e_atanh.c

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

/* atanh(x)
 * Method :
 *    1.Reduced x to positive by atanh(-x) = -atanh(x)
 *    2.For x>=0.5
 *                  1              2x                          x
 *  atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
 *                  2             1 - x                      1 - x
 *  
 *  For x<0.5
 *  atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
 *
 * Special cases:
 *  atanh(x) is NaN if |x| > 1 with signal;
 *  atanh(NaN) is that NaN with no signal;
 *  atanh(+-1) is +-INF with signal.
 *
 */

#include "math.h"
#include "math_private.h"

static const double one = 1.0, huge = 1e300;
static const double zero = 0.0;

double
atanh(double x)
{
    double t;
    int32_t hx,ix;
    u_int32_t lx;
    EXTRACT_WORDS(hx,lx,x);
    ix = hx&0x7fffffff;
    if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
        return (x-x)/(x-x);
    if(ix==0x3ff00000) 
        return x/zero;
    if(ix<0x3e300000&&(huge+x)>zero) return x;  /* x<2**-28 */
    SET_HIGH_WORD(x,ix);
    if(ix<0x3fe00000) {     /* x < 0.5 */
        t = x+x;
        t = 0.5*log1p(t+t*x/(one-x));
    } else 
        t = 0.5*log1p((x+x)/(one-x));
    if(hx>=0) return t; else return -t;
}