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

/* acoshl(x)
 * Method :
 *      Based on
 *              acoshl(x) = logl [ x + sqrtl(x*x-1) ]
 *      we have
 *              acoshl(x) := logl(x)+ln2,       if x is large; else
 *              acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
 *              acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
 *
 * Special cases:
 *      acoshl(x) is NaN with signal if x<1.
 *      acoshl(NaN) is NaN without signal.
 */

#include <math.h>

#include "math_private.h"

static const long double
one     = 1.0,
ln2     = 0.6931471805599453094172321214581766L;

long double
acoshl(long double x)
{
        long double t;
        u_int64_t lx;
        int64_t hx;
        GET_LDOUBLE_WORDS64(hx,lx,x);
        if(hx<0x3fff000000000000LL) {           /* x < 1 */
            return (x-x)/(x-x);
        } else if(hx >=0x4035000000000000LL) {  /* x > 2**54 */
            if(hx >=0x7fff000000000000LL) {     /* x is inf of NaN */
                return x+x;
            } else
                return logl(x)+ln2;     /* acoshl(huge)=logl(2x) */
        } else if(((hx-0x3fff000000000000LL)|lx)==0) {
            return 0.0L;                        /* acosh(1) = 0 */
        } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
            t=x*x;
            return logl(2.0L*x-one/(x+sqrtl(t-one)));
        } else {                        /* 1<x<2 */
            t = x-one;
            return log1pl(t+sqrtl(2.0L*t+t*t));
        }
}