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 /* Changes for 128-bit long double are
13 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
14 and are incorporated herein by permission of the author. The author
15 reserves the right to distribute this material elsewhere under different
16 copying permissions. These modifications are distributed here under
17 the following terms:
18
19 This library is free software; you can redistribute it and/or
20 modify it under the terms of the GNU Lesser General Public
21 License as published by the Free Software Foundation; either
22 version 2.1 of the License, or (at your option) any later version.
23
24 This library is distributed in the hope that it will be useful,
25 but WITHOUT ANY WARRANTY; without even the implied warranty of
26 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
27 Lesser General Public License for more details.
28
29 You should have received a copy of the GNU Lesser General Public
30 License along with this library; if not, see
31 <http://www.gnu.org/licenses/>. */
32
33 /* coshq(x)
34 * Method :
35 * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
36 * 1. Replace x by |x| (coshl(x) = coshl(-x)).
37 * 2.
38 * [ exp(x) - 1 ]^2
39 * 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
40 * 2*exp(x)
41 *
42 * exp(x) + 1/exp(x)
43 * ln2/2 <= x <= 22 : coshl(x) := -------------------
44 * 2
45 * 22 <= x <= lnovft : coshl(x) := expq(x)/2
46 * lnovft <= x <= ln2ovft: coshl(x) := expq(x/2)/2 * expq(x/2)
47 * ln2ovft < x : coshl(x) := huge*huge (overflow)
48 *
49 * Special cases:
50 * coshl(x) is |x| if x is +INF, -INF, or NaN.
51 * only coshl(0)=1 is exact for finite x.
52 */
53
54 #include "quadmath-imp.h"
55
56 static const __float128 one = 1.0, half = 0.5, huge = 1.0e4900Q,
57 ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
58
59 __float128
coshq(__float128 x)60 coshq (__float128 x)
61 {
62 __float128 t, w;
63 int32_t ex;
64 ieee854_float128 u;
65
66 u.value = x;
67 ex = u.words32.w0 & 0x7fffffff;
68
69 /* Absolute value of x. */
70 u.words32.w0 = ex;
71
72 /* x is INF or NaN */
73 if (ex >= 0x7fff0000)
74 return x * x;
75
76 /* |x| in [0,0.5*ln2], return 1+expm1q(|x|)^2/(2*expq(|x|)) */
77 if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
78 {
79 if (ex < 0x3fb80000) /* |x| < 2^-116 */
80 return one; /* cosh(tiny) = 1 */
81 t = expm1q (u.value);
82 w = one + t;
83
84 return one + (t * t) / (w + w);
85 }
86
87 /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
88 if (ex < 0x40044000)
89 {
90 t = expq (u.value);
91 return half * t + half / t;
92 }
93
94 /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
95 if (ex <= 0x400c62e3) /* 11356.375 */
96 return half * expq (u.value);
97
98 /* |x| in [log(maxdouble), overflowthresold] */
99 if (u.value <= ovf_thresh)
100 {
101 w = expq (half * u.value);
102 t = half * w;
103 return t * w;
104 }
105
106 /* |x| > overflowthresold, cosh(x) overflow */
107 return huge * huge;
108 }
109