1 /* Copyright JS Foundation and other contributors, http://js.foundation
2 *
3 * Licensed under the Apache License, Version 2.0 (the "License");
4 * you may not use this file except in compliance with the License.
5 * You may obtain a copy of the License at
6 *
7 * http://www.apache.org/licenses/LICENSE-2.0
8 *
9 * Unless required by applicable law or agreed to in writing, software
10 * distributed under the License is distributed on an "AS IS" BASIS
11 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 * See the License for the specific language governing permissions and
13 * limitations under the License.
14 *
15 * This file is based on work under the following copyright and permission
16 * notice:
17 *
18 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
19 *
20 * Developed at SunSoft, a Sun Microsystems, Inc. business.
21 * Permission to use, copy, modify, and distribute this
22 * software is freely granted, provided that this notice
23 * is preserved.
24 *
25 * @(#)e_sinh.c 1.3 95/01/18
26 */
27
28 #include "jerry-libm-internal.h"
29
30 /* __sinh(x)
31 * Method:
32 * mathematically sinh(x) if defined to be (exp(x) - exp(-x)) / 2
33 * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
34 * 2.
35 * E + E/(E+1)
36 * 0 <= x <= 22 : sinh(x) := -------------, E = expm1(x)
37 * 2
38 *
39 * 22 <= x <= lnovft : sinh(x) := exp(x) / 2
40 * lnovft <= x <= ln2ovft: sinh(x) := exp(x / 2) / 2 * exp(x / 2)
41 * ln2ovft < x : sinh(x) := x * shuge (overflow)
42 *
43 * Special cases:
44 * sinh(x) is |x| if x is +INF, -INF, or NaN.
45 * only sinh(0) = 0 is exact for finite x.
46 */
47
48 #define one 1.0
49 #define half 0.5
50 #define shuge 1.0e307
51
52 double
sinh(double x)53 sinh (double x)
54 {
55 double t, w, h;
56 int ix, jx;
57 unsigned lx;
58
59 /* High word of |x|. */
60 jx = __HI (x);
61 ix = jx & 0x7fffffff;
62
63 /* x is INF or NaN */
64 if (ix >= 0x7ff00000)
65 {
66 return x + x;
67 }
68
69 h = 0.5;
70 if (jx < 0)
71 {
72 h = -h;
73 }
74 /* |x| in [0,22], return sign(x) * 0.5 * (E + E / (E + 1))) */
75 if (ix < 0x40360000)
76 {
77 /* |x| < 22 */
78 if (ix < 0x3e300000)
79 {
80 /* |x| < 2**-28 */
81 if (shuge + x > one)
82 {
83 /* sinh(tiny) = tiny with inexact */
84 return x;
85 }
86 }
87 t = expm1 (fabs (x));
88 if (ix < 0x3ff00000)
89 {
90 return h * (2.0 * t - t * t / (t + one));
91 }
92 return h * (t + t / (t + one));
93 }
94
95 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
96 if (ix < 0x40862E42)
97 {
98 return h * exp (fabs (x));
99 }
100 /* |x| in [log(maxdouble), overflowthresold] */
101 lx = ((1 >> 29) + (unsigned int) x);
102 if (ix < 0x408633CE || ((ix == 0x408633ce) && (lx <= (unsigned) 0x8fb9f87d)))
103 {
104 w = exp (0.5 * fabs (x));
105 t = h * w;
106 return t * w;
107 }
108
109 /* |x| > overflowthresold, sinh(x) overflow */
110 return x * shuge;
111 } /* sinh */
112
113 #undef one
114 #undef half
115 #undef huge
116