Index: stable/10/lib/msun/Makefile =================================================================== --- stable/10/lib/msun/Makefile (revision 271778) +++ stable/10/lib/msun/Makefile (revision 271779) @@ -1,219 +1,220 @@ # @(#)Makefile 5.1beta 93/09/24 # $FreeBSD$ # # ==================================================== # 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. # ==================================================== # # .if ${MACHINE_CPUARCH} == "i386" ARCH_SUBDIR= i387 .else ARCH_SUBDIR= ${MACHINE_CPUARCH} .endif .include "${ARCH_SUBDIR}/Makefile.inc" .PATH: ${.CURDIR}/${ARCH_SUBDIR} .if ${MACHINE_CPUARCH} == "i386" || ${MACHINE_CPUARCH} == "amd64" .PATH: ${.CURDIR}/x86 CFLAGS+= -I${.CURDIR}/x86 .endif # long double format .if ${LDBL_PREC} == 64 .PATH: ${.CURDIR}/ld80 CFLAGS+= -I${.CURDIR}/ld80 .elif ${LDBL_PREC} == 113 .PATH: ${.CURDIR}/ld128 CFLAGS+= -I${.CURDIR}/ld128 .endif .PATH: ${.CURDIR}/bsdsrc .PATH: ${.CURDIR}/src .PATH: ${.CURDIR}/man LIB= m SHLIBDIR?= /lib SHLIB_MAJOR= 5 WARNS?= 1 IGNORE_PRAGMA= COMMON_SRCS= b_exp.c b_log.c b_tgamma.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_gamma.c e_gamma_r.c e_gammaf.c \ e_gammaf_r.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_rem_pio2.c \ e_rem_pio2f.c e_remainder.c e_remainderf.c e_scalb.c e_scalbf.c \ e_sinh.c e_sinhf.c e_sqrt.c e_sqrtf.c fenv.c \ imprecise.c \ k_cos.c k_cosf.c k_exp.c k_expf.c k_rem_pio2.c k_sin.c k_sinf.c \ k_tan.c k_tanf.c \ s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_carg.c s_cargf.c s_cargl.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_fabsf.c s_fdim.c \ s_finite.c s_finitef.c \ s_floor.c s_floorf.c s_fma.c s_fmaf.c \ s_fmax.c s_fmaxf.c s_fmaxl.c s_fmin.c \ s_fminf.c s_fminl.c s_frexp.c s_frexpf.c s_ilogb.c s_ilogbf.c \ s_ilogbl.c s_isfinite.c s_isnan.c s_isnormal.c \ s_llrint.c s_llrintf.c s_llround.c s_llroundf.c s_llroundl.c \ s_log1p.c s_log1pf.c s_logb.c s_logbf.c s_lrint.c s_lrintf.c \ s_lround.c s_lroundf.c s_lroundl.c s_modff.c \ s_nan.c s_nearbyint.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_roundl.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_significand.c s_significandf.c s_sin.c s_sinf.c \ s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c s_trunc.c s_truncf.c \ w_cabs.c w_cabsf.c w_drem.c w_dremf.c # Location of fpmath.h and _fpmath.h LIBCDIR= ${.CURDIR}/../libc .if exists(${LIBCDIR}/${MACHINE_ARCH}) LIBC_ARCH=${MACHINE_ARCH} .else LIBC_ARCH=${MACHINE_CPUARCH} .endif CFLAGS+= -I${.CURDIR}/src -I${LIBCDIR}/include \ -I${LIBCDIR}/${LIBC_ARCH} SYM_MAPS+= ${.CURDIR}/Symbol.map VERSION_DEF= ${LIBCDIR}/Versions.def SYMBOL_MAPS= ${SYM_MAPS} # C99 long double functions COMMON_SRCS+= s_copysignl.c s_fabsl.c s_llrintl.c s_lrintl.c s_modfl.c .if ${LDBL_PREC} != 53 # If long double != double use these; otherwise, we alias the double versions. COMMON_SRCS+= e_acoshl.c e_acosl.c e_asinl.c e_atan2l.c e_atanhl.c \ - e_fmodl.c e_hypotl.c e_remainderl.c e_sqrtl.c \ + e_coshl.c e_fmodl.c e_hypotl.c \ + e_remainderl.c e_sinhl.c e_sqrtl.c \ invtrig.c k_cosl.c k_sinl.c k_tanl.c \ s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c s_cprojl.c \ - s_csqrtl.c s_exp2l.c s_expl.c s_floorl.c s_fmal.c \ + s_csqrtl.c s_erfl.c s_exp2l.c s_expl.c s_floorl.c s_fmal.c \ s_frexpl.c s_logbl.c s_logl.c s_nanl.c s_nextafterl.c \ - s_nexttoward.c s_remquol.c s_rintl.c s_scalbnl.c \ - s_sinl.c s_tanl.c s_truncl.c w_cabsl.c + s_nexttoward.c s_remquol.c s_rintl.c s_roundl.c s_scalbnl.c \ + s_sinl.c s_tanhl.c s_tanl.c s_truncl.c w_cabsl.c .endif # C99 complex functions COMMON_SRCS+= catrig.c catrigf.c \ s_ccosh.c s_ccoshf.c s_cexp.c s_cexpf.c \ s_cimag.c s_cimagf.c s_cimagl.c \ s_conj.c s_conjf.c s_conjl.c \ s_cproj.c s_cprojf.c s_creal.c s_crealf.c s_creall.c \ s_csinh.c s_csinhf.c s_ctanh.c s_ctanhf.c # FreeBSD's C library supplies these functions: #COMMON_SRCS+= s_fabs.c s_frexp.c s_isnan.c s_ldexp.c s_modf.c # Exclude the generic versions of what we provide in the MD area. .if defined(ARCH_SRCS) .for i in ${ARCH_SRCS} COMMON_SRCS:= ${COMMON_SRCS:N${i:R}.c} .endfor .endif SRCS= ${COMMON_SRCS} ${ARCH_SRCS} INCS+= fenv.h math.h MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 \ ceil.3 cacos.3 ccos.3 ccosh.3 cexp.3 \ cimag.3 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \ feclearexcept.3 feenableexcept.3 fegetenv.3 \ fegetround.3 fenv.3 floor.3 \ fma.3 fmax.3 fmod.3 hypot.3 ieee.3 ieee_test.3 ilogb.3 j0.3 \ lgamma.3 log.3 lrint.3 lround.3 math.3 nan.3 \ nextafter.3 remainder.3 rint.3 \ round.3 scalbn.3 signbit.3 sin.3 sinh.3 sqrt.3 tan.3 tanh.3 trunc.3 \ complex.3 MLINKS+=acos.3 acosf.3 acos.3 acosl.3 MLINKS+=acosh.3 acoshf.3 acosh.3 acoshl.3 MLINKS+=asin.3 asinf.3 asin.3 asinl.3 MLINKS+=asinh.3 asinhf.3 asinh.3 asinhl.3 MLINKS+=atan.3 atanf.3 atan.3 atanl.3 MLINKS+=atanh.3 atanhf.3 atanh.3 atanhl.3 MLINKS+=atan2.3 atan2f.3 atan2.3 atan2l.3 \ atan2.3 carg.3 atan2.3 cargf.3 atan2.3 cargl.3 MLINKS+=cacos.3 cacosf.3 cacos.3 cacosh.3 cacos.3 cacoshf.3 \ cacos.3 casin.3 cacos.3 casinf.3 cacos.3 casinh.3 cacos.3 casinhf.3 \ cacos.3 catan.3 cacos.3 catanf.3 cacos.3 catanh.3 cacos.3 catanhf.3 MLINKS+=ccos.3 ccosf.3 ccos.3 csin.3 ccos.3 csinf.3 ccos.3 ctan.3 ccos.3 ctanf.3 MLINKS+=ccosh.3 ccoshf.3 ccosh.3 csinh.3 ccosh.3 csinhf.3 \ ccosh.3 ctanh.3 ccosh.3 ctanhf.3 MLINKS+=ceil.3 ceilf.3 ceil.3 ceill.3 MLINKS+=cexp.3 cexpf.3 MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \ cimag.3 conj.3 cimag.3 conjf.3 cimag.3 conjl.3 \ cimag.3 cproj.3 cimag.3 cprojf.3 cimag.3 cprojl.3 \ cimag.3 creal.3 cimag.3 crealf.3 cimag.3 creall.3 MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3 MLINKS+=cos.3 cosf.3 cos.3 cosl.3 -MLINKS+=cosh.3 coshf.3 +MLINKS+=cosh.3 coshf.3 cosh.3 coshl.3 MLINKS+=csqrt.3 csqrtf.3 csqrt.3 csqrtl.3 -MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3 +MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3 erf.3 erfl.3 erf.3 erfcl.3 MLINKS+=exp.3 expm1.3 exp.3 expm1f.3 exp.3 expm1l.3 exp.3 pow.3 exp.3 powf.3 \ exp.3 exp2.3 exp.3 exp2f.3 exp.3 exp2l.3 exp.3 expf.3 exp.3 expl.3 MLINKS+=fabs.3 fabsf.3 fabs.3 fabsl.3 MLINKS+=fdim.3 fdimf.3 fdim.3 fdiml.3 MLINKS+=feclearexcept.3 fegetexceptflag.3 feclearexcept.3 feraiseexcept.3 \ feclearexcept.3 fesetexceptflag.3 feclearexcept.3 fetestexcept.3 MLINKS+=feenableexcept.3 fedisableexcept.3 feenableexcept.3 fegetexcept.3 MLINKS+=fegetenv.3 feholdexcept.3 fegetenv.3 fesetenv.3 \ fegetenv.3 feupdateenv.3 MLINKS+=fegetround.3 fesetround.3 MLINKS+=floor.3 floorf.3 floor.3 floorl.3 MLINKS+=fma.3 fmaf.3 fma.3 fmal.3 MLINKS+=fmax.3 fmaxf.3 fmax.3 fmaxl.3 \ fmax.3 fmin.3 fmax.3 fminf.3 fmax.3 fminl.3 MLINKS+=fmod.3 fmodf.3 fmod.3 fmodl.3 MLINKS+=hypot.3 cabs.3 hypot.3 cabsf.3 hypot.3 cabsl.3 \ hypot.3 hypotf.3 hypot.3 hypotl.3 MLINKS+=ieee_test.3 scalb.3 ieee_test.3 scalbf.3 MLINKS+=ieee_test.3 significand.3 ieee_test.3 significandf.3 MLINKS+=ilogb.3 ilogbf.3 ilogb.3 ilogbl.3 \ ilogb.3 logb.3 ilogb.3 logbf.3 ilogb.3 logbl.3 MLINKS+=j0.3 j1.3 j0.3 jn.3 j0.3 y0.3 j0.3 y1.3 j0.3 y1f.3 j0.3 yn.3 MLINKS+=j0.3 j0f.3 j0.3 j1f.3 j0.3 jnf.3 j0.3 y0f.3 j0.3 ynf.3 MLINKS+=lgamma.3 gamma.3 lgamma.3 gammaf.3 lgamma.3 lgammaf.3 \ lgamma.3 tgamma.3 lgamma.3 tgammaf.3 MLINKS+=log.3 log10.3 log.3 log10f.3 log.3 log10l.3 \ log.3 log1p.3 log.3 log1pf.3 log.3 log1pl.3 \ log.3 logf.3 log.3 logl.3 \ log.3 log2.3 log.3 log2f.3 log.3 log2l.3 MLINKS+=lrint.3 llrint.3 lrint.3 llrintf.3 lrint.3 llrintl.3 \ lrint.3 lrintf.3 lrint.3 lrintl.3 MLINKS+=lround.3 llround.3 lround.3 llroundf.3 lround.3 llroundl.3 \ lround.3 lroundf.3 lround.3 lroundl.3 MLINKS+=nan.3 nanf.3 nan.3 nanl.3 MLINKS+=nextafter.3 nextafterf.3 nextafter.3 nextafterl.3 MLINKS+=nextafter.3 nexttoward.3 nextafter.3 nexttowardf.3 MLINKS+=nextafter.3 nexttowardl.3 MLINKS+=remainder.3 remainderf.3 remainder.3 remainderl.3 \ remainder.3 remquo.3 remainder.3 remquof.3 remainder.3 remquol.3 MLINKS+=rint.3 rintf.3 rint.3 rintl.3 \ rint.3 nearbyint.3 rint.3 nearbyintf.3 rint.3 nearbyintl.3 MLINKS+=round.3 roundf.3 round.3 roundl.3 MLINKS+=scalbn.3 scalbln.3 scalbn.3 scalblnf.3 scalbn.3 scalblnl.3 MLINKS+=scalbn.3 scalbnf.3 scalbn.3 scalbnl.3 MLINKS+=sin.3 sinf.3 sin.3 sinl.3 -MLINKS+=sinh.3 sinhf.3 +MLINKS+=sinh.3 sinhf.3 sinh.3 sinhl.3 MLINKS+=sqrt.3 cbrt.3 sqrt.3 cbrtf.3 sqrt.3 cbrtl.3 sqrt.3 sqrtf.3 \ sqrt.3 sqrtl.3 MLINKS+=tan.3 tanf.3 tan.3 tanl.3 -MLINKS+=tanh.3 tanhf.3 +MLINKS+=tanh.3 tanhf.3 tanh.3 tanhl.3 MLINKS+=trunc.3 truncf.3 trunc.3 truncl.3 .include Index: stable/10/lib/msun/Symbol.map =================================================================== --- stable/10/lib/msun/Symbol.map (revision 271778) +++ stable/10/lib/msun/Symbol.map (revision 271779) @@ -1,282 +1,282 @@ /* * $FreeBSD$ */ /* 7.0-CURRENT */ FBSD_1.0 { __fe_dfl_env; tgamma; acos; acosf; acosh; acoshf; asin; asinf; atan2; atan2f; atanh; atanhf; cosh; coshf; exp; expf; fmod; fmodf; gamma; gamma_r; gammaf; gammaf_r; hypot; hypotf; j0; y0; j0f; y0f; j1; y1; j1f; y1f; jn; yn; jnf; ynf; lgamma; lgamma_r; lgammaf; lgammaf_r; log; log10; log10f; logf; pow; powf; remainder; remainderf; scalb; scalbf; sinh; sinhf; sqrt; sqrtf; asinh; asinhf; atan; atanf; cbrt; cbrtf; ceil; ceilf; ceill; cimag; cimagf; cimagl; conj; conjf; conjl; copysign; copysignf; copysignl; cos; cosf; creal; crealf; creall; erf; erfc; erff; erfcf; exp2; exp2f; expm1; expm1f; fabs; fabsf; fabsl; fdim; fdimf; fdiml; finite; finitef; floor; floorf; floorl; fma; fmaf; fmal; fmax; fmaxf; fmaxl; fmin; fminf; fminl; frexp; frexpf; frexpl; ilogb; ilogbf; ilogbl; __isfinite; __isfinitef; __isfinitel; isnanf; __isnanl; __isnormal; __isnormalf; __isnormall; llrint; llrintf; llround; llroundf; llroundl; log1p; log1pf; logb; logbf; lrint; lrintf; lround; lroundf; lroundl; modff; modfl; nearbyint; nearbyintf; nextafter; nexttoward; nexttowardl; nextafterl; nextafterf; nexttowardf; remquo; remquof; rint; rintf; round; roundf; roundl; scalbln; scalblnf; scalblnl; scalbn; scalbnl; scalbnf; ldexpf; ldexpl; __signbit; __signbitf; __signbitl; signgam; significand; significandf; sin; sinf; tan; tanf; tanh; tanhf; trunc; truncf; truncl; cabs; cabsf; drem; dremf; }; /* First added in 8.0-CURRENT */ FBSD_1.1 { carg; cargf; csqrt; csqrtf; logbl; nan; nanf; nanl; llrintl; lrintl; nearbyintl; rintl; exp2l; sinl; cosl; tanl; tgammaf; sqrtl; hypotl; cabsl; csqrtl; remquol; remainderl; fmodl; acosl; asinl; atan2l; atanl; cargl; cproj; cprojf; cprojl; }; /* First added in 9.0-CURRENT */ FBSD_1.2 { __isnanf; cbrtl; cexp; cexpf; log2; log2f; }; /* First added in 10.0-CURRENT */ FBSD_1.3 { feclearexcept; fegetexceptflag; fetestexcept; fegetround; fesetround; fesetenv; acoshl; asinhl; atanhl; cacos; cacosf; cacosh; cacoshf; casin; casinf; casinh; casinhf; catan; catanf; catanh; catanhf; csin; csinf; csinh; csinhf; ccos; ccosf; ccosh; ccoshf; + coshl; ctan; ctanf; ctanh; ctanhf; + erfcl; + erfl; expl; expm1l; log10l; log1pl; log2l; logl; + sinhl; + tanhl; /* Implemented as weak aliases for imprecise versions */ - coshl; - erfcl; - erfl; lgammal; powl; - sinhl; - tanhl; tgammal; }; Index: stable/10/lib/msun/ld128/k_expl.h =================================================================== --- stable/10/lib/msun/ld128/k_expl.h (nonexistent) +++ stable/10/lib/msun/ld128/k_expl.h (revision 271779) @@ -0,0 +1,328 @@ +/* from: FreeBSD: head/lib/msun/ld128/s_expl.c 251345 2013-06-03 20:09:22Z kargl */ + +/*- + * Copyright (c) 2009-2013 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. + * + * Optimized by Bruce D. Evans. + */ + +#include +__FBSDID("$FreeBSD$"); + +/* + * ld128 version of k_expl.h. See ../ld80/s_expl.c for most comments. + * + * See ../src/e_exp.c and ../src/k_exp.h for precision-independent comments + * about the secondary kernels. + */ + +#define INTERVALS 128 +#define LOG2_INTERVALS 7 +#define BIAS (LDBL_MAX_EXP - 1) + +static const double +/* + * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must + * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest + * bits zero so that multiplication of it by n is exact. + */ +INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */ +L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */ +static const long double +/* 0x1.62e42fefa39ef35793c768000000p-8 */ +L1 = 5.41521234812457272982212595914567508e-3L; + +/* + * XXX values in hex in comments have been lost (or were never present) + * from here. + */ +static const long double +/* + * Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]: + * |exp(x) - p(x)| < 2**-124.9 + * (0.002708 is ln2/(2*INTERVALS) rounded up a little). + * + * XXX the coeffs aren't very carefully rounded, and I get 3.6 more bits. + */ +A2 = 0.5, +A3 = 1.66666666666666666666666666651085500e-1L, +A4 = 4.16666666666666666666666666425885320e-2L, +A5 = 8.33333333333333333334522877160175842e-3L, +A6 = 1.38888888888888888889971139751596836e-3L; + +static const double +A7 = 1.9841269841269470e-4, /* 0x1.a01a01a019f91p-13 */ +A8 = 2.4801587301585286e-5, /* 0x1.71de3ec75a967p-19 */ +A9 = 2.7557324277411235e-6, /* 0x1.71de3ec75a967p-19 */ +A10 = 2.7557333722375069e-7; /* 0x1.27e505ab56259p-22 */ + +static const struct { + /* + * hi must be rounded to at most 106 bits so that multiplication + * by r1 in expm1l() is exact, but it is rounded to 88 bits due to + * historical accidents. + * + * XXX it is wasteful to use long double for both hi and lo. ld128 + * exp2l() uses only float for lo (in a very differently organized + * table; ld80 exp2l() is different again. It uses 2 doubles in a + * table organized like this one. 1 double and 1 float would + * suffice). There are different packing/locality/alignment/caching + * problems with these methods. + * + * XXX C's bad %a format makes the bits unreadable. They happen + * to all line up for the hi values 1 before the point and 88 + * in 22 nybbles, but for the low values the nybbles are shifted + * randomly. + */ + long double hi; + long double lo; +} tbl[INTERVALS] = { + 0x1p0L, 0x0p0L, + 0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L, + 0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L, + 0x1.04315e86e7f84bd738f9a2p0L, 0xd.a47e6ed040bb4bfc05af6455e9b8p-96L, + 0x1.059b0d31585743ae7c548ep0L, 0xb.68ca417fe53e3495f7df4baf84a0p-92L, + 0x1.0706b29ddf6ddc6dc403a8p0L, 0x1.d87b27ed07cb8b092ac75e311753p-88L, + 0x1.0874518759bc808c35f25cp0L, 0x1.9427fa2b041b2d6829d8993a0d01p-88L, + 0x1.09e3ecac6f3834521e060cp0L, 0x5.84d6b74ba2e023da730e7fccb758p-92L, + 0x1.0b5586cf9890f6298b92b6p0L, 0x1.1842a98364291408b3ceb0a2a2bbp-88L, + 0x1.0cc922b7247f7407b705b8p0L, 0x9.3dc5e8aac564e6fe2ef1d431fd98p-92L, + 0x1.0e3ec32d3d1a2020742e4ep0L, 0x1.8af6a552ac4b358b1129e9f966a4p-88L, + 0x1.0fb66affed31af232091dcp0L, 0x1.8a1426514e0b627bda694a400a27p-88L, + 0x1.11301d0125b50a4ebbf1aep0L, 0xd.9318ceac5cc47ab166ee57427178p-92L, + 0x1.12abdc06c31cbfb92bad32p0L, 0x4.d68e2f7270bdf7cedf94eb1cb818p-92L, + 0x1.1429aaea92ddfb34101942p0L, 0x1.b2586d01844b389bea7aedd221d4p-88L, + 0x1.15a98c8a58e512480d573cp0L, 0x1.d5613bf92a2b618ee31b376c2689p-88L, + 0x1.172b83c7d517adcdf7c8c4p0L, 0x1.0eb14a792035509ff7d758693f24p-88L, + 0x1.18af9388c8de9bbbf70b9ap0L, 0x3.c2505c97c0102e5f1211941d2840p-92L, + 0x1.1a35beb6fcb753cb698f68p0L, 0x1.2d1c835a6c30724d5cfae31b84e5p-88L, + 0x1.1bbe084045cd39ab1e72b4p0L, 0x4.27e35f9acb57e473915519a1b448p-92L, + 0x1.1d4873168b9aa7805b8028p0L, 0x9.90f07a98b42206e46166cf051d70p-92L, + 0x1.1ed5022fcd91cb8819ff60p0L, 0x1.121d1e504d36c47474c9b7de6067p-88L, + 0x1.2063b88628cd63b8eeb028p0L, 0x1.50929d0fc487d21c2b84004264dep-88L, + 0x1.21f49917ddc962552fd292p0L, 0x9.4bdb4b61ea62477caa1dce823ba0p-92L, + 0x1.2387a6e75623866c1fadb0p0L, 0x1.c15cb593b0328566902df69e4de2p-88L, + 0x1.251ce4fb2a63f3582ab7dep0L, 0x9.e94811a9c8afdcf796934bc652d0p-92L, + 0x1.26b4565e27cdd257a67328p0L, 0x1.d3b249dce4e9186ddd5ff44e6b08p-92L, + 0x1.284dfe1f5638096cf15cf0p0L, 0x3.ca0967fdaa2e52d7c8106f2e262cp-92L, + 0x1.29e9df51fdee12c25d15f4p0L, 0x1.a24aa3bca890ac08d203fed80a07p-88L, + 0x1.2b87fd0dad98ffddea4652p0L, 0x1.8fcab88442fdc3cb6de4519165edp-88L, + 0x1.2d285a6e4030b40091d536p0L, 0xd.075384589c1cd1b3e4018a6b1348p-92L, + 0x1.2ecafa93e2f5611ca0f45cp0L, 0x1.523833af611bdcda253c554cf278p-88L, + 0x1.306fe0a31b7152de8d5a46p0L, 0x3.05c85edecbc27343629f502f1af2p-92L, + 0x1.32170fc4cd8313539cf1c2p0L, 0x1.008f86dde3220ae17a005b6412bep-88L, + 0x1.33c08b26416ff4c9c8610cp0L, 0x1.96696bf95d1593039539d94d662bp-88L, + 0x1.356c55f929ff0c94623476p0L, 0x3.73af38d6d8d6f9506c9bbc93cbc0p-92L, + 0x1.371a7373aa9caa7145502ep0L, 0x1.4547987e3e12516bf9c699be432fp-88L, + 0x1.38cae6d05d86585a9cb0d8p0L, 0x1.bed0c853bd30a02790931eb2e8f0p-88L, + 0x1.3a7db34e59ff6ea1bc9298p0L, 0x1.e0a1d336163fe2f852ceeb134067p-88L, + 0x1.3c32dc313a8e484001f228p0L, 0xb.58f3775e06ab66353001fae9fca0p-92L, + 0x1.3dea64c12342235b41223ep0L, 0x1.3d773fba2cb82b8244267c54443fp-92L, + 0x1.3fa4504ac801ba0bf701aap0L, 0x4.1832fb8c1c8dbdff2c49909e6c60p-92L, + 0x1.4160a21f72e29f84325b8ep0L, 0x1.3db61fb352f0540e6ba05634413ep-88L, + 0x1.431f5d950a896dc7044394p0L, 0x1.0ccec81e24b0caff7581ef4127f7p-92L, + 0x1.44e086061892d03136f408p0L, 0x1.df019fbd4f3b48709b78591d5cb5p-88L, + 0x1.46a41ed1d005772512f458p0L, 0x1.229d97df404ff21f39c1b594d3a8p-88L, + 0x1.486a2b5c13cd013c1a3b68p0L, 0x1.062f03c3dd75ce8757f780e6ec99p-88L, + 0x1.4a32af0d7d3de672d8bcf4p0L, 0x6.f9586461db1d878b1d148bd3ccb8p-92L, + 0x1.4bfdad5362a271d4397afep0L, 0xc.42e20e0363ba2e159c579f82e4b0p-92L, + 0x1.4dcb299fddd0d63b36ef1ap0L, 0x9.e0cc484b25a5566d0bd5f58ad238p-92L, + 0x1.4f9b2769d2ca6ad33d8b68p0L, 0x1.aa073ee55e028497a329a7333dbap-88L, + 0x1.516daa2cf6641c112f52c8p0L, 0x4.d822190e718226177d7608d20038p-92L, + 0x1.5342b569d4f81df0a83c48p0L, 0x1.d86a63f4e672a3e429805b049465p-88L, + 0x1.551a4ca5d920ec52ec6202p0L, 0x4.34ca672645dc6c124d6619a87574p-92L, + 0x1.56f4736b527da66ecb0046p0L, 0x1.64eb3c00f2f5ab3d801d7cc7272dp-88L, + 0x1.58d12d497c7fd252bc2b72p0L, 0x1.43bcf2ec936a970d9cc266f0072fp-88L, + 0x1.5ab07dd48542958c930150p0L, 0x1.91eb345d88d7c81280e069fbdb63p-88L, + 0x1.5c9268a5946b701c4b1b80p0L, 0x1.6986a203d84e6a4a92f179e71889p-88L, + 0x1.5e76f15ad21486e9be4c20p0L, 0x3.99766a06548a05829e853bdb2b52p-92L, + 0x1.605e1b976dc08b076f592ap0L, 0x4.86e3b34ead1b4769df867b9c89ccp-92L, + 0x1.6247eb03a5584b1f0fa06ep0L, 0x1.d2da42bb1ceaf9f732275b8aef30p-88L, + 0x1.6434634ccc31fc76f8714cp0L, 0x4.ed9a4e41000307103a18cf7a6e08p-92L, + 0x1.66238825522249127d9e28p0L, 0x1.b8f314a337f4dc0a3adf1787ff74p-88L, + 0x1.68155d44ca973081c57226p0L, 0x1.b9f32706bfe4e627d809a85dcc66p-88L, + 0x1.6a09e667f3bcc908b2fb12p0L, 0x1.66ea957d3e3adec17512775099dap-88L, + 0x1.6c012750bdabeed76a9980p0L, 0xf.4f33fdeb8b0ecd831106f57b3d00p-96L, + 0x1.6dfb23c651a2ef220e2cbep0L, 0x1.bbaa834b3f11577ceefbe6c1c411p-92L, + 0x1.6ff7df9519483cf87e1b4ep0L, 0x1.3e213bff9b702d5aa477c12523cep-88L, + 0x1.71f75e8ec5f73dd2370f2ep0L, 0xf.0acd6cb434b562d9e8a20adda648p-92L, + 0x1.73f9a48a58173bd5c9a4e6p0L, 0x8.ab1182ae217f3a7681759553e840p-92L, + 0x1.75feb564267c8bf6e9aa32p0L, 0x1.a48b27071805e61a17b954a2dad8p-88L, + 0x1.780694fde5d3f619ae0280p0L, 0x8.58b2bb2bdcf86cd08e35fb04c0f0p-92L, + 0x1.7a11473eb0186d7d51023ep0L, 0x1.6cda1f5ef42b66977960531e821bp-88L, + 0x1.7c1ed0130c1327c4933444p0L, 0x1.937562b2dc933d44fc828efd4c9cp-88L, + 0x1.7e2f336cf4e62105d02ba0p0L, 0x1.5797e170a1427f8fcdf5f3906108p-88L, + 0x1.80427543e1a11b60de6764p0L, 0x9.a354ea706b8e4d8b718a672bf7c8p-92L, + 0x1.82589994cce128acf88afap0L, 0xb.34a010f6ad65cbbac0f532d39be0p-92L, + 0x1.8471a4623c7acce52f6b96p0L, 0x1.c64095370f51f48817914dd78665p-88L, + 0x1.868d99b4492ec80e41d90ap0L, 0xc.251707484d73f136fb5779656b70p-92L, + 0x1.88ac7d98a669966530bcdep0L, 0x1.2d4e9d61283ef385de170ab20f96p-88L, + 0x1.8ace5422aa0db5ba7c55a0p0L, 0x1.92c9bb3e6ed61f2733304a346d8fp-88L, + 0x1.8cf3216b5448bef2aa1cd0p0L, 0x1.61c55d84a9848f8c453b3ca8c946p-88L, + 0x1.8f1ae991577362b982745cp0L, 0x7.2ed804efc9b4ae1458ae946099d4p-92L, + 0x1.9145b0b91ffc588a61b468p0L, 0x1.f6b70e01c2a90229a4c4309ea719p-88L, + 0x1.93737b0cdc5e4f4501c3f2p0L, 0x5.40a22d2fc4af581b63e8326efe9cp-92L, + 0x1.95a44cbc8520ee9b483694p0L, 0x1.a0fc6f7c7d61b2b3a22a0eab2cadp-88L, + 0x1.97d829fde4e4f8b9e920f8p0L, 0x1.1e8bd7edb9d7144b6f6818084cc7p-88L, + 0x1.9a0f170ca07b9ba3109b8cp0L, 0x4.6737beb19e1eada6825d3c557428p-92L, + 0x1.9c49182a3f0901c7c46b06p0L, 0x1.1f2be58ddade50c217186c90b457p-88L, + 0x1.9e86319e323231824ca78ep0L, 0x6.4c6e010f92c082bbadfaf605cfd4p-92L, + 0x1.a0c667b5de564b29ada8b8p0L, 0xc.ab349aa0422a8da7d4512edac548p-92L, + 0x1.a309bec4a2d3358c171f76p0L, 0x1.0daad547fa22c26d168ea762d854p-88L, + 0x1.a5503b23e255c8b424491cp0L, 0xa.f87bc8050a405381703ef7caff50p-92L, + 0x1.a799e1330b3586f2dfb2b0p0L, 0x1.58f1a98796ce8908ae852236ca94p-88L, + 0x1.a9e6b5579fdbf43eb243bcp0L, 0x1.ff4c4c58b571cf465caf07b4b9f5p-88L, + 0x1.ac36bbfd3f379c0db966a2p0L, 0x1.1265fc73e480712d20f8597a8e7bp-88L, + 0x1.ae89f995ad3ad5e8734d16p0L, 0x1.73205a7fbc3ae675ea440b162d6cp-88L, + 0x1.b0e07298db66590842acdep0L, 0x1.c6f6ca0e5dcae2aafffa7a0554cbp-88L, + 0x1.b33a2b84f15faf6bfd0e7ap0L, 0x1.d947c2575781dbb49b1237c87b6ep-88L, + 0x1.b59728de559398e3881110p0L, 0x1.64873c7171fefc410416be0a6525p-88L, + 0x1.b7f76f2fb5e46eaa7b081ap0L, 0xb.53c5354c8903c356e4b625aacc28p-92L, + 0x1.ba5b030a10649840cb3c6ap0L, 0xf.5b47f297203757e1cc6eadc8bad0p-92L, + 0x1.bcc1e904bc1d2247ba0f44p0L, 0x1.b3d08cd0b20287092bd59be4ad98p-88L, + 0x1.bf2c25bd71e088408d7024p0L, 0x1.18e3449fa073b356766dfb568ff4p-88L, + 0x1.c199bdd85529c2220cb12ap0L, 0x9.1ba6679444964a36661240043970p-96L, + 0x1.c40ab5fffd07a6d14df820p0L, 0xf.1828a5366fd387a7bdd54cdf7300p-92L, + 0x1.c67f12e57d14b4a2137fd2p0L, 0xf.2b301dd9e6b151a6d1f9d5d5f520p-96L, + 0x1.c8f6d9406e7b511acbc488p0L, 0x5.c442ddb55820171f319d9e5076a8p-96L, + 0x1.cb720dcef90691503cbd1ep0L, 0x9.49db761d9559ac0cb6dd3ed599e0p-92L, + 0x1.cdf0b555dc3f9c44f8958ep0L, 0x1.ac51be515f8c58bdfb6f5740a3a4p-88L, + 0x1.d072d4a07897b8d0f22f20p0L, 0x1.a158e18fbbfc625f09f4cca40874p-88L, + 0x1.d2f87080d89f18ade12398p0L, 0x9.ea2025b4c56553f5cdee4c924728p-92L, + 0x1.d5818dcfba48725da05aeap0L, 0x1.66e0dca9f589f559c0876ff23830p-88L, + 0x1.d80e316c98397bb84f9d04p0L, 0x8.805f84bec614de269900ddf98d28p-92L, + 0x1.da9e603db3285708c01a5ap0L, 0x1.6d4c97f6246f0ec614ec95c99392p-88L, + 0x1.dd321f301b4604b695de3cp0L, 0x6.30a393215299e30d4fb73503c348p-96L, + 0x1.dfc97337b9b5eb968cac38p0L, 0x1.ed291b7225a944efd5bb5524b927p-88L, + 0x1.e264614f5a128a12761fa0p0L, 0x1.7ada6467e77f73bf65e04c95e29dp-88L, + 0x1.e502ee78b3ff6273d13014p0L, 0x1.3991e8f49659e1693be17ae1d2f9p-88L, + 0x1.e7a51fbc74c834b548b282p0L, 0x1.23786758a84f4956354634a416cep-88L, + 0x1.ea4afa2a490d9858f73a18p0L, 0xf.5db301f86dea20610ceee13eb7b8p-92L, + 0x1.ecf482d8e67f08db0312fap0L, 0x1.949cef462010bb4bc4ce72a900dfp-88L, + 0x1.efa1bee615a27771fd21a8p0L, 0x1.2dac1f6dd5d229ff68e46f27e3dfp-88L, + 0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L, + 0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L, + 0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L, + 0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L, + 0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L +}; + +/* + * Kernel for expl(x). x must be finite and not tiny or huge. + * "tiny" is anything that would make us underflow (|A6*x^6| < ~LDBL_MIN). + * "huge" is anything that would make fn*L1 inexact (|x| > ~2**17*ln2). + */ +static inline void +__k_expl(long double x, long double *hip, long double *lop, int *kp) +{ + long double q, r, r1, t; + double dr, fn, r2; + int n, n2; + + /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */ + /* Use a specialized rint() to get fn. Assume round-to-nearest. */ + /* XXX assume no extra precision for the additions, as for trig fns. */ + /* XXX this set of comments is now quadruplicated. */ + /* XXX but see ../src/e_exp.c for a fix using double_t. */ + fn = (double)x * INV_L + 0x1.8p52 - 0x1.8p52; +#if defined(HAVE_EFFICIENT_IRINT) + n = irint(fn); +#else + n = (int)fn; +#endif + n2 = (unsigned)n % INTERVALS; + /* Depend on the sign bit being propagated: */ + *kp = n >> LOG2_INTERVALS; + r1 = x - fn * L1; + r2 = fn * -L2; + r = r1 + r2; + + /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */ + dr = r; + q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 + + dr * (A7 + dr * (A8 + dr * (A9 + dr * A10)))))))); + t = tbl[n2].lo + tbl[n2].hi; + *hip = tbl[n2].hi; + *lop = tbl[n2].lo + t * (q + r1); +} + +/* + * XXX: the rest of the functions are identical for ld80 and ld128. + * However, we should use scalbnl() for ld128, since long double + * multiplication is very slow on the only supported ld128 arch (sparc64). + */ + +static inline void +k_hexpl(long double x, long double *hip, long double *lop) +{ + float twopkm1; + int k; + + __k_expl(x, hip, lop, &k); + SET_FLOAT_WORD(twopkm1, 0x3f800000 + ((k - 1) << 23)); + *hip *= twopkm1; + *lop *= twopkm1; +} + +static inline long double +hexpl(long double x) +{ + long double hi, lo, twopkm2; + int k; + + twopkm2 = 1; + __k_expl(x, &hi, &lo, &k); + SET_LDBL_EXPSIGN(twopkm2, BIAS + k - 2); + return (lo + hi) * 2 * twopkm2; +} + +#ifdef _COMPLEX_H +/* + * See ../src/k_exp.c for details. + */ +static inline long double complex +__ldexp_cexpl(long double complex z, int expt) +{ + long double exp_x, hi, lo; + long double x, y, scale1, scale2; + int half_expt, k; + + x = creall(z); + y = cimagl(z); + __k_expl(x, &hi, &lo, &k); + + exp_x = (lo + hi) * 0x1p16382; + expt += k - 16382; + + scale1 = 1; + half_expt = expt / 2; + SET_LDBL_EXPSIGN(scale1, BIAS + half_expt); + scale2 = 1; + SET_LDBL_EXPSIGN(scale1, BIAS + expt - half_expt); + + return (cpackl(cos(y) * exp_x * scale1 * scale2, + sinl(y) * exp_x * scale1 * scale2)); +} +#endif /* _COMPLEX_H */ Property changes on: stable/10/lib/msun/ld128/k_expl.h ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: stable/10/lib/msun/ld128/s_erfl.c =================================================================== --- stable/10/lib/msun/ld128/s_erfl.c (nonexistent) +++ stable/10/lib/msun/ld128/s_erfl.c (revision 271779) @@ -0,0 +1,329 @@ +/* @(#)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 +__FBSDID("$FreeBSD$"); + +/* + * See s_erf.c for complete comments. + * + * Converted to long double by Steven G. Kargl. + */ +#include + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + +/* XXX Prevent compilers from erroneously constant folding these: */ +static const volatile long double tiny = 0x1p-10000L; + +static const double +half= 0.5, +one = 1, +two = 2; +/* + * In the domain [0, 2**-40], only the first term in the power series + * expansion of erf(x) is used. The magnitude of the first neglected + * terms is less than 2**-120. + */ +static const long double +efx = 1.28379167095512573896158903121545167e-01L, /* 0xecbff6a7, 0x481dd788, 0xb64d21a8, 0xeb06fc3f */ +efx8 = 1.02703333676410059116927122497236133e+00L, /* 0xecbff6a7, 0x481dd788, 0xb64d21a8, 0xeb06ff3f */ +/* + * Domain [0, 0.84375], range ~[-1.919e-38, 1.919e-38]: + * |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-125.29 + */ +pp0 = 1.28379167095512573896158903121545167e-01L, /* 0x3ffc06eb, 0xa8214db6, 0x88d71d48, 0xa7f6bfec */ +pp1 = -3.14931554396568573802046931159683404e-01L, /* 0xbffd427d, 0x6ada7263, 0x547eb096, 0x95f37463 */ +pp2 = -5.27514920282183487103576956956725309e-02L, /* 0xbffab023, 0xe5a271e3, 0xb0e79b01, 0x2f7ac962 */ +pp3 = -1.13202828509005281355609495523452713e-02L, /* 0xbff872f1, 0x6a5023a1, 0xe08b3884, 0x326af20f */ +pp4 = -9.18626155872522453865998391206048506e-04L, /* 0xbff4e19f, 0xea5fb024, 0x43247a37, 0xe430b06c */ +pp5 = -7.87518862406176274922506447157284230e-05L, /* 0xbff14a4f, 0x31a85fe0, 0x7fff2204, 0x09c49b37 */ +pp6 = -3.42357944472240436548115331090560881e-06L, /* 0xbfeccb81, 0x4b43c336, 0xcd2eb6c2, 0x903f2d87 */ +pp7 = -1.37317432573890412634717890726745428e-07L, /* 0xbfe826e3, 0x0e915eb6, 0x42aee414, 0xf7e36805 */ +pp8 = -2.71115170113861755855049008732113726e-09L, /* 0xbfe2749e, 0x2b94fd00, 0xecb4d166, 0x0efb91f8 */ +pp9 = -3.37925756196555959454018189718117864e-11L, /* 0xbfdc293e, 0x1d9060cb, 0xd043204a, 0x314cd7f0 */ +qq1 = 4.76672625471551170489978555182449450e-01L, /* 0x3ffde81c, 0xde6531f0, 0x76803bee, 0x526e29e9 */ +qq2 = 1.06713144672281502058807525850732240e-01L, /* 0x3ffbb518, 0xd7a6bb74, 0xcd9bdd33, 0x7601eee5 */ +qq3 = 1.47747613127513761102189201923147490e-02L, /* 0x3ff8e423, 0xae527e18, 0xf12cb447, 0x723b4749 */ +qq4 = 1.39939377672028671891148770908874816e-03L, /* 0x3ff56ed7, 0xba055d84, 0xc21b45c4, 0x388d1812 */ +qq5 = 9.44302939359455241271983309378738276e-05L, /* 0x3ff18c11, 0xc18c99a4, 0x86d0fe09, 0x46387b4c */ +qq6 = 4.56199342312522842161301671745365650e-06L, /* 0x3fed3226, 0x73421d05, 0x08875300, 0x32fa1432 */ +qq7 = 1.53019260483764773845294600092361197e-07L, /* 0x3fe8489b, 0x3a63f627, 0x2b9ad2ce, 0x26516e57 */ +qq8 = 3.25542691121324805094777901250005508e-09L, /* 0x3fe2bf6c, 0x26d93a29, 0x9142be7c, 0x9f1dd043 */ +qq9 = 3.37405581964478060434410167262684979e-11L; /* 0x3fdc28c8, 0xfb8fa1be, 0x10e57eec, 0xaa19e49f */ + +static const long double +erx = 8.42700792949714894142232424201210961e-01L, /* 0x3ffeaf76, 0x7a741088, 0xb0000000, 0x00000000 */ +/* + * Domain [0.84375, 1.25], range ~[-2.521e-36, 2.523e-36]: + * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-120.15 + */ +pa0 = -2.48010117891186017024438233323795897e-17L, /* 0xbfc7c97f, 0x77812279, 0x6c877f22, 0xef4bfb2e */ +pa1 = 4.15107497420594680894327969504526489e-01L, /* 0x3ffda911, 0xf096fbc2, 0x55662005, 0x2337fa64 */ +pa2 = -3.94180628087084846724448515851892609e-02L, /* 0xbffa42e9, 0xab54528c, 0xad529da1, 0x6efc2af3 */ +pa3 = 4.48897599625192107295954790681677462e-02L, /* 0x3ffa6fbc, 0xa65edba1, 0x0e4cbcea, 0x73ef9a31 */ +pa4 = 8.02069252143016600110972019232995528e-02L, /* 0x3ffb4887, 0x0e8b548e, 0x3230b417, 0x11b553b3 */ +pa5 = -1.02729816533435279443621120242391295e-02L, /* 0xbff850a0, 0x041de3ee, 0xd5bca6c9, 0x4ef5f9f2 */ +pa6 = 5.70777694530755634864821094419982095e-03L, /* 0x3ff77610, 0x9b501e10, 0x4c978382, 0x742df68f */ +pa7 = 1.22635150233075521018231779267077071e-03L, /* 0x3ff5417b, 0x0e623682, 0x60327da0, 0x96b9219e */ +pa8 = 5.36100234820204569428412542856666503e-04L, /* 0x3ff41912, 0x27ceb4c1, 0x1d3298ec, 0x84ced627 */ +pa9 = -1.97753571846365167177187858667583165e-04L, /* 0xbff29eb8, 0x23f5bcf3, 0x15c83c46, 0xe4fda98b */ +pa10 = 6.19333039900846970674794789568415105e-05L, /* 0x3ff103c4, 0x60f88e46, 0xc0c9fb02, 0x13cc7fc1 */ +pa11 = -5.40531400436645861492290270311751349e-06L, /* 0xbfed6abe, 0x9665f8a8, 0xdd0ad3ba, 0xe5dc0ee3 */ +qa1 = 9.05041313265490487793231810291907851e-01L, /* 0x3ffecf61, 0x93340222, 0xe9930620, 0xc4e61168 */ +qa2 = 6.79848064708886864767240880834868092e-01L, /* 0x3ffe5c15, 0x0ba858dc, 0xf7900ae9, 0xfea1e09a */ +qa3 = 4.04720609926471677581066689316516445e-01L, /* 0x3ffd9e6f, 0x145e9b00, 0x6d8c1749, 0xd2928623 */ +qa4 = 1.69183273898369996364661075664302225e-01L, /* 0x3ffc5a7c, 0xc2a363c1, 0xd6c19097, 0xef9b4063 */ +qa5 = 7.44476185988067992342479750486764248e-02L, /* 0x3ffb30ef, 0xfc7259ef, 0x1bcbb089, 0x686dd62d */ +qa6 = 2.02981172725892407200420389604788573e-02L, /* 0x3ff94c90, 0x7976cb0e, 0x21e1d36b, 0x0f09ca2b */ +qa7 = 6.94281866271607668268269403102277234e-03L, /* 0x3ff7c701, 0x2b193250, 0xc5d46ecc, 0x374843d8 */ +qa8 = 1.12952275469171559611651594706820034e-03L, /* 0x3ff52818, 0xfd2a7c06, 0xd13e38fd, 0xda4b34f5 */ +qa9 = 3.13736683241992737197226578597710179e-04L, /* 0x3ff348fa, 0x0cb48d18, 0x051f849b, 0x135ccf74 */ +qa10 = 1.17037675204033225470121134087771410e-05L, /* 0x3fee88b6, 0x98f47704, 0xa5d8f8f2, 0xc6422e11 */ +qa11 = 4.61312518293853991439362806880973592e-06L, /* 0x3fed3594, 0xe31db94f, 0x3592b693, 0xed4386b4 */ +qa12 = -1.02158572037456893687737553657431771e-06L; /* 0xbfeb123a, 0xd60d9b1e, 0x1f6fdeb9, 0x7dc8410a */ +/* + * Domain [1.25,2.85715], range ~[-2.922e-37,2.922e-37]: + * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-121.36 + */ +static const long double +ra0 = -9.86494292470069009555706994426014461e-03L, /* 0xbff84341, 0x239e8709, 0xe941b06a, 0xcb4b6ec5 */ +ra1 = -1.13580436992565640457579040117568870e+00L, /* 0xbfff22c4, 0x133f7c0d, 0x72d5e231, 0x2eb1ee3f */ +ra2 = -4.89744330295291950661185707066921755e+01L, /* 0xc00487cb, 0xa38b4fc2, 0xc136695b, 0xc1df8047 */ +ra3 = -1.10766149300215937173768072715352140e+03L, /* 0xc00914ea, 0x55e6beb3, 0xabc50e07, 0xb6e5664d */ +ra4 = -1.49991031232170934967642795601952100e+04L, /* 0xc00cd4b8, 0xd33243e6, 0xffbf6545, 0x3c57ef6e */ +ra5 = -1.29805749738318462882524181556996692e+05L, /* 0xc00ffb0d, 0xbfeed9b6, 0x5b2a3ff4, 0xe245bd3c */ +ra6 = -7.42828497044940065828871976644647850e+05L, /* 0xc0126ab5, 0x8fe7caca, 0x473352d9, 0xcd4e0c90 */ +ra7 = -2.85637299581890734287995171242421106e+06L, /* 0xc0145cad, 0xa7f76fe7, 0x3e358051, 0x1799f927 */ +ra8 = -7.40674797129824999383748865571026084e+06L, /* 0xc015c412, 0x6fe29c02, 0x298ad158, 0x7d24e45c */ +ra9 = -1.28653420911930973914078724204151759e+07L, /* 0xc016889e, 0x7c2eb0dc, 0x95d5863b, 0x0aa34dc3 */ +ra10 = -1.47198163599330179552932489109452638e+07L, /* 0xc016c136, 0x90b84923, 0xf9bcb497, 0x19bbd0f5 */ +ra11 = -1.07812992258382800318665248311522624e+07L, /* 0xc0164904, 0xe673a113, 0x35d7f079, 0xe13701f3 */ +ra12 = -4.83545565681708642630419905537756076e+06L, /* 0xc0152721, 0xfea094a8, 0x869eb39d, 0x413d6f13 */ +ra13 = -1.23956521201673964822976917356685286e+06L, /* 0xc0132ea0, 0xd3646baa, 0x2fe62b0d, 0xbae5ce85 */ +ra14 = -1.62289333553652417591275333240371812e+05L, /* 0xc0103cf8, 0xaab1e2d6, 0x4c25e014, 0x248d76ab */ +ra15 = -8.82890392601176969729168894389833110e+03L, /* 0xc00c13e7, 0x3b3d8f94, 0x6fbda6f6, 0xe7049a82 */ +ra16 = -1.22591866337261720023681535568334619e+02L, /* 0xc005ea5e, 0x12358891, 0xcfa712c5, 0x77f050d4 */ +sa1 = 6.44508918884710829371852723353794047e+01L, /* 0x400501cd, 0xb69a6c0f, 0x5716de14, 0x47161af6 */ +sa2 = 1.76118475473171481523704824327358534e+03L, /* 0x4009b84b, 0xd305829f, 0xc4c771b0, 0xbf1f7f9b */ +sa3 = 2.69448346969488374857087646131950188e+04L, /* 0x400da503, 0x56bacc05, 0x4fdba68d, 0x2cca27e6 */ +sa4 = 2.56826633369941456778326497384543763e+05L, /* 0x4010f59d, 0x51124428, 0x69c41de6, 0xbd0d5753 */ +sa5 = 1.60647413092257206847700054645905859e+06L, /* 0x40138834, 0xa2184244, 0x557a1bed, 0x68c9d556 */ +sa6 = 6.76963075165099718574753447122393797e+06L, /* 0x40159d2f, 0x7b01b0cc, 0x8bac9e95, 0x5d35d56e */ +sa7 = 1.94295690905361884290986932493647741e+07L, /* 0x40172878, 0xc1172d61, 0x3068501e, 0x2f3c71da */ +sa8 = 3.79774781017759149060839255547073541e+07L, /* 0x401821be, 0xc30d06fe, 0x410563d7, 0x032111fd */ +sa9 = 5.00659831846029484248302236457727397e+07L, /* 0x40187df9, 0x1f97a111, 0xc51d6ac2, 0x4b389793 */ +sa10 = 4.36486287620506484276130525941972541e+07L, /* 0x40184d03, 0x3a618ae0, 0x2a723357, 0xfa45c60a */ +sa11 = 2.43779678791333894255510508253951934e+07L, /* 0x401773fa, 0x6fe10ee2, 0xc467850d, 0xc6b7ff30 */ +sa12 = 8.30732360384443202039372372212966542e+06L, /* 0x4015fb09, 0xee6a5631, 0xdd98de7e, 0x8b00461a */ +sa13 = 1.60160846942050515734192397495105693e+06L, /* 0x40138704, 0x8782bf13, 0x5b8fb315, 0xa898abe5 */ +sa14 = 1.54255505242533291014555153757001825e+05L, /* 0x40102d47, 0xc0abc98e, 0x843c9490, 0xb4352440 */ +sa15 = 5.87949220002375547561467275493888824e+03L, /* 0x400b6f77, 0xe00d21d1, 0xec4d41e8, 0x2f8e1673 */ +sa16 = 4.97272976346793193860385983372237710e+01L; /* 0x40048dd1, 0x816c1b3f, 0x24f540a6, 0x4cfe03cc */ +/* + * Domain [2.85715,9], range ~[-7.886e-37,7.918e-37]: + * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-120 + */ +static const long double +rb0 = -9.86494292470008707171371994479162369e-3L, /* 0xbff84341, 0x239e86f4, 0x2f57e561, 0xf4469360 */ +rb1 = -1.57047326624110727986326503729442830L, /* 0xbfff920a, 0x8935bf73, 0x8803b894, 0x4656482d */ +rb2 = -1.03228196364885474342132255440317065e2L, /* 0xc0059ce9, 0xac4ed0ff, 0x2cff0ff7, 0x5e70d1ab */ +rb3 = -3.74000570653418227179358710865224376e3L, /* 0xc00ad380, 0x2ebf7835, 0xf6b07ed2, 0x861242f7 */ +rb4 = -8.35435477739098044190860390632813956e4L, /* 0xc00f4657, 0x8c3ae934, 0x3647d7b3, 0x80e76fb7 */ +rb5 = -1.21398672055223642118716640216747152e6L, /* 0xc0132862, 0x2b8761c8, 0x27d18c0f, 0x137c9463 */ +rb6 = -1.17669175877248796101665344873273970e7L, /* 0xc0166719, 0x0b2cea46, 0x81f14174, 0x11602ea5 */ +rb7 = -7.66108006086998253606773064264599615e7L, /* 0xc019243f, 0x3c26f4f0, 0x1cc05241, 0x3b953728 */ +rb8 = -3.32547117558141845968704725353130804e8L, /* 0xc01b3d24, 0x42d8ee26, 0x24ef6f3b, 0x604a8c65 */ +rb9 = -9.41561252426350696802167711221739746e8L, /* 0xc01cc0f8, 0xad23692a, 0x8ddb2310, 0xe9937145 */ +rb10 = -1.67157110805390944549427329626281063e9L, /* 0xc01d8e88, 0x9a903734, 0x09a55fa3, 0xd205c903 */ +rb11 = -1.74339631004410841337645931421427373e9L, /* 0xc01d9fa8, 0x77582d2a, 0xc183b8ab, 0x7e00cb05 */ +rb12 = -9.57655233596934915727573141357471703e8L, /* 0xc01cc8a5, 0x460cc685, 0xd0271fa0, 0x6a70e3da */ +rb13 = -2.26320062731339353035254704082495066e8L, /* 0xc01aafab, 0xd7d76721, 0xc9720e11, 0x6a8bd489 */ +rb14 = -1.42777302996263256686002973851837039e7L, /* 0xc016b3b8, 0xc499689f, 0x2b88d965, 0xc32414f9 */ +sb1 = 1.08512869705594540211033733976348506e2L, /* 0x4005b20d, 0x2db7528d, 0x00d20dcb, 0x858f6191 */ +sb2 = 5.02757713761390460534494530537572834e3L, /* 0x400b3a39, 0x3bf4a690, 0x3025d28d, 0xfd40a891 */ +sb3 = 1.31019107205412870059331647078328430e5L, /* 0x400fffcb, 0x1b71d05e, 0x3b28361d, 0x2a3c3690 */ +sb4 = 2.13021555152296846166736757455018030e6L, /* 0x40140409, 0x3c6984df, 0xc4491d7c, 0xb04aa08d */ +sb5 = 2.26649105281820861953868568619768286e7L, /* 0x401759d6, 0xce8736f0, 0xf28ad037, 0x2a901e0c */ +sb6 = 1.61071939490875921812318684143076081e8L, /* 0x401a3338, 0x686fb541, 0x6bd27d06, 0x4f95c9ac */ +sb7 = 7.66895673844301852676056750497991966e8L, /* 0x401c6daf, 0x31cec121, 0x54699126, 0x4bd9bf9e */ +sb8 = 2.41884450436101936436023058196042526e9L, /* 0x401e2059, 0x46b0b8d7, 0x87b64cbf, 0x78bc296d */ +sb9 = 4.92403055884071695093305291535107666e9L, /* 0x401f257e, 0xbe5ed739, 0x39e17346, 0xcadd2e55 */ +sb10 = 6.18627786365587486459633615573786416e9L, /* 0x401f70bb, 0x1be7a7e7, 0x6a45b5ae, 0x607c70f0 */ +sb11 = 4.45898013426501378097430226324743199e9L, /* 0x401f09c6, 0xa32643d7, 0xf1724620, 0x9ea46c32 */ +sb12 = 1.63006115763329848117160344854224975e9L, /* 0x401d84a3, 0x0996887f, 0x65a4f43b, 0x978c1d74 */ +sb13 = 2.39216717012421697446304015847567721e8L, /* 0x401ac845, 0x09a065c2, 0x30095da7, 0x9d72d6ae */ +sb14 = 7.84837329009278694937250358810225609e6L; /* 0x4015df06, 0xd5290e15, 0x63031fac, 0x4d9c894c */ +/* + * Domain [9,108], range ~[-5.324e-38,5.340e-38]: + * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-124 + */ +static const long double +rc0 = -9.86494292470008707171367567652935673e-3L, /* 0xbff84341, 0x239e86f4, 0x2f57e55b, 0x1aa10fd3 */ +rc1 = -1.26229447747315096406518846411562266L, /* 0xbfff4325, 0xbb1aab28, 0xda395cd9, 0xfb861c15 */ +rc2 = -6.13742634438922591780742637728666162e1L, /* 0xc004eafe, 0x7dd51cd8, 0x3c7c5928, 0x751e50cf */ +rc3 = -1.50455835478908280402912854338421517e3L, /* 0xc0097823, 0xbc15b9ab, 0x3d60745c, 0x523e80a5 */ +rc4 = -2.04415631865861549920184039902945685e4L, /* 0xc00d3f66, 0x40b3fc04, 0x5388f2ec, 0xb009e1f0 */ +rc5 = -1.57625662981714582753490610560037638e5L, /* 0xc01033dc, 0xd4dc95b6, 0xfd4da93b, 0xf355b4a9 */ +rc6 = -6.73473451616752528402917538033283794e5L, /* 0xc01248d8, 0x2e73a4f9, 0xcded49c5, 0xfa3bfeb7 */ +rc7 = -1.47433165421387483167186683764364857e6L, /* 0xc01367f1, 0xba77a8f7, 0xcfdd0dbb, 0x25d554b3 */ +rc8 = -1.38811981807868828563794929997744139e6L, /* 0xc01352e5, 0x7d16d9ad, 0xbbdcbf38, 0x38fbc5ea */ +rc9 = -3.59659700530831825640766479698155060e5L, /* 0xc0115f3a, 0xecd57f45, 0x21f8ad6c, 0x910a5958 */ +sc1 = 7.72730753022908298637508998072635696e1L, /* 0x40053517, 0xa10d52bc, 0xdabb55b6, 0xbd0328cd */ +sc2 = 2.36825757341694050500333261769082182e3L, /* 0x400a2808, 0x3e0a9b42, 0x82977842, 0x9c5de29e */ +sc3 = 3.72210540173034735352888847134073099e4L, /* 0x400e22ca, 0x1ba827ef, 0xac8390d7, 0x1fc39a41 */ +sc4 = 3.24136032646418336712461033591393412e5L, /* 0x40113c8a, 0x0216e100, 0xc59d1e44, 0xf0e68d9d */ +sc5 = 1.57836135851134393802505823370009175e6L, /* 0x40138157, 0x95bc7664, 0x17575961, 0xdbe58eeb */ +sc6 = 4.12881981392063738026679089714182355e6L, /* 0x4014f801, 0x9e82e8d2, 0xb8b3a70e, 0xfd84185d */ +sc7 = 5.24438427289213488410596395361544142e6L, /* 0x40154017, 0x81177109, 0x2aa6c3b0, 0x1f106625 */ +sc8 = 2.59909544563616121735963429710382149e6L, /* 0x40143d45, 0xbb90a9b1, 0x12bf9390, 0xa827a700 */ +sc9 = 2.80930665169282501639651995082335693e5L; /* 0x40111258, 0xaa92222e, 0xa97e3216, 0xa237fa6c */ + +long double +erfl(long double x) +{ + long double ax,R,S,P,Q,s,y,z,r; + uint64_t lx, llx; + int32_t i; + uint16_t hx; + + EXTRACT_LDBL128_WORDS(hx, lx, llx, x); + + if((hx & 0x7fff) == 0x7fff) { /* erfl(nan)=nan */ + i = (hx>>15)<<1; + return (1-i)+one/x; /* erfl(+-inf)=+-1 */ + } + + ax = fabsl(x); + if(ax < 0.84375) { + if(ax < 0x1p-40L) { + if(ax < 0x1p-16373L) + return (8*x+efx8*x)/8; /* avoid spurious underflow */ + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*(pp5+z*(pp6+z*(pp7+ + z*(pp8+z*pp9)))))))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*(qq6+z*(qq7+ + z*(qq8+z*qq9)))))))); + y = r/s; + return x + x*y; + } + if(ax < 1.25) { + s = ax-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*(pa7+ + s*(pa8+s*(pa9+s*(pa10+s*pa11)))))))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*(qa7+ + s*(qa8+s*(qa9+s*(qa10+s*(qa11+s*qa12))))))))))); + if(x>=0) return (erx + P/Q); else return (-erx - P/Q); + } + if (ax >= 9) { /* inf>|x|>= 9 */ + if(x>=0) return (one-tiny); else return (tiny-one); + } + s = one/(ax*ax); + if(ax < 2.85715) { /* |x| < 2.85715 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+ + s*(ra8+s*(ra9+s*(ra10+s*(ra11+s*(ra12+s*(ra13+s*(ra14+ + s*(ra15+s*ra16))))))))))))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+ + s*(sa8+s*(sa9+s*(sa10+s*(sa11+s*(sa12+s*(sa13+s*(sa14+ + s*(sa15+s*sa16))))))))))))))); + } else { /* |x| >= 2.85715 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*(rb7+ + s*(rb8+s*(rb9+s*(rb10+s*(rb11+s*(rb12+s*(rb13+ + s*rb14))))))))))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*(sb7+ + s*(sb8+s*(sb9+s*(sb10+s*(sb11+s*(sb12+s*(sb13+ + s*sb14))))))))))))); + } + z = (float)ax; + r = expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S); + if(x>=0) return (one-r/ax); else return (r/ax-one); +} + +long double +erfcl(long double x) +{ + long double ax,R,S,P,Q,s,y,z,r; + uint64_t lx, llx; + uint16_t hx; + + EXTRACT_LDBL128_WORDS(hx, lx, llx, x); + + if((hx & 0x7fff) == 0x7fff) { /* erfcl(nan)=nan */ + /* erfcl(+-inf)=0,2 */ + return ((hx>>15)<<1)+one/x; + } + + ax = fabsl(x); + if(ax < 0.84375L) { + if(ax < 0x1p-34L) + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*(pp5+z*(pp6+z*(pp7+ + z*(pp8+z*pp9)))))))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*(qq6+z*(qq7+ + z*(qq8+z*qq9)))))))); + y = r/s; + if(ax < 0.25L) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r; + } + } + if(ax < 1.25L) { + s = ax-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*(pa7+ + s*(pa8+s*(pa9+s*(pa10+s*pa11)))))))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*(qa7+ + s*(qa8+s*(qa9+s*(qa10+s*(qa11+s*qa12))))))))))); + if(x>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + + if(ax < 108) { /* |x| < 108 */ + s = one/(ax*ax); + if(ax < 2.85715) { /* |x| < 2.85715 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+ + s*(ra8+s*(ra9+s*(ra10+s*(ra11+s*(ra12+s*(ra13+s*(ra14+ + s*(ra15+s*ra16))))))))))))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+ + s*(sa8+s*(sa9+s*(sa10+s*(sa11+s*(sa12+s*(sa13+s*(sa14+ + s*(sa15+s*sa16))))))))))))))); + } else if(ax < 9) { + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*(rb7+ + s*(rb8+s*(rb9+s*(rb10+s*(rb11+s*(rb12+s*(rb13+ + s*rb14))))))))))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*(sb7+ + s*(sb8+s*(sb9+s*(sb10+s*(sb11+s*(sb12+s*(sb13+ + s*sb14))))))))))))); + } else { + if(x < -9) return two-tiny; /* x < -9 */ + R=rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*(rc5+s*(rc6+s*(rc7+ + s*(rc8+s*rc9)))))))); + S=one+s*(sc1+s*(sc2+s*(sc3+s*(sc4+s*(sc5+s*(sc6+s*(sc7+ + s*(sc8+s*sc9)))))))); + } + z = (float)ax; + r = expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S); + if(x>0) return r/ax; else return two-r/ax; + } else { + if(x>0) return tiny*tiny; else return two-tiny; + } +} Property changes on: stable/10/lib/msun/ld128/s_erfl.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: stable/10/lib/msun/ld128/s_expl.c =================================================================== --- stable/10/lib/msun/ld128/s_expl.c (revision 271778) +++ stable/10/lib/msun/ld128/s_expl.c (revision 271779) @@ -1,494 +1,326 @@ /*- * Copyright (c) 2009-2013 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. * * Optimized by Bruce D. Evans. */ #include __FBSDID("$FreeBSD$"); /* * ld128 version of s_expl.c. See ../ld80/s_expl.c for most comments. */ #include #include "fpmath.h" #include "math.h" #include "math_private.h" +#include "k_expl.h" -#define INTERVALS 128 -#define LOG2_INTERVALS 7 -#define BIAS (LDBL_MAX_EXP - 1) +/* XXX Prevent compilers from erroneously constant folding these: */ +static const volatile long double +huge = 0x1p10000L, +tiny = 0x1p-10000L; static const long double -huge = 0x1p10000L, twom10000 = 0x1p-10000L; -/* XXX Prevent gcc from erroneously constant folding this: */ -static volatile const long double tiny = 0x1p-10000L; static const long double /* log(2**16384 - 0.5) rounded towards zero: */ /* log(2**16384 - 0.5 + 1) rounded towards zero for expm1l() is the same: */ o_threshold = 11356.523406294143949491931077970763428L, /* log(2**(-16381-64-1)) rounded towards zero: */ u_threshold = -11433.462743336297878837243843452621503L; -static const double -/* - * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must - * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest - * bits zero so that multiplication of it by n is exact. - */ -INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */ -L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */ -static const long double -/* 0x1.62e42fefa39ef35793c768000000p-8 */ -L1 = 5.41521234812457272982212595914567508e-3L; - -static const long double -/* - * Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]: - * |exp(x) - p(x)| < 2**-124.9 - * (0.002708 is ln2/(2*INTERVALS) rounded up a little). - */ -A2 = 0.5, -A3 = 1.66666666666666666666666666651085500e-1L, -A4 = 4.16666666666666666666666666425885320e-2L, -A5 = 8.33333333333333333334522877160175842e-3L, -A6 = 1.38888888888888888889971139751596836e-3L; - -static const double -A7 = 1.9841269841269471e-4, -A8 = 2.4801587301585284e-5, -A9 = 2.7557324277411234e-6, -A10 = 2.7557333722375072e-7; - -static const struct { - /* - * hi must be rounded to at most 106 bits so that multiplication - * by r1 in expm1l() is exact, but it is rounded to 88 bits due to - * historical accidents. - */ - long double hi; - long double lo; -} tbl[INTERVALS] = { - 0x1p0L, 0x0p0L, - 0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L, - 0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L, - 0x1.04315e86e7f84bd738f9a2p0L, 0xd.a47e6ed040bb4bfc05af6455e9b8p-96L, - 0x1.059b0d31585743ae7c548ep0L, 0xb.68ca417fe53e3495f7df4baf84a0p-92L, - 0x1.0706b29ddf6ddc6dc403a8p0L, 0x1.d87b27ed07cb8b092ac75e311753p-88L, - 0x1.0874518759bc808c35f25cp0L, 0x1.9427fa2b041b2d6829d8993a0d01p-88L, - 0x1.09e3ecac6f3834521e060cp0L, 0x5.84d6b74ba2e023da730e7fccb758p-92L, - 0x1.0b5586cf9890f6298b92b6p0L, 0x1.1842a98364291408b3ceb0a2a2bbp-88L, - 0x1.0cc922b7247f7407b705b8p0L, 0x9.3dc5e8aac564e6fe2ef1d431fd98p-92L, - 0x1.0e3ec32d3d1a2020742e4ep0L, 0x1.8af6a552ac4b358b1129e9f966a4p-88L, - 0x1.0fb66affed31af232091dcp0L, 0x1.8a1426514e0b627bda694a400a27p-88L, - 0x1.11301d0125b50a4ebbf1aep0L, 0xd.9318ceac5cc47ab166ee57427178p-92L, - 0x1.12abdc06c31cbfb92bad32p0L, 0x4.d68e2f7270bdf7cedf94eb1cb818p-92L, - 0x1.1429aaea92ddfb34101942p0L, 0x1.b2586d01844b389bea7aedd221d4p-88L, - 0x1.15a98c8a58e512480d573cp0L, 0x1.d5613bf92a2b618ee31b376c2689p-88L, - 0x1.172b83c7d517adcdf7c8c4p0L, 0x1.0eb14a792035509ff7d758693f24p-88L, - 0x1.18af9388c8de9bbbf70b9ap0L, 0x3.c2505c97c0102e5f1211941d2840p-92L, - 0x1.1a35beb6fcb753cb698f68p0L, 0x1.2d1c835a6c30724d5cfae31b84e5p-88L, - 0x1.1bbe084045cd39ab1e72b4p0L, 0x4.27e35f9acb57e473915519a1b448p-92L, - 0x1.1d4873168b9aa7805b8028p0L, 0x9.90f07a98b42206e46166cf051d70p-92L, - 0x1.1ed5022fcd91cb8819ff60p0L, 0x1.121d1e504d36c47474c9b7de6067p-88L, - 0x1.2063b88628cd63b8eeb028p0L, 0x1.50929d0fc487d21c2b84004264dep-88L, - 0x1.21f49917ddc962552fd292p0L, 0x9.4bdb4b61ea62477caa1dce823ba0p-92L, - 0x1.2387a6e75623866c1fadb0p0L, 0x1.c15cb593b0328566902df69e4de2p-88L, - 0x1.251ce4fb2a63f3582ab7dep0L, 0x9.e94811a9c8afdcf796934bc652d0p-92L, - 0x1.26b4565e27cdd257a67328p0L, 0x1.d3b249dce4e9186ddd5ff44e6b08p-92L, - 0x1.284dfe1f5638096cf15cf0p0L, 0x3.ca0967fdaa2e52d7c8106f2e262cp-92L, - 0x1.29e9df51fdee12c25d15f4p0L, 0x1.a24aa3bca890ac08d203fed80a07p-88L, - 0x1.2b87fd0dad98ffddea4652p0L, 0x1.8fcab88442fdc3cb6de4519165edp-88L, - 0x1.2d285a6e4030b40091d536p0L, 0xd.075384589c1cd1b3e4018a6b1348p-92L, - 0x1.2ecafa93e2f5611ca0f45cp0L, 0x1.523833af611bdcda253c554cf278p-88L, - 0x1.306fe0a31b7152de8d5a46p0L, 0x3.05c85edecbc27343629f502f1af2p-92L, - 0x1.32170fc4cd8313539cf1c2p0L, 0x1.008f86dde3220ae17a005b6412bep-88L, - 0x1.33c08b26416ff4c9c8610cp0L, 0x1.96696bf95d1593039539d94d662bp-88L, - 0x1.356c55f929ff0c94623476p0L, 0x3.73af38d6d8d6f9506c9bbc93cbc0p-92L, - 0x1.371a7373aa9caa7145502ep0L, 0x1.4547987e3e12516bf9c699be432fp-88L, - 0x1.38cae6d05d86585a9cb0d8p0L, 0x1.bed0c853bd30a02790931eb2e8f0p-88L, - 0x1.3a7db34e59ff6ea1bc9298p0L, 0x1.e0a1d336163fe2f852ceeb134067p-88L, - 0x1.3c32dc313a8e484001f228p0L, 0xb.58f3775e06ab66353001fae9fca0p-92L, - 0x1.3dea64c12342235b41223ep0L, 0x1.3d773fba2cb82b8244267c54443fp-92L, - 0x1.3fa4504ac801ba0bf701aap0L, 0x4.1832fb8c1c8dbdff2c49909e6c60p-92L, - 0x1.4160a21f72e29f84325b8ep0L, 0x1.3db61fb352f0540e6ba05634413ep-88L, - 0x1.431f5d950a896dc7044394p0L, 0x1.0ccec81e24b0caff7581ef4127f7p-92L, - 0x1.44e086061892d03136f408p0L, 0x1.df019fbd4f3b48709b78591d5cb5p-88L, - 0x1.46a41ed1d005772512f458p0L, 0x1.229d97df404ff21f39c1b594d3a8p-88L, - 0x1.486a2b5c13cd013c1a3b68p0L, 0x1.062f03c3dd75ce8757f780e6ec99p-88L, - 0x1.4a32af0d7d3de672d8bcf4p0L, 0x6.f9586461db1d878b1d148bd3ccb8p-92L, - 0x1.4bfdad5362a271d4397afep0L, 0xc.42e20e0363ba2e159c579f82e4b0p-92L, - 0x1.4dcb299fddd0d63b36ef1ap0L, 0x9.e0cc484b25a5566d0bd5f58ad238p-92L, - 0x1.4f9b2769d2ca6ad33d8b68p0L, 0x1.aa073ee55e028497a329a7333dbap-88L, - 0x1.516daa2cf6641c112f52c8p0L, 0x4.d822190e718226177d7608d20038p-92L, - 0x1.5342b569d4f81df0a83c48p0L, 0x1.d86a63f4e672a3e429805b049465p-88L, - 0x1.551a4ca5d920ec52ec6202p0L, 0x4.34ca672645dc6c124d6619a87574p-92L, - 0x1.56f4736b527da66ecb0046p0L, 0x1.64eb3c00f2f5ab3d801d7cc7272dp-88L, - 0x1.58d12d497c7fd252bc2b72p0L, 0x1.43bcf2ec936a970d9cc266f0072fp-88L, - 0x1.5ab07dd48542958c930150p0L, 0x1.91eb345d88d7c81280e069fbdb63p-88L, - 0x1.5c9268a5946b701c4b1b80p0L, 0x1.6986a203d84e6a4a92f179e71889p-88L, - 0x1.5e76f15ad21486e9be4c20p0L, 0x3.99766a06548a05829e853bdb2b52p-92L, - 0x1.605e1b976dc08b076f592ap0L, 0x4.86e3b34ead1b4769df867b9c89ccp-92L, - 0x1.6247eb03a5584b1f0fa06ep0L, 0x1.d2da42bb1ceaf9f732275b8aef30p-88L, - 0x1.6434634ccc31fc76f8714cp0L, 0x4.ed9a4e41000307103a18cf7a6e08p-92L, - 0x1.66238825522249127d9e28p0L, 0x1.b8f314a337f4dc0a3adf1787ff74p-88L, - 0x1.68155d44ca973081c57226p0L, 0x1.b9f32706bfe4e627d809a85dcc66p-88L, - 0x1.6a09e667f3bcc908b2fb12p0L, 0x1.66ea957d3e3adec17512775099dap-88L, - 0x1.6c012750bdabeed76a9980p0L, 0xf.4f33fdeb8b0ecd831106f57b3d00p-96L, - 0x1.6dfb23c651a2ef220e2cbep0L, 0x1.bbaa834b3f11577ceefbe6c1c411p-92L, - 0x1.6ff7df9519483cf87e1b4ep0L, 0x1.3e213bff9b702d5aa477c12523cep-88L, - 0x1.71f75e8ec5f73dd2370f2ep0L, 0xf.0acd6cb434b562d9e8a20adda648p-92L, - 0x1.73f9a48a58173bd5c9a4e6p0L, 0x8.ab1182ae217f3a7681759553e840p-92L, - 0x1.75feb564267c8bf6e9aa32p0L, 0x1.a48b27071805e61a17b954a2dad8p-88L, - 0x1.780694fde5d3f619ae0280p0L, 0x8.58b2bb2bdcf86cd08e35fb04c0f0p-92L, - 0x1.7a11473eb0186d7d51023ep0L, 0x1.6cda1f5ef42b66977960531e821bp-88L, - 0x1.7c1ed0130c1327c4933444p0L, 0x1.937562b2dc933d44fc828efd4c9cp-88L, - 0x1.7e2f336cf4e62105d02ba0p0L, 0x1.5797e170a1427f8fcdf5f3906108p-88L, - 0x1.80427543e1a11b60de6764p0L, 0x9.a354ea706b8e4d8b718a672bf7c8p-92L, - 0x1.82589994cce128acf88afap0L, 0xb.34a010f6ad65cbbac0f532d39be0p-92L, - 0x1.8471a4623c7acce52f6b96p0L, 0x1.c64095370f51f48817914dd78665p-88L, - 0x1.868d99b4492ec80e41d90ap0L, 0xc.251707484d73f136fb5779656b70p-92L, - 0x1.88ac7d98a669966530bcdep0L, 0x1.2d4e9d61283ef385de170ab20f96p-88L, - 0x1.8ace5422aa0db5ba7c55a0p0L, 0x1.92c9bb3e6ed61f2733304a346d8fp-88L, - 0x1.8cf3216b5448bef2aa1cd0p0L, 0x1.61c55d84a9848f8c453b3ca8c946p-88L, - 0x1.8f1ae991577362b982745cp0L, 0x7.2ed804efc9b4ae1458ae946099d4p-92L, - 0x1.9145b0b91ffc588a61b468p0L, 0x1.f6b70e01c2a90229a4c4309ea719p-88L, - 0x1.93737b0cdc5e4f4501c3f2p0L, 0x5.40a22d2fc4af581b63e8326efe9cp-92L, - 0x1.95a44cbc8520ee9b483694p0L, 0x1.a0fc6f7c7d61b2b3a22a0eab2cadp-88L, - 0x1.97d829fde4e4f8b9e920f8p0L, 0x1.1e8bd7edb9d7144b6f6818084cc7p-88L, - 0x1.9a0f170ca07b9ba3109b8cp0L, 0x4.6737beb19e1eada6825d3c557428p-92L, - 0x1.9c49182a3f0901c7c46b06p0L, 0x1.1f2be58ddade50c217186c90b457p-88L, - 0x1.9e86319e323231824ca78ep0L, 0x6.4c6e010f92c082bbadfaf605cfd4p-92L, - 0x1.a0c667b5de564b29ada8b8p0L, 0xc.ab349aa0422a8da7d4512edac548p-92L, - 0x1.a309bec4a2d3358c171f76p0L, 0x1.0daad547fa22c26d168ea762d854p-88L, - 0x1.a5503b23e255c8b424491cp0L, 0xa.f87bc8050a405381703ef7caff50p-92L, - 0x1.a799e1330b3586f2dfb2b0p0L, 0x1.58f1a98796ce8908ae852236ca94p-88L, - 0x1.a9e6b5579fdbf43eb243bcp0L, 0x1.ff4c4c58b571cf465caf07b4b9f5p-88L, - 0x1.ac36bbfd3f379c0db966a2p0L, 0x1.1265fc73e480712d20f8597a8e7bp-88L, - 0x1.ae89f995ad3ad5e8734d16p0L, 0x1.73205a7fbc3ae675ea440b162d6cp-88L, - 0x1.b0e07298db66590842acdep0L, 0x1.c6f6ca0e5dcae2aafffa7a0554cbp-88L, - 0x1.b33a2b84f15faf6bfd0e7ap0L, 0x1.d947c2575781dbb49b1237c87b6ep-88L, - 0x1.b59728de559398e3881110p0L, 0x1.64873c7171fefc410416be0a6525p-88L, - 0x1.b7f76f2fb5e46eaa7b081ap0L, 0xb.53c5354c8903c356e4b625aacc28p-92L, - 0x1.ba5b030a10649840cb3c6ap0L, 0xf.5b47f297203757e1cc6eadc8bad0p-92L, - 0x1.bcc1e904bc1d2247ba0f44p0L, 0x1.b3d08cd0b20287092bd59be4ad98p-88L, - 0x1.bf2c25bd71e088408d7024p0L, 0x1.18e3449fa073b356766dfb568ff4p-88L, - 0x1.c199bdd85529c2220cb12ap0L, 0x9.1ba6679444964a36661240043970p-96L, - 0x1.c40ab5fffd07a6d14df820p0L, 0xf.1828a5366fd387a7bdd54cdf7300p-92L, - 0x1.c67f12e57d14b4a2137fd2p0L, 0xf.2b301dd9e6b151a6d1f9d5d5f520p-96L, - 0x1.c8f6d9406e7b511acbc488p0L, 0x5.c442ddb55820171f319d9e5076a8p-96L, - 0x1.cb720dcef90691503cbd1ep0L, 0x9.49db761d9559ac0cb6dd3ed599e0p-92L, - 0x1.cdf0b555dc3f9c44f8958ep0L, 0x1.ac51be515f8c58bdfb6f5740a3a4p-88L, - 0x1.d072d4a07897b8d0f22f20p0L, 0x1.a158e18fbbfc625f09f4cca40874p-88L, - 0x1.d2f87080d89f18ade12398p0L, 0x9.ea2025b4c56553f5cdee4c924728p-92L, - 0x1.d5818dcfba48725da05aeap0L, 0x1.66e0dca9f589f559c0876ff23830p-88L, - 0x1.d80e316c98397bb84f9d04p0L, 0x8.805f84bec614de269900ddf98d28p-92L, - 0x1.da9e603db3285708c01a5ap0L, 0x1.6d4c97f6246f0ec614ec95c99392p-88L, - 0x1.dd321f301b4604b695de3cp0L, 0x6.30a393215299e30d4fb73503c348p-96L, - 0x1.dfc97337b9b5eb968cac38p0L, 0x1.ed291b7225a944efd5bb5524b927p-88L, - 0x1.e264614f5a128a12761fa0p0L, 0x1.7ada6467e77f73bf65e04c95e29dp-88L, - 0x1.e502ee78b3ff6273d13014p0L, 0x1.3991e8f49659e1693be17ae1d2f9p-88L, - 0x1.e7a51fbc74c834b548b282p0L, 0x1.23786758a84f4956354634a416cep-88L, - 0x1.ea4afa2a490d9858f73a18p0L, 0xf.5db301f86dea20610ceee13eb7b8p-92L, - 0x1.ecf482d8e67f08db0312fap0L, 0x1.949cef462010bb4bc4ce72a900dfp-88L, - 0x1.efa1bee615a27771fd21a8p0L, 0x1.2dac1f6dd5d229ff68e46f27e3dfp-88L, - 0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L, - 0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L, - 0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L, - 0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L, - 0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L -}; - long double expl(long double x) { - union IEEEl2bits u, v; - long double q, r, r1, t, twopk, twopkp10000; - double dr, fn, r2; - int k, n, n2; + union IEEEl2bits u; + long double hi, lo, t, twopk; + int k; uint16_t hx, ix; + DOPRINT_START(&x); + /* Filter out exceptional cases. */ u.e = x; hx = u.xbits.expsign; ix = hx & 0x7fff; if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */ if (ix == BIAS + LDBL_MAX_EXP) { if (hx & 0x8000) /* x is -Inf or -NaN */ - return (-1 / x); - return (x + x); /* x is +Inf or +NaN */ + RETURNP(-1 / x); + RETURNP(x + x); /* x is +Inf or +NaN */ } if (x > o_threshold) - return (huge * huge); + RETURNP(huge * huge); if (x < u_threshold) - return (tiny * tiny); + RETURNP(tiny * tiny); } else if (ix < BIAS - 114) { /* |x| < 0x1p-114 */ - return (1 + x); /* 1 with inexact iff x != 0 */ + RETURN2P(1, x); /* 1 with inexact iff x != 0 */ } ENTERI(); - /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */ - /* Use a specialized rint() to get fn. Assume round-to-nearest. */ - /* XXX assume no extra precision for the additions, as for trig fns. */ - /* XXX this set of comments is now quadruplicated. */ - fn = (double)x * INV_L + 0x1.8p52 - 0x1.8p52; -#if defined(HAVE_EFFICIENT_IRINT) - n = irint(fn); -#else - n = (int)fn; -#endif - n2 = (unsigned)n % INTERVALS; - k = n >> LOG2_INTERVALS; - r1 = x - fn * L1; - r2 = fn * -L2; - r = r1 + r2; + twopk = 1; + __k_expl(x, &hi, &lo, &k); + t = SUM2P(hi, lo); - /* Prepare scale factors. */ + /* Scale by 2**k. */ /* XXX sparc64 multiplication is so slow that scalbnl() is faster. */ - v.e = 1; if (k >= LDBL_MIN_EXP) { - v.xbits.expsign = BIAS + k; - twopk = v.e; - } else { - v.xbits.expsign = BIAS + k + 10000; - twopkp10000 = v.e; - } - - /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */ - dr = r; - q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 + - dr * (A7 + dr * (A8 + dr * (A9 + dr * A10)))))))); - t = tbl[n2].lo + tbl[n2].hi; - t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi; - - /* Scale by 2**k. */ - if (k >= LDBL_MIN_EXP) { if (k == LDBL_MAX_EXP) RETURNI(t * 2 * 0x1p16383L); + SET_LDBL_EXPSIGN(twopk, BIAS + k); RETURNI(t * twopk); } else { - RETURNI(t * twopkp10000 * twom10000); + SET_LDBL_EXPSIGN(twopk, BIAS + k + 10000); + RETURNI(t * twopk * twom10000); } } /* * Our T1 and T2 are chosen to be approximately the points where method * A and method B have the same accuracy. Tang's T1 and T2 are the * points where method A's accuracy changes by a full bit. For Tang, * this drop in accuracy makes method A immediately less accurate than * method B, but our larger INTERVALS makes method A 2 bits more * accurate so it remains the most accurate method significantly * closer to the origin despite losing the full bit in our extended * range for it. * * Split the interval [T1, T2] into two intervals [T1, T3] and [T3, T2]. * Setting T3 to 0 would require the |x| < 0x1p-113 condition to appear * in both subintervals, so set T3 = 2**-5, which places the condition * into the [T1, T3] interval. + * + * XXX we now do this more to (partially) balance the number of terms + * in the C and D polys than to avoid checking the condition in both + * intervals. + * + * XXX these micro-optimizations are excessive. */ static const double T1 = -0.1659, /* ~-30.625/128 * log(2) */ T2 = 0.1659, /* ~30.625/128 * log(2) */ T3 = 0.03125; /* * Domain [-0.1659, 0.03125], range ~[2.9134e-44, 1.8404e-37]: * |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-122.03 +/* + * XXX none of the long double C or D coeffs except C10 is correctly printed. + * If you re-print their values in %.35Le format, the result is always + * different. For example, the last 2 digits in C3 should be 59, not 67. + * 67 is apparently from rounding an extra-precision value to 36 decimal + * places. */ static const long double C3 = 1.66666666666666666666666666666666667e-1L, C4 = 4.16666666666666666666666666666666645e-2L, C5 = 8.33333333333333333333333333333371638e-3L, C6 = 1.38888888888888888888888888891188658e-3L, C7 = 1.98412698412698412698412697235950394e-4L, C8 = 2.48015873015873015873015112487849040e-5L, C9 = 2.75573192239858906525606685484412005e-6L, C10 = 2.75573192239858906612966093057020362e-7L, C11 = 2.50521083854417203619031960151253944e-8L, C12 = 2.08767569878679576457272282566520649e-9L, C13 = 1.60590438367252471783548748824255707e-10L; +/* + * XXX this has 1 more coeff than needed. + * XXX can start the double coeffs but not the double mults at C10. + * With my coeffs (C10-C17 double; s = best_s): + * Domain [-0.1659, 0.03125], range ~[-1.1976e-37, 1.1976e-37]: + * |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65 + */ static const double C14 = 1.1470745580491932e-11, /* 0x1.93974a81dae30p-37 */ C15 = 7.6471620181090468e-13, /* 0x1.ae7f3820adab1p-41 */ C16 = 4.7793721460260450e-14, /* 0x1.ae7cd18a18eacp-45 */ C17 = 2.8074757356658877e-15, /* 0x1.949992a1937d9p-49 */ C18 = 1.4760610323699476e-16; /* 0x1.545b43aabfbcdp-53 */ /* * Domain [0.03125, 0.1659], range ~[-2.7676e-37, -1.0367e-38]: * |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-121.44 */ static const long double D3 = 1.66666666666666666666666666666682245e-1L, D4 = 4.16666666666666666666666666634228324e-2L, D5 = 8.33333333333333333333333364022244481e-3L, D6 = 1.38888888888888888888887138722762072e-3L, D7 = 1.98412698412698412699085805424661471e-4L, D8 = 2.48015873015873015687993712101479612e-5L, D9 = 2.75573192239858944101036288338208042e-6L, D10 = 2.75573192239853161148064676533754048e-7L, D11 = 2.50521083855084570046480450935267433e-8L, D12 = 2.08767569819738524488686318024854942e-9L, D13 = 1.60590442297008495301927448122499313e-10L; +/* + * XXX this has 1 more coeff than needed. + * XXX can start the double coeffs but not the double mults at D11. + * With my coeffs (D11-D16 double): + * Domain [0.03125, 0.1659], range ~[-1.1980e-37, 1.1980e-37]: + * |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65 + */ static const double D14 = 1.1470726176204336e-11, /* 0x1.93971dc395d9ep-37 */ D15 = 7.6478532249581686e-13, /* 0x1.ae892e3D16fcep-41 */ D16 = 4.7628892832607741e-14, /* 0x1.ad00Dfe41feccp-45 */ D17 = 3.0524857220358650e-15; /* 0x1.D7e8d886Df921p-49 */ long double expm1l(long double x) { union IEEEl2bits u, v; long double hx2_hi, hx2_lo, q, r, r1, t, twomk, twopk, x_hi; long double x_lo, x2; double dr, dx, fn, r2; int k, n, n2; uint16_t hx, ix; + DOPRINT_START(&x); + /* Filter out exceptional cases. */ u.e = x; hx = u.xbits.expsign; ix = hx & 0x7fff; if (ix >= BIAS + 7) { /* |x| >= 128 or x is NaN */ if (ix == BIAS + LDBL_MAX_EXP) { if (hx & 0x8000) /* x is -Inf or -NaN */ - return (-1 / x - 1); - return (x + x); /* x is +Inf or +NaN */ + RETURNP(-1 / x - 1); + RETURNP(x + x); /* x is +Inf or +NaN */ } if (x > o_threshold) - return (huge * huge); + RETURNP(huge * huge); /* * expm1l() never underflows, but it must avoid * unrepresentable large negative exponents. We used a * much smaller threshold for large |x| above than in * expl() so as to handle not so large negative exponents * in the same way as large ones here. */ if (hx & 0x8000) /* x <= -128 */ - return (tiny - 1); /* good for x < -114ln2 - eps */ + RETURN2P(tiny, -1); /* good for x < -114ln2 - eps */ } ENTERI(); if (T1 < x && x < T2) { x2 = x * x; dx = x; if (x < T3) { if (ix < BIAS - 113) { /* |x| < 0x1p-113 */ /* x (rounded) with inexact if x != 0: */ - RETURNI(x == 0 ? x : + RETURNPI(x == 0 ? x : (0x1p200 * x + fabsl(x)) * 0x1p-200); } q = x * x2 * C3 + x2 * x2 * (C4 + x * (C5 + x * (C6 + x * (C7 + x * (C8 + x * (C9 + x * (C10 + x * (C11 + x * (C12 + x * (C13 + dx * (C14 + dx * (C15 + dx * (C16 + dx * (C17 + dx * C18)))))))))))))); } else { q = x * x2 * D3 + x2 * x2 * (D4 + x * (D5 + x * (D6 + x * (D7 + x * (D8 + x * (D9 + x * (D10 + x * (D11 + x * (D12 + x * (D13 + dx * (D14 + dx * (D15 + dx * (D16 + dx * D17))))))))))))); } x_hi = (float)x; x_lo = x - x_hi; hx2_hi = x_hi * x_hi / 2; hx2_lo = x_lo * (x + x_hi) / 2; if (ix >= BIAS - 7) - RETURNI(hx2_lo + x_lo + q + (hx2_hi + x_hi)); + RETURN2PI(hx2_hi + x_hi, hx2_lo + x_lo + q); else - RETURNI(hx2_lo + q + hx2_hi + x); + RETURN2PI(x, hx2_lo + q + hx2_hi); } /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */ /* Use a specialized rint() to get fn. Assume round-to-nearest. */ fn = (double)x * INV_L + 0x1.8p52 - 0x1.8p52; #if defined(HAVE_EFFICIENT_IRINT) n = irint(fn); #else n = (int)fn; #endif n2 = (unsigned)n % INTERVALS; k = n >> LOG2_INTERVALS; r1 = x - fn * L1; r2 = fn * -L2; r = r1 + r2; /* Prepare scale factor. */ v.e = 1; v.xbits.expsign = BIAS + k; twopk = v.e; /* * Evaluate lower terms of * expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */ dr = r; q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 + dr * (A7 + dr * (A8 + dr * (A9 + dr * A10)))))))); t = tbl[n2].lo + tbl[n2].hi; if (k == 0) { - t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 + - (tbl[n2].hi - 1); + t = SUM2P(tbl[n2].hi - 1, tbl[n2].lo * (r1 + 1) + t * q + + tbl[n2].hi * r1); RETURNI(t); } if (k == -1) { - t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 + - (tbl[n2].hi - 2); + t = SUM2P(tbl[n2].hi - 2, tbl[n2].lo * (r1 + 1) + t * q + + tbl[n2].hi * r1); RETURNI(t / 2); } if (k < -7) { - t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi; + t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1)); RETURNI(t * twopk - 1); } if (k > 2 * LDBL_MANT_DIG - 1) { - t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi; + t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1)); if (k == LDBL_MAX_EXP) RETURNI(t * 2 * 0x1p16383L - 1); RETURNI(t * twopk - 1); } v.xbits.expsign = BIAS - k; twomk = v.e; if (k > LDBL_MANT_DIG - 1) - t = tbl[n2].lo - twomk + t * (q + r1) + tbl[n2].hi; + t = SUM2P(tbl[n2].hi, tbl[n2].lo - twomk + t * (q + r1)); else - t = tbl[n2].lo + t * (q + r1) + (tbl[n2].hi - twomk); + t = SUM2P(tbl[n2].hi - twomk, tbl[n2].lo + t * (q + r1)); RETURNI(t * twopk); } Index: stable/10/lib/msun/ld80/k_expl.h =================================================================== --- stable/10/lib/msun/ld80/k_expl.h (nonexistent) +++ stable/10/lib/msun/ld80/k_expl.h (revision 271779) @@ -0,0 +1,305 @@ +/* from: FreeBSD: head/lib/msun/ld80/s_expl.c 251343 2013-06-03 19:51:32Z kargl */ + +/*- + * Copyright (c) 2009-2013 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. + * + * Optimized by Bruce D. Evans. + */ + +#include +__FBSDID("$FreeBSD$"); + +/* + * See s_expl.c for more comments about __k_expl(). + * + * See ../src/e_exp.c and ../src/k_exp.h for precision-independent comments + * about the secondary kernels. + */ + +#define INTERVALS 128 +#define LOG2_INTERVALS 7 +#define BIAS (LDBL_MAX_EXP - 1) + +static const double +/* + * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must + * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest + * bits zero so that multiplication of it by n is exact. + */ +INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */ +L1 = 5.4152123484527692e-3, /* 0x162e42ff000000.0p-60 */ +L2 = -3.2819649005320973e-13, /* -0x1718432a1b0e26.0p-94 */ +/* + * Domain [-0.002708, 0.002708], range ~[-5.7136e-24, 5.7110e-24]: + * |exp(x) - p(x)| < 2**-77.2 + * (0.002708 is ln2/(2*INTERVALS) rounded up a little). + */ +A2 = 0.5, +A3 = 1.6666666666666119e-1, /* 0x15555555555490.0p-55 */ +A4 = 4.1666666666665887e-2, /* 0x155555555554e5.0p-57 */ +A5 = 8.3333354987869413e-3, /* 0x1111115b789919.0p-59 */ +A6 = 1.3888891738560272e-3; /* 0x16c16c651633ae.0p-62 */ + +/* + * 2^(i/INTERVALS) for i in [0,INTERVALS] is represented by two values where + * the first 53 bits of the significand are stored in hi and the next 53 + * bits are in lo. Tang's paper states that the trailing 6 bits of hi must + * be zero for his algorithm in both single and double precision, because + * the table is re-used in the implementation of expm1() where a floating + * point addition involving hi must be exact. Here hi is double, so + * converting it to long double gives 11 trailing zero bits. + */ +static const struct { + double hi; + double lo; +} tbl[INTERVALS] = { + 0x1p+0, 0x0p+0, + /* + * XXX hi is rounded down, and the formatting is not quite normal. + * But I rather like both. The 0x1.*p format is good for 4N+1 + * mantissa bits. Rounding down makes the lo terms positive, + * so that the columnar formatting can be simpler. + */ + 0x1.0163da9fb3335p+0, 0x1.b61299ab8cdb7p-54, + 0x1.02c9a3e778060p+0, 0x1.dcdef95949ef4p-53, + 0x1.04315e86e7f84p+0, 0x1.7ae71f3441b49p-53, + 0x1.059b0d3158574p+0, 0x1.d73e2a475b465p-55, + 0x1.0706b29ddf6ddp+0, 0x1.8db880753b0f6p-53, + 0x1.0874518759bc8p+0, 0x1.186be4bb284ffp-57, + 0x1.09e3ecac6f383p+0, 0x1.1487818316136p-54, + 0x1.0b5586cf9890fp+0, 0x1.8a62e4adc610bp-54, + 0x1.0cc922b7247f7p+0, 0x1.01edc16e24f71p-54, + 0x1.0e3ec32d3d1a2p+0, 0x1.03a1727c57b53p-59, + 0x1.0fb66affed31ap+0, 0x1.e464123bb1428p-53, + 0x1.11301d0125b50p+0, 0x1.49d77e35db263p-53, + 0x1.12abdc06c31cbp+0, 0x1.f72575a649ad2p-53, + 0x1.1429aaea92ddfp+0, 0x1.66820328764b1p-53, + 0x1.15a98c8a58e51p+0, 0x1.2406ab9eeab0ap-55, + 0x1.172b83c7d517ap+0, 0x1.b9bef918a1d63p-53, + 0x1.18af9388c8de9p+0, 0x1.777ee1734784ap-53, + 0x1.1a35beb6fcb75p+0, 0x1.e5b4c7b4968e4p-55, + 0x1.1bbe084045cd3p+0, 0x1.3563ce56884fcp-53, + 0x1.1d4873168b9aap+0, 0x1.e016e00a2643cp-54, + 0x1.1ed5022fcd91cp+0, 0x1.71033fec2243ap-53, + 0x1.2063b88628cd6p+0, 0x1.dc775814a8495p-55, + 0x1.21f49917ddc96p+0, 0x1.2a97e9494a5eep-55, + 0x1.2387a6e756238p+0, 0x1.9b07eb6c70573p-54, + 0x1.251ce4fb2a63fp+0, 0x1.ac155bef4f4a4p-55, + 0x1.26b4565e27cddp+0, 0x1.2bd339940e9d9p-55, + 0x1.284dfe1f56380p+0, 0x1.2d9e2b9e07941p-53, + 0x1.29e9df51fdee1p+0, 0x1.612e8afad1255p-55, + 0x1.2b87fd0dad98fp+0, 0x1.fbbd48ca71f95p-53, + 0x1.2d285a6e4030bp+0, 0x1.0024754db41d5p-54, + 0x1.2ecafa93e2f56p+0, 0x1.1ca0f45d52383p-56, + 0x1.306fe0a31b715p+0, 0x1.6f46ad23182e4p-55, + 0x1.32170fc4cd831p+0, 0x1.a9ce78e18047cp-55, + 0x1.33c08b26416ffp+0, 0x1.32721843659a6p-54, + 0x1.356c55f929ff0p+0, 0x1.928c468ec6e76p-53, + 0x1.371a7373aa9cap+0, 0x1.4e28aa05e8a8fp-53, + 0x1.38cae6d05d865p+0, 0x1.0b53961b37da2p-53, + 0x1.3a7db34e59ff6p+0, 0x1.d43792533c144p-53, + 0x1.3c32dc313a8e4p+0, 0x1.08003e4516b1ep-53, + 0x1.3dea64c123422p+0, 0x1.ada0911f09ebcp-55, + 0x1.3fa4504ac801bp+0, 0x1.417ee03548306p-53, + 0x1.4160a21f72e29p+0, 0x1.f0864b71e7b6cp-53, + 0x1.431f5d950a896p+0, 0x1.b8e088728219ap-53, + 0x1.44e086061892dp+0, 0x1.89b7a04ef80d0p-59, + 0x1.46a41ed1d0057p+0, 0x1.c944bd1648a76p-54, + 0x1.486a2b5c13cd0p+0, 0x1.3c1a3b69062f0p-56, + 0x1.4a32af0d7d3dep+0, 0x1.9cb62f3d1be56p-54, + 0x1.4bfdad5362a27p+0, 0x1.d4397afec42e2p-56, + 0x1.4dcb299fddd0dp+0, 0x1.8ecdbbc6a7833p-54, + 0x1.4f9b2769d2ca6p+0, 0x1.5a67b16d3540ep-53, + 0x1.516daa2cf6641p+0, 0x1.8225ea5909b04p-53, + 0x1.5342b569d4f81p+0, 0x1.be1507893b0d5p-53, + 0x1.551a4ca5d920ep+0, 0x1.8a5d8c4048699p-53, + 0x1.56f4736b527dap+0, 0x1.9bb2c011d93adp-54, + 0x1.58d12d497c7fdp+0, 0x1.295e15b9a1de8p-55, + 0x1.5ab07dd485429p+0, 0x1.6324c054647adp-54, + 0x1.5c9268a5946b7p+0, 0x1.c4b1b816986a2p-60, + 0x1.5e76f15ad2148p+0, 0x1.ba6f93080e65ep-54, + 0x1.605e1b976dc08p+0, 0x1.60edeb25490dcp-53, + 0x1.6247eb03a5584p+0, 0x1.63e1f40dfa5b5p-53, + 0x1.6434634ccc31fp+0, 0x1.8edf0e2989db3p-53, + 0x1.6623882552224p+0, 0x1.224fb3c5371e6p-53, + 0x1.68155d44ca973p+0, 0x1.038ae44f73e65p-57, + 0x1.6a09e667f3bccp+0, 0x1.21165f626cdd5p-53, + 0x1.6c012750bdabep+0, 0x1.daed533001e9ep-53, + 0x1.6dfb23c651a2ep+0, 0x1.e441c597c3775p-53, + 0x1.6ff7df9519483p+0, 0x1.9f0fc369e7c42p-53, + 0x1.71f75e8ec5f73p+0, 0x1.ba46e1e5de15ap-53, + 0x1.73f9a48a58173p+0, 0x1.7ab9349cd1562p-53, + 0x1.75feb564267c8p+0, 0x1.7edd354674916p-53, + 0x1.780694fde5d3fp+0, 0x1.866b80a02162dp-54, + 0x1.7a11473eb0186p+0, 0x1.afaa2047ed9b4p-53, + 0x1.7c1ed0130c132p+0, 0x1.f124cd1164dd6p-54, + 0x1.7e2f336cf4e62p+0, 0x1.05d02ba15797ep-56, + 0x1.80427543e1a11p+0, 0x1.6c1bccec9346bp-53, + 0x1.82589994cce12p+0, 0x1.159f115f56694p-53, + 0x1.8471a4623c7acp+0, 0x1.9ca5ed72f8c81p-53, + 0x1.868d99b4492ecp+0, 0x1.01c83b21584a3p-53, + 0x1.88ac7d98a6699p+0, 0x1.994c2f37cb53ap-54, + 0x1.8ace5422aa0dbp+0, 0x1.6e9f156864b27p-54, + 0x1.8cf3216b5448bp+0, 0x1.de55439a2c38bp-53, + 0x1.8f1ae99157736p+0, 0x1.5cc13a2e3976cp-55, + 0x1.9145b0b91ffc5p+0, 0x1.114c368d3ed6ep-53, + 0x1.93737b0cdc5e4p+0, 0x1.e8a0387e4a814p-53, + 0x1.95a44cbc8520ep+0, 0x1.d36906d2b41f9p-53, + 0x1.97d829fde4e4fp+0, 0x1.173d241f23d18p-53, + 0x1.9a0f170ca07b9p+0, 0x1.7462137188ce7p-53, + 0x1.9c49182a3f090p+0, 0x1.c7c46b071f2bep-56, + 0x1.9e86319e32323p+0, 0x1.824ca78e64c6ep-56, + 0x1.a0c667b5de564p+0, 0x1.6535b51719567p-53, + 0x1.a309bec4a2d33p+0, 0x1.6305c7ddc36abp-54, + 0x1.a5503b23e255cp+0, 0x1.1684892395f0fp-53, + 0x1.a799e1330b358p+0, 0x1.bcb7ecac563c7p-54, + 0x1.a9e6b5579fdbfp+0, 0x1.0fac90ef7fd31p-54, + 0x1.ac36bbfd3f379p+0, 0x1.81b72cd4624ccp-53, + 0x1.ae89f995ad3adp+0, 0x1.7a1cd345dcc81p-54, + 0x1.b0e07298db665p+0, 0x1.2108559bf8deep-53, + 0x1.b33a2b84f15fap+0, 0x1.ed7fa1cf7b290p-53, + 0x1.b59728de55939p+0, 0x1.1c7102222c90ep-53, + 0x1.b7f76f2fb5e46p+0, 0x1.d54f610356a79p-53, + 0x1.ba5b030a10649p+0, 0x1.0819678d5eb69p-53, + 0x1.bcc1e904bc1d2p+0, 0x1.23dd07a2d9e84p-55, + 0x1.bf2c25bd71e08p+0, 0x1.0811ae04a31c7p-53, + 0x1.c199bdd85529cp+0, 0x1.11065895048ddp-55, + 0x1.c40ab5fffd07ap+0, 0x1.b4537e083c60ap-54, + 0x1.c67f12e57d14bp+0, 0x1.2884dff483cadp-54, + 0x1.c8f6d9406e7b5p+0, 0x1.1acbc48805c44p-56, + 0x1.cb720dcef9069p+0, 0x1.503cbd1e949dbp-56, + 0x1.cdf0b555dc3f9p+0, 0x1.889f12b1f58a3p-53, + 0x1.d072d4a07897bp+0, 0x1.1a1e45e4342b2p-53, + 0x1.d2f87080d89f1p+0, 0x1.15bc247313d44p-53, + 0x1.d5818dcfba487p+0, 0x1.2ed02d75b3707p-55, + 0x1.d80e316c98397p+0, 0x1.7709f3a09100cp-53, + 0x1.da9e603db3285p+0, 0x1.c2300696db532p-54, + 0x1.dd321f301b460p+0, 0x1.2da5778f018c3p-54, + 0x1.dfc97337b9b5ep+0, 0x1.72d195873da52p-53, + 0x1.e264614f5a128p+0, 0x1.424ec3f42f5b5p-53, + 0x1.e502ee78b3ff6p+0, 0x1.39e8980a9cc8fp-55, + 0x1.e7a51fbc74c83p+0, 0x1.2d522ca0c8de2p-54, + 0x1.ea4afa2a490d9p+0, 0x1.0b1ee7431ebb6p-53, + 0x1.ecf482d8e67f0p+0, 0x1.1b60625f7293ap-53, + 0x1.efa1bee615a27p+0, 0x1.dc7f486a4b6b0p-54, + 0x1.f252b376bba97p+0, 0x1.3a1a5bf0d8e43p-54, + 0x1.f50765b6e4540p+0, 0x1.9d3e12dd8a18bp-54, + 0x1.f7bfdad9cbe13p+0, 0x1.1227697fce57bp-53, + 0x1.fa7c1819e90d8p+0, 0x1.74853f3a5931ep-55, + 0x1.fd3c22b8f71f1p+0, 0x1.2eb74966579e7p-57 +}; + +/* + * Kernel for expl(x). x must be finite and not tiny or huge. + * "tiny" is anything that would make us underflow (|A6*x^6| < ~LDBL_MIN). + * "huge" is anything that would make fn*L1 inexact (|x| > ~2**17*ln2). + */ +static inline void +__k_expl(long double x, long double *hip, long double *lop, int *kp) +{ + long double fn, q, r, r1, r2, t, z; + int n, n2; + + /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */ + /* Use a specialized rint() to get fn. Assume round-to-nearest. */ + fn = x * INV_L + 0x1.8p63 - 0x1.8p63; + r = x - fn * L1 - fn * L2; /* r = r1 + r2 done independently. */ +#if defined(HAVE_EFFICIENT_IRINTL) + n = irintl(fn); +#elif defined(HAVE_EFFICIENT_IRINT) + n = irint(fn); +#else + n = (int)fn; +#endif + n2 = (unsigned)n % INTERVALS; + /* Depend on the sign bit being propagated: */ + *kp = n >> LOG2_INTERVALS; + r1 = x - fn * L1; + r2 = fn * -L2; + + /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */ + z = r * r; +#if 0 + q = r2 + z * (A2 + r * A3) + z * z * (A4 + r * A5) + z * z * z * A6; +#else + q = r2 + z * A2 + z * r * (A3 + r * A4 + z * (A5 + r * A6)); +#endif + t = (long double)tbl[n2].lo + tbl[n2].hi; + *hip = tbl[n2].hi; + *lop = tbl[n2].lo + t * (q + r1); +} + +static inline void +k_hexpl(long double x, long double *hip, long double *lop) +{ + float twopkm1; + int k; + + __k_expl(x, hip, lop, &k); + SET_FLOAT_WORD(twopkm1, 0x3f800000 + ((k - 1) << 23)); + *hip *= twopkm1; + *lop *= twopkm1; +} + +static inline long double +hexpl(long double x) +{ + long double hi, lo, twopkm2; + int k; + + twopkm2 = 1; + __k_expl(x, &hi, &lo, &k); + SET_LDBL_EXPSIGN(twopkm2, BIAS + k - 2); + return (lo + hi) * 2 * twopkm2; +} + +#ifdef _COMPLEX_H +/* + * See ../src/k_exp.c for details. + */ +static inline long double complex +__ldexp_cexpl(long double complex z, int expt) +{ + long double exp_x, hi, lo; + long double x, y, scale1, scale2; + int half_expt, k; + + x = creall(z); + y = cimagl(z); + __k_expl(x, &hi, &lo, &k); + + exp_x = (lo + hi) * 0x1p16382; + expt += k - 16382; + + scale1 = 1; + half_expt = expt / 2; + SET_LDBL_EXPSIGN(scale1, BIAS + half_expt); + scale2 = 1; + SET_LDBL_EXPSIGN(scale1, BIAS + expt - half_expt); + + return (cpackl(cos(y) * exp_x * scale1 * scale2, + sinl(y) * exp_x * scale1 * scale2)); +} +#endif /* _COMPLEX_H */ Property changes on: stable/10/lib/msun/ld80/k_expl.h ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: stable/10/lib/msun/ld80/s_erfl.c =================================================================== --- stable/10/lib/msun/ld80/s_erfl.c (nonexistent) +++ stable/10/lib/msun/ld80/s_erfl.c (revision 271779) @@ -0,0 +1,337 @@ +/* @(#)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 +__FBSDID("$FreeBSD$"); + +/* + * See s_erf.c for complete comments. + * + * Converted to long double by Steven G. Kargl. + */ +#include +#ifdef __i386__ +#include +#endif + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + +/* XXX Prevent compilers from erroneously constant folding: */ +static const volatile long double tiny = 0x1p-10000L; + +static const double +half= 0.5, +one = 1, +two = 2; +/* + * In the domain [0, 2**-34], only the first term in the power series + * expansion of erf(x) is used. The magnitude of the first neglected + * terms is less than 2**-102. + */ +static const union IEEEl2bits +efxu = LD80C(0x8375d410a6db446c, -3, 1.28379167095512573902e-1L), +efx8u = LD80C(0x8375d410a6db446c, 0, 1.02703333676410059122e+0L), +/* + * Domain [0, 0.84375], range ~[-1.423e-22, 1.423e-22]: + * |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-72.573 + */ +pp0u = LD80C(0x8375d410a6db446c, -3, 1.28379167095512573902e-1L), +pp1u = LD80C(0xa46c7d09ec3d0cec, -2, -3.21140201054840180596e-1L), +pp2u = LD80C(0x9b31e66325576f86, -5, -3.78893851760347812082e-2L), +pp3u = LD80C(0x804ac72c9a0b97dd, -7, -7.83032847030604679616e-3L), +pp4u = LD80C(0x9f42bcbc3d5a601d, -12, -3.03765663857082048459e-4L), +pp5u = LD80C(0x9ec4ad6193470693, -16, -1.89266527398167917502e-5L), +qq1u = LD80C(0xdb4b8eb713188d6b, -2, 4.28310832832310510579e-1L), +qq2u = LD80C(0xa5750835b2459bd1, -4, 8.07896272074540216658e-2L), +qq3u = LD80C(0x8b85d6bd6a90b51c, -7, 8.51579638189385354266e-3L), +qq4u = LD80C(0x87332f82cff4ff96, -11, 5.15746855583604912827e-4L), +qq5u = LD80C(0x83466cb6bf9dca00, -16, 1.56492109706256700009e-5L), +qq6u = LD80C(0xf5bf98c2f996bf63, -24, 1.14435527803073879724e-7L); +#define efx (efxu.e) +#define efx8 (efx8u.e) +#define pp0 (pp0u.e) +#define pp1 (pp1u.e) +#define pp2 (pp2u.e) +#define pp3 (pp3u.e) +#define pp4 (pp4u.e) +#define pp5 (pp5u.e) +#define qq1 (qq1u.e) +#define qq2 (qq2u.e) +#define qq3 (qq3u.e) +#define qq4 (qq4u.e) +#define qq5 (qq5u.e) +#define qq6 (qq6u.e) +static const union IEEEl2bits +erxu = LD80C(0xd7bb3d0000000000, -1, 8.42700779438018798828e-1L), +/* + * Domain [0.84375, 1.25], range ~[-8.132e-22, 8.113e-22]: + * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-71.762 + */ +pa0u = LD80C(0xe8211158da02c692, -27, 1.35116960705131296711e-8L), +pa1u = LD80C(0xd488f89f36988618, -2, 4.15107507167065612570e-1L), +pa2u = LD80C(0xece74f8c63fa3942, -4, -1.15675565215949226989e-1L), +pa3u = LD80C(0xc8d31e020727c006, -4, 9.80589241379624665791e-2L), +pa4u = LD80C(0x985d5d5fafb0551f, -5, 3.71984145558422368847e-2L), +pa5u = LD80C(0xa5b6c4854d2f5452, -8, -5.05718799340957673661e-3L), +pa6u = LD80C(0x85c8d58fe3993a47, -8, 4.08277919612202243721e-3L), +pa7u = LD80C(0xddbfbc23677b35cf, -13, 2.11476292145347530794e-4L), +qa1u = LD80C(0xb8a977896f5eff3f, -1, 7.21335860303380361298e-1L), +qa2u = LD80C(0x9fcd662c3d4eac86, -1, 6.24227891731886593333e-1L), +qa3u = LD80C(0x9d0b618eac67ba07, -2, 3.06727455774491855801e-1L), +qa4u = LD80C(0x881a4293f6d6c92d, -3, 1.32912674218195890535e-1L), +qa5u = LD80C(0xbab144f07dea45bf, -5, 4.55792134233613027584e-2L), +qa6u = LD80C(0xa6c34ba438bdc900, -7, 1.01783980070527682680e-2L), +qa7u = LD80C(0x8fa866dc20717a91, -9, 2.19204436518951438183e-3L); +#define erx (erxu.e) +#define pa0 (pa0u.e) +#define pa1 (pa1u.e) +#define pa2 (pa2u.e) +#define pa3 (pa3u.e) +#define pa4 (pa4u.e) +#define pa5 (pa5u.e) +#define pa6 (pa6u.e) +#define pa7 (pa7u.e) +#define qa1 (qa1u.e) +#define qa2 (qa2u.e) +#define qa3 (qa3u.e) +#define qa4 (qa4u.e) +#define qa5 (qa5u.e) +#define qa6 (qa6u.e) +#define qa7 (qa7u.e) +static const union IEEEl2bits +/* + * Domain [1.25,2.85715], range ~[-2.334e-22,2.334e-22]: + * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-71.860 + */ +ra0u = LD80C(0xa1a091e0fb4f335a, -7, -9.86494298915814308249e-3L), +ra1u = LD80C(0xc2b0d045ae37df6b, -1, -7.60510460864878271275e-1L), +ra2u = LD80C(0xf2cec3ee7da636c5, 3, -1.51754798236892278250e+1L), +ra3u = LD80C(0x813cc205395adc7d, 7, -1.29237335516455333420e+2L), +ra4u = LD80C(0x8737c8b7b4062c2f, 9, -5.40871625829510494776e+2L), +ra5u = LD80C(0x8ffe5383c08d4943, 10, -1.15194769466026108551e+3L), +ra6u = LD80C(0x983573e64d5015a9, 10, -1.21767039790249025544e+3L), +ra7u = LD80C(0x92a794e763a6d4db, 9, -5.86618463370624636688e+2L), +ra8u = LD80C(0xd5ad1fae77c3d9a3, 6, -1.06838132335777049840e+2L), +ra9u = LD80C(0x934c1a247807bb9c, 2, -4.60303980944467334806e+0L), +sa1u = LD80C(0xd342f90012bb1189, 4, 2.64077014928547064865e+1L), +sa2u = LD80C(0x839be13d9d5da883, 8, 2.63217811300123973067e+2L), +sa3u = LD80C(0x9f8cba6d1ae1b24b, 10, 1.27639775710344617587e+3L), +sa4u = LD80C(0xcaa83f403713e33e, 11, 3.24251544209971162003e+3L), +sa5u = LD80C(0x8796aff2f3c47968, 12, 4.33883591261332837874e+3L), +sa6u = LD80C(0xb6ef97f9c753157b, 11, 2.92697460344182158454e+3L), +sa7u = LD80C(0xe02aee5f83773d1c, 9, 8.96670799139389559818e+2L), +sa8u = LD80C(0xc82b83855b88e07e, 6, 1.00084987800048510018e+2L), +sa9u = LD80C(0x92f030aefadf28ad, 1, 2.29591004455459083843e+0L); +#define ra0 (ra0u.e) +#define ra1 (ra1u.e) +#define ra2 (ra2u.e) +#define ra3 (ra3u.e) +#define ra4 (ra4u.e) +#define ra5 (ra5u.e) +#define ra6 (ra6u.e) +#define ra7 (ra7u.e) +#define ra8 (ra8u.e) +#define ra9 (ra9u.e) +#define sa1 (sa1u.e) +#define sa2 (sa2u.e) +#define sa3 (sa3u.e) +#define sa4 (sa4u.e) +#define sa5 (sa5u.e) +#define sa6 (sa6u.e) +#define sa7 (sa7u.e) +#define sa8 (sa8u.e) +#define sa9 (sa9u.e) +/* + * Domain [2.85715,7], range ~[-8.323e-22,8.390e-22]: + * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-70.326 + */ +static const union IEEEl2bits +rb0u = LD80C(0xa1a091cf43abcd26, -7, -9.86494292470284646962e-3L), +rb1u = LD80C(0xd19d2df1cbb8da0a, -1, -8.18804618389296662837e-1L), +rb2u = LD80C(0x9a4dd1383e5daf5b, 4, -1.92879967111618594779e+1L), +rb3u = LD80C(0xbff0ae9fc0751de6, 7, -1.91940164551245394969e+2L), +rb4u = LD80C(0xdde08465310b472b, 9, -8.87508080766577324539e+2L), +rb5u = LD80C(0xe796e1d38c8c70a9, 10, -1.85271506669474503781e+3L), +rb6u = LD80C(0xbaf655a76e0ab3b5, 10, -1.49569795581333675349e+3L), +rb7u = LD80C(0x95d21e3e75503c21, 8, -2.99641547972948019157e+2L), +sb1u = LD80C(0x814487ed823c8cbd, 5, 3.23169247732868256569e+1L), +sb2u = LD80C(0xbe4bfbb1301304be, 8, 3.80593618534539961773e+2L), +sb3u = LD80C(0x809c4ade46b927c7, 11, 2.05776827838541292848e+3L), +sb4u = LD80C(0xa55284359f3395a8, 12, 5.29031455540062116327e+3L), +sb5u = LD80C(0xbcfa72da9b820874, 12, 6.04730608102312640462e+3L), +sb6u = LD80C(0x9d09a35988934631, 11, 2.51260238030767176221e+3L), +sb7u = LD80C(0xd675bbe542c159fa, 7, 2.14459898308561015684e+2L); +#define rb0 (rb0u.e) +#define rb1 (rb1u.e) +#define rb2 (rb2u.e) +#define rb3 (rb3u.e) +#define rb4 (rb4u.e) +#define rb5 (rb5u.e) +#define rb6 (rb6u.e) +#define rb7 (rb7u.e) +#define sb1 (sb1u.e) +#define sb2 (sb2u.e) +#define sb3 (sb3u.e) +#define sb4 (sb4u.e) +#define sb5 (sb5u.e) +#define sb6 (sb6u.e) +#define sb7 (sb7u.e) +/* + * Domain [7,108], range ~[-4.422e-22,4.422e-22]: + * |log(x*erfc(x)) + x**2 + 0.5625 - rc(x)/sc(x)| < 2**-70.938 + */ +static const union IEEEl2bits +/* err = -4.422092275318925082e-22 -70.937689 */ +rc0u = LD80C(0xa1a091cf437a17ad, -7, -9.86494292470008707260e-3L), +rc1u = LD80C(0xbe79c5a978122b00, -1, -7.44045595049165939261e-1L), +rc2u = LD80C(0xdb26f9bbe31a2794, 3, -1.36970155085888424425e+1L), +rc3u = LD80C(0xb5f69a38f5747ac8, 6, -9.09816453742625888546e+1L), +rc4u = LD80C(0xd79676d970d0a21a, 7, -2.15587750997584074147e+2L), +rc5u = LD80C(0xfe528153c45ec97c, 6, -1.27161142938347796666e+2L), +sc1u = LD80C(0xc5e8cd46d5604a96, 4, 2.47386727842204312937e+1L), +sc2u = LD80C(0xc5f0f5a5484520eb, 7, 1.97941248254913378865e+2L), +sc3u = LD80C(0x964e3c7b34db9170, 9, 6.01222441484087787522e+2L), +sc4u = LD80C(0x99be1b89faa0596a, 9, 6.14970430845978077827e+2L), +sc5u = LD80C(0xf80dfcbf37ffc5ea, 6, 1.24027318931184605891e+2L); +#define rc0 (rc0u.e) +#define rc1 (rc1u.e) +#define rc2 (rc2u.e) +#define rc3 (rc3u.e) +#define rc4 (rc4u.e) +#define rc5 (rc5u.e) +#define sc1 (sc1u.e) +#define sc2 (sc2u.e) +#define sc3 (sc3u.e) +#define sc4 (sc4u.e) +#define sc5 (sc5u.e) + +long double +erfl(long double x) +{ + long double ax,R,S,P,Q,s,y,z,r; + uint64_t lx; + int32_t i; + uint16_t hx; + + EXTRACT_LDBL80_WORDS(hx, lx, x); + + if((hx & 0x7fff) == 0x7fff) { /* erfl(nan)=nan */ + i = (hx>>15)<<1; + return (1-i)+one/x; /* erfl(+-inf)=+-1 */ + } + + ENTERI(); + + ax = fabsl(x); + if(ax < 0.84375) { + if(ax < 0x1p-34L) { + if(ax < 0x1p-16373L) + RETURNI((8*x+efx8*x)/8); /* avoid spurious underflow */ + RETURNI(x + efx*x); + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*pp5)))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*qq6))))); + y = r/s; + RETURNI(x + x*y); + } + if(ax < 1.25) { + s = ax-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*pa7)))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*qa7)))))); + if(x>=0) RETURNI(erx + P/Q); else RETURNI(-erx - P/Q); + } + if(ax >= 7) { /* inf>|x|>= 7 */ + if(x>=0) RETURNI(one-tiny); else RETURNI(tiny-one); + } + s = one/(ax*ax); + if(ax < 2.85715) { /* |x| < 2.85715 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+ + s*(ra8+s*ra9)))))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+ + s*(sa8+s*sa9)))))))); + } else { /* |x| >= 2.85715 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*rb7)))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*sb7)))))); + } + z=(float)ax; + r=expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S); + if(x>=0) RETURNI(one-r/ax); else RETURNI(r/ax-one); +} + +long double +erfcl(long double x) +{ + long double ax,R,S,P,Q,s,y,z,r; + uint64_t lx; + uint16_t hx; + + EXTRACT_LDBL80_WORDS(hx, lx, x); + + if((hx & 0x7fff) == 0x7fff) { /* erfcl(nan)=nan */ + /* erfcl(+-inf)=0,2 */ + return ((hx>>15)<<1)+one/x; + } + + ENTERI(); + + ax = fabsl(x); + if(ax < 0.84375L) { + if(ax < 0x1p-34L) + RETURNI(one-x); + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*pp5)))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*qq6))))); + y = r/s; + if(ax < 0.25L) { /* x<1/4 */ + RETURNI(one-(x+x*y)); + } else { + r = x*y; + r += (x-half); + RETURNI(half - r); + } + } + if(ax < 1.25L) { + s = ax-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*pa7)))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*qa7)))))); + if(x>=0) { + z = one-erx; RETURNI(z - P/Q); + } else { + z = (erx+P/Q); RETURNI(one+z); + } + } + + if(ax < 108) { /* |x| < 108 */ + s = one/(ax*ax); + if(ax < 2.85715) { /* |x| < 2.85715 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+ + s*(ra8+s*ra9)))))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+ + s*(sa8+s*sa9)))))))); + } else if(ax < 7) { /* | |x| < 7 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*rb7)))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*sb7)))))); + } else { + if(x < -7) RETURNI(two-tiny);/* x < -7 */ + R=rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*rc5)))); + S=one+s*(sc1+s*(sc2+s*(sc3+s*(sc4+s*sc5)))); + } + z = (float)ax; + r = expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S); + if(x>0) RETURNI(r/ax); else RETURNI(two-r/ax); + } else { + if(x>0) RETURNI(tiny*tiny); else RETURNI(two-tiny); + } +} Property changes on: stable/10/lib/msun/ld80/s_erfl.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: stable/10/lib/msun/ld80/s_expl.c =================================================================== --- stable/10/lib/msun/ld80/s_expl.c (revision 271778) +++ stable/10/lib/msun/ld80/s_expl.c (revision 271779) @@ -1,469 +1,284 @@ /*- * Copyright (c) 2009-2013 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. * * Optimized by Bruce D. Evans. */ #include __FBSDID("$FreeBSD$"); /** * Compute the exponential of x for Intel 80-bit format. This is based on: * * PTP Tang, "Table-driven implementation of the exponential function * in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 15, * 144-157 (1989). * * where the 32 table entries have been expanded to INTERVALS (see below). */ #include #ifdef __i386__ #include #endif #include "fpmath.h" #include "math.h" #include "math_private.h" +#include "k_expl.h" -#define INTERVALS 128 -#define LOG2_INTERVALS 7 -#define BIAS (LDBL_MAX_EXP - 1) +/* XXX Prevent compilers from erroneously constant folding these: */ +static const volatile long double +huge = 0x1p10000L, +tiny = 0x1p-10000L; static const long double -huge = 0x1p10000L, twom10000 = 0x1p-10000L; -/* XXX Prevent gcc from erroneously constant folding this: */ -static volatile const long double tiny = 0x1p-10000L; static const union IEEEl2bits /* log(2**16384 - 0.5) rounded towards zero: */ /* log(2**16384 - 0.5 + 1) rounded towards zero for expm1l() is the same: */ o_thresholdu = LD80C(0xb17217f7d1cf79ab, 13, 11356.5234062941439488L), #define o_threshold (o_thresholdu.e) /* log(2**(-16381-64-1)) rounded towards zero: */ u_thresholdu = LD80C(0xb21dfe7f09e2baa9, 13, -11399.4985314888605581L); #define u_threshold (u_thresholdu.e) -static const double -/* - * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must - * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest - * bits zero so that multiplication of it by n is exact. - */ -INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */ -L1 = 5.4152123484527692e-3, /* 0x162e42ff000000.0p-60 */ -L2 = -3.2819649005320973e-13, /* -0x1718432a1b0e26.0p-94 */ -/* - * Domain [-0.002708, 0.002708], range ~[-5.7136e-24, 5.7110e-24]: - * |exp(x) - p(x)| < 2**-77.2 - * (0.002708 is ln2/(2*INTERVALS) rounded up a little). - */ -A2 = 0.5, -A3 = 1.6666666666666119e-1, /* 0x15555555555490.0p-55 */ -A4 = 4.1666666666665887e-2, /* 0x155555555554e5.0p-57 */ -A5 = 8.3333354987869413e-3, /* 0x1111115b789919.0p-59 */ -A6 = 1.3888891738560272e-3; /* 0x16c16c651633ae.0p-62 */ - -/* - * 2^(i/INTERVALS) for i in [0,INTERVALS] is represented by two values where - * the first 53 bits of the significand are stored in hi and the next 53 - * bits are in lo. Tang's paper states that the trailing 6 bits of hi must - * be zero for his algorithm in both single and double precision, because - * the table is re-used in the implementation of expm1() where a floating - * point addition involving hi must be exact. Here hi is double, so - * converting it to long double gives 11 trailing zero bits. - */ -static const struct { - double hi; - double lo; -} tbl[INTERVALS] = { - 0x1p+0, 0x0p+0, - 0x1.0163da9fb3335p+0, 0x1.b61299ab8cdb7p-54, - 0x1.02c9a3e778060p+0, 0x1.dcdef95949ef4p-53, - 0x1.04315e86e7f84p+0, 0x1.7ae71f3441b49p-53, - 0x1.059b0d3158574p+0, 0x1.d73e2a475b465p-55, - 0x1.0706b29ddf6ddp+0, 0x1.8db880753b0f6p-53, - 0x1.0874518759bc8p+0, 0x1.186be4bb284ffp-57, - 0x1.09e3ecac6f383p+0, 0x1.1487818316136p-54, - 0x1.0b5586cf9890fp+0, 0x1.8a62e4adc610bp-54, - 0x1.0cc922b7247f7p+0, 0x1.01edc16e24f71p-54, - 0x1.0e3ec32d3d1a2p+0, 0x1.03a1727c57b53p-59, - 0x1.0fb66affed31ap+0, 0x1.e464123bb1428p-53, - 0x1.11301d0125b50p+0, 0x1.49d77e35db263p-53, - 0x1.12abdc06c31cbp+0, 0x1.f72575a649ad2p-53, - 0x1.1429aaea92ddfp+0, 0x1.66820328764b1p-53, - 0x1.15a98c8a58e51p+0, 0x1.2406ab9eeab0ap-55, - 0x1.172b83c7d517ap+0, 0x1.b9bef918a1d63p-53, - 0x1.18af9388c8de9p+0, 0x1.777ee1734784ap-53, - 0x1.1a35beb6fcb75p+0, 0x1.e5b4c7b4968e4p-55, - 0x1.1bbe084045cd3p+0, 0x1.3563ce56884fcp-53, - 0x1.1d4873168b9aap+0, 0x1.e016e00a2643cp-54, - 0x1.1ed5022fcd91cp+0, 0x1.71033fec2243ap-53, - 0x1.2063b88628cd6p+0, 0x1.dc775814a8495p-55, - 0x1.21f49917ddc96p+0, 0x1.2a97e9494a5eep-55, - 0x1.2387a6e756238p+0, 0x1.9b07eb6c70573p-54, - 0x1.251ce4fb2a63fp+0, 0x1.ac155bef4f4a4p-55, - 0x1.26b4565e27cddp+0, 0x1.2bd339940e9d9p-55, - 0x1.284dfe1f56380p+0, 0x1.2d9e2b9e07941p-53, - 0x1.29e9df51fdee1p+0, 0x1.612e8afad1255p-55, - 0x1.2b87fd0dad98fp+0, 0x1.fbbd48ca71f95p-53, - 0x1.2d285a6e4030bp+0, 0x1.0024754db41d5p-54, - 0x1.2ecafa93e2f56p+0, 0x1.1ca0f45d52383p-56, - 0x1.306fe0a31b715p+0, 0x1.6f46ad23182e4p-55, - 0x1.32170fc4cd831p+0, 0x1.a9ce78e18047cp-55, - 0x1.33c08b26416ffp+0, 0x1.32721843659a6p-54, - 0x1.356c55f929ff0p+0, 0x1.928c468ec6e76p-53, - 0x1.371a7373aa9cap+0, 0x1.4e28aa05e8a8fp-53, - 0x1.38cae6d05d865p+0, 0x1.0b53961b37da2p-53, - 0x1.3a7db34e59ff6p+0, 0x1.d43792533c144p-53, - 0x1.3c32dc313a8e4p+0, 0x1.08003e4516b1ep-53, - 0x1.3dea64c123422p+0, 0x1.ada0911f09ebcp-55, - 0x1.3fa4504ac801bp+0, 0x1.417ee03548306p-53, - 0x1.4160a21f72e29p+0, 0x1.f0864b71e7b6cp-53, - 0x1.431f5d950a896p+0, 0x1.b8e088728219ap-53, - 0x1.44e086061892dp+0, 0x1.89b7a04ef80d0p-59, - 0x1.46a41ed1d0057p+0, 0x1.c944bd1648a76p-54, - 0x1.486a2b5c13cd0p+0, 0x1.3c1a3b69062f0p-56, - 0x1.4a32af0d7d3dep+0, 0x1.9cb62f3d1be56p-54, - 0x1.4bfdad5362a27p+0, 0x1.d4397afec42e2p-56, - 0x1.4dcb299fddd0dp+0, 0x1.8ecdbbc6a7833p-54, - 0x1.4f9b2769d2ca6p+0, 0x1.5a67b16d3540ep-53, - 0x1.516daa2cf6641p+0, 0x1.8225ea5909b04p-53, - 0x1.5342b569d4f81p+0, 0x1.be1507893b0d5p-53, - 0x1.551a4ca5d920ep+0, 0x1.8a5d8c4048699p-53, - 0x1.56f4736b527dap+0, 0x1.9bb2c011d93adp-54, - 0x1.58d12d497c7fdp+0, 0x1.295e15b9a1de8p-55, - 0x1.5ab07dd485429p+0, 0x1.6324c054647adp-54, - 0x1.5c9268a5946b7p+0, 0x1.c4b1b816986a2p-60, - 0x1.5e76f15ad2148p+0, 0x1.ba6f93080e65ep-54, - 0x1.605e1b976dc08p+0, 0x1.60edeb25490dcp-53, - 0x1.6247eb03a5584p+0, 0x1.63e1f40dfa5b5p-53, - 0x1.6434634ccc31fp+0, 0x1.8edf0e2989db3p-53, - 0x1.6623882552224p+0, 0x1.224fb3c5371e6p-53, - 0x1.68155d44ca973p+0, 0x1.038ae44f73e65p-57, - 0x1.6a09e667f3bccp+0, 0x1.21165f626cdd5p-53, - 0x1.6c012750bdabep+0, 0x1.daed533001e9ep-53, - 0x1.6dfb23c651a2ep+0, 0x1.e441c597c3775p-53, - 0x1.6ff7df9519483p+0, 0x1.9f0fc369e7c42p-53, - 0x1.71f75e8ec5f73p+0, 0x1.ba46e1e5de15ap-53, - 0x1.73f9a48a58173p+0, 0x1.7ab9349cd1562p-53, - 0x1.75feb564267c8p+0, 0x1.7edd354674916p-53, - 0x1.780694fde5d3fp+0, 0x1.866b80a02162dp-54, - 0x1.7a11473eb0186p+0, 0x1.afaa2047ed9b4p-53, - 0x1.7c1ed0130c132p+0, 0x1.f124cd1164dd6p-54, - 0x1.7e2f336cf4e62p+0, 0x1.05d02ba15797ep-56, - 0x1.80427543e1a11p+0, 0x1.6c1bccec9346bp-53, - 0x1.82589994cce12p+0, 0x1.159f115f56694p-53, - 0x1.8471a4623c7acp+0, 0x1.9ca5ed72f8c81p-53, - 0x1.868d99b4492ecp+0, 0x1.01c83b21584a3p-53, - 0x1.88ac7d98a6699p+0, 0x1.994c2f37cb53ap-54, - 0x1.8ace5422aa0dbp+0, 0x1.6e9f156864b27p-54, - 0x1.8cf3216b5448bp+0, 0x1.de55439a2c38bp-53, - 0x1.8f1ae99157736p+0, 0x1.5cc13a2e3976cp-55, - 0x1.9145b0b91ffc5p+0, 0x1.114c368d3ed6ep-53, - 0x1.93737b0cdc5e4p+0, 0x1.e8a0387e4a814p-53, - 0x1.95a44cbc8520ep+0, 0x1.d36906d2b41f9p-53, - 0x1.97d829fde4e4fp+0, 0x1.173d241f23d18p-53, - 0x1.9a0f170ca07b9p+0, 0x1.7462137188ce7p-53, - 0x1.9c49182a3f090p+0, 0x1.c7c46b071f2bep-56, - 0x1.9e86319e32323p+0, 0x1.824ca78e64c6ep-56, - 0x1.a0c667b5de564p+0, 0x1.6535b51719567p-53, - 0x1.a309bec4a2d33p+0, 0x1.6305c7ddc36abp-54, - 0x1.a5503b23e255cp+0, 0x1.1684892395f0fp-53, - 0x1.a799e1330b358p+0, 0x1.bcb7ecac563c7p-54, - 0x1.a9e6b5579fdbfp+0, 0x1.0fac90ef7fd31p-54, - 0x1.ac36bbfd3f379p+0, 0x1.81b72cd4624ccp-53, - 0x1.ae89f995ad3adp+0, 0x1.7a1cd345dcc81p-54, - 0x1.b0e07298db665p+0, 0x1.2108559bf8deep-53, - 0x1.b33a2b84f15fap+0, 0x1.ed7fa1cf7b290p-53, - 0x1.b59728de55939p+0, 0x1.1c7102222c90ep-53, - 0x1.b7f76f2fb5e46p+0, 0x1.d54f610356a79p-53, - 0x1.ba5b030a10649p+0, 0x1.0819678d5eb69p-53, - 0x1.bcc1e904bc1d2p+0, 0x1.23dd07a2d9e84p-55, - 0x1.bf2c25bd71e08p+0, 0x1.0811ae04a31c7p-53, - 0x1.c199bdd85529cp+0, 0x1.11065895048ddp-55, - 0x1.c40ab5fffd07ap+0, 0x1.b4537e083c60ap-54, - 0x1.c67f12e57d14bp+0, 0x1.2884dff483cadp-54, - 0x1.c8f6d9406e7b5p+0, 0x1.1acbc48805c44p-56, - 0x1.cb720dcef9069p+0, 0x1.503cbd1e949dbp-56, - 0x1.cdf0b555dc3f9p+0, 0x1.889f12b1f58a3p-53, - 0x1.d072d4a07897bp+0, 0x1.1a1e45e4342b2p-53, - 0x1.d2f87080d89f1p+0, 0x1.15bc247313d44p-53, - 0x1.d5818dcfba487p+0, 0x1.2ed02d75b3707p-55, - 0x1.d80e316c98397p+0, 0x1.7709f3a09100cp-53, - 0x1.da9e603db3285p+0, 0x1.c2300696db532p-54, - 0x1.dd321f301b460p+0, 0x1.2da5778f018c3p-54, - 0x1.dfc97337b9b5ep+0, 0x1.72d195873da52p-53, - 0x1.e264614f5a128p+0, 0x1.424ec3f42f5b5p-53, - 0x1.e502ee78b3ff6p+0, 0x1.39e8980a9cc8fp-55, - 0x1.e7a51fbc74c83p+0, 0x1.2d522ca0c8de2p-54, - 0x1.ea4afa2a490d9p+0, 0x1.0b1ee7431ebb6p-53, - 0x1.ecf482d8e67f0p+0, 0x1.1b60625f7293ap-53, - 0x1.efa1bee615a27p+0, 0x1.dc7f486a4b6b0p-54, - 0x1.f252b376bba97p+0, 0x1.3a1a5bf0d8e43p-54, - 0x1.f50765b6e4540p+0, 0x1.9d3e12dd8a18bp-54, - 0x1.f7bfdad9cbe13p+0, 0x1.1227697fce57bp-53, - 0x1.fa7c1819e90d8p+0, 0x1.74853f3a5931ep-55, - 0x1.fd3c22b8f71f1p+0, 0x1.2eb74966579e7p-57 -}; - long double expl(long double x) { - union IEEEl2bits u, v; - long double fn, q, r, r1, r2, t, twopk, twopkp10000; - long double z; - int k, n, n2; + union IEEEl2bits u; + long double hi, lo, t, twopk; + int k; uint16_t hx, ix; + DOPRINT_START(&x); + /* Filter out exceptional cases. */ u.e = x; hx = u.xbits.expsign; ix = hx & 0x7fff; if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */ if (ix == BIAS + LDBL_MAX_EXP) { if (hx & 0x8000) /* x is -Inf, -NaN or unsupported */ - return (-1 / x); - return (x + x); /* x is +Inf, +NaN or unsupported */ + RETURNP(-1 / x); + RETURNP(x + x); /* x is +Inf, +NaN or unsupported */ } if (x > o_threshold) - return (huge * huge); + RETURNP(huge * huge); if (x < u_threshold) - return (tiny * tiny); - } else if (ix < BIAS - 65) { /* |x| < 0x1p-65 (includes pseudos) */ - return (1 + x); /* 1 with inexact iff x != 0 */ + RETURNP(tiny * tiny); + } else if (ix < BIAS - 75) { /* |x| < 0x1p-75 (includes pseudos) */ + RETURN2P(1, x); /* 1 with inexact iff x != 0 */ } ENTERI(); - /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */ - /* Use a specialized rint() to get fn. Assume round-to-nearest. */ - fn = x * INV_L + 0x1.8p63 - 0x1.8p63; - r = x - fn * L1 - fn * L2; /* r = r1 + r2 done independently. */ -#if defined(HAVE_EFFICIENT_IRINTL) - n = irintl(fn); -#elif defined(HAVE_EFFICIENT_IRINT) - n = irint(fn); -#else - n = (int)fn; -#endif - n2 = (unsigned)n % INTERVALS; - /* Depend on the sign bit being propagated: */ - k = n >> LOG2_INTERVALS; - r1 = x - fn * L1; - r2 = fn * -L2; + twopk = 1; + __k_expl(x, &hi, &lo, &k); + t = SUM2P(hi, lo); - /* Prepare scale factors. */ - v.e = 1; - if (k >= LDBL_MIN_EXP) { - v.xbits.expsign = BIAS + k; - twopk = v.e; - } else { - v.xbits.expsign = BIAS + k + 10000; - twopkp10000 = v.e; - } - - /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */ - z = r * r; - q = r2 + z * (A2 + r * A3) + z * z * (A4 + r * A5) + z * z * z * A6; - t = (long double)tbl[n2].lo + tbl[n2].hi; - t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi; - /* Scale by 2**k. */ if (k >= LDBL_MIN_EXP) { if (k == LDBL_MAX_EXP) RETURNI(t * 2 * 0x1p16383L); + SET_LDBL_EXPSIGN(twopk, BIAS + k); RETURNI(t * twopk); } else { - RETURNI(t * twopkp10000 * twom10000); + SET_LDBL_EXPSIGN(twopk, BIAS + k + 10000); + RETURNI(t * twopk * twom10000); } } /** * Compute expm1l(x) for Intel 80-bit format. This is based on: * * PTP Tang, "Table-driven implementation of the Expm1 function * in IEEE floating-point arithmetic," ACM Trans. Math. Soft., 18, * 211-222 (1992). */ /* * Our T1 and T2 are chosen to be approximately the points where method * A and method B have the same accuracy. Tang's T1 and T2 are the * points where method A's accuracy changes by a full bit. For Tang, * this drop in accuracy makes method A immediately less accurate than * method B, but our larger INTERVALS makes method A 2 bits more * accurate so it remains the most accurate method significantly * closer to the origin despite losing the full bit in our extended * range for it. */ static const double T1 = -0.1659, /* ~-30.625/128 * log(2) */ T2 = 0.1659; /* ~30.625/128 * log(2) */ /* - * Domain [-0.1659, 0.1659], range ~[-1.2027e-22, 3.4417e-22]: - * |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-71.2 + * Domain [-0.1659, 0.1659], range ~[-2.6155e-22, 2.5507e-23]: + * |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-71.6 + * + * XXX the coeffs aren't very carefully rounded, and I get 2.8 more bits, + * but unlike for ld128 we can't drop any terms. */ static const union IEEEl2bits B3 = LD80C(0xaaaaaaaaaaaaaaab, -3, 1.66666666666666666671e-1L), B4 = LD80C(0xaaaaaaaaaaaaaaac, -5, 4.16666666666666666712e-2L); static const double B5 = 8.3333333333333245e-3, /* 0x1.111111111110cp-7 */ B6 = 1.3888888888888861e-3, /* 0x1.6c16c16c16c0ap-10 */ B7 = 1.9841269841532042e-4, /* 0x1.a01a01a0319f9p-13 */ B8 = 2.4801587302069236e-5, /* 0x1.a01a01a03cbbcp-16 */ B9 = 2.7557316558468562e-6, /* 0x1.71de37fd33d67p-19 */ B10 = 2.7557315829785151e-7, /* 0x1.27e4f91418144p-22 */ B11 = 2.5063168199779829e-8, /* 0x1.ae94fabdc6b27p-26 */ B12 = 2.0887164654459567e-9; /* 0x1.1f122d6413fe1p-29 */ long double expm1l(long double x) { union IEEEl2bits u, v; long double fn, hx2_hi, hx2_lo, q, r, r1, r2, t, twomk, twopk, x_hi; long double x_lo, x2, z; long double x4; int k, n, n2; uint16_t hx, ix; + DOPRINT_START(&x); + /* Filter out exceptional cases. */ u.e = x; hx = u.xbits.expsign; ix = hx & 0x7fff; if (ix >= BIAS + 6) { /* |x| >= 64 or x is NaN */ if (ix == BIAS + LDBL_MAX_EXP) { if (hx & 0x8000) /* x is -Inf, -NaN or unsupported */ - return (-1 / x - 1); - return (x + x); /* x is +Inf, +NaN or unsupported */ + RETURNP(-1 / x - 1); + RETURNP(x + x); /* x is +Inf, +NaN or unsupported */ } if (x > o_threshold) - return (huge * huge); + RETURNP(huge * huge); /* * expm1l() never underflows, but it must avoid * unrepresentable large negative exponents. We used a * much smaller threshold for large |x| above than in * expl() so as to handle not so large negative exponents * in the same way as large ones here. */ if (hx & 0x8000) /* x <= -64 */ - return (tiny - 1); /* good for x < -65ln2 - eps */ + RETURN2P(tiny, -1); /* good for x < -65ln2 - eps */ } ENTERI(); if (T1 < x && x < T2) { - if (ix < BIAS - 64) { /* |x| < 0x1p-64 (includes pseudos) */ + if (ix < BIAS - 74) { /* |x| < 0x1p-74 (includes pseudos) */ /* x (rounded) with inexact if x != 0: */ - RETURNI(x == 0 ? x : + RETURNPI(x == 0 ? x : (0x1p100 * x + fabsl(x)) * 0x1p-100); } x2 = x * x; x4 = x2 * x2; q = x4 * (x2 * (x4 * /* * XXX the number of terms is no longer good for * pairwise grouping of all except B3, and the * grouping is no longer from highest down. */ (x2 * B12 + (x * B11 + B10)) + (x2 * (x * B9 + B8) + (x * B7 + B6))) + (x * B5 + B4.e)) + x2 * x * B3.e; x_hi = (float)x; x_lo = x - x_hi; hx2_hi = x_hi * x_hi / 2; hx2_lo = x_lo * (x + x_hi) / 2; if (ix >= BIAS - 7) - RETURNI(hx2_lo + x_lo + q + (hx2_hi + x_hi)); + RETURN2PI(hx2_hi + x_hi, hx2_lo + x_lo + q); else - RETURNI(hx2_lo + q + hx2_hi + x); + RETURN2PI(x, hx2_lo + q + hx2_hi); } /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */ /* Use a specialized rint() to get fn. Assume round-to-nearest. */ fn = x * INV_L + 0x1.8p63 - 0x1.8p63; #if defined(HAVE_EFFICIENT_IRINTL) n = irintl(fn); #elif defined(HAVE_EFFICIENT_IRINT) n = irint(fn); #else n = (int)fn; #endif n2 = (unsigned)n % INTERVALS; k = n >> LOG2_INTERVALS; r1 = x - fn * L1; r2 = fn * -L2; r = r1 + r2; /* Prepare scale factor. */ v.e = 1; v.xbits.expsign = BIAS + k; twopk = v.e; /* * Evaluate lower terms of * expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */ z = r * r; q = r2 + z * (A2 + r * A3) + z * z * (A4 + r * A5) + z * z * z * A6; t = (long double)tbl[n2].lo + tbl[n2].hi; if (k == 0) { - t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 + - (tbl[n2].hi - 1); + t = SUM2P(tbl[n2].hi - 1, tbl[n2].lo * (r1 + 1) + t * q + + tbl[n2].hi * r1); RETURNI(t); } if (k == -1) { - t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 + - (tbl[n2].hi - 2); + t = SUM2P(tbl[n2].hi - 2, tbl[n2].lo * (r1 + 1) + t * q + + tbl[n2].hi * r1); RETURNI(t / 2); } if (k < -7) { - t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi; + t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1)); RETURNI(t * twopk - 1); } if (k > 2 * LDBL_MANT_DIG - 1) { - t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi; + t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1)); if (k == LDBL_MAX_EXP) RETURNI(t * 2 * 0x1p16383L - 1); RETURNI(t * twopk - 1); } v.xbits.expsign = BIAS - k; twomk = v.e; if (k > LDBL_MANT_DIG - 1) - t = tbl[n2].lo - twomk + t * (q + r1) + tbl[n2].hi; + t = SUM2P(tbl[n2].hi, tbl[n2].lo - twomk + t * (q + r1)); else - t = tbl[n2].lo + t * (q + r1) + (tbl[n2].hi - twomk); + t = SUM2P(tbl[n2].hi - twomk, tbl[n2].lo + t * (q + r1)); RETURNI(t * twopk); } Index: stable/10/lib/msun/man/cosh.3 =================================================================== --- stable/10/lib/msun/man/cosh.3 (revision 271778) +++ stable/10/lib/msun/man/cosh.3 (revision 271779) @@ -1,69 +1,73 @@ .\" Copyright (c) 1989, 1991 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. .\" 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: @(#)cosh.3 5.1 (Berkeley) 5/2/91 .\" $FreeBSD$ .\" -.Dd January 14, 2005 +.Dd August 17, 2013 .Dt COSH 3 .Os .Sh NAME .Nm cosh , -.Nm coshf +.Nm coshf , +.Nm coshl .Nd hyperbolic cosine functions .Sh LIBRARY .Lb libm .Sh SYNOPSIS .In math.h .Ft double .Fn cosh "double x" .Ft float .Fn coshf "float x" +.Ft long double +.Fn coshl "long double x" .Sh DESCRIPTION The -.Fn cosh -and the -.Fn coshf +.Fn cosh , +.Fn coshf , +and +.Fn coshl functions compute the hyperbolic cosine of .Fa x . .Sh SEE ALSO .Xr acos 3 , .Xr asin 3 , .Xr atan 3 , .Xr atan2 3 , .Xr ccosh 3 , .Xr cos 3 , .Xr math 3 , .Xr sin 3 , .Xr sinh 3 , .Xr tan 3 , .Xr tanh 3 .Sh STANDARDS The .Fn cosh function conforms to .St -isoC . Index: stable/10/lib/msun/man/erf.3 =================================================================== --- stable/10/lib/msun/man/erf.3 (revision 271778) +++ stable/10/lib/msun/man/erf.3 (revision 271779) @@ -1,93 +1,98 @@ .\" Copyright (c) 1985, 1991 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. .\" 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: @(#)erf.3 6.4 (Berkeley) 4/20/91 .\" $FreeBSD$ .\" -.Dd April 20, 1991 +.Dd July 13, 2014 .Dt ERF 3 .Os .Sh NAME .Nm erf , .Nm erff , +.Nm erfl , .Nm erfc , -.Nm erfcf +.Nm erfcf , +.Nm erfcl .Nd error function operators .Sh LIBRARY .Lb libm .Sh SYNOPSIS .In math.h .Ft double .Fn erf "double x" .Ft float .Fn erff "float x" +.Ft "long double" +.Fn erfl "long double x" .Ft double .Fn erfc "double x" .Ft float .Fn erfcf "float x" +.Ft "long double" +.Fn erfcl "long double x" .Sh DESCRIPTION These functions calculate the error function of .Fa x . .Pp The -.Fn erf -and the -.Fn erff +.Fn erf , +.Fn erff , +and +.Fn erfl functions calculate the error function of x; where .Bd -ragged -offset indent .if n \{\ erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} .if t \{\ erf\|(x) := (2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} .Ed .Pp The -.Fn erfc -and the -.Fn erfcf +.Fn erfc , +.Fn erfcf , +and +.Fn erfcl functions calculate the complementary error function of .Fa x ; that is .Fn erfc subtracts the result of the error function .Fn erf x from 1.0. -This is useful, since for large -.Fa x -places disappear. .Sh SEE ALSO .Xr math 3 .Sh HISTORY The .Fn erf and .Fn erfc functions appeared in .Bx 4.3 . Index: stable/10/lib/msun/man/sinh.3 =================================================================== --- stable/10/lib/msun/man/sinh.3 (revision 271778) +++ stable/10/lib/msun/man/sinh.3 (revision 271779) @@ -1,68 +1,73 @@ .\" Copyright (c) 1991 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. .\" 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: @(#)sinh.3 6.6 (Berkeley) 4/19/91 .\" $FreeBSD$ -.Dd January 14, 2005 +.\" +.Dd August 17, 2013 .Dt SINH 3 .Os .Sh NAME .Nm sinh , -.Nm sinhf +.Nm sinhf , +.Nm sinhl .Nd hyperbolic sine function .Sh LIBRARY .Lb libm .Sh SYNOPSIS .In math.h .Ft double .Fn sinh "double x" .Ft float .Fn sinhf "float x" +.Ft long double +.Fn sinhl "long double x" .Sh DESCRIPTION The -.Fn sinh -and the -.Fn sinhf +.Fn sinh , +.Fn sinhf , +and +.Fn sinhl functions compute the hyperbolic sine of .Fa x . .Sh SEE ALSO .Xr acos 3 , .Xr asin 3 , .Xr atan 3 , .Xr atan2 3 , .Xr cos 3 , .Xr cosh 3 , .Xr csinh 3 , .Xr math 3 , .Xr sin 3 , .Xr tan 3 , .Xr tanh 3 .Sh STANDARDS The .Fn sinh function conforms to .St -isoC . Index: stable/10/lib/msun/man/tanh.3 =================================================================== --- stable/10/lib/msun/man/tanh.3 (revision 271778) +++ stable/10/lib/msun/man/tanh.3 (revision 271779) @@ -1,77 +1,82 @@ .\" Copyright (c) 1991 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. .\" 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: @(#)tanh.3 5.1 (Berkeley) 5/2/91 .\" $FreeBSD$ .\" -.Dd May 2, 1991 +.Dd August 17, 2013 .Dt TANH 3 .Os .Sh NAME .Nm tanh , -.Nm tanhf +.Nm tanhf , +.Nm tanhl .Nd hyperbolic tangent functions .Sh LIBRARY .Lb libm .Sh SYNOPSIS .In math.h .Ft double .Fn tanh "double x" .Ft float .Fn tanhf "float x" +.Ft long double +.Fn tanhl "long double x" .Sh DESCRIPTION The -.Fn tanh -and the -.Fn tanhf +.Fn tanh , +.Fn tanhf , +and +.Fn tanhl functions compute the hyperbolic tangent of .Fa x . For a discussion of error due to roundoff, see .Xr math 3 . .Sh RETURN VALUES The -.Fn tanh +.Fn tanh , +.Fn tanhf , and the -.Fn tanhf +.Fn tanhl functions return the hyperbolic tangent value. .Sh SEE ALSO .Xr acos 3 , .Xr asin 3 , .Xr atan 3 , .Xr atan2 3 , .Xr cos 3 , .Xr cosh 3 , .Xr ctanh 3 , .Xr math 3 , .Xr sin 3 , .Xr sinh 3 , .Xr tan 3 .Sh STANDARDS The .Fn tanh function conforms to .St -isoC . Index: stable/10/lib/msun/src/e_cosh.c =================================================================== --- stable/10/lib/msun/src/e_cosh.c (revision 271778) +++ stable/10/lib/msun/src/e_cosh.c (revision 271779) @@ -1,79 +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 __FBSDID("$FreeBSD$"); /* __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 "math.h" #include "math_private.h" static const double one = 1.0, half=0.5, huge = 1.0e300; 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) +__weak_reference(cosh, coshl); +#endif Index: stable/10/lib/msun/src/e_coshl.c =================================================================== --- stable/10/lib/msun/src/e_coshl.c (nonexistent) +++ stable/10/lib/msun/src/e_coshl.c (revision 271779) @@ -0,0 +1,130 @@ +/* from: FreeBSD: head/lib/msun/src/e_coshl.c XXX */ + +/* + * ==================================================== + * 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 +__FBSDID("$FreeBSD$"); + +/* + * See e_cosh.c for complete comments. + * + * Converted to long double by Bruce D. Evans. + */ + +#include +#ifdef __i386__ +#include +#endif + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" +#include "k_expl.h" + +#if LDBL_MAX_EXP != 0x4000 +/* We also require the usual expsign encoding. */ +#error "Unsupported long double format" +#endif + +#define BIAS (LDBL_MAX_EXP - 1) + +static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L; +#if LDBL_MANT_DIG == 64 +/* + * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]: + * |cosh(x) - c(x)| < 2**-68.8 + */ +static const union IEEEl2bits +C4u = LD80C(0xaaaaaaaaaaaaac78, -5, 4.16666666666666682297e-2L); +#define C4 C4u.e +static const double +C2 = 0.5, +C6 = 1.3888888888888616e-3, /* 0x16c16c16c16b99.0p-62 */ +C8 = 2.4801587301767953e-5, /* 0x1a01a01a027061.0p-68 */ +C10 = 2.7557319163300398e-7, /* 0x127e4fb6c9b55f.0p-74 */ +C12 = 2.0876768371393075e-9, /* 0x11eed99406a3f4.0p-81 */ +C14 = 1.1469537039374480e-11, /* 0x1938c67cd18c48.0p-89 */ +C16 = 4.8473490896852041e-14; /* 0x1b49c429701e45.0p-97 */ +#elif LDBL_MANT_DIG == 113 +/* + * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]: + * |cosh(x) - c(x)| < 2**-121.69 + */ +static const long double +C4 = 4.16666666666666666666666666666666225e-2L, /* 0x1555555555555555555555555554e.0p-117L */ +C6 = 1.38888888888888888888888888889434831e-3L, /* 0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */ +C8 = 2.48015873015873015873015871870962089e-5L, /* 0x1a01a01a01a01a01a01a017af2756.0p-128L */ +C10 = 2.75573192239858906525574318600800201e-7L, /* 0x127e4fb7789f5c72ef01c8a040640.0p-134L */ +C12 = 2.08767569878680989791444691755468269e-9L, /* 0x11eed8eff8d897b543d0679607399.0p-141L */ +C14= 1.14707455977297247387801189650495351e-11L, /* 0x193974a8c07c9d24ae169a7fa9b54.0p-149L */ +C16 = 4.77947733238737883626416876486279985e-14L; /* 0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */ +static const double +C2 = 0.5, +C18 = 1.5619206968597871e-16, /* 0x16827863b9900b.0p-105 */ +C20 = 4.1103176218528049e-19, /* 0x1e542ba3d3c269.0p-114 */ +C22 = 8.8967926401641701e-22, /* 0x10ce399542a014.0p-122 */ +C24 = 1.6116681626523904e-24, /* 0x1f2c981d1f0cb7.0p-132 */ +C26 = 2.5022374732804632e-27; /* 0x18c7ecf8b2c4a0.0p-141 */ +#else +#error "Unsupported long double format" +#endif /* LDBL_MANT_DIG == 64 */ + +/* log(2**16385 - 0.5) rounded up: */ +static const float +o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */ + +long double +coshl(long double x) +{ + long double hi,lo,x2,x4; + double dx2; + uint16_t ix; + + GET_LDBL_EXPSIGN(ix,x); + ix &= 0x7fff; + + /* x is INF or NaN */ + if(ix>=0x7fff) return x*x; + + ENTERI(); + + /* |x| < 1, return 1 or c(x) */ + if(ix<0x3fff) { + if (ix o_threshold, cosh(x) overflow */ + RETURNI(huge*huge); +} Property changes on: stable/10/lib/msun/src/e_coshl.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: stable/10/lib/msun/src/e_lgamma_r.c =================================================================== --- stable/10/lib/msun/src/e_lgamma_r.c (revision 271778) +++ stable/10/lib/msun/src/e_lgamma_r.c (revision 271779) @@ -1,297 +1,295 @@ /* @(#)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 __FBSDID("$FreeBSD$"); /* __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 "math.h" #include "math_private.h" +static const volatile double vzero = 0; + static const double -two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +zero= 0.00000000000000000000e+00, 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) +/* + * Compute sin(pi*x) without actually doing the pi*x multiplication. + * sin_pi(x) is only called for x < 0 and |x| < 2**(p-1) where p is + * the precision of x. + */ +static double +sin_pi(double x) { + volatile double vz; double y,z; - int n,ix; + int n; - GET_HIGH_WORD(ix,x); - ix &= 0x7fffffff; + y = -x; - if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); - y = -x; /* x is assume negative */ + vz = y+0x1p52; /* depend on 0 <= y < 0x1p52 */ + z = vz-0x1p52; /* rint(y) for the above range */ + if (z == y) + return zero; - /* - * 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; - } - } + vz = y+0x1p50; + GET_LOW_WORD(n,vz); /* bits for rounded y (units 0.25) */ + z = vz-0x1p50; /* y rounded to a multiple of 0.25 */ + if (z > y) { + z -= 0.25; /* adjust to round down */ + n--; + } + n &= 7; /* octant of y mod 2 */ + y = y - z + n * 0.25; /* y mod 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; } 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; + int i,ix,lx; 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|lx)==0) return one/vzero; 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; + return one/vzero; t = sin_pi(x); - if(t==zero) return one/zero; /* -integer */ + if(t==zero) return one/vzero; /* -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; } Index: stable/10/lib/msun/src/e_lgammaf_r.c =================================================================== --- stable/10/lib/msun/src/e_lgammaf_r.c (revision 271778) +++ stable/10/lib/msun/src/e_lgammaf_r.c (revision 271779) @@ -1,230 +1,223 @@ /* 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 __FBSDID("$FreeBSD$"); #include "math.h" #include "math_private.h" +static const volatile float vzero = 0; + static const float -two23= 8.3886080000e+06, /* 0x4b000000 */ +zero= 0.0000000000e+00, 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) +static float +sin_pif(float x) { + volatile float vz; float y,z; - int n,ix; + int n; - GET_FLOAT_WORD(ix,x); - ix &= 0x7fffffff; + y = -x; - if(ix<0x3e800000) return __kernel_sindf(pi*x); - y = -x; /* x is assume negative */ + vz = y+0x1p23F; /* depend on 0 <= y < 0x1p23 */ + z = vz-0x1p23F; /* rintf(y) for the above range */ + if (z == y) + return zero; - /* - * 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; - } - } + vz = y+0x1p21F; + GET_FLOAT_WORD(n,vz); /* bits for rounded y (units 0.25) */ + z = vz-0x1p21F; /* y rounded to a multiple of 0.25 */ + if (z > y) { + z -= 0.25F; /* adjust to round down */ + n--; + } + n &= 7; /* octant of y mod 2 */ + y = y - z + n * 0.25F; /* y mod 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; } 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==0) return one/vzero; 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; + return one/vzero; t = sin_pif(x); - if(t==zero) return one/zero; /* -integer */ + if(t==zero) return one/vzero; /* -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; } Index: stable/10/lib/msun/src/e_pow.c =================================================================== --- stable/10/lib/msun/src/e_pow.c (revision 271778) +++ stable/10/lib/msun/src/e_pow.c (revision 271779) @@ -1,306 +1,306 @@ /* @(#)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 __FBSDID("$FreeBSD$"); /* __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 + * 2. Perform y*log2(x) = n+y' by simulating multi-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 + * 3. (anything) ** NAN is NAN except 1 ** NAN = 1 * 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 + * 9. +-1 ** +-INF is 1 * 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 "math.h" #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*/ 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 */ + return one; /* (-1)**+-inf is 1 */ 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==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; } Index: stable/10/lib/msun/src/e_sinh.c =================================================================== --- stable/10/lib/msun/src/e_sinh.c (revision 271778) +++ stable/10/lib/msun/src/e_sinh.c (revision 271779) @@ -1,73 +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 __FBSDID("$FreeBSD$"); /* __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 "math.h" #include "math_private.h" static const double one = 1.0, shuge = 1.0e307; 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) +__weak_reference(sinh, sinhl); +#endif Index: stable/10/lib/msun/src/e_sinhl.c =================================================================== --- stable/10/lib/msun/src/e_sinhl.c (nonexistent) +++ stable/10/lib/msun/src/e_sinhl.c (revision 271779) @@ -0,0 +1,131 @@ +/* from: FreeBSD: head/lib/msun/src/e_sinhl.c XXX */ + +/* + * ==================================================== + * 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 +__FBSDID("$FreeBSD$"); + +/* + * See e_sinh.c for complete comments. + * + * Converted to long double by Bruce D. Evans. + */ + +#include +#ifdef __i386__ +#include +#endif + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" +#include "k_expl.h" + +#if LDBL_MAX_EXP != 0x4000 +/* We also require the usual expsign encoding. */ +#error "Unsupported long double format" +#endif + +#define BIAS (LDBL_MAX_EXP - 1) + +static const long double shuge = 0x1p16383L; +#if LDBL_MANT_DIG == 64 +/* + * Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]: + * |sinh(x)/x - s(x)| < 2**-70.3 + */ +static const union IEEEl2bits +S3u = LD80C(0xaaaaaaaaaaaaaaaa, -3, 1.66666666666666666658e-1L); +#define S3 S3u.e +static const double +S5 = 8.3333333333333332e-3, /* 0x11111111111111.0p-59 */ +S7 = 1.9841269841270074e-4, /* 0x1a01a01a01a070.0p-65 */ +S9 = 2.7557319223873889e-6, /* 0x171de3a5565fe6.0p-71 */ +S11 = 2.5052108406704084e-8, /* 0x1ae6456857530f.0p-78 */ +S13 = 1.6059042748655297e-10, /* 0x161245fa910697.0p-85 */ +S15 = 7.6470006914396920e-13, /* 0x1ae7ce4eff2792.0p-93 */ +S17 = 2.8346142308424267e-15; /* 0x19882ce789ffc6.0p-101 */ +#elif LDBL_MANT_DIG == 113 +/* + * Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]: + * |sinh(x)/x - s(x)| < 2**-118.0 + */ +static const long double +S3 = 1.66666666666666666666666666666666033e-1L, /* 0x1555555555555555555555555553b.0p-115L */ +S5 = 8.33333333333333333333333333337643193e-3L, /* 0x111111111111111111111111180f5.0p-119L */ +S7 = 1.98412698412698412698412697391263199e-4L, /* 0x1a01a01a01a01a01a01a0176aad11.0p-125L */ +S9 = 2.75573192239858906525574406205464218e-6L, /* 0x171de3a556c7338faac243aaa9592.0p-131L */ +S11 = 2.50521083854417187749675637460977997e-8L, /* 0x1ae64567f544e38fe59b3380d7413.0p-138L */ +S13 = 1.60590438368216146368737762431552702e-10L, /* 0x16124613a86d098059c7620850fc2.0p-145L */ +S15 = 7.64716373181980539786802470969096440e-13L, /* 0x1ae7f3e733b814193af09ce723043.0p-153L */ +S17 = 2.81145725434775409870584280722701574e-15L; /* 0x1952c77030c36898c3fd0b6dfc562.0p-161L */ +static const double +S19= 8.2206352435411005e-18, /* 0x12f49b4662b86d.0p-109 */ +S21= 1.9572943931418891e-20, /* 0x171b8f2fab9628.0p-118 */ +S23 = 3.8679983530666939e-23, /* 0x17617002b73afc.0p-127 */ +S25 = 6.5067867911512749e-26; /* 0x1423352626048a.0p-136 */ +#else +#error "Unsupported long double format" +#endif /* LDBL_MANT_DIG == 64 */ + +/* log(2**16385 - 0.5) rounded up: */ +static const float +o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */ + +long double +sinhl(long double x) +{ + long double hi,lo,x2,x4; + double dx2,s; + int16_t ix,jx; + + GET_LDBL_EXPSIGN(jx,x); + ix = jx&0x7fff; + + /* x is INF or NaN */ + if(ix>=0x7fff) return x+x; + + ENTERI(); + + s = 1; + if (jx<0) s = -1; + + /* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */ + if (ix<0x4005) { /* |x|<64 */ + if (ix1) RETURNI(x); /* sinh(tiny) = tiny with inexact */ + if (ix<0x3fff) { /* |x|<1 */ + x2 = x*x; +#if LDBL_MANT_DIG == 64 + x4 = x2*x2; + RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) + + ((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x); +#elif LDBL_MANT_DIG == 113 + dx2 = x2; + RETURNI(((((((((((S25*dx2 + S23)*dx2 + + S21)*x2 + S19)*x2 + + S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 + + S5)* (x2*x*x2) + + S3*(x2*x) + x); +#endif + } + k_hexpl(fabsl(x), &hi, &lo); + RETURNI(s*(lo - 0.25/(hi + lo) + hi)); + } + + /* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */ + if (fabsl(x) <= o_threshold) + RETURNI(s*hexpl(fabsl(x))); + + /* |x| > o_threshold, sinh(x) overflow */ + return x*shuge; +} Property changes on: stable/10/lib/msun/src/e_sinhl.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: stable/10/lib/msun/src/imprecise.c =================================================================== --- stable/10/lib/msun/src/imprecise.c (revision 271778) +++ stable/10/lib/msun/src/imprecise.c (revision 271779) @@ -1,69 +1,64 @@ /*- * Copyright (c) 2013 David Chisnall * 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 #include /* * If long double is not the same size as double, then these will lose * precision and we should emit a warning whenever something links against * them. */ #if (LDBL_MANT_DIG > 53) #define WARN_IMPRECISE(x) \ __warn_references(x, # x " has lower than advertised precision"); #else #define WARN_IMPRECISE(x) #endif /* * Declare the functions as weak variants so that other libraries providing * real versions can override them. */ #define DECLARE_WEAK(x)\ __weak_reference(imprecise_## x, x);\ WARN_IMPRECISE(x) long double imprecise_powl(long double x, long double y) { return pow(x, y); } DECLARE_WEAK(powl); #define DECLARE_IMPRECISE(f) \ long double imprecise_ ## f ## l(long double v) { return f(v); }\ DECLARE_WEAK(f ## l) -DECLARE_IMPRECISE(cosh); -DECLARE_IMPRECISE(erfc); -DECLARE_IMPRECISE(erf); DECLARE_IMPRECISE(lgamma); -DECLARE_IMPRECISE(sinh); -DECLARE_IMPRECISE(tanh); DECLARE_IMPRECISE(tgamma); Index: stable/10/lib/msun/src/math.h =================================================================== --- stable/10/lib/msun/src/math.h (revision 271778) +++ stable/10/lib/msun/src/math.h (revision 271779) @@ -1,526 +1,507 @@ /* * ==================================================== * 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 * $FreeBSD$ */ #ifndef _MATH_H_ #define _MATH_H_ #include #include #include /* * 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; #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 #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 #if (__STDC_VERSION__ >= 201112L && defined(__clang__)) || \ __has_extension(c_generic_selections) #define __fp_type_select(x, f, d, ld) _Generic((x), \ float: f(x), \ double: d(x), \ long double: ld(x), \ volatile float: f(x), \ volatile double: d(x), \ volatile long double: ld(x), \ volatile const float: f(x), \ volatile const double: d(x), \ volatile const long double: ld(x), \ const float: f(x), \ const double: d(x), \ const long double: ld(x)) #elif __GNUC_PREREQ__(3, 1) && !defined(__cplusplus) #define __fp_type_select(x, f, d, ld) __builtin_choose_expr( \ __builtin_types_compatible_p(__typeof(x), long double), ld(x), \ __builtin_choose_expr( \ __builtin_types_compatible_p(__typeof(x), double), d(x), \ __builtin_choose_expr( \ __builtin_types_compatible_p(__typeof(x), float), f(x), (void)0))) #else #define __fp_type_select(x, f, d, ld) \ ((sizeof(x) == sizeof(float)) ? f(x) \ : (sizeof(x) == sizeof(double)) ? d(x) \ : ld(x)) #endif #define fpclassify(x) \ __fp_type_select(x, __fpclassifyf, __fpclassifyd, __fpclassifyl) #define isfinite(x) __fp_type_select(x, __isfinitef, __isfinite, __isfinitel) #define isinf(x) __fp_type_select(x, __isinff, __isinf, __isinfl) #define isnan(x) \ __fp_type_select(x, __inline_isnanf, __inline_isnan, __inline_isnanl) #define isnormal(x) __fp_type_select(x, __isnormalf, __isnormal, __isnormall) #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) __fp_type_select(x, __signbitf, __signbit, __signbitl) 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) extern int signgam; #endif /* __BSD_VISIBLE || __XSI_VISIBLE */ #if __BSD_VISIBLE #if 0 /* Old value from 4.4BSD-Lite math.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. */ __BEGIN_DECLS /* * ANSI/POSIX */ int __fpclassifyd(double) __pure2; int __fpclassifyf(float) __pure2; int __fpclassifyl(long double) __pure2; int __isfinitef(float) __pure2; int __isfinite(double) __pure2; int __isfinitel(long double) __pure2; int __isinff(float) __pure2; int __isinf(double) __pure2; int __isinfl(long double) __pure2; int __isnormalf(float) __pure2; int __isnormal(double) __pure2; int __isnormall(long double) __pure2; int __signbit(double) __pure2; int __signbitf(float) __pure2; int __signbitl(long double) __pure2; static __inline int __inline_isnan(__const double __x) { return (__x != __x); } static __inline int __inline_isnanf(__const float __x) { return (__x != __x); } static __inline int __inline_isnanl(__const long double __x) { return (__x != __x); } /* * Version 2 of the Single UNIX Specification (UNIX98) defined isnan() and * isinf() as functions taking double. C99, and the subsequent POSIX revisions * (SUSv3, POSIX.1-2001, define it as a macro that accepts any real floating * point type. If we are targeting SUSv2 and C99 or C11 (or C++11) then we * expose the newer definition, assuming that the language spec takes * precedence over the operating system interface spec. */ #if __XSI_VISIBLE > 0 && __XSI_VISIBLE < 600 && __ISO_C_VISIBLE < 1999 #undef isinf #undef isnan int isinf(double); int isnan(double); #endif double acos(double); double asin(double); double atan(double); double atan2(double, double); double cos(double); double sin(double); double tan(double); double cosh(double); double sinh(double); double tanh(double); double exp(double); double frexp(double, int *); /* fundamentally !__pure2 */ double ldexp(double, int); double log(double); double log10(double); double modf(double, double *); /* fundamentally !__pure2 */ double pow(double, double); double sqrt(double); double ceil(double); double fabs(double) __pure2; double floor(double); double fmod(double, double); /* * These functions are not in C90. */ #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE double acosh(double); double asinh(double); double atanh(double); double cbrt(double); double erf(double); double erfc(double); double exp2(double); double expm1(double); double fma(double, double, double); double hypot(double, double); int ilogb(double) __pure2; double lgamma(double); long long llrint(double); long long llround(double); double log1p(double); double log2(double); double logb(double); long lrint(double); long lround(double); double nan(const char *) __pure2; double nextafter(double, double); double remainder(double, double); double remquo(double, double, int *); double rint(double); #endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */ #if __BSD_VISIBLE || __XSI_VISIBLE double j0(double); double j1(double); double jn(int, double); double y0(double); double y1(double); double yn(int, double); #if __XSI_VISIBLE <= 500 || __BSD_VISIBLE double gamma(double); #endif #if __XSI_VISIBLE <= 600 || __BSD_VISIBLE double scalb(double, double); #endif #endif /* __BSD_VISIBLE || __XSI_VISIBLE */ #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 double copysign(double, double) __pure2; double fdim(double, double); double fmax(double, double) __pure2; double fmin(double, double) __pure2; double nearbyint(double); double round(double); double scalbln(double, long); double scalbn(double, int); double tgamma(double); double trunc(double); #endif /* * BSD math library entry points */ #if __BSD_VISIBLE double drem(double, double); int finite(double) __pure2; int isnanf(float) __pure2; /* * Reentrant version of gamma & lgamma; passes signgam back by reference * as the second argument; user must allocate space for signgam. */ double gamma_r(double, int *); double lgamma_r(double, int *); /* * IEEE Test Vector */ double significand(double); #endif /* __BSD_VISIBLE */ /* float versions of ANSI/POSIX functions */ #if __ISO_C_VISIBLE >= 1999 float acosf(float); float asinf(float); float atanf(float); float atan2f(float, float); float cosf(float); float sinf(float); float tanf(float); float coshf(float); float sinhf(float); float tanhf(float); float exp2f(float); float expf(float); float expm1f(float); float frexpf(float, int *); /* fundamentally !__pure2 */ int ilogbf(float) __pure2; float ldexpf(float, int); float log10f(float); float log1pf(float); float log2f(float); float logf(float); float modff(float, float *); /* fundamentally !__pure2 */ float powf(float, float); float sqrtf(float); float ceilf(float); float fabsf(float) __pure2; float floorf(float); float fmodf(float, float); float roundf(float); float erff(float); float erfcf(float); float hypotf(float, float); float lgammaf(float); float tgammaf(float); float acoshf(float); float asinhf(float); float atanhf(float); float cbrtf(float); float logbf(float); float copysignf(float, float) __pure2; long long llrintf(float); long long llroundf(float); long lrintf(float); long lroundf(float); float nanf(const char *) __pure2; float nearbyintf(float); float nextafterf(float, float); float remainderf(float, float); float remquof(float, float, int *); float rintf(float); float scalblnf(float, long); float scalbnf(float, int); float truncf(float); float fdimf(float, float); float fmaf(float, float, float); float fmaxf(float, float) __pure2; float fminf(float, float) __pure2; #endif /* * float versions of BSD math library entry points */ #if __BSD_VISIBLE float dremf(float, float); int finitef(float) __pure2; float gammaf(float); float j0f(float); float j1f(float); float jnf(int, float); float scalbf(float, float); float y0f(float); float y1f(float); float ynf(int, float); /* * Float versions of reentrant version of gamma & lgamma; passes * signgam back by reference as the second argument; user must * allocate space for signgam. */ float gammaf_r(float, int *); float lgammaf_r(float, int *); /* * float version of IEEE Test Vector */ float significandf(float); #endif /* __BSD_VISIBLE */ /* * long double versions of ISO/POSIX math functions */ #if __ISO_C_VISIBLE >= 1999 long double acoshl(long double); long double acosl(long double); long double asinhl(long double); long double asinl(long double); long double atan2l(long double, long double); long double atanhl(long double); long double atanl(long double); long double cbrtl(long double); long double ceill(long double); long double copysignl(long double, long double) __pure2; +long double coshl(long double); long double cosl(long double); +long double erfcl(long double); +long double erfl(long double); long double exp2l(long double); long double expl(long double); long double expm1l(long double); long double fabsl(long double) __pure2; long double fdiml(long double, long double); long double floorl(long double); long double fmal(long double, long double, long double); long double fmaxl(long double, long double) __pure2; long double fminl(long double, long double) __pure2; long double fmodl(long double, long double); long double frexpl(long double value, int *); /* fundamentally !__pure2 */ long double hypotl(long double, long double); int ilogbl(long double) __pure2; long double ldexpl(long double, int); +long double lgammal(long double); long long llrintl(long double); long long llroundl(long double); long double log10l(long double); long double log1pl(long double); long double log2l(long double); long double logbl(long double); long double logl(long double); long lrintl(long double); long lroundl(long double); long double modfl(long double, long double *); /* fundamentally !__pure2 */ long double nanl(const char *) __pure2; long double nearbyintl(long double); long double nextafterl(long double, long double); double nexttoward(double, long double); float nexttowardf(float, long double); long double nexttowardl(long double, long double); +long double powl(long double, long double); long double remainderl(long double, long double); long double remquol(long double, long double, int *); long double rintl(long double); long double roundl(long double); long double scalblnl(long double, long); long double scalbnl(long double, int); +long double sinhl(long double); long double sinl(long double); long double sqrtl(long double); +long double tanhl(long double); long double tanl(long double); +long double tgammal(long double); long double truncl(long double); #endif /* __ISO_C_VISIBLE >= 1999 */ __END_DECLS #endif /* !_MATH_H_ */ - -/* separate header for cmath */ -#ifndef _MATH_EXTRA_H_ -#if __ISO_C_VISIBLE >= 1999 -#if _DECLARE_C99_LDBL_MATH - -#define _MATH_EXTRA_H_ - -/* - * extra long double versions of math functions for C99 and cmath - */ -__BEGIN_DECLS - -long double coshl(long double); -long double erfcl(long double); -long double erfl(long double); -long double lgammal(long double); -long double powl(long double, long double); -long double sinhl(long double); -long double tanhl(long double); -long double tgammal(long double); - -__END_DECLS - -#endif /* !_DECLARE_C99_LDBL_MATH */ -#endif /* __ISO_C_VISIBLE >= 1999 */ -#endif /* !_MATH_EXTRA_H_ */ Index: stable/10/lib/msun/src/s_erf.c =================================================================== --- stable/10/lib/msun/src/s_erf.c (revision 271778) +++ stable/10/lib/msun/src/s_erf.c (revision 271779) @@ -1,301 +1,309 @@ /* @(#)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 __FBSDID("$FreeBSD$"); /* 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 "math.h" #include "math_private.h" +/* XXX Prevent compilers from erroneously constant folding: */ +static const volatile double tiny= 1e-300; + 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 */ +half= 0.5, +one = 1, +two = 2, +/* c = (float)0.84506291151 */ erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ /* - * Coefficients for approximation to erf on [0,0.84375] + * In the domain [0, 2**-28], only the first term in the power series + * expansion of erf(x) is used. The magnitude of the first neglected + * terms is less than 2**-84. */ efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ 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] + * 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] + * 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] + * 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 */ 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 (8*x+efx8*x)/8; /* avoid spurious 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))))))); + 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)))))); + 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; } +#if (LDBL_MANT_DIG == 53) +__weak_reference(erf, erfl); +#endif + 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))))))); + 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)))))); + 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); + 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) +__weak_reference(erfc, erfcl); +#endif Index: stable/10/lib/msun/src/s_erff.c =================================================================== --- stable/10/lib/msun/src/s_erff.c (revision 271778) +++ stable/10/lib/msun/src/s_erff.c (revision 271779) @@ -1,182 +1,181 @@ /* 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 __FBSDID("$FreeBSD$"); #include "math.h" #include "math_private.h" +/* XXX Prevent compilers from erroneously constant folding: */ +static const volatile float tiny = 1e-30; + static const float -tiny = 1e-30, -half= 5.0000000000e-01, /* 0x3F000000 */ -one = 1.0000000000e+00, /* 0x3F800000 */ -two = 2.0000000000e+00, /* 0x40000000 */ +half= 0.5, +one = 1, +two = 2, +erx = 8.42697144e-01, /* 0x3f57bb00 */ /* - * Coefficients for approximation to erf on [0,0.84375] + * In the domain [0, 2**-14], only the first term in the power series + * expansion of erf(x) is used. The magnitude of the first neglected + * terms is less than 2**-42. */ -efx = 1.2837916613e-01, /* 0x3e0375d4 */ -efx8= 1.0270333290e+00, /* 0x3f8375d4 */ +efx = 1.28379166e-01, /* 0x3e0375d4 */ +efx8= 1.02703333e+00, /* 0x3f8375d4 */ /* - * Domain [0, 0.84375], range ~[-5.4446e-10,5.5197e-10]: - * |(erf(x) - x)/x - p(x)/q(x)| < 2**-31. + * Domain [0, 0.84375], range ~[-5.4419e-10, 5.5179e-10]: + * |(erf(x) - x)/x - pp(x)/qq(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 */ +pp0 = 1.28379166e-01, /* 0x3e0375d4 */ +pp1 = -3.36030394e-01, /* 0xbeac0c2d */ +pp2 = -1.86261395e-03, /* 0xbaf422f4 */ +qq1 = 3.12324315e-01, /* 0x3e9fe8f9 */ +qq2 = 2.16070414e-02, /* 0x3cb10140 */ +qq3 = -1.98859372e-03, /* 0xbb025311 */ /* - * Domain [0.84375, 1.25], range ~[-1.953e-11,1.940e-11]: - * |(erf(x) - erx) - p(x)/q(x)| < 2**-36. + * Domain [0.84375, 1.25], range ~[-1.023e-9, 1.023e-9]: + * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-31 */ -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 */ +pa0 = 3.65041046e-06, /* 0x3674f993 */ +pa1 = 4.15109307e-01, /* 0x3ed48935 */ +pa2 = -2.09395722e-01, /* 0xbe566bd5 */ +pa3 = 8.67677554e-02, /* 0x3db1b34b */ +qa1 = 4.95560974e-01, /* 0x3efdba2b */ +qa2 = 3.71248513e-01, /* 0x3ebe1449 */ +qa3 = 3.92478965e-02, /* 0x3d20c267 */ /* - * 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 + * Domain [1.25,1/0.35], range ~[-4.821e-9, 4.927e-9]: + * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-28 */ -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 */ +ra0 = -9.88156721e-03, /* 0xbc21e64c */ +ra1 = -5.43658376e-01, /* 0xbf0b2d32 */ +ra2 = -1.66828310e+00, /* 0xbfd58a4d */ +ra3 = -6.91554189e-01, /* 0xbf3109b2 */ +sa1 = 4.48581553e+00, /* 0x408f8bcd */ +sa2 = 4.10799170e+00, /* 0x408374ab */ +sa3 = 5.53855181e-01, /* 0x3f0dc974 */ /* - * 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 + * Domain [2.85715, 11], range ~[-1.484e-9, 1.505e-9]: + * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-30 */ -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 */ +rb0 = -9.86496918e-03, /* 0xbc21a0ae */ +rb1 = -5.48049808e-01, /* 0xbf0c4cfe */ +rb2 = -1.84115684e+00, /* 0xbfebab07 */ +sb1 = 4.87132740e+00, /* 0x409be1ea */ +sb2 = 3.04982710e+00, /* 0x4043305e */ +sb3 = -7.61900663e-01; /* 0xbf430bec */ 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 */ + if(ix>=0x7f800000) { /* erff(nan)=nan */ i = ((u_int32_t)hx>>31)<<1; - return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ + return (float)(1-i)+one/x; /* erff(+-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))); + Q = one+s*(qa1+s*(qa2+s*qa3)); 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 */ + if(ix< 0x4036db8c) { /* |x| < 2.85715 ~ 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))); + S=one+s*(sa1+s*(sa2+s*sa3)); + } else { /* |x| >= 2.85715 ~ 1/0.35 */ + R=rb0+s*(rb1+s*rb2); + S=one+s*(sb1+s*(sb2+s*sb3)); } 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; } 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 */ + if(ix>=0x7f800000) { /* erfcf(nan)=nan */ + /* erfcf(+-inf)=0,2 */ return (float)(((u_int32_t)hx>>31)<<1)+one/x; } if(ix < 0x3f580000) { /* |x|<0.84375 */ if(ix < 0x33800000) /* |x|<2**-24 */ 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))); + Q = one+s*(qa1+s*(qa2+s*qa3)); if(hx>=0) { z = one-erx; return z - P/Q; } else { z = erx+P/Q; return one+z; } } if (ix < 0x41300000) { /* |x|<11 */ 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(ix< 0x4036db8c) { /* |x| < 2.85715 ~ 1/.35 */ + R=ra0+s*(ra1+s*(ra2+s*ra3)); + S=one+s*(sa1+s*(sa2+s*sa3)); + } else { /* |x| >= 2.85715 ~ 1/.35 */ 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))); + R=rb0+s*(rb1+s*rb2); + S=one+s*(sb1+s*(sb2+s*sb3)); } 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; } } Index: stable/10/lib/msun/src/s_round.c =================================================================== --- stable/10/lib/msun/src/s_round.c (revision 271778) +++ stable/10/lib/msun/src/s_round.c (revision 271779) @@ -1,51 +1,60 @@ /*- * 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 __FBSDID("$FreeBSD$"); -#include +#include +#include "math.h" +#include "math_private.h" + double round(double x) { double t; + uint32_t hx; - if (!isfinite(x)) - return (x); + GET_HIGH_WORD(hx, x); + if ((hx & 0x7fffffff) == 0x7ff00000) + return (x + x); - if (x >= 0.0) { + if (!(hx & 0x80000000)) { t = floor(x); if (t - x <= -0.5) - t += 1.0; + t += 1; return (t); } else { t = floor(-x); if (t + x <= -0.5) - t += 1.0; + t += 1; return (-t); } } + +#if (LDBL_MANT_DIG == 53) +__weak_reference(round, roundl); +#endif Index: stable/10/lib/msun/src/s_roundf.c =================================================================== --- stable/10/lib/msun/src/s_roundf.c (revision 271778) +++ stable/10/lib/msun/src/s_roundf.c (revision 271779) @@ -1,51 +1,54 @@ /*- * 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 __FBSDID("$FreeBSD$"); -#include +#include "math.h" +#include "math_private.h" float roundf(float x) { float t; + uint32_t hx; - if (!isfinite(x)) - return (x); + GET_FLOAT_WORD(hx, x); + if ((hx & 0x7fffffff) == 0x7f800000) + return (x + x); - if (x >= 0.0) { + if (!(hx & 0x80000000)) { t = floorf(x); - if (t - x <= -0.5) - t += 1.0; + if (t - x <= -0.5F) + t += 1; return (t); } else { t = floorf(-x); - if (t + x <= -0.5) - t += 1.0; + if (t + x <= -0.5F) + t += 1; return (-t); } } Index: stable/10/lib/msun/src/s_roundl.c =================================================================== --- stable/10/lib/msun/src/s_roundl.c (revision 271778) +++ stable/10/lib/msun/src/s_roundl.c (revision 271779) @@ -1,51 +1,62 @@ /*- * 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 __FBSDID("$FreeBSD$"); -#include +#include +#ifdef __i386__ +#include +#endif +#include "fpmath.h" +#include "math.h" +#include "math_private.h" + long double roundl(long double x) { long double t; + uint16_t hx; - if (!isfinite(x)) - return (x); + GET_LDBL_EXPSIGN(hx, x); + if ((hx & 0x7fff) == 0x7fff) + return (x + x); - if (x >= 0.0) { + ENTERI(); + + if (!(hx & 0x8000)) { t = floorl(x); - if (t - x <= -0.5) - t += 1.0; - return (t); + if (t - x <= -0.5L) + t += 1; + RETURNI(t); } else { t = floorl(-x); - if (t + x <= -0.5) - t += 1.0; - return (-t); + if (t + x <= -0.5L) + t += 1; + RETURNI(-t); } } Index: stable/10/lib/msun/src/s_tanh.c =================================================================== --- stable/10/lib/msun/src/s_tanh.c (revision 271778) +++ stable/10/lib/msun/src/s_tanh.c (revision 271779) @@ -1,77 +1,84 @@ /* @(#)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 __FBSDID("$FreeBSD$"); /* 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 "math.h" #include "math_private.h" -static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300; +static const volatile double tiny = 1.0e-300; +static const double one = 1.0, two = 2.0, huge = 1.0e300; 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) +__weak_reference(tanh, tanhl); +#endif Index: stable/10/lib/msun/src/s_tanhf.c =================================================================== --- stable/10/lib/msun/src/s_tanhf.c (revision 271778) +++ stable/10/lib/msun/src/s_tanhf.c (revision 271779) @@ -1,55 +1,57 @@ /* 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 __FBSDID("$FreeBSD$"); #include "math.h" #include "math_private.h" -static const float one=1.0, two=2.0, tiny = 1.0e-30, huge = 1.0e30; +static const volatile float tiny = 1.0e-30; +static const float one=1.0, two=2.0, huge = 1.0e30; + 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; } Index: stable/10/lib/msun/src/s_tanhl.c =================================================================== --- stable/10/lib/msun/src/s_tanhl.c (nonexistent) +++ stable/10/lib/msun/src/s_tanhl.c (revision 271779) @@ -0,0 +1,172 @@ +/* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */ + +/* @(#)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 +__FBSDID("$FreeBSD$"); + +/* + * See s_tanh.c for complete comments. + * + * Converted to long double by Bruce D. Evans. + */ + +#include +#ifdef __i386__ +#include +#endif + +#include "math.h" +#include "math_private.h" +#include "fpmath.h" +#include "k_expl.h" + +#if LDBL_MAX_EXP != 0x4000 +/* We also require the usual expsign encoding. */ +#error "Unsupported long double format" +#endif + +#define BIAS (LDBL_MAX_EXP - 1) + +static const volatile double tiny = 1.0e-300; +static const double one = 1.0; +#if LDBL_MANT_DIG == 64 +/* + * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]: + * |tanh(x)/x - t(x)| < 2**-72.3 + */ +static const union IEEEl2bits +T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L); +#define T3 T3u.e +static const double +T5 = 1.3333333333333314e-1, /* 0x1111111111110a.0p-55 */ +T7 = -5.3968253968210485e-2, /* -0x1ba1ba1ba1a1a1.0p-57 */ +T9 = 2.1869488531393817e-2, /* 0x1664f488172022.0p-58 */ +T11 = -8.8632352345964591e-3, /* -0x1226e34bc138d5.0p-59 */ +T13 = 3.5921169709993771e-3, /* 0x1d6d371d3e400f.0p-61 */ +T15 = -1.4555786415756001e-3, /* -0x17d923aa63814d.0p-62 */ +T17 = 5.8645267876296793e-4, /* 0x13378589b85aa7.0p-63 */ +T19 = -2.1121033571392224e-4; /* -0x1baf0af80c4090.0p-65 */ +#elif LDBL_MANT_DIG == 113 +/* + * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]: + * |tanh(x)/x - t(x)| < 2**121.6 + */ +static const long double +T3 = -3.33333333333333333333333333333332980e-1L, /* -0x1555555555555555555555555554e.0p-114L */ +T5 = 1.33333333333333333333333333332707260e-1L, /* 0x1111111111111111111111110ab7b.0p-115L */ +T7 = -5.39682539682539682539682535723482314e-2L, /* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */ +T9 = 2.18694885361552028218693591149061717e-2L, /* 0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */ +T11 = -8.86323552990219656883762347736381851e-3L, /* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */ +T13 = 3.59212803657248101358314398220822722e-3L, /* 0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */ +T15 = -1.45583438705131796512568010348874662e-3L; /* -0x17da36452b75e150c44cc34253b34.0p-122L */ +static const double +T17 = 5.9002744094556621e-4, /* 0x1355824803668e.0p-63 */ +T19 = -2.3912911424260516e-4, /* -0x1f57d7734c8dde.0p-65 */ +T21 = 9.6915379535512898e-5, /* 0x1967e18ad6a6ca.0p-66 */ +T23 = -3.9278322983156353e-5, /* -0x1497d8e6b75729.0p-67 */ +T25 = 1.5918887220143869e-5, /* 0x10b1319998cafa.0p-68 */ +T27 = -6.4514295231630956e-6, /* -0x1b0f2b71b218eb.0p-70 */ +T29 = 2.6120754043964365e-6, /* 0x15e963a3cf3a39.0p-71 */ +T31 = -1.0407567231003314e-6, /* -0x1176041e656869.0p-72 */ +T33 = 3.4744117554063574e-7; /* 0x1750fe732cab9c.0p-74 */ +#endif /* LDBL_MANT_DIG == 64 */ + +static inline long double +divl(long double a, long double b, long double c, long double d, + long double e, long double f) +{ + long double inv, r; + float fr, fw; + + _2sumF(a, c); + b = b + c; + _2sumF(d, f); + e = e + f; + + inv = 1 / (d + e); + + r = (a + b) * inv; + fr = r; + r = fr; + + fw = d + e; + e = d - fw + e; + d = fw; + + r = r + (a - d * r + b - e * r) * inv; + + return r; +} + +long double +tanhl(long double x) +{ + long double hi,lo,s,x2,x4,z; + double dx2; + int16_t jx,ix; + + GET_LDBL_EXPSIGN(jx,x); + ix = jx&0x7fff; + + /* x is INF or NaN */ + if(ix>=0x7fff) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + ENTERI(); + + /* |x| < 40 */ + if (ix < 0x4004 || fabsl(x) < 40) { /* |x|<40 */ + if (__predict_false(ix= 40, return +-1 */ + } else { + z = one - tiny; /* raise inexact flag */ + } + s = 1; + if (jx<0) s = -1; + RETURNI(s*z); +} Property changes on: stable/10/lib/msun/src/s_tanhl.c ___________________________________________________________________ Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +FreeBSD=%H \ No newline at end of property Added: svn:mime-type ## -0,0 +1 ## +text/plain \ No newline at end of property Index: stable/10 =================================================================== --- stable/10 (revision 271778) +++ stable/10 (revision 271779) Property changes on: stable/10 ___________________________________________________________________ Modified: svn:mergeinfo ## -0,0 +0,1 ## Merged /head:r257770,257818,257823,260066-260067,260089,260145,268587-268590,268593,268597,269758,270845,270847,270893,270932,270947,271147