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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 filesrs-1.0
Szabolcs Nagy
14 years ago
3 changed files with 83 additions and 173 deletions
@ -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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GET_HIGH_WORD(jx, x); |
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ix = jx & 0x7fffffff; |
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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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/* 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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/* 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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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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