* 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
This commit is contained in:
Steve Kargl
parent
5f63fbd67f
commit
a48e1f224c
@ -96,13 +96,14 @@ COMMON_SRCS+= s_copysignl.c s_fabsl.c s_llrintl.c s_lrintl.c s_modfl.c
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.if ${LDBL_PREC} != 53
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# If long double != double use these; otherwise, we alias the double versions.
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COMMON_SRCS+= e_acoshl.c e_acosl.c e_asinl.c e_atan2l.c e_atanhl.c \
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e_fmodl.c e_hypotl.c e_remainderl.c e_sqrtl.c \
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e_coshl.c e_fmodl.c e_hypotl.c \
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e_remainderl.c e_sinhl.c e_sqrtl.c \
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invtrig.c k_cosl.c k_sinl.c k_tanl.c \
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s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c s_cprojl.c \
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s_csqrtl.c s_exp2l.c s_expl.c s_floorl.c s_fmal.c \
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s_frexpl.c s_logbl.c s_logl.c s_nanl.c s_nextafterl.c \
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s_nexttoward.c s_remquol.c s_rintl.c s_roundl.c s_scalbnl.c \
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s_sinl.c s_tanl.c s_truncl.c w_cabsl.c
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s_nexttoward.c s_remquol.c s_rintl.c s_roundl.c s_scalbnl.c \
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s_sinl.c s_tanhl.c s_tanl.c s_truncl.c w_cabsl.c
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.endif
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# C99 complex functions
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@ -160,7 +161,7 @@ MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \
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cimag.3 creal.3 cimag.3 crealf.3 cimag.3 creall.3
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MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3
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MLINKS+=cos.3 cosf.3 cos.3 cosl.3
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MLINKS+=cosh.3 coshf.3
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MLINKS+=cosh.3 coshf.3 cosh.3 coshl.3
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MLINKS+=csqrt.3 csqrtf.3 csqrt.3 csqrtl.3
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MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3
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MLINKS+=exp.3 expm1.3 exp.3 expm1f.3 exp.3 expm1l.3 exp.3 pow.3 exp.3 powf.3 \
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@ -208,11 +209,11 @@ MLINKS+=round.3 roundf.3 round.3 roundl.3
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MLINKS+=scalbn.3 scalbln.3 scalbn.3 scalblnf.3 scalbn.3 scalblnl.3
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MLINKS+=scalbn.3 scalbnf.3 scalbn.3 scalbnl.3
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MLINKS+=sin.3 sinf.3 sin.3 sinl.3
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MLINKS+=sinh.3 sinhf.3
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MLINKS+=sinh.3 sinhf.3 sinh.3 sinhl.3
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MLINKS+=sqrt.3 cbrt.3 sqrt.3 cbrtf.3 sqrt.3 cbrtl.3 sqrt.3 sqrtf.3 \
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sqrt.3 sqrtl.3
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MLINKS+=tan.3 tanf.3 tan.3 tanl.3
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MLINKS+=tanh.3 tanhf.3
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MLINKS+=tanh.3 tanhf.3 tanh.3 tanhl.3
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MLINKS+=trunc.3 truncf.3 trunc.3 truncl.3
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.include <bsd.lib.mk>
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@ -260,6 +260,7 @@ FBSD_1.3 {
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ccosf;
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ccosh;
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ccoshf;
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coshl;
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ctan;
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ctanf;
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ctanh;
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@ -270,13 +271,12 @@ FBSD_1.3 {
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log1pl;
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log2l;
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logl;
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sinhl;
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tanhl;
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/* Implemented as weak aliases for imprecise versions */
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coshl;
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erfcl;
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erfl;
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lgammal;
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powl;
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sinhl;
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tanhl;
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tgammal;
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};
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@ -28,12 +28,13 @@
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.\" from: @(#)cosh.3 5.1 (Berkeley) 5/2/91
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.\" $FreeBSD$
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.\"
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.Dd January 14, 2005
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.Dd August 17, 2013
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.Dt COSH 3
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.Os
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.Sh NAME
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.Nm cosh ,
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.Nm coshf
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.Nm coshf ,
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.Nm coshl
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.Nd hyperbolic cosine functions
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.Sh LIBRARY
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.Lb libm
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@ -43,11 +44,14 @@
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.Fn cosh "double x"
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.Ft float
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.Fn coshf "float x"
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.Ft long double
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.Fn coshl "long double x"
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.Sh DESCRIPTION
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The
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.Fn cosh
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.Fn cosh ,
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.Fn coshf ,
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and the
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.Fn coshf
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.Fn coshl
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functions compute the hyperbolic cosine of
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.Fa x .
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.Sh SEE ALSO
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@ -42,11 +42,14 @@
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.Fn sinh "double x"
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.Ft float
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.Fn sinhf "float x"
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.Ft long double
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.Fn sinhl "long double x"
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.Sh DESCRIPTION
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The
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.Fn sinh
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.Fn sinh ,
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.Fn sinhf ,
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and the
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.Fn sinhf
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.Fn sinhl
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functions compute the hyperbolic sine of
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.Fa x .
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.Sh SEE ALSO
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@ -28,12 +28,13 @@
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.\" from: @(#)tanh.3 5.1 (Berkeley) 5/2/91
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.\" $FreeBSD$
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.\"
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.Dd May 2, 1991
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.Dd August 17, 2013
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.Dt TANH 3
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.Os
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.Sh NAME
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.Nm tanh ,
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.Nm tanhf
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.Nm tanhf ,
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.Nm tanhl
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.Nd hyperbolic tangent functions
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.Sh LIBRARY
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.Lb libm
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@ -43,20 +44,24 @@
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.Fn tanh "double x"
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.Ft float
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.Fn tanhf "float x"
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.Ft long double
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.Fn tanhl "long double x"
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.Sh DESCRIPTION
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The
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.Fn tanh
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.Fn tanh ,
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.Fn tanhf ,
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and the
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.Fn tanhf
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.Fn tanhl
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functions compute the hyperbolic tangent of
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.Fa x .
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For a discussion of error due to roundoff, see
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.Xr math 3 .
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.Sh RETURN VALUES
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The
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.Fn tanh
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.Fn tanh ,
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.Fn tanhf ,
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and the
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.Fn tanhf
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.Fn tanhl
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functions return the hyperbolic tangent value.
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.Sh SEE ALSO
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.Xr acos 3 ,
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@ -35,6 +35,8 @@ __FBSDID("$FreeBSD$");
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* only cosh(0)=1 is exact for finite x.
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*/
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#include <float.h>
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#include "math.h"
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#include "math_private.h"
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@ -77,3 +79,7 @@ __ieee754_cosh(double x)
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/* |x| > overflowthresold, cosh(x) overflow */
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return huge*huge;
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}
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#if (LDBL_MANT_DIG == 53)
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__weak_reference(cosh, coshl);
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#endif
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130
lib/msun/src/e_coshl.c
Normal file
130
lib/msun/src/e_coshl.c
Normal file
@ -0,0 +1,130 @@
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/* from: FreeBSD: head/lib/msun/src/e_coshl.c XXX */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/*
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* See e_cosh.c for complete comments.
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*
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* Converted to long double by Bruce D. Evans.
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*/
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#include <float.h>
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#ifdef __i386__
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#include <ieeefp.h>
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#endif
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#include "fpmath.h"
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#include "math.h"
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#include "math_private.h"
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#include "k_expl.h"
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#if LDBL_MAX_EXP != 0x4000
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/* We also require the usual expsign encoding. */
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#error "Unsupported long double format"
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#endif
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#define BIAS (LDBL_MAX_EXP - 1)
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static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L;
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#if LDBL_MANT_DIG == 64
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/*
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* Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]:
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* |cosh(x) - c(x)| < 2**-68.8
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*/
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static const union IEEEl2bits
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C4u = LD80C(0xaaaaaaaaaaaaac78, -5, 4.16666666666666682297e-2L);
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#define C4 C4u.e
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static const double
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C2 = 0.5,
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C6 = 1.3888888888888616e-3, /* 0x16c16c16c16b99.0p-62 */
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C8 = 2.4801587301767953e-5, /* 0x1a01a01a027061.0p-68 */
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C10 = 2.7557319163300398e-7, /* 0x127e4fb6c9b55f.0p-74 */
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C12 = 2.0876768371393075e-9, /* 0x11eed99406a3f4.0p-81 */
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C14 = 1.1469537039374480e-11, /* 0x1938c67cd18c48.0p-89 */
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C16 = 4.8473490896852041e-14; /* 0x1b49c429701e45.0p-97 */
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#elif LDBL_MANT_DIG == 113
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/*
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* Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]:
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* |cosh(x) - c(x)| < 2**-121.69
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*/
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static const long double
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C4 = 4.16666666666666666666666666666666225e-2L, /* 0x1555555555555555555555555554e.0p-117L */
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C6 = 1.38888888888888888888888888889434831e-3L, /* 0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */
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C8 = 2.48015873015873015873015871870962089e-5L, /* 0x1a01a01a01a01a01a01a017af2756.0p-128L */
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C10 = 2.75573192239858906525574318600800201e-7L, /* 0x127e4fb7789f5c72ef01c8a040640.0p-134L */
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C12 = 2.08767569878680989791444691755468269e-9L, /* 0x11eed8eff8d897b543d0679607399.0p-141L */
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C14= 1.14707455977297247387801189650495351e-11L, /* 0x193974a8c07c9d24ae169a7fa9b54.0p-149L */
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C16 = 4.77947733238737883626416876486279985e-14L; /* 0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */
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static const double
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C2 = 0.5,
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C18 = 1.5619206968597871e-16, /* 0x16827863b9900b.0p-105 */
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C20 = 4.1103176218528049e-19, /* 0x1e542ba3d3c269.0p-114 */
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C22 = 8.8967926401641701e-22, /* 0x10ce399542a014.0p-122 */
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C24 = 1.6116681626523904e-24, /* 0x1f2c981d1f0cb7.0p-132 */
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C26 = 2.5022374732804632e-27; /* 0x18c7ecf8b2c4a0.0p-141 */
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#else
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#error "Unsupported long double format"
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#endif /* LDBL_MANT_DIG == 64 */
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/* log(2**16385 - 0.5) rounded towards up: */
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static const float
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o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */
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long double
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coshl(long double x)
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{
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long double hi,lo,x2,x4;
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double dx2;
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uint16_t ix;
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GET_LDBL_EXPSIGN(ix,x);
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ix &= 0x7fff;
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/* x is INF or NaN */
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if(ix>=0x7fff) return x*x;
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ENTERI();
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/* |x| < 1, return 1 or c(x) */
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if(ix<0x3fff) {
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if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x| < TINY */
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RETURNI(1+tiny); /* cosh(tiny) = 1(+) with inexact */
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x2 = x*x;
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#if LDBL_MANT_DIG == 64
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x4 = x2*x2;
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RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) +
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((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1);
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#elif LDBL_MANT_DIG == 113
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dx2 = x2;
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RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 +
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C20)*x2 + C18)*x2 +
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C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 +
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C4)*(x2*x2) + C2*x2 + 1);
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#endif
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}
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/* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */
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if (ix < 0x4005) {
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k_hexpl(fabsl(x), &hi, &lo);
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RETURNI(lo + 0.25/(hi + lo) + hi);
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}
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/* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */
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if (fabsl(x) <= o_threshold)
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RETURNI(hexpl(fabsl(x)));
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/* |x| > o_threshold, cosh(x) overflow */
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RETURNI(huge*huge);
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}
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@ -32,6 +32,8 @@ __FBSDID("$FreeBSD$");
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* only sinh(0)=0 is exact for finite x.
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*/
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#include <float.h>
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#include "math.h"
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#include "math_private.h"
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@ -71,3 +73,7 @@ __ieee754_sinh(double x)
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/* |x| > overflowthresold, sinh(x) overflow */
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return x*shuge;
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}
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#if (LDBL_MANT_DIG == 53)
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__weak_reference(sinh, sinhl);
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#endif
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131
lib/msun/src/e_sinhl.c
Normal file
131
lib/msun/src/e_sinhl.c
Normal file
@ -0,0 +1,131 @@
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/* from: FreeBSD: head/lib/msun/src/e_sinhl.c XXX */
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/*
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* ====================================================
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||||
* 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.
|
||||
* ====================================================
|
||||
*/
|
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
|
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|
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/*
|
||||
* See e_sinh.c for complete comments.
|
||||
*
|
||||
* Converted to long double by Bruce D. Evans.
|
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*/
|
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|
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#include <float.h>
|
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#ifdef __i386__
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#include <ieeefp.h>
|
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#endif
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#include "fpmath.h"
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#include "math.h"
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#include "math_private.h"
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#include "k_expl.h"
|
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#if LDBL_MAX_EXP != 0x4000
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/* We also require the usual expsign encoding. */
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#error "Unsupported long double format"
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#endif
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#define BIAS (LDBL_MAX_EXP - 1)
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static const long double shuge = 0x1p16383L;
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#if LDBL_MANT_DIG == 64
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/*
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* Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]:
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* |sinh(x)/x - s(x)| < 2**-70.3
|
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*/
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static const union IEEEl2bits
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S3u = LD80C(0xaaaaaaaaaaaaaaaa, -3, 1.66666666666666666658e-1L);
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#define S3 S3u.e
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static const double
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S5 = 8.3333333333333332e-3, /* 0x11111111111111.0p-59 */
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S7 = 1.9841269841270074e-4, /* 0x1a01a01a01a070.0p-65 */
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S9 = 2.7557319223873889e-6, /* 0x171de3a5565fe6.0p-71 */
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S11 = 2.5052108406704084e-8, /* 0x1ae6456857530f.0p-78 */
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S13 = 1.6059042748655297e-10, /* 0x161245fa910697.0p-85 */
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S15 = 7.6470006914396920e-13, /* 0x1ae7ce4eff2792.0p-93 */
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S17 = 2.8346142308424267e-15; /* 0x19882ce789ffc6.0p-101 */
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#elif LDBL_MANT_DIG == 113
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/*
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* Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]:
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* |sinh(x)/x - s(x)| < 2**-118.0
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*/
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static const long double
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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 (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x|<TINY */
|
||||
if(shuge+x>1) 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;
|
||||
}
|
||||
@ -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);
|
||||
|
||||
@ -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
|
||||
|
||||
@ -37,6 +37,8 @@ __FBSDID("$FreeBSD$");
|
||||
* only tanh(0)=0 is exact for finite argument.
|
||||
*/
|
||||
|
||||
#include <float.h>
|
||||
|
||||
#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
|
||||
|
||||
164
lib/msun/src/s_tanhl.c
Normal file
164
lib/msun/src/s_tanhl.c
Normal file
@ -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 <sys/cdefs.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
/*
|
||||
* See s_tanh.c for complete comments.
|
||||
*
|
||||
* Converted to long double by Bruce D. Evans.
|
||||
*/
|
||||
|
||||
#include <float.h>
|
||||
#ifdef __i386__
|
||||
#include <ieeefp.h>
|
||||
#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<BIAS-(LDBL_MANT_DIG+1)/2)) { /* |x|<TINY */
|
||||
/* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
|
||||
return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
|
||||
}
|
||||
if (fabsl(x) < 0.25) { /* |x|<0.25 */
|
||||
x2 = x*x;
|
||||
#if LDBL_MANT_DIG == 64
|
||||
x4 = x2*x2;
|
||||
RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
|
||||
((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
|
||||
T3*(x2*x) + x);
|
||||
#elif LDBL_MANT_DIG == 113
|
||||
dx2 = x2;
|
||||
RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
|
||||
T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
|
||||
T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
|
||||
(x2*x*x2) +
|
||||
T3*(x2*x) + x);
|
||||
#endif
|
||||
}
|
||||
k_hexpl(2*fabsl(x), &hi, &lo);
|
||||
if (fabsl(x) < 1.5) /* |x|<1.5 */
|
||||
z = divl(hi, lo, -0.5, hi, lo, 0.5);
|
||||
else
|
||||
z = one - one/(lo+0.5+hi);
|
||||
/* |x| >= 40, return +-1 */
|
||||
} else {
|
||||
z = one - tiny; /* raise inexact flag */
|
||||
}
|
||||
s = 1;
|
||||
if (jx<0) s = -1;
|
||||
RETURNI(s*z);
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user