s_tanh.c

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/* @(#)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.
 * ====================================================
 */

/* 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;
}