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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 #pragma weak __cosh = cosh
30
31 /* INDENT OFF */
32 /*
33 * cosh(x)
34 * Code originated from 4.3bsd.
35 * Modified by K.C. Ng for SUN 4.0 libm.
36 * Method :
37 * 1. Replace x by |x| (cosh(x) = cosh(-x)).
38 * 2.
39 * [ exp(x) - 1 ]^2
40 * 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
41 * 2*exp(x)
42 *
43 * exp(x) + 1/exp(x)
44 * 0.3465 <= x <= 22 : cosh(x) := -------------------
45 * 2
46 * 22 <= x <= lnovft : cosh(x) := exp(x)/2
47 * lnovft <= x < INF : cosh(x) := scalbn(exp(x-1024*ln2),1023)
48 *
49 * Note: .3465 is a number near one half of ln2.
50 *
51 * Special cases:
52 * cosh(x) is |x| if x is +INF, -INF, or NaN.
53 * only cosh(0)=1 is exact for finite x.
54 */
55 /* INDENT ON */
56
57 #include "libm.h"
58
59 static const double
60 ln2 = 6.93147180559945286227e-01,
61 ln2hi = 6.93147180369123816490e-01,
62 ln2lo = 1.90821492927058770002e-10,
63 lnovft = 7.09782712893383973096e+02;
64
65 double
cosh(double x)66 cosh(double x) {
67 double t, w;
68
69 w = fabs(x);
70 if (!finite(w))
71 return (w * w);
72 if (w < 0.3465) {
73 t = expm1(w);
74 w = 1.0 + t;
75 if (w != 1.0)
76 w = 1.0 + (t * t) / (w + w);
77 return (w);
78 } else if (w < 22.0) {
79 t = exp(w);
80 return (0.5 * (t + 1.0 / t));
81 } else if (w <= lnovft) {
82 return (0.5 * exp(w));
83 } else {
84 w = (w - 1024 * ln2hi) - 1024 * ln2lo;
85 if (w >= ln2)
86 return (_SVID_libm_err(x, x, 5));
87 else
88 return (scalbn(exp(w), 1023));
89 }
90 }
91