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/* e_acoshl.c -- long double version of e_acosh.c.

 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.

 */

/*

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

 * 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.

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

 */

/* __ieee754_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 "quadmath-imp.h"

static const __float128

one     = 1.0Q,

ln2     = 0.6931471805599453094172321214581766Q;

__float128

acoshq (__float128 x)

{

        __float128 t;

        uint64_t lx;

        int64_t hx;

        GET_FLT128_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 logq(x)+ln2;     /* acoshl(huge)=logl(2x) */

        } else if(((hx-0x3fff000000000000LL)|lx)==0) {

            return 0.0Q;                        /* acosh(1) = 0 */

        } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */

            t=x*x;

            return logq(2.0Q*x-one/(x+sqrtq(t-one)));

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

            t = x-one;

            return log1pq(t+sqrtq(2.0Q*t+t*t));

        }

}