1/*
2 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26/* __ieee754_cosh(x)
27 * Method :
28 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
29 * 1. Replace x by |x| (cosh(x) = cosh(-x)).
30 * 2.
31 * [ exp(x) - 1 ]^2
32 * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
33 * 2*exp(x)
34 *
35 * exp(x) + 1/exp(x)
36 * ln2/2 <= x <= 22 : cosh(x) := -------------------
37 * 2
38 * 22 <= x <= lnovft : cosh(x) := exp(x)/2
39 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
40 * ln2ovft < x : cosh(x) := huge*huge (overflow)
41 *
42 * Special cases:
43 * cosh(x) is |x| if x is +INF, -INF, or NaN.
44 * only cosh(0)=1 is exact for finite x.
45 */
46
47#include "fdlibm.h"
48
49#ifdef __STDC__
50static const double one = 1.0, half=0.5, huge = 1.0e300;
51#else
52static double one = 1.0, half=0.5, huge = 1.0e300;
53#endif
54
55#ifdef __STDC__
56 double __ieee754_cosh(double x)
57#else
58 double __ieee754_cosh(x)
59 double x;
60#endif
61{
62 double t,w;
63 int ix;
64 unsigned lx;
65
66 /* High word of |x|. */
67 ix = __HI(x);
68 ix &= 0x7fffffff;
69
70 /* x is INF or NaN */
71 if(ix>=0x7ff00000) return x*x;
72
73 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
74 if(ix<0x3fd62e43) {
75 t = expm1(fabs(x));
76 w = one+t;
77 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
78 return one+(t*t)/(w+w);
79 }
80
81 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
82 if (ix < 0x40360000) {
83 t = __ieee754_exp(fabs(x));
84 return half*t+half/t;
85 }
86
87 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
88 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
89
90 /* |x| in [log(maxdouble), overflowthresold] */
91 lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
92 if (ix<0x408633CE ||
93 ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
94 w = __ieee754_exp(half*fabs(x));
95 t = half*w;
96 return t*w;
97 }
98
99 /* |x| > overflowthresold, cosh(x) overflow */
100 return huge*huge;
101}
102