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_acosh.c 1.3 95/01/18
26 */
27
28 #include "jerry-libm-internal.h"
29
30 /* acosh(x)
31 * Method :
32 * Based on
33 * acosh(x) = log [ x + sqrt(x * x - 1) ]
34 * we have
35 * acosh(x) := log(x) + ln2, if x is large; else
36 * acosh(x) := log(2x - 1 / (sqrt(x * x - 1) + x)), if x > 2; else
37 * acosh(x) := log1p(t + sqrt(2.0 * t + t * t)); where t = x - 1.
38 *
39 * Special cases:
40 * acosh(x) is NaN with signal if x < 1.
41 * acosh(NaN) is NaN without signal.
42 */
43
44 #define one 1.0
45 #define ln2 6.93147180559945286227e-01 /* 0x3FE62E42, 0xFEFA39EF */
46
47 double
acosh(double x)48 acosh (double x)
49 {
50 double t;
51 int hx;
52 hx = __HI (x);
53 if (hx < 0x3ff00000)
54 {
55 /* x < 1 */
56 return NAN;
57 }
58 else if (hx >= 0x41b00000)
59 {
60 /* x > 2**28 */
61 if (hx >= 0x7ff00000)
62 {
63 /* x is inf of NaN */
64 return x + x;
65 }
66 else
67 {
68 /* acosh(huge) = log(2x) */
69 return log (x) + ln2;
70 }
71 }
72 else if (((hx - 0x3ff00000) | __LO (x)) == 0)
73 {
74 /* acosh(1) = 0 */
75 return 0.0;
76 }
77 else if (hx > 0x40000000)
78 {
79 /* 2**28 > x > 2 */
80 t = x * x;
81 return log (2.0 * x - one / (x + sqrt (t - one)));
82 }
83 else
84 {
85 /* 1 < x < 2 */
86 t = x - one;
87 return log1p (t + sqrt (2.0 * t + t * t));
88 }
89 } /* acosh */
90
91 #undef one
92 #undef ln2
93