atanh.c

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/* @(#)e_atanh.c 1.3 95/01/18 */

/*
 * Copyright (c) 2015-2017 Carsten Sonne Larsen  <cs@innolan.dk>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * The origin source code can be obtained from:
 * http://www.netlib.org/fdlibm/e_atanh.c
 * 
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 *
 */

#include "prim.h"
#include "math.h"

#ifdef _WIN32
#pragma warning( disable : 4146 )
#endif

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

/**
 * @brief   Inverse hyperbolic tangent function.
 * @version 1.3
 * @date    95/01/18
 * @details
 * <pre>
 * 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.
 * </pre>
 * @copyright Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 * @license   Developed at SunSoft, a Sun Microsystems, Inc. business. Permission
 *            to use, copy, modify, and distribute this software is freely granted,
 *            provided that this notice is preserved.
 */

double atanh(double x)
{
    double t;
    sword hx,ix;
    uword lx;
    GET_HIGH_WORD(hx,x);
    GET_LOW_WORD(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);       /* x <- |x| */
    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;
}