120 lines
2.6 KiB
C
120 lines
2.6 KiB
C
|
|
/* @(#)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.
|
|
* ====================================================
|
|
*/
|
|
|
|
/*
|
|
|
|
FUNCTION
|
|
<<tanh>>, <<tanhf>>---hyperbolic tangent
|
|
|
|
INDEX
|
|
tanh
|
|
INDEX
|
|
tanhf
|
|
|
|
SYNOPSIS
|
|
#include <math.h>
|
|
double tanh(double <[x]>);
|
|
float tanhf(float <[x]>);
|
|
|
|
DESCRIPTION
|
|
|
|
<<tanh>> computes the hyperbolic tangent of
|
|
the argument <[x]>. Angles are specified in radians.
|
|
|
|
<<tanh(<[x]>)>> is defined as
|
|
. sinh(<[x]>)/cosh(<[x]>)
|
|
|
|
<<tanhf>> is identical, save that it takes and returns <<float>> values.
|
|
|
|
RETURNS
|
|
The hyperbolic tangent of <[x]> is returned.
|
|
|
|
PORTABILITY
|
|
<<tanh>> is ANSI C. <<tanhf>> is an extension.
|
|
|
|
*/
|
|
|
|
/* 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 "fdlibm.h"
|
|
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
|
|
#ifdef __STDC__
|
|
static const volatile double one=1.0, two=2.0, tiny = 1.0e-300;
|
|
#else
|
|
static double volatile 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;
|
|
}
|
|
|
|
#endif /* _DOUBLE_IS_32BITS */
|