e_acosh.c revision 1dc9e472e19acfe6dc7f41e429236e7eef7ceda1 
1
2/* @(#)e_acosh.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 *
13 */
14
15#ifndef lint
16static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_acosh.c,v 1.8 2005/02/04 18:26:05 das Exp $";
17#endif
18
19/* __ieee754_acosh(x)
20 * Method :
21 *	Based on
22 *		acosh(x) = log [ x + sqrt(x*x-1) ]
23 *	we have
24 *		acosh(x) := log(x)+ln2,	if x is large; else
25 *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
26 *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
27 *
28 * Special cases:
29 *	acosh(x) is NaN with signal if x<1.
30 *	acosh(NaN) is NaN without signal.
31 */
32
33#include "math.h"
34#include "math_private.h"
35
36static const double
37one	= 1.0,
38ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
39
40double
41__ieee754_acosh(double x)
42{
43	double t;
44	int32_t hx;
45	u_int32_t lx;
46	EXTRACT_WORDS(hx,lx,x);
47	if(hx<0x3ff00000) {		/* x < 1 */
48	    return (x-x)/(x-x);
49	} else if(hx >=0x41b00000) {	/* x > 2**28 */
50	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
51	        return x+x;
52	    } else
53		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
54	} else if(((hx-0x3ff00000)|lx)==0) {
55	    return 0.0;			/* acosh(1) = 0 */
56	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
57	    t=x*x;
58	    return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
59	} else {			/* 1<x<2 */
60	    t = x-one;
61	    return log1p(t+sqrt(2.0*t+t*t));
62	}
63}
64