1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /*
13 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
14 *
15 * Permission to use, copy, modify, and distribute this software for any
16 * purpose with or without fee is hereby granted, provided that the above
17 * copyright notice and this permission notice appear in all copies.
18 *
19 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
20 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
21 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
22 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
23 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
24 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
25 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
26 */
27
28 /* coshl(x)
29 * Method :
30 * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
31 * 1. Replace x by |x| (coshl(x) = coshl(-x)).
32 * 2.
33 * [ exp(x) - 1 ]^2
34 * 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
35 * 2*exp(x)
36 *
37 * exp(x) + 1/exp(x)
38 * ln2/2 <= x <= 22 : coshl(x) := -------------------
39 * 2
40 * 22 <= x <= lnovft : coshl(x) := expl(x)/2
41 * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2)
42 * ln2ovft < x : coshl(x) := huge*huge (overflow)
43 *
44 * Special cases:
45 * coshl(x) is |x| if x is +INF, -INF, or NaN.
46 * only coshl(0)=1 is exact for finite x.
47 */
48
49 static const long double one = 1.0L, half = 0.5L, huge = 1.0e4900L,
50 ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
51
52 long double
coshl(long double x)53 coshl(long double x)
54 {
55 long double t, w;
56 int32_t ex;
57 ieee_quad_shape_type u;
58
59 u.value = x;
60 ex = u.parts32.mswhi & 0x7fffffff;
61
62 /* Absolute value of x. */
63 u.parts32.mswhi = ex;
64
65 /* x is INF or NaN */
66 if (ex >= 0x7fff0000)
67 return x * x;
68
69 /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
70 if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
71 {
72 if (ex < 0x3fb80000) /* |x| < 2^-116 */
73 return one; /* cosh(tiny) = 1 */
74 t = expm1l (u.value);
75 w = one + t;
76
77 return one + (t * t) / (w + w);
78 }
79
80 /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
81 if (ex < 0x40044000)
82 {
83 t = expl (u.value);
84 return half * t + half / t;
85 }
86
87 /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
88 if (ex <= 0x400c62e3) /* 11356.375 */
89 return half * expl (u.value);
90
91 /* |x| in [log(maxdouble), overflowthresold] */
92 if (u.value <= ovf_thresh)
93 {
94 w = expl (half * u.value);
95 t = half * w;
96 return t * w;
97 }
98
99 /* |x| > overflowthresold, cosh(x) overflow */
100 return __math_oflowl(0);
101 }
102
