/* @(#)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 <LibConfig.h> | |
#include <sys/EfiCdefs.h> | |
#if defined(LIBM_SCCS) && !defined(lint) | |
__RCSID("$NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $"); | |
#endif | |
/* 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**-55 : tanh(x) := x*(one+x) | |
* -t | |
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) | |
* t + 2 | |
* 2 | |
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) | |
* t + 2 | |
* 22.0 < x <= INF : tanh(x) := 1. | |
* | |
* Special cases: | |
* tanh(NaN) is NaN; | |
* only tanh(0)=0 is exact for finite argument. | |
*/ | |
#include "math.h" | |
#include "math_private.h" | |
static const double one=1.0, two=2.0, tiny = 1.0e-300; | |
double | |
tanh(double x) | |
{ | |
double t,z; | |
int32_t jx,ix; | |
/* High word of |x|. */ | |
GET_HIGH_WORD(jx,x); | |
ix = jx&0x7fffffff; | |
/* x is INF or NaN */ | |
if(ix>=0x7ff00000) { | |
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ | |
else return one/x-one; /* tanh(NaN) = NaN */ | |
} | |
/* |x| < 22 */ | |
if (ix < 0x40360000) { /* |x|<22 */ | |
if (ix<0x3c800000) /* |x|<2**-55 */ | |
return x*(one+x); /* tanh(small) = small */ | |
if (ix>=0x3ff00000) { /* |x|>=1 */ | |
t = expm1(two*fabs(x)); | |
z = one - two/(t+two); | |
} else { | |
t = expm1(-two*fabs(x)); | |
z= -t/(t+two); | |
} | |
/* |x| > 22, return +-1 */ | |
} else { | |
z = one - tiny; /* raised inexact flag */ | |
} | |
return (jx>=0)? z: -z; | |
} |