1/*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22/*
23 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24 */
25/*
26 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27 * Use is subject to license terms.
28 */
29
30#pragma weak __acosh = acosh
31
32/* INDENT OFF */
33/*
34 * acosh(x)
35 * Method :
36 *	Based on
37 *		acosh(x) = log [ x + sqrt(x*x-1) ]
38 *	we have
39 *		acosh(x) := log(x)+ln2,	if x is large; else
40 *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x > 2; else
41 *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t = x-1.
42 *
43 * Special cases:
44 *	acosh(x) is NaN with signal if x < 1.
45 *	acosh(NaN) is NaN without signal.
46 */
47/* INDENT ON */
48
49#include "libm_protos.h"	/* _SVID_libm_error */
50#include "libm_macros.h"
51#include <math.h>
52
53static const double
54	one = 1.0,
55	ln2 = 6.93147180559945286227e-01;	/* 3FE62E42, FEFA39EF */
56
57double
58acosh(double x) {
59	double t;
60	int hx;
61
62	hx = ((int *) &x)[HIWORD];
63	if (hx < 0x3ff00000) {	/* x < 1 */
64		if (isnan(x))
65#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
66			return (hx >= 0xfff80000 ? x : (x - x) / (x - x));
67			/* assumes sparc-like QNaN */
68#else
69			return (x - x) / (x - x);
70#endif
71		else
72			return (_SVID_libm_err(x, x, 29));
73	} else if (hx >= 0x41b00000) {
74		/* x > 2**28 */
75		if (hx >= 0x7ff00000) {	/* x is inf of NaN */
76#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
77			return (hx >= 0x7ff80000 ? x : x + x);
78			/* assumes sparc-like QNaN */
79#else
80			return (x + x);
81#endif
82		} else	/* acosh(huge)=log(2x) */
83			return (log(x) + ln2);
84	} else if (((hx - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) {
85		return (0.0);	/* acosh(1) = 0 */
86	} else if (hx > 0x40000000) {
87		/* 2**28 > x > 2 */
88		t = x * x;
89		return (log(2.0 * x - one / (x + sqrt(t - one))));
90	} else {
91		/* 1 < x < 2 */
92		t = x - one;
93		return (log1p(t + sqrt(2.0 * t + t * t)));
94	}
95}
96