e_acosh.c

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

/* acosh(x)
 * 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.
 */

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

static const double 
one = 1.0,
ln2 = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */

double
acosh(double x)
{   
    double t;
    int32_t hx;
    u_int32_t lx;
    EXTRACT_WORDS(hx,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));
    }
}