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 | /* __ieee754_coshl(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) := expl(x)/2 |
46 | * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(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 <math.h> |
55 | #include <math_private.h> |
56 | |
57 | static const _Float128 one = 1.0, half = 0.5, huge = L(1.0e4900), |
58 | ovf_thresh = L(1.1357216553474703894801348310092223067821E4); |
59 | |
60 | _Float128 |
61 | __ieee754_coshl (_Float128 x) |
62 | { |
63 | _Float128 t, w; |
64 | int32_t ex; |
65 | ieee854_long_double_shape_type u; |
66 | |
67 | u.value = x; |
68 | ex = u.parts32.w0 & 0x7fffffff; |
69 | |
70 | /* Absolute value of x. */ |
71 | u.parts32.w0 = ex; |
72 | |
73 | /* x is INF or NaN */ |
74 | if (ex >= 0x7fff0000) |
75 | return x * x; |
76 | |
77 | /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ |
78 | if (ex < 0x3ffd62e4) /* 0.3465728759765625 */ |
79 | { |
80 | if (ex < 0x3fb80000) /* |x| < 2^-116 */ |
81 | return one; /* cosh(tiny) = 1 */ |
82 | t = __expm1l (u.value); |
83 | w = one + t; |
84 | |
85 | return one + (t * t) / (w + w); |
86 | } |
87 | |
88 | /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ |
89 | if (ex < 0x40044000) |
90 | { |
91 | t = __ieee754_expl (u.value); |
92 | return half * t + half / t; |
93 | } |
94 | |
95 | /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ |
96 | if (ex <= 0x400c62e3) /* 11356.375 */ |
97 | return half * __ieee754_expl (u.value); |
98 | |
99 | /* |x| in [log(maxdouble), overflowthresold] */ |
100 | if (u.value <= ovf_thresh) |
101 | { |
102 | w = __ieee754_expl (half * u.value); |
103 | t = half * w; |
104 | return t * w; |
105 | } |
106 | |
107 | /* |x| > overflowthresold, cosh(x) overflow */ |
108 | return huge * huge; |
109 | } |
110 | strong_alias (__ieee754_coshl, __coshl_finite) |
111 | |