e_acoshl.c revision 2116 
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[] = "$Id: e_acosh.c,v 1.6 1994/08/18 23:04:54 jtc Exp $";
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
34#ifdef __STDC__
35static const double
36#else
37static double
38#endif
39one	= 1.0,
40ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
41
42#ifdef __STDC__
43	double __ieee754_acosh(double x)
44#else
45	double __ieee754_acosh(x)
46	double x;
47#endif
48{
49	double t;
50	int32_t hx;
51	u_int32_t lx;
52	EXTRACT_WORDS(hx,lx,x);
53	if(hx<0x3ff00000) {		/* x < 1 */
54	    return (x-x)/(x-x);
55	} else if(hx >=0x41b00000) {	/* x > 2**28 */
56	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
57	        return x+x;
58	    } else
59		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
60	} else if(((hx-0x3ff00000)|lx)==0) {
61	    return 0.0;			/* acosh(1) = 0 */
62	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
63	    t=x*x;
64	    return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
65	} else {			/* 1<x<2 */
66	    t = x-one;
67	    return log1p(t+sqrt(2.0*t+t*t));
68	}
69}
70