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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.

 * ====================================================

 */

#if defined(LIBM_SCCS) && !defined(lint)

static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $";

#endif

/* __ieee754_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"

#ifdef __STDC__

static const double

#else

static double

#endif

one     = 1.0,

ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */

#ifdef __STDC__

        double __ieee754_acosh(double x)

#else

        double __ieee754_acosh(x)

        double x;

#endif

{

        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 __ieee754_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 __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));

        } else {                        /* 1<x<2 */

            t = x-one;

            return log1p(t+sqrt(2.0*t+t*t));

        }

}