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