0,0 → 1,87 |
/* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */ |
/* @(#)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. |
* ==================================================== |
*/ |
|
#if defined(LIBM_SCCS) && !defined(lint) |
static char rcsid[] = "$Id: s_tanh.c,v 1.5 1994/08/18 23:10:22 jtc 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" |
|
#ifdef __STDC__ |
static const double one=1.0, two=2.0, tiny = 1.0e-300; |
#else |
static double one=1.0, two=2.0, tiny = 1.0e-300; |
#endif |
|
#ifdef __STDC__ |
double tanh(double x) |
#else |
double tanh(x) |
double x; |
#endif |
{ |
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; |
} |