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