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
53 static const double
54 one = 1.0,
55 ln2 = 6.93147180559945286227e-01; /* 3FE62E42, FEFA39EF */
56
57 double
acosh(double x)58 acosh(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