xref: /third_party/jerryscript/jerry-libm/cosh.c (revision 425bb815) 
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_cosh.c 1.3 95/01/18
26 */
27
28#include "jerry-libm-internal.h"
29
30/* cosh(x)
31 * Method:
32 * mathematically cosh(x) if defined to be (exp(x) + exp(-x)) / 2
33 *  1. Replace x by |x| (cosh(x) = cosh(-x)).
34 *  2.
35 *                                                 [ exp(x) - 1 ]^2
36 *      0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
37 *                                                     2*exp(x)
38 *
39 *                                             exp(x) +  1/exp(x)
40 *      ln2/2    <= x <= 22     :  cosh(x) := -------------------
41 *                                                    2
42 *
43 *      22       <= x <= lnovft :  cosh(x) := exp(x)/2
44 *      lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
45 *      ln2ovft  <  x           :  cosh(x) := huge * huge (overflow)
46 *
47 * Special cases:
48 *  cosh(x) is |x| if x is +INF, -INF, or NaN.
49 *  only cosh(0) = 1 is exact for finite x.
50 */
51
52#define one 1.0
53#define half 0.5
54#define huge 1.0e300
55
56double
57cosh (double x)
58{
59  double t, w;
60  int ix;
61  unsigned lx;
62
63  /* High word of |x|. */
64  ix = __HI (x);
65  ix &= 0x7fffffff;
66
67  /* x is INF or NaN */
68  if (ix >= 0x7ff00000)
69  {
70    return x * x;
71  }
72  /* |x| in [0, 0.5 * ln2], return 1 + expm1(|x|)^2 / (2 * exp(|x|)) */
73  if (ix < 0x3fd62e43)
74  {
75    t = expm1 (fabs (x));
76    w = one + t;
77    if (ix < 0x3c800000)
78    {
79      /* cosh(tiny) = 1 */
80      return w;
81    }
82    return one + (t * t) / (w + w);
83  }
84
85  /* |x| in [0.5 * ln2, 22], return (exp(|x|) + 1 / exp(|x|) / 2; */
86  if (ix < 0x40360000)
87  {
88    t = exp (fabs (x));
89    return half * t + half / t;
90  }
91
92  /* |x| in [22, log(maxdouble)] return half * exp(|x|) */
93  if (ix < 0x40862E42)
94  {
95    return half * exp (fabs (x));
96  }
97  /* |x| in [log(maxdouble), overflowthresold] */
98  lx = ((1 >> 29) + (unsigned int) x);
99  if ((ix < 0x408633CE) ||
100      ((ix == 0x408633ce) && (lx <= (unsigned) 0x8fb9f87d)))
101  {
102    w = exp (half * fabs (x));
103    t = half * w;
104    return t * w;
105  }
106
107  /* |x| > overflowthresold, cosh(x) overflow */
108  return huge * huge;
109} /* cosh */
110
111#undef one
112#undef half
113#undef huge
114