asinh.c

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/* @(#)s_asinh.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/s_asinh.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"

static const double
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
huge=  1.00000000000000000000e+300;

/**
 * @brief     Inverse hyperbolic sine function.
 * @version   1.3
 * @date      95/01/18
 * @details
 * <pre>
 * Method :
 *  Based on
 *      asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
 *  we have
 *  asinh(x) := x  if  1+x*x=1,
 *       := sign(x)*(log(x)+ln2)) for large |x|, else
 *       := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
 *       := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
 * </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 asinh(double x)
{
    double t,w;
    sword hx,ix;
    GET_HIGH_WORD(hx,x);
    ix = hx&0x7fffffff;
    if(ix>=0x7ff00000) return x+x;  /* x is inf or NaN */
    if(ix< 0x3e300000) {    /* |x|<2**-28 */
        if(huge+x>one) return x;    /* return x inexact except 0 */
    }
    if(ix>0x41b00000) { /* |x| > 2**28 */
        w = log(fabs(x))+ln2;
    } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
        t = fabs(x);
        w = log(2.0*t+one/(sqrt(x*x+one)+t));
    } else {        /* 2.0 > |x| > 2**-28 */
        t = x*x;
        w =log1p(fabs(x)+t/(one+sqrt(one+t)));
    }
    if(hx>0) return w;
    else return -w;
}