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/* @(#)e_acosh.c 5.1 93/09/24 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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#ifndef lint
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static char rcsid[] = "$\Id: e_acosh.c,v 1.2 1995/05/30 05:47:53 rgrimes Exp $";
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#endif
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/* __ieee754_acosh(x)
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 * Method :
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 *      Based on
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 *              acosh(x) = log [ x + sqrt(x*x-1) ]
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 *      we have
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 *              acosh(x) := log(x)+ln2, if x is large; else
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 *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
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 *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
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 *
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 * Special cases:
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 *      acosh(x) is NaN with signal if x<1.
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 *      acosh(NaN) is NaN without signal.
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 */
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#include "math.h"
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#include "math_private.h"
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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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one     = 1.0,
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ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
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#ifdef __STDC__
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        double __ieee754_acosh(double x)
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#else
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        double __ieee754_acosh(x)
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        double x;
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#endif
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{
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        double t;
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        int32_t hx;
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        u_int32_t lx;
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        EXTRACT_WORDS(hx,lx,x);
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        if(hx<0x3ff00000) {             /* x < 1 */
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            return (x-x)/(x-x);
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        } else if(hx >=0x41b00000) {    /* x > 2**28 */
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            if(hx >=0x7ff00000) {       /* x is inf of NaN */
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                return x+x;
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            } else
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                return __ieee754_log(x)+ln2;    /* acosh(huge)=log(2x) */
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        } else if(((hx-0x3ff00000)|lx)==0) {
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            return 0.0;                 /* acosh(1) = 0 */
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        } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
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            t=x*x;
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            return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
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        } else {                        /* 1<x<2 */
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            t = x-one;
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            return log1p(t+sqrt(2.0*t+t*t));
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        }
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}