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

/* tanhl(x)
 * Return the Hyperbolic Tangent of x
 *
 * Method :
 *                                      x    -x
 *                                     e  - e
 *      0. tanhl(x) is defined to be -----------
 *                                      x    -x
 *                                     e  + e
 *      1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
 *      2.  0      <= x <= 2**-55 : tanhl(x) := x*(one+x)
 *                                               -t
 *          2**-55 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
 *                                              t + 2
 *                                                    2
 *          1      <= x <=  23.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
 *                                                  t + 2
 *          23.0   <  x <= INF    : tanhl(x) := 1.
 *
 * Special cases:
 *      tanhl(NaN) is NaN;
 *      only tanhl(0)=0 is exact for finite argument.
 */

#include <math.h>

#include "math_private.h"

static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;

long double
tanhl(long double x)
{
        long double t,z;
        int32_t se;
        u_int32_t jj0,jj1,ix;

    /* High word of |x|. */
        GET_LDOUBLE_WORDS(se,jj0,jj1,x);
        ix = se&0x7fff;

    /* x is INF or NaN */
        if(ix==0x7fff) {
            /* for NaN it's not important which branch: tanhl(NaN) = NaN */
            if (se&0x8000) return one/x-one;    /* tanhl(-inf)= -1; */
            else           return one/x+one;    /* tanhl(+inf)=+1 */
        }

    /* |x| < 23 */
        if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {/* |x|<23 */
            if ((ix|jj0|jj1) == 0)
                return x;               /* x == +- 0 */
            if (ix<0x3fc8)              /* |x|<2**-55 */
                return x*(one+tiny);    /* tanh(small) = small */
            if (ix>=0x3fff) {   /* |x|>=1  */
                t = expm1l(two*fabsl(x));
                z = one - two/(t+two);
            } else {
                t = expm1l(-two*fabsl(x));
                z= -t/(t+two);
            }
    /* |x| > 23, return +-1 */
        } else {
            z = one - tiny;             /* raised inexact flag */
        }
        return (se&0x8000)? -z: z;
}