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math: tanh.c cleanup similar to sinh, cosh

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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 files
This commit is contained in:
Szabolcs Nagy
2012-12-16 19:52:42 +01:00
parent f143458223
commit e42a977fe5
3 changed files with 83 additions and 173 deletions
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94
src/math/tanh.c
View File

@ -1,73 +1,41 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_tanh.c */
/*
* ====================================================
* 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.
* ====================================================
*/
/* Tanh(x)
* Return the Hyperbolic Tangent of x
*
* Method :
* x -x
* e - e
* 0. tanh(x) is defined to be -----------
* x -x
* e + e
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
* 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0
* -t
* 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
* t + 2
* 2
* 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
* t + 2
* 22 <= x <= INF : tanh(x) := 1.
*
* Special cases:
* tanh(NaN) is NaN;
* only tanh(0)=0 is exact for finite argument.
*/
#include "libm.h"
static const double tiny = 1.0e-300, huge = 1.0e300;
/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
* = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
* = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
*/
double tanh(double x)
{
double t,z;
int32_t jx,ix;
union {double f; uint64_t i;} u = {.f = x};
uint32_t w;
int sign;
double t;
GET_HIGH_WORD(jx, x);
ix = jx & 0x7fffffff;
/* x = |x| */
sign = u.i >> 63;
u.i &= (uint64_t)-1/2;
x = u.f;
w = u.i >> 32;
/* x is INF or NaN */
if (ix >= 0x7ff00000) {
if (jx >= 0)
return 1.0f/x + 1.0f; /* tanh(+-inf)=+-1 */
else
return 1.0f/x - 1.0f; /* tanh(NaN) = NaN */
}
if (ix < 0x40360000) { /* |x| < 22 */
if (ix < 0x3e300000) { /* |x| < 2**-28 */
/* tanh(tiny) = tiny with inexact */
if (huge+x > 1.0f)
return x;
}
if (ix >= 0x3ff00000) { /* |x| >= 1 */
t = expm1(2.0f*fabs(x));
z = 1.0f - 2.0f/(t+2.0f);
if (w > 0x3fe193ea) {
/* |x| > log(3)/2 ~= 0.5493 or nan */
if (w > 0x40340000) {
/* |x| > 20 or nan */
/* note: this branch avoids raising overflow */
/* raise inexact if x!=+-inf and handle nan */
t = 1 + 0/(x + 0x1p-120f);
} else {
t = expm1(-2.0f*fabs(x));
z= -t/(t+2.0f);
t = expm1(2*x);
t = 1 - 2/(t+2);
}
} else { /* |x| >= 22, return +-1 */
z = 1.0f - tiny; /* raise inexact */
} else if (w > 0x3fd058ae) {
/* |x| > log(5/3)/2 ~= 0.2554 */
t = expm1(2*x);
t = t/(t+2);
} else {
/* |x| is small, up to 2ulp error in [0.1,0.2554] */
t = expm1(-2*x);
t = -t/(t+2);
}
return jx >= 0 ? z : -z;
return sign ? -t : t;
}