# e_acosh.c   [plain text]

/* @(#)e_acosh.c 5.1 93/09/24 */
/*
* ====================================================
*
* 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.
* ====================================================
*/

#include <sys/cdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("\$NetBSD: e_acosh.c,v 1.11 1999/07/02 15:37:38 simonb Exp \$");
#endif

/* __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 double
one	= 1.0,
ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */

#define __ieee754_log log
#define __ieee754_sqrt sqrt

double acosh(double x)
{
double t;
int32_t hx;
u_int32_t lx;
EXTRACT_WORDS(hx,lx,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)|lx)==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+__ieee754_sqrt(t-one)));
} else {			/* 1<x<2 */
t = x-one;
return log1p(t+sqrt(2.0*t+t*t));
}
}