acosh.c

Go to the documentation of this file.

/* @(#)e_acosh.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_acosh.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 = 1.0,
ln2 = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */

/**
 * @brief     Inverse hyperbolic cosine function.
 * @version   1.3
 * @date      95/01/18
 * @details
 * <pre>
 * Method :
 *  Based on
 *      acosh(x) = log [ x + sqrt(x*x-1) ]
 *  we have
 *      acosh(x) := log(x)+ln2, if x is large; else
 *      acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
 *      acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
 *
 * Special cases:
 *  acosh(x) is NaN with signal if x<1.
 *  acosh(NaN) is NaN without 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 acosh(double x)
{
    double t;
    sword hx, lx;
    GET_HIGH_WORD(hx,x);
    GET_LOW_WORD(lx,x);

    if(hx<0x3ff00000) {     /* x < 1 */
        return (x-x)/(x-x);
    } else if(hx >=0x41b00000) {    /* x > 2**28 */
        if(hx >=0x7ff00000) {   /* x is inf of NaN */
            return x+x;
        } else
            return log(x)+ln2;  /* acosh(huge)=log(2x) */
    } else if(((hx-0x3ff00000)|lx)==0) {
        return 0.0;         /* acosh(1) = 0 */
    } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
        t=x*x;
        return log(2.0*x-one/(x+sqrt(t-one)));
    } else {            /* 1<x<2 */
        t = x-one;
        return log1p(t+sqrt(2.0*t+t*t));
    }
}