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 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __coshl = coshl
32
33 #include "libm.h"
34 #include "longdouble.h"
35
36 /*
37 * COSH(X)
38 * RETURN THE HYPERBOLIC COSINE OF X
39 *
40 * Method :
41 * 1. Replace x by |x| (COSH(x) = COSH(-x)).
42 * 2.
43 * [ EXP(x) - 1 ]^2
44 * 0 <= x <= 0.3465 : COSH(x) := 1 + -------------------
45 * 2*EXP(x)
46 *
47 * EXP(x) + 1/EXP(x)
48 * 0.3465 <= x <= thresh : COSH(x) := -------------------
49 * 2
50 * thresh <= x <= lnovft : COSH(x) := EXP(x)/2
51 * lnovft <= x < INF : COSH(x) := SCALBN(EXP(x-MEP1*ln2),ME)
52 *
53 *
54 * here
55 * 0.3465 a number that is near one half of ln2.
56 * thresh a number such that
57 * EXP(thresh)+EXP(-thresh)=EXP(thresh)
58 * lnovft logarithm of the overflow threshold
59 * = MEP1*ln2 chopped to machine precision.
60 * ME maximum exponent
61 * MEP1 maximum exponent plus 1
62 *
63 * Special cases:
64 * COSH(x) is |x| if x is +INF, -INF, or NaN.
65 * only COSH(0)=1 is exact for finite x.
66 */
67
68 static const long double C[] = {
69 0.5L,
70 1.0L,
71 0.3465L,
72 45.0L,
73 1.135652340629414394879149e+04L,
74 7.004447686242549087858985e-16L,
75 2.710505431213761085018632e-20L, /* 2^-65 */
76 };
77
78 #define half C[0]
79 #define one C[1]
80 #define thr1 C[2]
81 #define thr2 C[3]
82 #define lnovft C[4]
83 #define lnovlo C[5]
84 #define tinyl C[6]
85
86 long double
87 coshl(long double x)
88 {
89 long double w, t;
90
91 w = fabsl(x);
92
93 if (!finitel(w))
94 return (w + w); /* x is INF or NaN */
95
96 if (w < thr1) {
97 if (w < tinyl)
98 return (one + w); /* inexact+directed rounding */
99
100 t = expm1l(w);
101 w = one + t;
102 w = one + (t * t) / (w + w);
103 return (w);
104 }
105
106 if (w < thr2) {
107 t = expl(w);
108 return (half * (t + one / t));
109 }
110
111 if (w <= lnovft)
112 return (half * expl(w));
113
114 return (scalbnl(expl((w - lnovft) - lnovlo), 16383));
115 }