e_atanh.c

/*
 *                               POK header
 * 
 * The following file is a part of the POK project. Any modification should
 * made according to the POK licence. You CANNOT use this file or a part of
 * this file is this part of a file for your own project
 *
 * For more information on the POK licence, please see our LICENCE FILE
 *
 * Please follow the coding guidelines described in doc/CODING_GUIDELINES
 *
 *                                      Copyright (c) 2007-2009 POK team 
 *
 * Created by julien on Fri Jan 30 14:41:34 2009 
 */

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

/* __ieee754_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.
 *
 */
#ifdef POK_NEEDS_LIBMATH

#include <libm.h>
#include "math_private.h"

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

static const double zero = 0.0;

double
__ieee754_atanh(double x)
{
        double t;
        int32_t hx,ix;
        uint32_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;
}
#endif