1
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, 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
14/* acosh(x)
15 * Method :
16 *	Based on
17 *		acosh(x) = log [ x + sqrt(x*x-1) ]
18 *	we have
19 *		acosh(x) := log(x)+ln2,	if x is large; else
20 *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
21 *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
22 *
23 * Special cases:
24 *	acosh(x) is NaN with signal if x<1.
25 *	acosh(NaN) is NaN without signal.
26 */
27
28#include <float.h>
29
30#include "math.h"
31#include "math_private.h"
32
33static const double
34one	= 1.0,
35ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
36
37double
38acosh(double x)
39{
40	double t;
41	int32_t hx;
42	u_int32_t lx;
43	EXTRACT_WORDS(hx,lx,x);
44	if(hx<0x3ff00000) {		/* x < 1 */
45	    return (x-x)/(x-x);
46	} else if(hx >=0x41b00000) {	/* x > 2**28 */
47	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
48	        return x+x;
49	    } else
50		return log(x)+ln2;	/* acosh(huge)=log(2x) */
51	} else if(((hx-0x3ff00000)|lx)==0) {
52	    return 0.0;			/* acosh(1) = 0 */
53	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
54	    t=x*x;
55	    return log(2.0*x-one/(x+sqrt(t-one)));
56	} else {			/* 1<x<2 */
57	    t = x-one;
58	    return log1p(t+sqrt(2.0*t+t*t));
59	}
60}
61
62#if LDBL_MANT_DIG == 53
63__weak_reference(acosh, acoshl);
64#endif
65