math: tanh.c cleanup similar to sinh, cosh
comments are kept in the double version of the function compared to fdlibm/freebsd we partition the domain into one more part and select different threshold points: now the [log(5/3)/2,log(3)/2] and [log(3)/2,inf] domains should have <1.5ulp error (so only the last bit may be wrong, assuming good exp, expm1) (note that log(3)/2 and log(5/3)/2 are the points where tanh changes resolution: tanh(log(3)/2)=0.5, tanh(log(5/3)/2)=0.25) for some x < log(5/3)/2 (~=0.2554) the error can be >1.5ulp but it should be <2ulp (the freebsd code had some >2ulp errors in [0.255,1]) even with the extra logic the new code produces smaller object files
This commit is contained in:
Szabolcs Nagy
parent
f143458223
commit
e42a977fe5
3 changed files with 83 additions and 173 deletions
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@ -1,73 +1,41 @@
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/* origin: FreeBSD /usr/src/lib/msun/src/s_tanh.c */
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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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/* Tanh(x)
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* Return the Hyperbolic Tangent of x
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*
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* Method :
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* x -x
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* e - e
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* 0. tanh(x) is defined to be -----------
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* x -x
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* e + e
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* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
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* 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0
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* -t
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* 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
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* t + 2
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* 2
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* 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
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* t + 2
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* 22 <= x <= INF : tanh(x) := 1.
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*
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* Special cases:
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* tanh(NaN) is NaN;
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* only tanh(0)=0 is exact for finite argument.
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*/
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#include "libm.h"
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static const double tiny = 1.0e-300, huge = 1.0e300;
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/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
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* = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
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* = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
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*/
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double tanh(double x)
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{
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double t,z;
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int32_t jx,ix;
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union {double f; uint64_t i;} u = {.f = x};
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uint32_t w;
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int sign;
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double t;
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GET_HIGH_WORD(jx, x);
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ix = jx & 0x7fffffff;
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/* x = |x| */
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sign = u.i >> 63;
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u.i &= (uint64_t)-1/2;
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x = u.f;
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w = u.i >> 32;
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/* x is INF or NaN */
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if (ix >= 0x7ff00000) {
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if (jx >= 0)
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return 1.0f/x + 1.0f; /* tanh(+-inf)=+-1 */
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else
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return 1.0f/x - 1.0f; /* tanh(NaN) = NaN */
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}
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if (ix < 0x40360000) { /* |x| < 22 */
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if (ix < 0x3e300000) { /* |x| < 2**-28 */
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/* tanh(tiny) = tiny with inexact */
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if (huge+x > 1.0f)
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return x;
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}
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if (ix >= 0x3ff00000) { /* |x| >= 1 */
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t = expm1(2.0f*fabs(x));
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z = 1.0f - 2.0f/(t+2.0f);
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if (w > 0x3fe193ea) {
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/* |x| > log(3)/2 ~= 0.5493 or nan */
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if (w > 0x40340000) {
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/* |x| > 20 or nan */
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/* note: this branch avoids raising overflow */
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/* raise inexact if x!=+-inf and handle nan */
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t = 1 + 0/(x + 0x1p-120f);
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} else {
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t = expm1(-2.0f*fabs(x));
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z= -t/(t+2.0f);
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t = expm1(2*x);
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t = 1 - 2/(t+2);
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}
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} else { /* |x| >= 22, return +-1 */
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z = 1.0f - tiny; /* raise inexact */
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} else if (w > 0x3fd058ae) {
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/* |x| > log(5/3)/2 ~= 0.2554 */
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t = expm1(2*x);
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t = t/(t+2);
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} else {
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/* |x| is small, up to 2ulp error in [0.1,0.2554] */
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t = expm1(-2*x);
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t = -t/(t+2);
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}
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return jx >= 0 ? z : -z;
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return sign ? -t : t;
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}
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@ -1,55 +1,35 @@
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/* origin: FreeBSD /usr/src/lib/msun/src/s_tanhf.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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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 "libm.h"
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static const float
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tiny = 1.0e-30,
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huge = 1.0e30;
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float tanhf(float x)
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{
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float t,z;
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int32_t jx,ix;
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union {float f; uint32_t i;} u = {.f = x};
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uint32_t w;
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int sign;
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float t;
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GET_FLOAT_WORD(jx, x);
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ix = jx & 0x7fffffff;
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/* x = |x| */
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sign = u.i >> 31;
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u.i &= 0x7fffffff;
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x = u.f;
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w = u.i;
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/* x is INF or NaN */
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if(ix >= 0x7f800000) {
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if (jx >= 0)
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return 1.0f/x + 1.0f; /* tanh(+-inf)=+-1 */
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else
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return 1.0f/x - 1.0f; /* tanh(NaN) = NaN */
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}
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if (ix < 0x41100000) { /* |x| < 9 */
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if (ix < 0x39800000) { /* |x| < 2**-12 */
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/* tanh(tiny) = tiny with inexact */
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if (huge+x > 1.0f)
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return x;
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}
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if (ix >= 0x3f800000) { /* |x|>=1 */
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t = expm1f(2.0f*fabsf(x));
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z = 1.0f - 2.0f/(t+2.0f);
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if (w > 0x3f0c9f54) {
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/* |x| > log(3)/2 ~= 0.5493 or nan */
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if (w > 0x41200000) {
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/* |x| > 10 */
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t = 1 + 0/(x + 0x1p-120f);
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} else {
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t = expm1f(-2.0f*fabsf(x));
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z = -t/(t+2.0f);
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t = expm1f(2*x);
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t = 1 - 2/(t+2);
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}
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} else { /* |x| >= 9, return +-1 */
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z = 1.0f - tiny; /* raise inexact */
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} else if (w > 0x3e82c578) {
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/* |x| > log(5/3)/2 ~= 0.2554 */
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t = expm1f(2*x);
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t = t/(t+2);
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} else {
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/* |x| is small */
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t = expm1f(-2*x);
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t = -t/(t+2);
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}
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return jx >= 0 ? z : -z;
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return sign ? -t : t;
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}
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@ -1,38 +1,3 @@
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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_tanhl.c */
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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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/* tanhl(x)
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* Return the Hyperbolic Tangent of x
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*
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* Method :
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* x -x
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* e - e
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* 0. tanhl(x) is defined to be -----------
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* x -x
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* e + e
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* 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
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* 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x)
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* -t
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* 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
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* t + 2
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* 2
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* 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
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* t + 2
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* 23.0 < x <= INF : tanhl(x) := 1.
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*
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* Special cases:
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* tanhl(NaN) is NaN;
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* only tanhl(0)=0 is exact for finite argument.
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*/
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#include "libm.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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@ -41,43 +6,40 @@ long double tanhl(long double x)
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return tanh(x);
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}
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#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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static const long double tiny = 1.0e-4900L;
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long double tanhl(long double x)
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{
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long double t,z;
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int32_t se;
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uint32_t jj0,jj1,ix;
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union {
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long double f;
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struct{uint64_t m; uint16_t se; uint16_t pad;} i;
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} u = {.f = x};
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unsigned ex = u.i.se & 0x7fff;
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unsigned sign = u.i.se & 0x8000;
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uint32_t w;
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long double t;
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/* High word of |x|. */
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GET_LDOUBLE_WORDS(se, jj0, jj1, x);
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ix = se & 0x7fff;
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/* x = |x| */
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u.i.se = ex;
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x = u.f;
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w = u.i.m >> 32;
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/* x is INF or NaN */
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if (ix == 0x7fff) {
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/* for NaN it's not important which branch: tanhl(NaN) = NaN */
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if (se & 0x8000)
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return 1.0/x-1.0; /* tanhl(-inf)= -1; */
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return 1.0/x+1.0; /* tanhl(+inf)= +1 */
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}
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/* |x| < 23 */
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if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {
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if ((ix|jj0|jj1) == 0) /* x == +- 0 */
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return x;
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if (ix < 0x3fc8) /* |x| < 2**-55 */
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return x*(1.0+tiny); /* tanh(small) = small */
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if (ix >= 0x3fff) { /* |x| >= 1 */
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t = expm1l(2.0*fabsl(x));
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z = 1.0 - 2.0/(t+2.0);
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if (ex > 0x3ffe || (ex == 0x3ffe && w > 0x8c9f53d5)) {
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/* |x| > log(3)/2 ~= 0.5493 or nan */
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if (ex >= 0x3fff+5) {
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/* |x| >= 32 */
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t = 1 + 0/(x + 0x1p-120f);
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} else {
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t = expm1l(-2.0*fabsl(x));
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z = -t/(t+2.0);
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t = expm1l(2*x);
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t = 1 - 2/(t+2);
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}
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/* |x| > 23, return +-1 */
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} else if (ex > 0x3ffd || (ex == 0x3ffd && w > 0x82c577d4)) {
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/* |x| > log(5/3)/2 ~= 0.2554 */
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t = expm1l(2*x);
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t = t/(t+2);
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} else {
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z = 1.0 - tiny; /* raise inexact flag */
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/* |x| is small */
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t = expm1l(-2*x);
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t = -t/(t+2);
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}
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return se & 0x8000 ? -z : z;
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return sign ? -t : t;
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}
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#endif
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