# shithub: 9ferno

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```/* derived from /netlib/fdlibm */

/* @(#)s_tanh.c 1.3 95/01/18 */
/*
* ====================================================
*
* Developed at SunSoft, 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**-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"

static const double one=1.0, two=2.0, tiny = 1.0e-300;

double tanh(double x)
{
double t,z;
int jx,ix;

/* High word of |x|. */
jx = __HI(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;
}
```