From a48e1f224c561c156d130496638b5defbb3081d0 Mon Sep 17 00:00:00 2001 From: Steve Kargl Date: Mon, 30 Dec 2013 01:06:21 +0000 Subject: [PATCH] * Makefile: . Hook coshl, sinhl, and tanhl into libm. . Create symbolic links for corresponding manpages. . While here remove a nearby extraneous space. * Symbol.map: * src/math.h: . Move coshl, sinhl, and tanhl to their proper locations. * man/cosh.3: * man/sinh.3: * man/tanh.3: . Update the manpages. * src/e_cosh.c: * src/e_sinh.c: * src/s_tanh.c: . Add weak reference for LBDL_MANT_DIG==53 targets. * src/imprecise.c: . Remove the coshl, sinhl, and tanhl kludge. * src/e_coshl.c: . ld80 and ld128 implementation of coshl(). * src/e_sinhl.c: . ld80 and ld128 implementation of sinhl(). * src/s_tanhl.c: . ld80 and ld128 implementation of tanhl(). Obtained from: bde (mostly), das and kargl --- lib/msun/Makefile | 13 ++-- lib/msun/Symbol.map | 6 +- lib/msun/man/cosh.3 | 12 ++- lib/msun/man/sinh.3 | 7 +- lib/msun/man/tanh.3 | 17 ++-- lib/msun/src/e_cosh.c | 6 ++ lib/msun/src/e_coshl.c | 130 +++++++++++++++++++++++++++++++ lib/msun/src/e_sinh.c | 6 ++ lib/msun/src/e_sinhl.c | 131 +++++++++++++++++++++++++++++++ lib/msun/src/imprecise.c | 3 - lib/msun/src/math.h | 6 +- lib/msun/src/s_tanh.c | 6 ++ lib/msun/src/s_tanhl.c | 164 +++++++++++++++++++++++++++++++++++++++ 13 files changed, 480 insertions(+), 27 deletions(-) create mode 100644 lib/msun/src/e_coshl.c create mode 100644 lib/msun/src/e_sinhl.c create mode 100644 lib/msun/src/s_tanhl.c diff --git a/lib/msun/Makefile b/lib/msun/Makefile index 3533dd233f92..f57610f553ab 100644 --- a/lib/msun/Makefile +++ b/lib/msun/Makefile @@ -96,13 +96,14 @@ 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_frexpl.c s_logbl.c s_logl.c s_nanl.c s_nextafterl.c \ - s_nexttoward.c s_remquol.c s_rintl.c s_roundl.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 @@ -160,7 +161,7 @@ MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.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+=exp.3 expm1.3 exp.3 expm1f.3 exp.3 expm1l.3 exp.3 pow.3 exp.3 powf.3 \ @@ -208,11 +209,11 @@ 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 diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map index 037659dff0a3..c36472bafb02 100644 --- a/lib/msun/Symbol.map +++ b/lib/msun/Symbol.map @@ -260,6 +260,7 @@ FBSD_1.3 { ccosf; ccosh; ccoshf; + coshl; ctan; ctanf; ctanh; @@ -270,13 +271,12 @@ FBSD_1.3 { log1pl; log2l; logl; + sinhl; + tanhl; /* Implemented as weak aliases for imprecise versions */ - coshl; erfcl; erfl; lgammal; powl; - sinhl; - tanhl; tgammal; }; diff --git a/lib/msun/man/cosh.3 b/lib/msun/man/cosh.3 index 96abc5aa7c9f..e2d28b61d5c7 100644 --- a/lib/msun/man/cosh.3 +++ b/lib/msun/man/cosh.3 @@ -28,12 +28,13 @@ .\" 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 @@ -43,11 +44,14 @@ .Fn cosh "double x" .Ft float .Fn coshf "float x" +.Ft long double +.Fn coshl "long double x" .Sh DESCRIPTION The -.Fn cosh +.Fn cosh , +.Fn coshf , and the -.Fn coshf +.Fn coshl functions compute the hyperbolic cosine of .Fa x . .Sh SEE ALSO diff --git a/lib/msun/man/sinh.3 b/lib/msun/man/sinh.3 index 02944ccc3a6a..f69d9d78d12c 100644 --- a/lib/msun/man/sinh.3 +++ b/lib/msun/man/sinh.3 @@ -42,11 +42,14 @@ .Fn sinh "double x" .Ft float .Fn sinhf "float x" +.Ft long double +.Fn sinhl "long double x" .Sh DESCRIPTION The -.Fn sinh +.Fn sinh , +.Fn sinhf , and the -.Fn sinhf +.Fn sinhl functions compute the hyperbolic sine of .Fa x . .Sh SEE ALSO diff --git a/lib/msun/man/tanh.3 b/lib/msun/man/tanh.3 index 6fb185c418b6..e1fc11a529d9 100644 --- a/lib/msun/man/tanh.3 +++ b/lib/msun/man/tanh.3 @@ -28,12 +28,13 @@ .\" 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 @@ -43,20 +44,24 @@ .Fn tanh "double x" .Ft float .Fn tanhf "float x" +.Ft long double +.Fn tanhl "long double x" .Sh DESCRIPTION The -.Fn tanh +.Fn tanh , +.Fn tanhf , and the -.Fn tanhf +.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 , diff --git a/lib/msun/src/e_cosh.c b/lib/msun/src/e_cosh.c index a36369545d9b..246b5fbec860 100644 --- a/lib/msun/src/e_cosh.c +++ b/lib/msun/src/e_cosh.c @@ -35,6 +35,8 @@ __FBSDID("$FreeBSD$"); * only cosh(0)=1 is exact for finite x. */ +#include + #include "math.h" #include "math_private.h" @@ -77,3 +79,7 @@ __ieee754_cosh(double x) /* |x| > overflowthresold, cosh(x) overflow */ return huge*huge; } + +#if (LDBL_MANT_DIG == 53) +__weak_reference(cosh, coshl); +#endif diff --git a/lib/msun/src/e_coshl.c b/lib/msun/src/e_coshl.c new file mode 100644 index 000000000000..a4b0d840a1b7 --- /dev/null +++ b/lib/msun/src/e_coshl.c @@ -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 towards 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); +} diff --git a/lib/msun/src/e_sinh.c b/lib/msun/src/e_sinh.c index 17442d0d152a..6c01f4a3c8e3 100644 --- a/lib/msun/src/e_sinh.c +++ b/lib/msun/src/e_sinh.c @@ -32,6 +32,8 @@ __FBSDID("$FreeBSD$"); * only sinh(0)=0 is exact for finite x. */ +#include + #include "math.h" #include "math_private.h" @@ -71,3 +73,7 @@ __ieee754_sinh(double x) /* |x| > overflowthresold, sinh(x) overflow */ return x*shuge; } + +#if (LDBL_MANT_DIG == 53) +__weak_reference(sinh, sinhl); +#endif diff --git a/lib/msun/src/e_sinhl.c b/lib/msun/src/e_sinhl.c new file mode 100644 index 000000000000..2187b13dd3dc --- /dev/null +++ b/lib/msun/src/e_sinhl.c @@ -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 towards 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; +} diff --git a/lib/msun/src/imprecise.c b/lib/msun/src/imprecise.c index a7503bf1c234..5bd3d642955b 100644 --- a/lib/msun/src/imprecise.c +++ b/lib/msun/src/imprecise.c @@ -60,10 +60,7 @@ DECLARE_WEAK(powl); 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); diff --git a/lib/msun/src/math.h b/lib/msun/src/math.h index 1bd931c318f3..fc4becc98403 100644 --- a/lib/msun/src/math.h +++ b/lib/msun/src/math.h @@ -451,6 +451,7 @@ 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 exp2l(long double); long double expl(long double); @@ -488,8 +489,10 @@ 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 truncl(long double); @@ -510,13 +513,10 @@ __END_DECLS */ __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 diff --git a/lib/msun/src/s_tanh.c b/lib/msun/src/s_tanh.c index 96e35656ba27..f7b71c5c68c6 100644 --- a/lib/msun/src/s_tanh.c +++ b/lib/msun/src/s_tanh.c @@ -37,6 +37,8 @@ __FBSDID("$FreeBSD$"); * only tanh(0)=0 is exact for finite argument. */ +#include + #include "math.h" #include "math_private.h" @@ -75,3 +77,7 @@ tanh(double x) } return (jx>=0)? z: -z; } + +#if (LDBL_MANT_DIG == 53) +__weak_reference(tanh, tanhl); +#endif diff --git a/lib/msun/src/s_tanhl.c b/lib/msun/src/s_tanhl.c new file mode 100644 index 000000000000..f42a70f51996 --- /dev/null +++ b/lib/msun/src/s_tanhl.c @@ -0,0 +1,164 @@ +/* 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, w; + float fr, fw; + uint32_t hx; + + _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(); + + if (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); +}