/* @(#)e_acosh.c 1.3 95/01/18 */

/*

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

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunSoft, 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 "fdlibm.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;

	int hx;

	hx = __HI(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)|__LO(x))==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+sqrt(t-one)));

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

	    t = x-one;

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

	}

}