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
47double
48acosh (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