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/* 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 one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300;
double tanh(double x)
{
double t,z;
int32_t jx,ix;
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 */
}
if (ix < 0x40360000) { /* |x| < 22 */
if (ix < 0x3e300000) { /* |x| < 2**-28 */
/* tanh(tiny) = tiny with inexact */
if (huge+x > one)
return x;
}
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);
}
} else { /* |x| >= 22, return +-1 */
z = one - tiny; /* raise inexact */
}
return jx >= 0 ? z : -z;
}
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