e_acosh.c revision 97407 
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#ifndef lint
14static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_acosh.c 97407 2002-05-28 17:03:12Z alfred $";
15#endif
16
17/* __ieee754_acosh(x)
18 * Method :
19 *	Based on
20 *		acosh(x) = log [ x + sqrt(x*x-1) ]
21 *	we have
22 *		acosh(x) := log(x)+ln2,	if x is large; else
23 *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
24 *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
25 *
26 * Special cases:
27 *	acosh(x) is NaN with signal if x<1.
28 *	acosh(NaN) is NaN without signal.
29 */
30
31#include "math.h"
32#include "math_private.h"
33
34static const double
35one	= 1.0,
36ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
37
38double
39__ieee754_acosh(double x)
40{
41	double t;
42	int32_t hx;
43	u_int32_t lx;
44	EXTRACT_WORDS(hx,lx,x);
45	if(hx<0x3ff00000) {		/* x < 1 */
46	    return (x-x)/(x-x);
47	} else if(hx >=0x41b00000) {	/* x > 2**28 */
48	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
49	        return x+x;
50	    } else
51		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
52	} else if(((hx-0x3ff00000)|lx)==0) {
53	    return 0.0;			/* acosh(1) = 0 */
54	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
55	    t=x*x;
56	    return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
57	} else {			/* 1<x<2 */
58	    t = x-one;
59	    return log1p(t+__ieee754_sqrt(2.0*t+t*t));
60	}
61}
62