514.5), 22515, 0, 0, 0); + check_long ("lround (-22514.5) == -22515", FUNC(lround) (-22514.5), -22515, 0, 0, 0); +#ifndef TEST_FLOAT + check_long ("lround (2097152.5) == 2097153", FUNC(lround) (2097152.5), 2097153, 0, 0, 0); + check_long ("lround (-2097152.5) == -2097153", FUNC(lround) (-2097152.5), -2097153, 0, 0, 0); +#endif + print_max_error ("lround", 0, 0); +} + + +static void +llround_test (void) +{ + init_max_error (); + + check_longlong ("llround (0) == 0", FUNC(llround) (0), 0, 0, 0, 0); + check_longlong ("llround (-0) == 0", FUNC(llround) (minus_zero), 0, 0, 0, 0); + check_longlong ("llround (0.2) == 0.0", FUNC(llround) (0.2L), 0.0, 0, 0, 0); + check_longlong ("llround (-0.2) == 0", FUNC(llround) (-0.2L), 0, 0, 0, 0); + check_longlong ("llround (0.5) == 1", FUNC(llround) (0.5), 1, 0, 0, 0); + check_longlong ("llround (-0.5) == -1", FUNC(llround) (-0.5), -1, 0, 0, 0); + check_longlong ("llround (0.8) == 1", FUNC(llround) (0.8L), 1, 0, 0, 0); + check_longlong ("llround (-0.8) == -1", FUNC(llround) (-0.8L), -1, 0, 0, 0); + check_longlong ("llround (1.5) == 2", FUNC(llround) (1.5), 2, 0, 0, 0); + check_longlong ("llround (-1.5) == -2", FUNC(llround) (-1.5), -2, 0, 0, 0); + check_longlong ("llround (22514.5) == 22515", FUNC(llround) (22514.5), 22515, 0, 0, 0); + check_longlong ("llround (-22514.5) == -22515", FUNC(llround) (-22514.5), -22515, 0, 0, 0); +#ifndef TEST_FLOAT + check_longlong ("llround (2097152.5) == 2097153", FUNC(llround) (2097152.5), 2097153, 0, 0, 0); + check_longlong ("llround (-2097152.5) == -2097153", FUNC(llround) (-2097152.5), -2097153, 0, 0, 0); + check_longlong ("llround (34359738368.5) == 34359738369ll", FUNC(llround) (34359738368.5), 34359738369ll, 0, 0, 0); + check_longlong ("llround (-34359738368.5) == -34359738369ll", FUNC(llround) (-34359738368.5), -34359738369ll, 0, 0, 0); +#endif + + /* Test boundary conditions. */ + /* 0x1FFFFF */ + check_longlong ("llround (2097151.0) == 2097151LL", FUNC(llround) (2097151.0), 2097151LL, 0, 0, 0); + /* 0x800000 */ + check_longlong ("llround (8388608.0) == 8388608LL", FUNC(llround) (8388608.0), 8388608LL, 0, 0, 0); + /* 0x1000000 */ + check_longlong ("llround (16777216.0) == 16777216LL", FUNC(llround) (16777216.0), 16777216LL, 0, 0, 0); + /* 0x20000000000 */ + check_longlong ("llround (2199023255552.0) == 2199023255552LL", FUNC(llround) (2199023255552.0), 2199023255552LL, 0, 0, 0); + /* 0x40000000000 */ + check_longlong ("llround (4398046511104.0) == 4398046511104LL", FUNC(llround) (4398046511104.0), 4398046511104LL, 0, 0, 0); + /* 0x10000000000000 */ + check_longlong ("llround (4503599627370496.0) == 4503599627370496LL", FUNC(llround) (4503599627370496.0), 4503599627370496LL, 0, 0, 0); + /* 0x10000080000000 */ + check_longlong ("llrint (4503601774854144.0) == 4503601774854144LL", FUNC(llrint) (4503601774854144.0), 4503601774854144LL, 0, 0, 0); + /* 0x20000000000000 */ + check_longlong ("llround (9007199254740992.0) == 9007199254740992LL", FUNC(llround) (9007199254740992.0), 9007199254740992LL, 0, 0, 0); + /* 0x80000000000000 */ + check_longlong ("llround (36028797018963968.0) == 36028797018963968LL", FUNC(llround) (36028797018963968.0), 36028797018963968LL, 0, 0, 0); + /* 0x100000000000000 */ + check_longlong ("llround (72057594037927936.0) == 72057594037927936LL", FUNC(llround) (72057594037927936.0), 72057594037927936LL, 0, 0, 0); + +#ifndef TEST_FLOAT + /* 0x100000000 */ + check_longlong ("llround (4294967295.5) == 4294967296LL", FUNC(llround) (4294967295.5), 4294967296LL, 0, 0, 0); + /* 0x200000000 */ + check_longlong ("llround (8589934591.5) == 8589934592LL", FUNC(llround) (8589934591.5), 8589934592LL, 0, 0, 0); +#endif + + print_max_error ("llround", 0, 0); +} + +static void +modf_test (void) +{ + FLOAT x; + + init_max_error (); + + check_float ("modf (inf, &x) == 0", FUNC(modf) (plus_infty, &x), 0, 0, 0, 0); + check_float ("modf (inf, &x) sets x to plus_infty", x, plus_infty, 0, 0, 0); + check_float ("modf (-inf, &x) == -0", FUNC(modf) (minus_infty, &x), minus_zero, 0, 0, 0); + check_float ("modf (-inf, &x) sets x to minus_infty", x, minus_infty, 0, 0, 0); + check_float ("modf (NaN, &x) == NaN", FUNC(modf) (nan_value, &x), nan_value, 0, 0, 0); + check_float ("modf (NaN, &x) sets x to nan_value", x, nan_value, 0, 0, 0); + check_float ("modf (0, &x) == 0", FUNC(modf) (0, &x), 0, 0, 0, 0); + check_float ("modf (0, &x) sets x to 0", x, 0, 0, 0, 0); + check_float ("modf (1.5, &x) == 0.5", FUNC(modf) (1.5, &x), 0.5, 0, 0, 0); + check_float ("modf (1.5, &x) sets x to 1", x, 1, 0, 0, 0); + check_float ("modf (2.5, &x) == 0.5", FUNC(modf) (2.5, &x), 0.5, 0, 0, 0); + check_float ("modf (2.5, &x) sets x to 2", x, 2, 0, 0, 0); + check_float ("modf (-2.5, &x) == -0.5", FUNC(modf) (-2.5, &x), -0.5, 0, 0, 0); + check_float ("modf (-2.5, &x) sets x to -2", x, -2, 0, 0, 0); + check_float ("modf (20, &x) == 0", FUNC(modf) (20, &x), 0, 0, 0, 0); + check_float ("modf (20, &x) sets x to 20", x, 20, 0, 0, 0); + check_float ("modf (21, &x) == 0", FUNC(modf) (21, &x), 0, 0, 0, 0); + check_float ("modf (21, &x) sets x to 21", x, 21, 0, 0, 0); + check_float ("modf (89.5, &x) == 0.5", FUNC(modf) (89.5, &x), 0.5, 0, 0, 0); + check_float ("modf (89.5, &x) sets x to 89", x, 89, 0, 0, 0); + + print_max_error ("modf", 0, 0); +} + +static void +nearbyint_test (void) +{ + init_max_error (); + + check_float ("nearbyint (0.0) == 0.0", FUNC(nearbyint) (0.0), 0.0, 0, 0, 0); + check_float ("nearbyint (-0) == -0", FUNC(nearbyint) (minus_zero), minus_zero, 0, 0, 0); + check_float ("nearbyint (inf) == inf", FUNC(nearbyint) (plus_infty), plus_infty, 0, 0, 0); + check_float ("nearbyint (-inf) == -inf", FUNC(nearbyint) (minus_infty), minus_infty, 0, 0, 0); + check_float ("nearbyint (NaN) == NaN", FUNC(nearbyint) (nan_value), nan_value, 0, 0, 0); + + /* Default rounding mode is round to nearest. */ + check_float ("nearbyint (0.5) == 0.0", FUNC(nearbyint) (0.5), 0.0, 0, 0, 0); + check_float ("nearbyint (1.5) == 2.0", FUNC(nearbyint) (1.5), 2.0, 0, 0, 0); + check_float ("nearbyint (-0.5) == -0", FUNC(nearbyint) (-0.5), minus_zero, 0, 0, 0); + check_float ("nearbyint (-1.5) == -2.0", FUNC(nearbyint) (-1.5), -2.0, 0, 0, 0); + + print_max_error ("nearbyint", 0, 0); +} + +static void +nextafter_test (void) +{ + + init_max_error (); + + check_float ("nextafter (0, 0) == 0", FUNC(nextafter) (0, 0), 0, 0, 0, 0); + check_float ("nextafter (-0, 0) == 0", FUNC(nextafter) (minus_zero, 0), 0, 0, 0, 0); + check_float ("nextafter (0, -0) == -0", FUNC(nextafter) (0, minus_zero), minus_zero, 0, 0, 0); + check_float ("nextafter (-0, -0) == -0", FUNC(nextafter) (minus_zero, minus_zero), minus_zero, 0, 0, 0); + + check_float ("nextafter (9, 9) == 9", FUNC(nextafter) (9, 9), 9, 0, 0, 0); + check_float ("nextafter (-9, -9) == -9", FUNC(nextafter) (-9, -9), -9, 0, 0, 0); + check_float ("nextafter (inf, inf) == inf", FUNC(nextafter) (plus_infty, plus_infty), plus_infty, 0, 0, 0); + check_float ("nextafter (-inf, -inf) == -inf", FUNC(nextafter) (minus_infty, minus_infty), minus_infty, 0, 0, 0); + + check_float ("nextafter (NaN, 1.1) == NaN", FUNC(nextafter) (nan_value, 1.1L), nan_value, 0, 0, 0); + check_float ("nextafter (1.1, NaN) == NaN", FUNC(nextafter) (1.1L, nan_value), nan_value, 0, 0, 0); + check_float ("nextafter (NaN, NaN) == NaN", FUNC(nextafter) (nan_value, nan_value), nan_value, 0, 0, 0); + + /* XXX We need the hexadecimal FP number representation here for further + tests. */ + + print_max_error ("nextafter", 0, 0); +} + + +#if 0 /* XXX scp XXX */ +static void +nexttoward_test (void) +{ + init_max_error (); + check_float ("nexttoward (0, 0) == 0", FUNC(nexttoward) (0, 0), 0, 0, 0, 0); + check_float ("nexttoward (-0, 0) == 0", FUNC(nexttoward) (minus_zero, 0), 0, 0, 0, 0); + check_float ("nexttoward (0, -0) == -0", FUNC(nexttoward) (0, minus_zero), minus_zero, 0, 0, 0); + check_float ("nexttoward (-0, -0) == -0", FUNC(nexttoward) (minus_zero, minus_zero), minus_zero, 0, 0, 0); + + check_float ("nexttoward (9, 9) == 9", FUNC(nexttoward) (9, 9), 9, 0, 0, 0); + check_float ("nexttoward (-9, -9) == -9", FUNC(nexttoward) (-9, -9), -9, 0, 0, 0); + check_float ("nexttoward (inf, inf) == inf", FUNC(nexttoward) (plus_infty, plus_infty), plus_infty, 0, 0, 0); + check_float ("nexttoward (-inf, -inf) == -inf", FUNC(nexttoward) (minus_infty, minus_infty), minus_infty, 0, 0, 0); + + check_float ("nexttoward (NaN, 1.1) == NaN", FUNC(nexttoward) (nan_value, 1.1L), nan_value, 0, 0, 0); + check_float ("nexttoward (1.1, NaN) == NaN", FUNC(nexttoward) (1.1L, nan_value), nan_value, 0, 0, 0); + check_float ("nexttoward (NaN, NaN) == NaN", FUNC(nexttoward) (nan_value, nan_value), nan_value, 0, 0, 0); + + /* XXX We need the hexadecimal FP number representation here for further + tests. */ + + print_max_error ("nexttoward", 0, 0); +} +#endif + + +static void +pow_test (void) +{ + + errno = 0; + FUNC(pow) (0, 0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("pow (0, 0) == 1", FUNC(pow) (0, 0), 1, 0, 0, 0); + check_float ("pow (0, -0) == 1", FUNC(pow) (0, minus_zero), 1, 0, 0, 0); + check_float ("pow (-0, 0) == 1", FUNC(pow) (minus_zero, 0), 1, 0, 0, 0); + check_float ("pow (-0, -0) == 1", FUNC(pow) (minus_zero, minus_zero), 1, 0, 0, 0); + + check_float ("pow (10, 0) == 1", FUNC(pow) (10, 0), 1, 0, 0, 0); + check_float ("pow (10, -0) == 1", FUNC(pow) (10, minus_zero), 1, 0, 0, 0); + check_float ("pow (-10, 0) == 1", FUNC(pow) (-10, 0), 1, 0, 0, 0); + check_float ("pow (-10, -0) == 1", FUNC(pow) (-10, minus_zero), 1, 0, 0, 0); + + check_float ("pow (NaN, 0) == 1", FUNC(pow) (nan_value, 0), 1, 0, 0, 0); + check_float ("pow (NaN, -0) == 1", FUNC(pow) (nan_value, minus_zero), 1, 0, 0, 0); + + +#ifndef TEST_INLINE + check_float ("pow (1.1, inf) == inf", FUNC(pow) (1.1L, plus_infty), plus_infty, 0, 0, 0); + check_float ("pow (inf, inf) == inf", FUNC(pow) (plus_infty, plus_infty), plus_infty, 0, 0, 0); + check_float ("pow (-1.1, inf) == inf", FUNC(pow) (-1.1L, plus_infty), plus_infty, 0, 0, 0); + check_float ("pow (-inf, inf) == inf", FUNC(pow) (minus_infty, plus_infty), plus_infty, 0, 0, 0); + + check_float ("pow (0.9, inf) == 0", FUNC(pow) (0.9L, plus_infty), 0, 0, 0, 0); + check_float ("pow (1e-7, inf) == 0", FUNC(pow) (1e-7L, plus_infty), 0, 0, 0, 0); + check_float ("pow (-0.9, inf) == 0", FUNC(pow) (-0.9L, plus_infty), 0, 0, 0, 0); + check_float ("pow (-1e-7, inf) == 0", FUNC(pow) (-1e-7L, plus_infty), 0, 0, 0, 0); + + check_float ("pow (1.1, -inf) == 0", FUNC(pow) (1.1L, minus_infty), 0, 0, 0, 0); + check_float ("pow (inf, -inf) == 0", FUNC(pow) (plus_infty, minus_infty), 0, 0, 0, 0); + check_float ("pow (-1.1, -inf) == 0", FUNC(pow) (-1.1L, minus_infty), 0, 0, 0, 0); + check_float ("pow (-inf, -inf) == 0", FUNC(pow) (minus_infty, minus_infty), 0, 0, 0, 0); + + check_float ("pow (0.9, -inf) == inf", FUNC(pow) (0.9L, minus_infty), plus_infty, 0, 0, 0); + check_float ("pow (1e-7, -inf) == inf", FUNC(pow) (1e-7L, minus_infty), plus_infty, 0, 0, 0); + check_float ("pow (-0.9, -inf) == inf", FUNC(pow) (-0.9L, minus_infty), plus_infty, 0, 0, 0); + check_float ("pow (-1e-7, -inf) == inf", FUNC(pow) (-1e-7L, minus_infty), plus_infty, 0, 0, 0); + + check_float ("pow (inf, 1e-7) == inf", FUNC(pow) (plus_infty, 1e-7L), plus_infty, 0, 0, 0); + check_float ("pow (inf, 1) == inf", FUNC(pow) (plus_infty, 1), plus_infty, 0, 0, 0); + check_float ("pow (inf, 1e7) == inf", FUNC(pow) (plus_infty, 1e7L), plus_infty, 0, 0, 0); + + check_float ("pow (inf, -1e-7) == 0", FUNC(pow) (plus_infty, -1e-7L), 0, 0, 0, 0); + check_float ("pow (inf, -1) == 0", FUNC(pow) (plus_infty, -1), 0, 0, 0, 0); + check_float ("pow (inf, -1e7) == 0", FUNC(pow) (plus_infty, -1e7L), 0, 0, 0, 0); + + check_float ("pow (-inf, 1) == -inf", FUNC(pow) (minus_infty, 1), minus_infty, 0, 0, 0); + check_float ("pow (-inf, 11) == -inf", FUNC(pow) (minus_infty, 11), minus_infty, 0, 0, 0); + check_float ("pow (-inf, 1001) == -inf", FUNC(pow) (minus_infty, 1001), minus_infty, 0, 0, 0); + + check_float ("pow (-inf, 2) == inf", FUNC(pow) (minus_infty, 2), plus_infty, 0, 0, 0); + check_float ("pow (-inf, 12) == inf", FUNC(pow) (minus_infty, 12), plus_infty, 0, 0, 0); + check_float ("pow (-inf, 1002) == inf", FUNC(pow) (minus_infty, 1002), plus_infty, 0, 0, 0); + check_float ("pow (-inf, 0.1) == inf", FUNC(pow) (minus_infty, 0.1L), plus_infty, 0, 0, 0); + check_float ("pow (-inf, 1.1) == inf", FUNC(pow) (minus_infty, 1.1L), plus_infty, 0, 0, 0); + check_float ("pow (-inf, 11.1) == inf", FUNC(pow) (minus_infty, 11.1L), plus_infty, 0, 0, 0); + check_float ("pow (-inf, 1001.1) == inf", FUNC(pow) (minus_infty, 1001.1L), plus_infty, 0, 0, 0); + + check_float ("pow (-inf, -1) == -0", FUNC(pow) (minus_infty, -1), minus_zero, 0, 0, 0); + check_float ("pow (-inf, -11) == -0", FUNC(pow) (minus_infty, -11), minus_zero, 0, 0, 0); + check_float ("pow (-inf, -1001) == -0", FUNC(pow) (minus_infty, -1001), minus_zero, 0, 0, 0); + + check_float ("pow (-inf, -2) == 0", FUNC(pow) (minus_infty, -2), 0, 0, 0, 0); + check_float ("pow (-inf, -12) == 0", FUNC(pow) (minus_infty, -12), 0, 0, 0, 0); + check_float ("pow (-inf, -1002) == 0", FUNC(pow) (minus_infty, -1002), 0, 0, 0, 0); + check_float ("pow (-inf, -0.1) == 0", FUNC(pow) (minus_infty, -0.1L), 0, 0, 0, 0); + check_float ("pow (-inf, -1.1) == 0", FUNC(pow) (minus_infty, -1.1L), 0, 0, 0, 0); + check_float ("pow (-inf, -11.1) == 0", FUNC(pow) (minus_infty, -11.1L), 0, 0, 0, 0); + check_float ("pow (-inf, -1001.1) == 0", FUNC(pow) (minus_infty, -1001.1L), 0, 0, 0, 0); +#endif + + check_float ("pow (NaN, NaN) == NaN", FUNC(pow) (nan_value, nan_value), nan_value, 0, 0, 0); + check_float ("pow (0, NaN) == NaN", FUNC(pow) (0, nan_value), nan_value, 0, 0, 0); + check_float ("pow (1, NaN) == 1", FUNC(pow) (1, nan_value), 1, 0, 0, 0); + check_float ("pow (-1, NaN) == NaN", FUNC(pow) (-1, nan_value), nan_value, 0, 0, 0); + check_float ("pow (NaN, 1) == NaN", FUNC(pow) (nan_value, 1), nan_value, 0, 0, 0); + check_float ("pow (NaN, -1) == NaN", FUNC(pow) (nan_value, -1), nan_value, 0, 0, 0); + + /* pow (x, NaN) == NaN. */ + check_float ("pow (3.0, NaN) == NaN", FUNC(pow) (3.0, nan_value), nan_value, 0, 0, 0); + + check_float ("pow (1, inf) == 1", FUNC(pow) (1, plus_infty), 1, 0, 0, 0); + check_float ("pow (-1, inf) == 1", FUNC(pow) (-1, plus_infty), 1, 0, 0, 0); + check_float ("pow (1, -inf) == 1", FUNC(pow) (1, minus_infty), 1, 0, 0, 0); + check_float ("pow (-1, -inf) == 1", FUNC(pow) (-1, minus_infty), 1, 0, 0, 0); + + check_float ("pow (-0.1, 1.1) == NaN plus invalid exception", FUNC(pow) (-0.1L, 1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("pow (-0.1, -1.1) == NaN plus invalid exception", FUNC(pow) (-0.1L, -1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("pow (-10.1, 1.1) == NaN plus invalid exception", FUNC(pow) (-10.1L, 1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("pow (-10.1, -1.1) == NaN plus invalid exception", FUNC(pow) (-10.1L, -1.1L), nan_value, 0, 0, INVALID_EXCEPTION); + + check_float ("pow (0, -1) == inf plus division by zero exception", FUNC(pow) (0, -1), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("pow (0, -11) == inf plus division by zero exception", FUNC(pow) (0, -11), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("pow (-0, -1) == -inf plus division by zero exception", FUNC(pow) (minus_zero, -1), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("pow (-0, -11) == -inf plus division by zero exception", FUNC(pow) (minus_zero, -11), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + check_float ("pow (0, -2) == inf plus division by zero exception", FUNC(pow) (0, -2), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("pow (0, -11.1) == inf plus division by zero exception", FUNC(pow) (0, -11.1L), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("pow (-0, -2) == inf plus division by zero exception", FUNC(pow) (minus_zero, -2), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("pow (-0, -11.1) == inf plus division by zero exception", FUNC(pow) (minus_zero, -11.1L), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + + + check_float ("pow (0, 1) == 0", FUNC(pow) (0, 1), 0, 0, 0, 0); + check_float ("pow (0, 11) == 0", FUNC(pow) (0, 11), 0, 0, 0, 0); + + check_float ("pow (-0, 1) == -0", FUNC(pow) (minus_zero, 1), minus_zero, 0, 0, 0); + check_float ("pow (-0, 11) == -0", FUNC(pow) (minus_zero, 11), minus_zero, 0, 0, 0); + + + check_float ("pow (0, 2) == 0", FUNC(pow) (0, 2), 0, 0, 0, 0); + check_float ("pow (0, 11.1) == 0", FUNC(pow) (0, 11.1L), 0, 0, 0, 0); + + + check_float ("pow (-0, 2) == 0", FUNC(pow) (minus_zero, 2), 0, 0, 0, 0); + check_float ("pow (-0, 11.1) == 0", FUNC(pow) (minus_zero, 11.1L), 0, 0, 0, 0); + +#ifndef TEST_INLINE + /* pow (x, +inf) == +inf for |x| > 1. */ + check_float ("pow (1.5, inf) == inf", FUNC(pow) (1.5, plus_infty), plus_infty, 0, 0, 0); + + /* pow (x, +inf) == +0 for |x| < 1. */ + check_float ("pow (0.5, inf) == 0.0", FUNC(pow) (0.5, plus_infty), 0.0, 0, 0, 0); + + /* pow (x, -inf) == +0 for |x| > 1. */ + check_float ("pow (1.5, -inf) == 0.0", FUNC(pow) (1.5, minus_infty), 0.0, 0, 0, 0); + + /* pow (x, -inf) == +inf for |x| < 1. */ + check_float ("pow (0.5, -inf) == inf", FUNC(pow) (0.5, minus_infty), plus_infty, 0, 0, 0); +#endif + + /* pow (+inf, y) == +inf for y > 0. */ + check_float ("pow (inf, 2) == inf", FUNC(pow) (plus_infty, 2), plus_infty, 0, 0, 0); + + /* pow (+inf, y) == +0 for y < 0. */ + check_float ("pow (inf, -1) == 0.0", FUNC(pow) (plus_infty, -1), 0.0, 0, 0, 0); + + /* pow (-inf, y) == -inf for y an odd integer > 0. */ + check_float ("pow (-inf, 27) == -inf", FUNC(pow) (minus_infty, 27), minus_infty, 0, 0, 0); + + /* pow (-inf, y) == +inf for y > 0 and not an odd integer. */ + check_float ("pow (-inf, 28) == inf", FUNC(pow) (minus_infty, 28), plus_infty, 0, 0, 0); + + /* pow (-inf, y) == -0 for y an odd integer < 0. */ + check_float ("pow (-inf, -3) == -0", FUNC(pow) (minus_infty, -3), minus_zero, 0, 0, 0); + /* pow (-inf, y) == +0 for y < 0 and not an odd integer. */ + check_float ("pow (-inf, -2.0) == 0.0", FUNC(pow) (minus_infty, -2.0), 0.0, 0, 0, 0); + + /* pow (+0, y) == +0 for y an odd integer > 0. */ + check_float ("pow (0.0, 27) == 0.0", FUNC(pow) (0.0, 27), 0.0, 0, 0, 0); + + /* pow (-0, y) == -0 for y an odd integer > 0. */ + check_float ("pow (-0, 27) == -0", FUNC(pow) (minus_zero, 27), minus_zero, 0, 0, 0); + + /* pow (+0, y) == +0 for y > 0 and not an odd integer. */ + check_float ("pow (0.0, 4) == 0.0", FUNC(pow) (0.0, 4), 0.0, 0, 0, 0); + + /* pow (-0, y) == +0 for y > 0 and not an odd integer. */ + check_float ("pow (-0, 4) == 0.0", FUNC(pow) (minus_zero, 4), 0.0, 0, 0, 0); + + check_float ("pow (0.7, 1.2) == 0.65180494056638638188", FUNC(pow) (0.7L, 1.2L), 0.65180494056638638188L, DELTA1398, 0, 0); + +#if defined TEST_DOUBLE || defined TEST_LDOUBLE + check_float ("pow (-7.49321e+133, -9.80818e+16) == 0", FUNC(pow) (-7.49321e+133, -9.80818e+16), 0, 0, 0, 0); +#endif + + print_max_error ("pow", DELTApow, 0); +} + +static void +remainder_test (void) +{ + errno = 0; + FUNC(remainder) (1.625, 1.0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("remainder (1, 0) == NaN plus invalid exception", FUNC(remainder) (1, 0), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("remainder (1, -0) == NaN plus invalid exception", FUNC(remainder) (1, minus_zero), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("remainder (inf, 1) == NaN plus invalid exception", FUNC(remainder) (plus_infty, 1), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("remainder (-inf, 1) == NaN plus invalid exception", FUNC(remainder) (minus_infty, 1), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("remainder (NaN, NaN) == NaN", FUNC(remainder) (nan_value, nan_value), nan_value, 0, 0, 0); + + check_float ("remainder (1.625, 1.0) == -0.375", FUNC(remainder) (1.625, 1.0), -0.375, 0, 0, 0); + check_float ("remainder (-1.625, 1.0) == 0.375", FUNC(remainder) (-1.625, 1.0), 0.375, 0, 0, 0); + check_float ("remainder (1.625, -1.0) == -0.375", FUNC(remainder) (1.625, -1.0), -0.375, 0, 0, 0); + check_float ("remainder (-1.625, -1.0) == 0.375", FUNC(remainder) (-1.625, -1.0), 0.375, 0, 0, 0); + check_float ("remainder (5.0, 2.0) == 1.0", FUNC(remainder) (5.0, 2.0), 1.0, 0, 0, 0); + check_float ("remainder (3.0, 2.0) == -1.0", FUNC(remainder) (3.0, 2.0), -1.0, 0, 0, 0); + + print_max_error ("remainder", 0, 0); +} + +static void +remquo_test (void) +{ + /* x is needed. */ + int x; + + errno = 0; + FUNC(remquo) (1.625, 1.0, &x); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("remquo (1, 0, &x) == NaN plus invalid exception", FUNC(remquo) (1, 0, &x), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("remquo (1, -0, &x) == NaN plus invalid exception", FUNC(remquo) (1, minus_zero, &x), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("remquo (inf, 1, &x) == NaN plus invalid exception", FUNC(remquo) (plus_infty, 1, &x), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("remquo (-inf, 1, &x) == NaN plus invalid exception", FUNC(remquo) (minus_infty, 1, &x), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("remquo (NaN, NaN, &x) == NaN", FUNC(remquo) (nan_value, nan_value, &x), nan_value, 0, 0, 0); + + check_float ("remquo (1.625, 1.0, &x) == -0.375", FUNC(remquo) (1.625, 1.0, &x), -0.375, 0, 0, 0); + check_int ("remquo (1.625, 1.0, &x) sets x to 2", x, 2, 0, 0, 0); + check_float ("remquo (-1.625, 1.0, &x) == 0.375", FUNC(remquo) (-1.625, 1.0, &x), 0.375, 0, 0, 0); + check_int ("remquo (-1.625, 1.0, &x) sets x to -2", x, -2, 0, 0, 0); + check_float ("remquo (1.625, -1.0, &x) == -0.375", FUNC(remquo) (1.625, -1.0, &x), -0.375, 0, 0, 0); + check_int ("remquo (1.625, -1.0, &x) sets x to -2", x, -2, 0, 0, 0); + check_float ("remquo (-1.625, -1.0, &x) == 0.375", FUNC(remquo) (-1.625, -1.0, &x), 0.375, 0, 0, 0); + check_int ("remquo (-1.625, -1.0, &x) sets x to 2", x, 2, 0, 0, 0); + + check_float ("remquo (5, 2, &x) == 1", FUNC(remquo) (5, 2, &x), 1, 0, 0, 0); + check_int ("remquo (5, 2, &x) sets x to 2", x, 2, 0, 0, 0); + check_float ("remquo (3, 2, &x) == -1", FUNC(remquo) (3, 2, &x), -1, 0, 0, 0); + check_int ("remquo (3, 2, &x) sets x to 2", x, 2, 0, 0, 0); + + print_max_error ("remquo", 0, 0); +} + +static void +rint_test (void) +{ + init_max_error (); + + check_float ("rint (0.0) == 0.0", FUNC(rint) (0.0), 0.0, 0, 0, 0); + check_float ("rint (-0) == -0", FUNC(rint) (minus_zero), minus_zero, 0, 0, 0); + check_float ("rint (inf) == inf", FUNC(rint) (plus_infty), plus_infty, 0, 0, 0); + check_float ("rint (-inf) == -inf", FUNC(rint) (minus_infty), minus_infty, 0, 0, 0); + + /* Default rounding mode is round to even. */ + check_float ("rint (0.5) == 0.0", FUNC(rint) (0.5), 0.0, 0, 0, 0); + check_float ("rint (1.5) == 2.0", FUNC(rint) (1.5), 2.0, 0, 0, 0); + check_float ("rint (2.5) == 2.0", FUNC(rint) (2.5), 2.0, 0, 0, 0); + check_float ("rint (3.5) == 4.0", FUNC(rint) (3.5), 4.0, 0, 0, 0); + check_float ("rint (4.5) == 4.0", FUNC(rint) (4.5), 4.0, 0, 0, 0); + check_float ("rint (-0.5) == -0.0", FUNC(rint) (-0.5), -0.0, 0, 0, 0); + check_float ("rint (-1.5) == -2.0", FUNC(rint) (-1.5), -2.0, 0, 0, 0); + check_float ("rint (-2.5) == -2.0", FUNC(rint) (-2.5), -2.0, 0, 0, 0); + check_float ("rint (-3.5) == -4.0", FUNC(rint) (-3.5), -4.0, 0, 0, 0); + check_float ("rint (-4.5) == -4.0", FUNC(rint) (-4.5), -4.0, 0, 0, 0); + + print_max_error ("rint", 0, 0); +} + +static void +round_test (void) +{ + init_max_error (); + + check_float ("round (0) == 0", FUNC(round) (0), 0, 0, 0, 0); + check_float ("round (-0) == -0", FUNC(round) (minus_zero), minus_zero, 0, 0, 0); + check_float ("round (0.2) == 0.0", FUNC(round) (0.2L), 0.0, 0, 0, 0); + check_float ("round (-0.2) == -0", FUNC(round) (-0.2L), minus_zero, 0, 0, 0); + check_float ("round (0.5) == 1.0", FUNC(round) (0.5), 1.0, 0, 0, 0); + check_float ("round (-0.5) == -1.0", FUNC(round) (-0.5), -1.0, 0, 0, 0); + check_float ("round (0.8) == 1.0", FUNC(round) (0.8L), 1.0, 0, 0, 0); + check_float ("round (-0.8) == -1.0", FUNC(round) (-0.8L), -1.0, 0, 0, 0); + check_float ("round (1.5) == 2.0", FUNC(round) (1.5), 2.0, 0, 0, 0); + check_float ("round (-1.5) == -2.0", FUNC(round) (-1.5), -2.0, 0, 0, 0); + check_float ("round (2097152.5) == 2097153", FUNC(round) (2097152.5), 2097153, 0, 0, 0); + check_float ("round (-2097152.5) == -2097153", FUNC(round) (-2097152.5), -2097153, 0, 0, 0); + + print_max_error ("round", 0, 0); +} + + +static void +scalbn_test (void) +{ + + init_max_error (); + + check_float ("scalbn (0, 0) == 0", FUNC(scalbn) (0, 0), 0, 0, 0, 0); + check_float ("scalbn (-0, 0) == -0", FUNC(scalbn) (minus_zero, 0), minus_zero, 0, 0, 0); + + check_float ("scalbn (inf, 1) == inf", FUNC(scalbn) (plus_infty, 1), plus_infty, 0, 0, 0); + check_float ("scalbn (-inf, 1) == -inf", FUNC(scalbn) (minus_infty, 1), minus_infty, 0, 0, 0); + check_float ("scalbn (NaN, 1) == NaN", FUNC(scalbn) (nan_value, 1), nan_value, 0, 0, 0); + + check_float ("scalbn (0.8, 4) == 12.8", FUNC(scalbn) (0.8L, 4), 12.8L, 0, 0, 0); + check_float ("scalbn (-0.854375, 5) == -27.34", FUNC(scalbn) (-0.854375L, 5), -27.34L, 0, 0, 0); + + check_float ("scalbn (1, 0) == 1", FUNC(scalbn) (1, 0L), 1, 0, 0, 0); + + print_max_error ("scalbn", 0, 0); +} + +static void +scalbln_test (void) +{ + + init_max_error (); + + check_float ("scalbln (0, 0) == 0", FUNC(scalbln) (0, 0), 0, 0, 0, 0); + check_float ("scalbln (-0, 0) == -0", FUNC(scalbln) (minus_zero, 0), minus_zero, 0, 0, 0); + + check_float ("scalbln (inf, 1) == inf", FUNC(scalbln) (plus_infty, 1), plus_infty, 0, 0, 0); + check_float ("scalbln (-inf, 1) == -inf", FUNC(scalbln) (minus_infty, 1), minus_infty, 0, 0, 0); + check_float ("scalbln (NaN, 1) == NaN", FUNC(scalbln) (nan_value, 1), nan_value, 0, 0, 0); + + check_float ("scalbln (0.8, 4) == 12.8", FUNC(scalbln) (0.8L, 4), 12.8L, 0, 0, 0); + check_float ("scalbln (-0.854375, 5) == -27.34", FUNC(scalbln) (-0.854375L, 5), -27.34L, 0, 0, 0); + + check_float ("scalbln (1, 0) == 1", FUNC(scalbln) (1, 0L), 1, 0, 0, 0); + + print_max_error ("scalbn", 0, 0); +} + +static void +signbit_test (void) +{ + + init_max_error (); + + check_bool ("signbit (0) == false", signbit (0.0), 0, 0, 0, 0); + check_bool ("signbit (-0) == true", signbit (minus_zero), 1, 0, 0, 0); + check_bool ("signbit (inf) == false", signbit (plus_infty), 0, 0, 0, 0); + check_bool ("signbit (-inf) == true", signbit (minus_infty), 1, 0, 0, 0); + + /* signbit (x) != 0 for x < 0. */ + check_bool ("signbit (-1) == true", signbit (-1.0), 1, 0, 0, 0); + /* signbit (x) == 0 for x >= 0. */ + check_bool ("signbit (1) == false", signbit (1.0), 0, 0, 0, 0); + + print_max_error ("signbit", 0, 0); +} + +static void +sin_test (void) +{ + errno = 0; + FUNC(sin) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("sin (0) == 0", FUNC(sin) (0), 0, 0, 0, 0); + check_float ("sin (-0) == -0", FUNC(sin) (minus_zero), minus_zero, 0, 0, 0); + check_float ("sin (inf) == NaN plus invalid exception", FUNC(sin) (plus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("sin (-inf) == NaN plus invalid exception", FUNC(sin) (minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("sin (NaN) == NaN", FUNC(sin) (nan_value), nan_value, 0, 0, 0); + + check_float ("sin (pi/6) == 0.5", FUNC(sin) (M_PI_6l), 0.5, 0, 0, 0); + check_float ("sin (-pi/6) == -0.5", FUNC(sin) (-M_PI_6l), -0.5, 0, 0, 0); + check_float ("sin (pi/2) == 1", FUNC(sin) (M_PI_2l), 1, 0, 0, 0); + check_float ("sin (-pi/2) == -1", FUNC(sin) (-M_PI_2l), -1, 0, 0, 0); + check_float ("sin (0.7) == 0.64421768723769105367261435139872014", FUNC(sin) (0.7L), 0.64421768723769105367261435139872014L, DELTA1524, 0, 0); + + print_max_error ("sin", DELTAsin, 0); + +} + + +static void +sincos_test (void) +{ + FLOAT sin_res, cos_res; + + errno = 0; + FUNC(sincos) (0, &sin_res, &cos_res); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + /* sincos is treated differently because it returns void. */ + FUNC (sincos) (0, &sin_res, &cos_res); + check_float ("sincos (0, &sin_res, &cos_res) puts 0 in sin_res", sin_res, 0, 0, 0, 0); + check_float ("sincos (0, &sin_res, &cos_res) puts 1 in cos_res", cos_res, 1, 0, 0, 0); + + FUNC (sincos) (minus_zero, &sin_res, &cos_res); + check_float ("sincos (-0, &sin_res, &cos_res) puts -0 in sin_res", sin_res, minus_zero, 0, 0, 0); + check_float ("sincos (-0, &sin_res, &cos_res) puts 1 in cos_res", cos_res, 1, 0, 0, 0); + FUNC (sincos) (plus_infty, &sin_res, &cos_res); + check_float ("sincos (inf, &sin_res, &cos_res) puts NaN in sin_res plus invalid exception", sin_res, nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("sincos (inf, &sin_res, &cos_res) puts NaN in cos_res", cos_res, nan_value, 0, 0, 0); + FUNC (sincos) (minus_infty, &sin_res, &cos_res); + check_float ("sincos (-inf, &sin_res, &cos_res) puts NaN in sin_res plus invalid exception", sin_res, nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("sincos (-inf, &sin_res, &cos_res) puts NaN in cos_res", cos_res, nan_value, 0, 0, 0); + FUNC (sincos) (nan_value, &sin_res, &cos_res); + check_float ("sincos (NaN, &sin_res, &cos_res) puts NaN in sin_res", sin_res, nan_value, 0, 0, 0); + check_float ("sincos (NaN, &sin_res, &cos_res) puts NaN in cos_res", cos_res, nan_value, 0, 0, 0); + + FUNC (sincos) (M_PI_2l, &sin_res, &cos_res); + check_float ("sincos (pi/2, &sin_res, &cos_res) puts 1 in sin_res", sin_res, 1, 0, 0, 0); + check_float ("sincos (pi/2, &sin_res, &cos_res) puts 0 in cos_res", cos_res, 0, DELTA1536, 0, 0); + FUNC (sincos) (M_PI_6l, &sin_res, &cos_res); + check_float ("sincos (pi/6, &sin_res, &cos_res) puts 0.5 in sin_res", sin_res, 0.5, 0, 0, 0); + check_float ("sincos (pi/6, &sin_res, &cos_res) puts 0.86602540378443864676372317075293616 in cos_res", cos_res, 0.86602540378443864676372317075293616L, 0, 0, 0); + FUNC (sincos) (M_PI_6l*2.0, &sin_res, &cos_res); + check_float ("sincos (M_PI_6l*2.0, &sin_res, &cos_res) puts 0.86602540378443864676372317075293616 in sin_res", sin_res, 0.86602540378443864676372317075293616L, DELTA1539, 0, 0); + check_float ("sincos (M_PI_6l*2.0, &sin_res, &cos_res) puts 0.5 in cos_res", cos_res, 0.5, DELTA1540, 0, 0); + FUNC (sincos) (0.7L, &sin_res, &cos_res); + check_float ("sincos (0.7, &sin_res, &cos_res) puts 0.64421768723769105367261435139872014 in sin_res", sin_res, 0.64421768723769105367261435139872014L, DELTA1541, 0, 0); + check_float ("sincos (0.7, &sin_res, &cos_res) puts 0.76484218728448842625585999019186495 in cos_res", cos_res, 0.76484218728448842625585999019186495L, DELTA1542, 0, 0); + + print_max_error ("sincos", DELTAsincos, 0); +} + +static void +sinh_test (void) +{ + errno = 0; + FUNC(sinh) (0.7L); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + check_float ("sinh (0) == 0", FUNC(sinh) (0), 0, 0, 0, 0); + check_float ("sinh (-0) == -0", FUNC(sinh) (minus_zero), minus_zero, 0, 0, 0); + +#ifndef TEST_INLINE + check_float ("sinh (inf) == inf", FUNC(sinh) (plus_infty), plus_infty, 0, 0, 0); + check_float ("sinh (-inf) == -inf", FUNC(sinh) (minus_infty), minus_infty, 0, 0, 0); +#endif + check_float ("sinh (NaN) == NaN", FUNC(sinh) (nan_value), nan_value, 0, 0, 0); + + check_float ("sinh (0.7) == 0.75858370183953350346", FUNC(sinh) (0.7L), 0.75858370183953350346L, DELTA1548, 0, 0); +#if 0 /* XXX scp XXX */ + check_float ("sinh (0x8p-32) == 1.86264514923095703232705808926175479e-9", FUNC(sinh) (0x8p-32L), 1.86264514923095703232705808926175479e-9L, 0, 0, 0); +#endif + + print_max_error ("sinh", DELTAsinh, 0); +} + +static void +sqrt_test (void) +{ + errno = 0; + FUNC(sqrt) (1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("sqrt (0) == 0", FUNC(sqrt) (0), 0, 0, 0, 0); + check_float ("sqrt (NaN) == NaN", FUNC(sqrt) (nan_value), nan_value, 0, 0, 0); + check_float ("sqrt (inf) == inf", FUNC(sqrt) (plus_infty), plus_infty, 0, 0, 0); + + check_float ("sqrt (-0) == -0", FUNC(sqrt) (minus_zero), minus_zero, 0, 0, 0); + + /* sqrt (x) == NaN plus invalid exception for x < 0. */ + check_float ("sqrt (-1) == NaN plus invalid exception", FUNC(sqrt) (-1), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("sqrt (-inf) == NaN plus invalid exception", FUNC(sqrt) (minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("sqrt (NaN) == NaN", FUNC(sqrt) (nan_value), nan_value, 0, 0, 0); + + check_float ("sqrt (2209) == 47", FUNC(sqrt) (2209), 47, 0, 0, 0); + check_float ("sqrt (4) == 2", FUNC(sqrt) (4), 2, 0, 0, 0); + check_float ("sqrt (2) == M_SQRT2l", FUNC(sqrt) (2), M_SQRT2l, 0, 0, 0); + check_float ("sqrt (0.25) == 0.5", FUNC(sqrt) (0.25), 0.5, 0, 0, 0); + check_float ("sqrt (6642.25) == 81.5", FUNC(sqrt) (6642.25), 81.5, 0, 0, 0); + check_float ("sqrt (15239.9025) == 123.45", FUNC(sqrt) (15239.9025L), 123.45L, DELTA1562, 0, 0); + check_float ("sqrt (0.7) == 0.83666002653407554797817202578518747", FUNC(sqrt) (0.7L), 0.83666002653407554797817202578518747L, 0, 0, 0); + + print_max_error ("sqrt", DELTAsqrt, 0); +} + +static void +tan_test (void) +{ + errno = 0; + FUNC(tan) (0); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("tan (0) == 0", FUNC(tan) (0), 0, 0, 0, 0); + check_float ("tan (-0) == -0", FUNC(tan) (minus_zero), minus_zero, 0, 0, 0); + check_float ("tan (inf) == NaN plus invalid exception", FUNC(tan) (plus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("tan (-inf) == NaN plus invalid exception", FUNC(tan) (minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("tan (NaN) == NaN", FUNC(tan) (nan_value), nan_value, 0, 0, 0); + + check_float ("tan (pi/4) == 1", FUNC(tan) (M_PI_4l), 1, DELTA1569, 0, 0); + check_float ("tan (0.7) == 0.84228838046307944812813500221293775", FUNC(tan) (0.7L), 0.84228838046307944812813500221293775L, DELTA1570, 0, 0); + + print_max_error ("tan", DELTAtan, 0); +} + +static void +tanh_test (void) +{ + errno = 0; + FUNC(tanh) (0.7L); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + init_max_error (); + + check_float ("tanh (0) == 0", FUNC(tanh) (0), 0, 0, 0, 0); + check_float ("tanh (-0) == -0", FUNC(tanh) (minus_zero), minus_zero, 0, 0, 0); + +#ifndef TEST_INLINE + check_float ("tanh (inf) == 1", FUNC(tanh) (plus_infty), 1, 0, 0, 0); + check_float ("tanh (-inf) == -1", FUNC(tanh) (minus_infty), -1, 0, 0, 0); +#endif + check_float ("tanh (NaN) == NaN", FUNC(tanh) (nan_value), nan_value, 0, 0, 0); + + check_float ("tanh (0.7) == 0.60436777711716349631", FUNC(tanh) (0.7L), 0.60436777711716349631L, DELTA1576, 0, 0); + check_float ("tanh (-0.7) == -0.60436777711716349631", FUNC(tanh) (-0.7L), -0.60436777711716349631L, DELTA1577, 0, 0); + + check_float ("tanh (1.0) == 0.7615941559557648881194582826047935904", FUNC(tanh) (1.0L), 0.7615941559557648881194582826047935904L, 0, 0, 0); + check_float ("tanh (-1.0) == -0.7615941559557648881194582826047935904", FUNC(tanh) (-1.0L), -0.7615941559557648881194582826047935904L, 0, 0, 0); + + /* 2^-57 */ + check_float ("tanh (6.938893903907228377647697925567626953125e-18) == 6.938893903907228377647697925567626953125e-18", FUNC(tanh) (6.938893903907228377647697925567626953125e-18L), 6.938893903907228377647697925567626953125e-18L, 0, 0, 0); + + print_max_error ("tanh", DELTAtanh, 0); +} + +static void +tgamma_test (void) +{ + errno = 0; + FUNC(tgamma) (1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + feclearexcept (FE_ALL_EXCEPT); + + init_max_error (); + + check_float ("tgamma (inf) == inf", FUNC(tgamma) (plus_infty), plus_infty, 0, 0, 0); + check_float ("tgamma (0) == inf plus divide-by-zero", FUNC(tgamma) (0), plus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("tgamma (-0) == inf plus divide-by-zero", FUNC(tgamma) (minus_zero), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + /* tgamma (x) == NaN plus invalid exception for integer x <= 0. */ + check_float ("tgamma (-2) == NaN plus invalid exception", FUNC(tgamma) (-2), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("tgamma (-inf) == NaN plus invalid exception", FUNC(tgamma) (minus_infty), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("tgamma (NaN) == NaN", FUNC(tgamma) (nan_value), nan_value, 0, 0, 0); + + check_float ("tgamma (0.5) == sqrt (pi)", FUNC(tgamma) (0.5), M_SQRT_PIl, DELTA1587, 0, 0); + check_float ("tgamma (-0.5) == -2 sqrt (pi)", FUNC(tgamma) (-0.5), -M_2_SQRT_PIl, DELTA1588, 0, 0); + + check_float ("tgamma (1) == 1", FUNC(tgamma) (1), 1, 0, 0, 0); + check_float ("tgamma (4) == 6", FUNC(tgamma) (4), 6, DELTA1590, 0, 0); + + check_float ("tgamma (0.7) == 1.29805533264755778568", FUNC(tgamma) (0.7L), 1.29805533264755778568L, DELTA1591, 0, 0); + check_float ("tgamma (1.2) == 0.91816874239976061064", FUNC(tgamma) (1.2L), 0.91816874239976061064L, 0, 0, 0); + + print_max_error ("tgamma", DELTAtgamma, 0); +} + +static void +trunc_test (void) +{ + init_max_error (); + + check_float ("trunc (inf) == inf", FUNC(trunc) (plus_infty), plus_infty, 0, 0, 0); + check_float ("trunc (-inf) == -inf", FUNC(trunc) (minus_infty), minus_infty, 0, 0, 0); + check_float ("trunc (NaN) == NaN", FUNC(trunc) (nan_value), nan_value, 0, 0, 0); + + check_float ("trunc (0) == 0", FUNC(trunc) (0), 0, 0, 0, 0); + check_float ("trunc (-0) == -0", FUNC(trunc) (minus_zero), minus_zero, 0, 0, 0); + check_float ("trunc (0.625) == 0", FUNC(trunc) (0.625), 0, 0, 0, 0); + check_float ("trunc (-0.625) == -0", FUNC(trunc) (-0.625), minus_zero, 0, 0, 0); + check_float ("trunc (1) == 1", FUNC(trunc) (1), 1, 0, 0, 0); + check_float ("trunc (-1) == -1", FUNC(trunc) (-1), -1, 0, 0, 0); + check_float ("trunc (1.625) == 1", FUNC(trunc) (1.625), 1, 0, 0, 0); + check_float ("trunc (-1.625) == -1", FUNC(trunc) (-1.625), -1, 0, 0, 0); + + check_float ("trunc (1048580.625) == 1048580", FUNC(trunc) (1048580.625L), 1048580L, 0, 0, 0); + check_float ("trunc (-1048580.625) == -1048580", FUNC(trunc) (-1048580.625L), -1048580L, 0, 0, 0); + + check_float ("trunc (8388610.125) == 8388610.0", FUNC(trunc) (8388610.125L), 8388610.0L, 0, 0, 0); + check_float ("trunc (-8388610.125) == -8388610.0", FUNC(trunc) (-8388610.125L), -8388610.0L, 0, 0, 0); + + check_float ("trunc (4294967296.625) == 4294967296.0", FUNC(trunc) (4294967296.625L), 4294967296.0L, 0, 0, 0); + check_float ("trunc (-4294967296.625) == -4294967296.0", FUNC(trunc) (-4294967296.625L), -4294967296.0L, 0, 0, 0); + + + print_max_error ("trunc", 0, 0); +} + +static void +y0_test (void) +{ + FLOAT s, c; + errno = 0; + FUNC (sincos) (0, &s, &c); + if (errno == ENOSYS) + /* Required function not implemented. */ + return; + FUNC(y0) (1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + /* y0 is the Bessel function of the second kind of order 0 */ + init_max_error (); + + check_float ("y0 (-1.0) == NaN", FUNC(y0) (-1.0), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("y0 (0.0) == -inf", FUNC(y0) (0.0), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("y0 (NaN) == NaN", FUNC(y0) (nan_value), nan_value, 0, 0, 0); + check_float ("y0 (inf) == 0", FUNC(y0) (plus_infty), 0, 0, 0, 0); + + check_float ("y0 (0.1) == -1.5342386513503668441", FUNC(y0) (0.1L), -1.5342386513503668441L, DELTA1614, 0, 0); + check_float ("y0 (0.7) == -0.19066492933739506743", FUNC(y0) (0.7L), -0.19066492933739506743L, DELTA1615, 0, 0); + check_float ("y0 (1.0) == 0.088256964215676957983", FUNC(y0) (1.0), 0.088256964215676957983L, DELTA1616, 0, 0); + check_float ("y0 (1.5) == 0.38244892379775884396", FUNC(y0) (1.5), 0.38244892379775884396L, DELTA1617, 0, 0); + check_float ("y0 (2.0) == 0.51037567264974511960", FUNC(y0) (2.0), 0.51037567264974511960L, DELTA1618, 0, 0); + check_float ("y0 (8.0) == 0.22352148938756622053", FUNC(y0) (8.0), 0.22352148938756622053L, DELTA1619, 0, 0); + check_float ("y0 (10.0) == 0.055671167283599391424", FUNC(y0) (10.0), 0.055671167283599391424L, DELTA1620, 0, 0); + + print_max_error ("y0", DELTAy0, 0); +} + + +static void +y1_test (void) +{ + FLOAT s, c; + errno = 0; + FUNC (sincos) (0, &s, &c); + if (errno == ENOSYS) + /* Required function not implemented. */ + return; + FUNC(y1) (1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + /* y1 is the Bessel function of the second kind of order 1 */ + init_max_error (); + + check_float ("y1 (-1.0) == NaN", FUNC(y1) (-1.0), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("y1 (0.0) == -inf", FUNC(y1) (0.0), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("y1 (inf) == 0", FUNC(y1) (plus_infty), 0, 0, 0, 0); + check_float ("y1 (NaN) == NaN", FUNC(y1) (nan_value), nan_value, 0, 0, 0); + + check_float ("y1 (0.1) == -6.4589510947020269877", FUNC(y1) (0.1L), -6.4589510947020269877L, DELTA1625, 0, 0); + check_float ("y1 (0.7) == -1.1032498719076333697", FUNC(y1) (0.7L), -1.1032498719076333697L, DELTA1626, 0, 0); + check_float ("y1 (1.0) == -0.78121282130028871655", FUNC(y1) (1.0), -0.78121282130028871655L, DELTA1627, 0, 0); + check_float ("y1 (1.5) == -0.41230862697391129595", FUNC(y1) (1.5), -0.41230862697391129595L, DELTA1628, 0, 0); + check_float ("y1 (2.0) == -0.10703243154093754689", FUNC(y1) (2.0), -0.10703243154093754689L, DELTA1629, 0, 0); + check_float ("y1 (8.0) == -0.15806046173124749426", FUNC(y1) (8.0), -0.15806046173124749426L, DELTA1630, 0, 0); + check_float ("y1 (10.0) == 0.24901542420695388392", FUNC(y1) (10.0), 0.24901542420695388392L, DELTA1631, 0, 0); + + print_max_error ("y1", DELTAy1, 0); +} + +static void +yn_test (void) +{ + FLOAT s, c; + errno = 0; + FUNC (sincos) (0, &s, &c); + if (errno == ENOSYS) + /* Required function not implemented. */ + return; + FUNC(yn) (1, 1); + if (errno == ENOSYS) + /* Function not implemented. */ + return; + + /* yn is the Bessel function of the second kind of order n */ + init_max_error (); + + /* yn (0, x) == y0 (x) */ + check_float ("yn (0, -1.0) == NaN", FUNC(yn) (0, -1.0), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("yn (0, 0.0) == -inf", FUNC(yn) (0, 0.0), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("yn (0, NaN) == NaN", FUNC(yn) (0, nan_value), nan_value, 0, 0, 0); + check_float ("yn (0, inf) == 0", FUNC(yn) (0, plus_infty), 0, 0, 0, 0); + + check_float ("yn (0, 0.1) == -1.5342386513503668441", FUNC(yn) (0, 0.1L), -1.5342386513503668441L, DELTA1636, 0, 0); + check_float ("yn (0, 0.7) == -0.19066492933739506743", FUNC(yn) (0, 0.7L), -0.19066492933739506743L, DELTA1637, 0, 0); + check_float ("yn (0, 1.0) == 0.088256964215676957983", FUNC(yn) (0, 1.0), 0.088256964215676957983L, DELTA1638, 0, 0); + check_float ("yn (0, 1.5) == 0.38244892379775884396", FUNC(yn) (0, 1.5), 0.38244892379775884396L, DELTA1639, 0, 0); + check_float ("yn (0, 2.0) == 0.51037567264974511960", FUNC(yn) (0, 2.0), 0.51037567264974511960L, DELTA1640, 0, 0); + check_float ("yn (0, 8.0) == 0.22352148938756622053", FUNC(yn) (0, 8.0), 0.22352148938756622053L, DELTA1641, 0, 0); + check_float ("yn (0, 10.0) == 0.055671167283599391424", FUNC(yn) (0, 10.0), 0.055671167283599391424L, DELTA1642, 0, 0); + + /* yn (1, x) == y1 (x) */ + check_float ("yn (1, -1.0) == NaN", FUNC(yn) (1, -1.0), nan_value, 0, 0, INVALID_EXCEPTION); + check_float ("yn (1, 0.0) == -inf", FUNC(yn) (1, 0.0), minus_infty, 0, 0, DIVIDE_BY_ZERO_EXCEPTION); + check_float ("yn (1, inf) == 0", FUNC(yn) (1, plus_infty), 0, 0, 0, 0); + check_float ("yn (1, NaN) == NaN", FUNC(yn) (1, nan_value), nan_value, 0, 0, 0); + + check_float ("yn (1, 0.1) == -6.4589510947020269877", FUNC(yn) (1, 0.1L), -6.4589510947020269877L, DELTA1647, 0, 0); + check_float ("yn (1, 0.7) == -1.1032498719076333697", FUNC(yn) (1, 0.7L), -1.1032498719076333697L, DELTA1648, 0, 0); + check_float ("yn (1, 1.0) == -0.78121282130028871655", FUNC(yn) (1, 1.0), -0.78121282130028871655L, DELTA1649, 0, 0); + check_float ("yn (1, 1.5) == -0.41230862697391129595", FUNC(yn) (1, 1.5), -0.41230862697391129595L, DELTA1650, 0, 0); + check_float ("yn (1, 2.0) == -0.10703243154093754689", FUNC(yn) (1, 2.0), -0.10703243154093754689L, DELTA1651, 0, 0); + check_float ("yn (1, 8.0) == -0.15806046173124749426", FUNC(yn) (1, 8.0), -0.15806046173124749426L, DELTA1652, 0, 0); + check_float ("yn (1, 10.0) == 0.24901542420695388392", FUNC(yn) (1, 10.0), 0.24901542420695388392L, DELTA1653, 0, 0); + + /* yn (3, x) */ + check_float ("yn (3, inf) == 0", FUNC(yn) (3, plus_infty), 0, 0, 0, 0); + check_float ("yn (3, NaN) == NaN", FUNC(yn) (3, nan_value), nan_value, 0, 0, 0); + + check_float ("yn (3, 0.1) == -5099.3323786129048894", FUNC(yn) (3, 0.1L), -5099.3323786129048894L, DELTA1656, 0, 0); + check_float ("yn (3, 0.7) == -15.819479052819633505", FUNC(yn) (3, 0.7L), -15.819479052819633505L, DELTA1657, 0, 0); + check_float ("yn (3, 1.0) == -5.8215176059647288478", FUNC(yn) (3, 1.0), -5.8215176059647288478L, 0, 0, 0); + check_float ("yn (3, 2.0) == -1.1277837768404277861", FUNC(yn) (3, 2.0), -1.1277837768404277861L, DELTA1659, 0, 0); + check_float ("yn (3, 10.0) == -0.25136265718383732978", FUNC(yn) (3, 10.0), -0.25136265718383732978L, DELTA1660, 0, 0); + + /* yn (10, x) */ + check_float ("yn (10, inf) == 0", FUNC(yn) (10, plus_infty), 0, 0, 0, 0); + check_float ("yn (10, NaN) == NaN", FUNC(yn) (10, nan_value), nan_value, 0, 0, 0); + + check_float ("yn (10, 0.1) == -0.11831335132045197885e19", FUNC(yn) (10, 0.1L), -0.11831335132045197885e19L, DELTA1663, 0, 0); + check_float ("yn (10, 0.7) == -0.42447194260703866924e10", FUNC(yn) (10, 0.7L), -0.42447194260703866924e10L, DELTA1664, 0, 0); + check_float ("yn (10, 1.0) == -0.12161801427868918929e9", FUNC(yn) (10, 1.0), -0.12161801427868918929e9L, DELTA1665, 0, 0); + check_float ("yn (10, 2.0) == -129184.54220803928264", FUNC(yn) (10, 2.0), -129184.54220803928264L, DELTA1666, 0, 0); + check_float ("yn (10, 10.0) == -0.35981415218340272205", FUNC(yn) (10, 10.0), -0.35981415218340272205L, DELTA1667, 0, 0); + + print_max_error ("yn", DELTAyn, 0); + +} + + + +static void +initialize (void) +{ + plus_zero = 0.0; + nan_value = plus_zero / plus_zero; /* Suppress GCC warning */ + + minus_zero = FUNC(copysign) (0.0, -1.0); + plus_infty = CHOOSE (HUGE_VALL, HUGE_VAL, HUGE_VALF, + HUGE_VALL, HUGE_VAL, HUGE_VALF); + minus_infty = CHOOSE (-HUGE_VALL, -HUGE_VAL, -HUGE_VALF, + -HUGE_VALL, -HUGE_VAL, -HUGE_VALF); + + (void) &plus_zero; + (void) &nan_value; + (void) &minus_zero; + (void) &plus_infty; + (void) &minus_infty; + + /* Clear all exceptions. From now on we must not get random exceptions. */ + feclearexcept (FE_ALL_EXCEPT); +} + +#if 0 /* XXX scp XXX */ +/* Definitions of arguments for argp functions. */ +static const struct argp_option options[] = +{ + { "verbose", 'v', "NUMBER", 0, "Level of verbosity (0..3)"}, + { "ulps-file", 'u', NULL, 0, "Output ulps to file ULPs"}, + { "no-max-error", 'f', NULL, 0, + "Don't output maximal errors of functions"}, + { "no-points", 'p', NULL, 0, + "Don't output results of functions invocations"}, + { "ignore-max-ulp", 'i', "yes/no", 0, + "Ignore given maximal errors"}, + { NULL, 0, NULL, 0, NULL } +}; + +/* Short description of program. */ +static const char doc[] = "Math test suite: " TEST_MSG ; + +/* Prototype for option handler. */ +static error_t parse_opt (int key, char *arg, struct argp_state *state); + +/* Data structure to communicate with argp functions. */ +static struct argp argp = +{ + options, parse_opt, NULL, doc, +}; + + +/* Handle program arguments. */ +static error_t +parse_opt (int key, char *arg, struct argp_state *state) +{ + switch (key) + { + case 'f': + output_max_error = 0; + break; + case 'i': + if (strcmp (arg, "yes") == 0) + ignore_max_ulp = 1; + else if (strcmp (arg, "no") == 0) + ignore_max_ulp = 0; + break; + case 'p': + output_points = 0; + break; + case 'u': + output_ulps = 1; + break; + case 'v': + if (optarg) + verbose = (unsigned int) strtoul (optarg, NULL, 0); + else + verbose = 3; + break; + default: + return ARGP_ERR_UNKNOWN; + } + return 0; +} +#endif + +#if 0 +/* function to check our ulp calculation. */ +void +check_ulp (void) +{ + int i; + + FLOAT u, diff, ulp; + /* This gives one ulp. */ + u = FUNC(nextafter) (10, 20); + check_equal (10.0, u, 1, &diff, &ulp); + printf ("One ulp: % .4" PRINTF_NEXPR "\n", ulp); + + /* This gives one more ulp. */ + u = FUNC(nextafter) (u, 20); + check_equal (10.0, u, 2, &diff, &ulp); + printf ("two ulp: % .4" PRINTF_NEXPR "\n", ulp); + + /* And now calculate 100 ulp. */ + for (i = 2; i < 100; i++) + u = FUNC(nextafter) (u, 20); + check_equal (10.0, u, 100, &diff, &ulp); + printf ("100 ulp: % .4" PRINTF_NEXPR "\n", ulp); +} +#endif + +int +main (int argc, char **argv) +{ +#if 0 /* XXX scp XXX */ + int remaining; +#endif + + verbose = 1; + output_ulps = 0; + output_max_error = 1; + output_points = 1; + /* XXX set to 0 for releases. */ + ignore_max_ulp = 0; + +#if 0 /* XXX scp XXX */ + /* Parse and process arguments. */ + argp_parse (&argp, argc, argv, 0, &remaining, NULL); + + if (remaining != argc) + { + fprintf (stderr, "wrong number of arguments"); + argp_help (&argp, stdout, ARGP_HELP_SEE, program_invocation_short_name); + exit (EXIT_FAILURE); + } +#endif + + if (output_ulps) + { + ulps_file = fopen ("ULPs", "a"); + if (ulps_file == NULL) + { + perror ("can't open file `ULPs' for writing: "); + exit (1); + } + } + + + initialize (); + printf (TEST_MSG); + +#if 0 + check_ulp (); +#endif + + /* Keep the tests a wee bit ordered (according to ISO C99). */ + /* Classification macros: */ + fpclassify_test (); + isfinite_test (); + isnormal_test (); + signbit_test (); + + /* Trigonometric functions: */ + acos_test (); + asin_test (); + atan_test (); + atan2_test (); + cos_test (); + sin_test (); + sincos_test (); + tan_test (); + + /* Hyperbolic functions: */ + acosh_test (); + asinh_test (); + atanh_test (); + cosh_test (); + sinh_test (); + tanh_test (); + + /* Exponential and logarithmic functions: */ + exp_test (); +#if 0 /* XXX scp XXX */ + exp10_test (); +#endif + exp2_test (); + expm1_test (); + frexp_test (); + ldexp_test (); + log_test (); + log10_test (); + log1p_test (); + log2_test (); + logb_test (); + modf_test (); + ilogb_test (); + scalbn_test (); + scalbln_test (); + + /* Power and absolute value functions: */ + cbrt_test (); + fabs_test (); + hypot_test (); + pow_test (); + sqrt_test (); + + /* Error and gamma functions: */ + erf_test (); + erfc_test (); + gamma_test (); + lgamma_test (); + tgamma_test (); + + /* Nearest integer functions: */ + ceil_test (); + floor_test (); + nearbyint_test (); + rint_test (); + lrint_test (); + llrint_test (); + round_test (); + lround_test (); + llround_test (); + trunc_test (); + + /* Remainder functions: */ + fmod_test (); + remainder_test (); + remquo_test (); + + /* Manipulation functions: */ + copysign_test (); + nextafter_test (); +#if 0 /* XXX scp XXX */ + nexttoward_test (); +#endif + + /* maximum, minimum and positive difference functions */ + fdim_test (); + fmax_test (); + fmin_test (); + + /* Multiply and add: */ + fma_test (); + +#if 0 /* XXX scp XXX */ + /* Complex functions: */ + cabs_test (); + cacos_test (); + cacosh_test (); + carg_test (); + casin_test (); + casinh_test (); + catan_test (); + catanh_test (); + ccos_test (); + ccosh_test (); + cexp_test (); + cimag_test (); + clog10_test (); + clog_test (); + conj_test (); + cpow_test (); + cproj_test (); + creal_test (); + csin_test (); + csinh_test (); + csqrt_test (); + ctan_test (); + ctanh_test (); +#endif + + /* Bessel functions: */ + j0_test (); + j1_test (); + jn_test (); + y0_test (); + y1_test (); + yn_test (); + + if (output_ulps) + fclose (ulps_file); + + printf ("\nTest suite completed:\n"); + printf (" %d test cases plus %d tests for exception flags executed.\n", + noTests, noExcTests); + if (noXFails) + printf (" %d expected failures occurred.\n", noXFails); + if (noXPasses) + printf (" %d unexpected passes occurred.\n", noXPasses); + if (noErrors) + { + printf (" %d errors occurred.\n", noErrors); + return 1; + } + printf (" All tests passed successfully.\n"); + + return 0; +} + +/* + * Local Variables: + * mode:c + * End: + */ diff --git a/openlibm/test/test-211.c b/openlibm/test/test-211.c new file mode 100644 index 0000000..8bec4e9 --- /dev/null +++ b/openlibm/test/test-211.c @@ -0,0 +1,12 @@ +#include +#include +#include + +int +main() +{ + float x = 0xd.65874p-4f; + float y = 4.0f; + float z = powf (x, y); + assert(z==0x1.f74424p-2); +} diff --git a/openlibm/test/test-double.c b/openlibm/test/test-double.c new file mode 100644 index 0000000..4d239a7 --- /dev/null +++ b/openlibm/test/test-double.c @@ -0,0 +1,34 @@ +/* Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Andreas Jaeger , 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, write to the Free + Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA + 02111-1307 USA. */ + +#define FUNC(function) function +#define FLOAT double +#define TEST_MSG "testing double (without inline functions)\n" +#define MATHCONST(x) x +#define CHOOSE(Clongdouble,Cdouble,Cfloat,Cinlinelongdouble,Cinlinedouble,Cinlinefloat) Cdouble +#define PRINTF_EXPR "e" +#define PRINTF_XEXPR "a" +#define PRINTF_NEXPR "f" +#define TEST_DOUBLE 1 + +#ifndef __NO_MATH_INLINES +# define __NO_MATH_INLINES +#endif + +#include "libm-test.c" diff --git a/openlibm/test/test-float.c b/openlibm/test/test-float.c new file mode 100644 index 0000000..26a4213 --- /dev/null +++ b/openlibm/test/test-float.c @@ -0,0 +1,34 @@ +/* Copyright (C) 1997, 1999 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Andreas Jaeger , 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, write to the Free + Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA + 02111-1307 USA. */ + +#define FUNC(function) function ## f +#define FLOAT float +#define TEST_MSG "testing float (without inline functions)\n" +#define MATHCONST(x) x +#define CHOOSE(Clongdouble,Cdouble,Cfloat,Cinlinelongdouble,Cinlinedouble,Cinlinefloat) Cfloat +#define PRINTF_EXPR "e" +#define PRINTF_XEXPR "a" +#define PRINTF_NEXPR "f" +#define TEST_FLOAT 1 + +#ifndef __NO_MATH_INLINES +# define __NO_MATH_INLINES +#endif + +#include "libm-test.c" diff --git a/openlibm/wasm32/Make.files b/openlibm/wasm32/Make.files new file mode 100644 index 0000000..e69de29 diff --git a/openlibm/wasm32/assert.h b/openlibm/wasm32/assert.h new file mode 100644 index 0000000..5c6205b --- /dev/null +++ b/openlibm/wasm32/assert.h @@ -0,0 +1 @@ +#define assert(x) ((void)0) diff --git a/openlibm/wasm32/float.h b/openlibm/wasm32/float.h new file mode 100644 index 0000000..c82ecbd --- /dev/null +++ b/openlibm/wasm32/float.h @@ -0,0 +1,33 @@ +#pragma once + +#define FLT_RADIX 2 + +#define FLT_TRUE_MIN 1.40129846432481707092e-45F +#define FLT_MIN 1.17549435082228750797e-38F +#define FLT_MAX 3.40282346638528859812e+38F +#define FLT_EPSILON 1.1920928955078125e-07F + +#define FLT_MANT_DIG 24 +#define FLT_MIN_EXP (-125) +#define FLT_MAX_EXP 128 +#define FLT_HAS_SUBNORM 1 + +#define FLT_DIG 6 +#define FLT_DECIMAL_DIG 9 +#define FLT_MIN_10_EXP (-37) +#define FLT_MAX_10_EXP 38 + +#define DBL_TRUE_MIN 4.94065645841246544177e-324 +#define DBL_MIN 2.22507385850720138309e-308 +#define DBL_MAX 1.79769313486231570815e+308 +#define DBL_EPSILON 2.22044604925031308085e-16 + +#define DBL_MANT_DIG 53 +#define DBL_MIN_EXP (-1021) +#define DBL_MAX_EXP 1024 +#define DBL_HAS_SUBNORM 1 + +#define DBL_DIG 15 +#define DBL_DECIMAL_DIG 17 +#define DBL_MIN_10_EXP (-307) +#define DBL_MAX_10_EXP 308 diff --git a/openlibm/wasm32/limits.h b/openlibm/wasm32/limits.h new file mode 100644 index 0000000..1f8d124 --- /dev/null +++ b/openlibm/wasm32/limits.h @@ -0,0 +1,9 @@ +#include + +#define INT_MIN INT32_MIN +#define INT_MAX INT32_MAX +#define LONG_MIN INT32_MIN +#define LONG_MAX INT32_MAX +#define LLONG_MIN INT64_MIN +#define LLONG_MAX INT64_MAX + diff --git a/openlibm/wasm32/stdint.h b/openlibm/wasm32/stdint.h new file mode 100644 index 0000000..3996e5b --- /dev/null +++ b/openlibm/wasm32/stdint.h @@ -0,0 +1,43 @@ +#pragma once + +typedef unsigned char uint8_t; +typedef unsigned short uint16_t; +typedef unsigned int uint32_t; +typedef unsigned long long uint64_t; + +typedef char int8_t; +typedef short int16_t; +typedef int int32_t; +typedef long long int64_t; + +typedef unsigned int uintptr_t; +typedef int intptr_t; + +_Static_assert(sizeof (uint8_t) == 1, "invalid size"); +_Static_assert(sizeof (uint16_t) == 2, "invalid size"); +_Static_assert(sizeof (uint32_t) == 4, "invalid size"); +_Static_assert(sizeof (uint64_t) == 8, "invalid size"); + +_Static_assert(sizeof (int8_t) == 1, "invalid size"); +_Static_assert(sizeof (int16_t) == 2, "invalid size"); +_Static_assert(sizeof (int32_t) == 4, "invalid size"); +_Static_assert(sizeof (int64_t) == 8, "invalid size"); + +_Static_assert(sizeof (uintptr_t) == sizeof (intptr_t), "invalid size"); +_Static_assert(sizeof (uintptr_t) == sizeof (void*), "invalid size"); +_Static_assert(sizeof (uintptr_t) == 4, "invalid size"); + +#define UINT8_MAX 0xFF +#define UINT16_MAX 0xFFFF +#define UINT32_MAX 0xFFFFFFFFUL +#define UINT64_MAX 0xFFFFFFFFFFFFFFFFULL + +#define INT8_MAX 0x7F +#define INT16_MAX 0x7FFF +#define INT32_MAX 0x7FFFFFFF +#define INT64_MAX 0x7FFFFFFFFFFFFFFF + +#define INT8_MIN (-0x80) +#define INT16_MIN (-0x8000) +#define INT32_MIN (-0x80000000L) +#define INT64_MIN (-0x8000000000000000LL) diff --git a/printf.c b/printf.c new file mode 100644 index 0000000..cebfe40 --- /dev/null +++ b/printf.c @@ -0,0 +1,12 @@ +#include +#include + +int printf(const char *restrict fmt, ...) +{ + int ret; + va_list ap; + va_start(ap, fmt); + ret = vfprintf(stdout, fmt, ap); + va_end(ap); + return ret; +} diff --git a/serial.c b/serial.c new file mode 100644 index 0000000..4779588 --- /dev/null +++ b/serial.c @@ -0,0 +1,47 @@ +#include +#include +#include + +#define DEFAULT_BAUDRATE 115200 + +void gilbraltar_serial_init(void) { + uint32_t baudrate = DEFAULT_BAUDRATE; + uint32_t clock_rate = gilbraltar_get_clock(2); + uint32_t baud16 = baudrate * 16; + uint32_t int_div = clock_rate / baud16; + uint32_t fract_div_2 = (clock_rate % baud16) * 8 / baudrate; + uint32_t fract_div = fract_div_2 / 2 + fract_div_2 % 2; + + write32(ARM_UART0_IMSC, 0); + write32(ARM_UART0_ICR, 0x7ff); + write32(ARM_UART0_IBRD, int_div); + write32(ARM_UART0_FBRD, fract_div); + write32(ARM_UART0_LCRH, (1 << 4) | (3 << 5)); + write32(ARM_UART0_CR, (1 << 0) | (1 << 8) | (1 << 9)); +} + +void gilbraltar_serial_send(uint8_t chr) { + while (1) + if (!(read32(ARM_UART0_FR) & 0x20)) break; + + write32(ARM_UART0_DR, chr); +} + +uint8_t gilbraltar_serial_recv(void) { + while (1) + if (!(read32(ARM_UART0_FR) & 0x10)) break; + + return (read32(ARM_UART0_DR) & 0xff); +} + +void gilbraltar_serial_puts(const char *str) { + while (*str) gilbraltar_serial_send(*str++); +} + +void gilbraltar_serial_putchar(int chr) { + gilbraltar_serial_send(chr & 0xff); +} + +void gilbraltar_serial_write(const char *str, size_t len) { + while (len--) gilbraltar_serial_send(*str++); +} diff --git a/startup.S b/startup.S new file mode 100644 index 0000000..7ec81e3 --- /dev/null +++ b/startup.S @@ -0,0 +1,105 @@ +/* startup.S + * + * Copyright (C) 2014-2024 R. Stange + * Copyright (C) 2024 Romain Calascibetta + */ + +#include + + .macro armv8_switch_to_el1_m, xreg1, xreg2 + /* Initialize Generic Timers */ + mrs \xreg1, cnthctl_el2 + orr \xreg1, \xreg1, #0x3 /* Enable EL1 access to timers */ + msr cnthctl_el2, \xreg1 + msr cntvoff_el2, xzr + + /* Initialize MPID/MIPDR registers */ + mrs \xreg1, midr_el1 + mrs \xreg2, mpidr_el1 + msr vpidr_el2, \xreg1 + msr vmpidr_el2, \xreg2 + + /* Disable coprocessor traps */ + mov \xreg1, #0x33ff + msr cptr_el2, \xreg1 /* Disable coprocessor traps to EL2 */ + msr hstr_el2, xzr /* Disable coprocessor trap to EL2 */ + mov \xreg1, #3 << 20 + msr cpacr_el1, \xreg1 /* Enable FP/SIMD at EL1 */ + + /* Initalize HCR_EL2 */ + mov \xreg1, #(1 << 31) /* 64bit EL1 */ + msr hcr_el2, \xreg1 + + /* SCTLR_EL1 initialization + * + * Setting RES1 bits [39, 28, 23, 22, 20, 11] to 1 + * and RES0 bits [31, 30, 27, 21, 17, 13, 10, 6] to 1 + * and UCI, EE, E0E, WXN, nTWE, nTWI, UCT, DZE, I, UMA, SED, ITD, CP15BEN, + * SA0, SA, C and M to 0 + */ + mov \xreg1, #0x0800 + movk \xreg1, #0x30d0, lsl #16 + msr sctlr_el1, \xreg1 + + /* Return to the EL1_SP1 mode from EL2 */ + mov \xreg1, #0x3c4 + msr spsr_el2, \xreg1 /* EL1_SP0 | D | A | I | F */ + adr \xreg1, 1f + msr elr_el2, \xreg1 + eret +1: + + .endm + + .section .init + .globl _start + +_start: // normally entered from armstub8 in EL2 after boot +// ldr x0, =MEM_KERNEL_STACK +// mov sp, x0 +// b gilbraltar_sysinit + mrs x0, CurrentEL // Check if already in EL1t mode? + cmp x0, #4 + beq 1f + + ldr x0, =MEM_EXCEPTION_STACK // IRQ, FIQ and exception handler run in EL1h + msr sp_el1, x0 + ldr x0, =VectorTable // init exception vector table for EL2 + msr vbar_el2, x0 + armv8_switch_to_el1_m x0, x1 +1: + ldr x0, =MEM_KERNEL_STACK // main thread runs in EL1t and use sp_el0 + mov sp, x0 + ldr x0, =VectorTable // init exception vector table + msr vbar_el1, x0 + b gilbraltar_sysinit + +/* Multicore + * .globl _start_secondary + * _start_secondary: + * mrs x2, mpidr_el1 // read affinity + * lsr x2, x2, #8 // CPU ID is Aff1 in Cortex-A76 + * and x2, x2, #CORES-1 // Get CPU ID + * mrs x0, CurrentEL + * cmp x0, #4 + * beq 1f + * + * mov x1, #EXCEPTION_STACK_SIZE // calculate exception stack offset for core + * mul x1, x1, x2 + * ldr x0, =MEM_EXCEPTION_STACK // IRC, FIQ, and exception handler run in EL1h + * add x0, x0, x1 + * msr sp_el1, x0 // init their stack + * + * armv8_switch_to_el1_m x0, x1 + * 1: + * mov x1, #KERNEL_STACK_SIZE // calculate kernel stack offset for the core + * mul x1, x1, x2 + * ldr x0, =MEM_KERNEL_STACK // main thread runs in EL1t and use sp_el0 + * add x0, x0, x1 + * mov sp, x0 // init its stack + * + * ldr x0, =VectorTable // init exception vector table + * msr vbar_el1, x0 + * + * b sysinit_secondary + */ diff --git a/test/test01.c b/test/test01.c new file mode 100644 index 0000000..48705a4 --- /dev/null +++ b/test/test01.c @@ -0,0 +1,15 @@ +#include +#include + +/* The kernel should start and the LED should blink. + * The time between blinks should be "fairly" long (around 1s). + */ + +void main(void) { + while (1) { + gilbraltar_led(false); + gilbraltar_delay_hot_loop(0x3f0000); + gilbraltar_led(true); + gilbraltar_delay_hot_loop(0x3f0000); + } +} diff --git a/test/test02.c b/test/test02.c new file mode 100644 index 0000000..1e21641 --- /dev/null +++ b/test/test02.c @@ -0,0 +1,9 @@ +#include + +/* The kernel should start and you should see + * "Hello World!" in your terminal! + */ +void main(void) { + gilbraltar_serial_init(); + gilbraltar_serial_puts("Hello World!\r\n"); +} diff --git a/test/test03.c b/test/test03.c new file mode 100644 index 0000000..589da7f --- /dev/null +++ b/test/test03.c @@ -0,0 +1,28 @@ +#include +#include + +extern char _etext[]; + +void main(void) { + gilbraltar_log(INFO, " _____ _ _ _ _ _ \r\n"); + gilbraltar_log(INFO, "| __|_| | |_ ___ ___| | |_ ___ ___ \r\n"); + gilbraltar_log(INFO, "| | | | | . | _| .'| | _| .'| _|\r\n"); + gilbraltar_log(INFO, "|_____|_|_|___|_| |__,|_|_| |__,|_| \r\n"); + gilbraltar_log(INFO, " BL31 @ 0x%08x - 0x%08x\r\n", 0x0, 0x8000); + gilbraltar_log(INFO, " EL3 stack @ 0x%08x\r\n", 0x6f000); + gilbraltar_log(INFO, " kernel @ 0x%08x - 0x%08lx\r\n", + MEM_KERNEL_START, (uintptr_t) _etext); + gilbraltar_log(INFO, " stack @ 0x%08x - 0x%08x\r\n", + MEM_KERNEL_STACK - KERNEL_STACK_SIZE, MEM_KERNEL_STACK); + gilbraltar_log(INFO, "exception stack @ 0x%08x - 0x%08x\r\n", + MEM_EXCEPTION_STACK - EXCEPTION_STACK_SIZE, + MEM_EXCEPTION_STACK); + gilbraltar_log(INFO, " irq stack @ 0x%08x - 0x%08x\r\n", + MEM_IRQ_STACK - EXCEPTION_STACK_SIZE, MEM_IRQ_STACK); + gilbraltar_log(INFO, " fiq stack @ 0x%08x - 0x%08x\r\n", + MEM_FIQ_STACK - EXCEPTION_STACK_SIZE, MEM_FIQ_STACK); + gilbraltar_log(INFO, " pages table @ 0x%08x - 0x%08x\r\n", MEM_PAGE_TABLE1, + MEM_PAGE_TABLE1_END); + gilbraltar_log(INFO, "coherent region @ 0x%08x - 0x%08x\r\n", + MEM_COHERENT_REGION, MEM_COHERENT_REGION + 4 * MEGABYTE); +} diff --git a/timer.c b/timer.c new file mode 100644 index 0000000..eeba853 --- /dev/null +++ b/timer.c @@ -0,0 +1,25 @@ +#include /* for ARM_SYSTIMER_CLO */ +#include /* for read32() */ +#include /* for uint32_t */ +#include /* for CLOCKHZ */ + +void gilbraltar_delay_hot_loop(uint32_t cycle) { + volatile uint32_t v; + for (v = 0; v < cycle; v++) + ; +} + +void gilbraltar_delay_us(uint32_t us) { + if (us > 0) { + uint32_t ticks = us * (CLOCKHZ / 1000000) + 1; + uint32_t s = read32(ARM_SYSTIMER_CLO); + + while (read32(ARM_SYSTIMER_CLO) - s < ticks) + ; + } +} + +void gilbraltar_delay_ms(uint32_t ms) { + if (ms > 0) + gilbraltar_delay_us(ms * 1000); +}