1/* @(#)e_acosh.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13#include <sys/cdefs.h>
14#if defined(LIBM_SCCS) && !defined(lint)
15__RCSID("$NetBSD: e_acosh.c,v 1.11 1999/07/02 15:37:38 simonb Exp $");
16#endif
17
18/* __ieee754_acosh(x)
19 * Method :
20 *	Based on
21 *		acosh(x) = log [ x + sqrt(x*x-1) ]
22 *	we have
23 *		acosh(x) := log(x)+ln2,	if x is large; else
24 *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
25 *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
26 *
27 * Special cases:
28 *	acosh(x) is NaN with signal if x<1.
29 *	acosh(NaN) is NaN without signal.
30 */
31
32#include "math.h"
33#include "math_private.h"
34
35static const double
36one	= 1.0,
37ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
38
39double
40__ieee754_acosh(double x)
41{
42	double t;
43	int32_t hx;
44	u_int32_t lx;
45	EXTRACT_WORDS(hx,lx,x);
46	if(hx<0x3ff00000) {		/* x < 1 */
47	    return (x-x)/(x-x);
48	} else if(hx >=0x41b00000) {	/* x > 2**28 */
49	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
50	        return x+x;
51	    } else
52		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
53	} else if(((hx-0x3ff00000)|lx)==0) {
54	    return 0.0;			/* acosh(1) = 0 */
55	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
56	    t=x*x;
57	    return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
58	} else {			/* 1<x<2 */
59	    t = x-one;
60	    return log1p(t+sqrt(2.0*t+t*t));
61	}
62}
63