/* @(#)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.

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

 */

/* __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>

static const long double

one	= 1.0L,

ln2	= M_LN2l;

long double

__ieee754_acoshl(long double x)

{

	long double t;

	int64_t hx;

	uint64_t lx;

	double xhi, xlo;

	ldbl_unpack (x, &xhi, &xlo;;

	EXTRACT_WORDS64 (hx, xhi);

	EXTRACT_WORDS64 (lx, xlo);

	if(hx<0x3ff0000000000000LL) {		/* x < 1 */

	    return (x-x)/(x-x);

	} else if(hx >=0x4370000000000000LL) {	/* x >= 2**56 */

	    if(hx >=0x7ff0000000000000LL) {	/* x is inf of NaN */

		return x+x;

	    } else

		return __ieee754_logl(x)+ln2;	/* acosh(huge)=log(2x) */

	} else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) {

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

	} else if (hx > 0x4000000000000000LL) {	/* 2**56 > x > 2 */

	    t=x*x;

	    return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one)));

	} else {			/* 1

	    t = x-one;

	    return __log1pl(t+sqrtl(2.0*t+t*t));

	}

}

strong_alias (__ieee754_acoshl, __acoshl_finite)