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e_cosh.c
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1 
2 /* @(#)e_cosh.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  */
13 
14 /* __ieee754_cosh(x)
15  * Method :
16  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
17  * 1. Replace x by |x| (cosh(x) = cosh(-x)).
18  * 2.
19  * [ exp(x) - 1 ]^2
20  * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
21  * 2*exp(x)
22  *
23  * exp(x) + 1/exp(x)
24  * ln2/2 <= x <= 22 : cosh(x) := -------------------
25  * 2
26  * 22 <= x <= lnovft : cosh(x) := exp(x)/2
27  * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
28  * ln2ovft < x : cosh(x) := huge*huge (overflow)
29  *
30  * Special cases:
31  * cosh(x) is |x| if x is +INF, -INF, or NaN.
32  * only cosh(0)=1 is exact for finite x.
33  */
34 
35 #include "fdlibm.h"
36 
37 #ifdef __STDC__
38 static const double one = 1.0, half=0.5, huge = 1.0e300;
39 #else
40 static double one = 1.0, half=0.5, huge = 1.0e300;
41 #endif
42 
43 #ifdef __STDC__
44  double __ieee754_cosh(double x)
45 #else
46  double __ieee754_cosh(x)
47  double x;
48 #endif
49 {
50  double t,w;
51  int ix;
52  unsigned lx;
53 
54  /* High word of |x|. */
55  ix = __HI(x);
56  ix &= 0x7fffffff;
57 
58  /* x is INF or NaN */
59  if(ix>=0x7ff00000) return x*x;
60 
61  /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
62  if(ix<0x3fd62e43) {
63  t = expm1(fabs(x));
64  w = one+t;
65  if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
66  return one+(t*t)/(w+w);
67  }
68 
69  /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
70  if (ix < 0x40360000) {
71  t = __ieee754_exp(fabs(x));
72  return half*t+half/t;
73  }
74 
75  /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
76  if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
77 
78  /* |x| in [log(maxdouble), overflowthresold] */
79  lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
80  if ((ix<0x408633CE) ||
81  ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
82  w = __ieee754_exp(half*fabs(x));
83  t = half*w;
84  return t*w;
85  }
86 
87  /* |x| > overflowthresold, cosh(x) overflow */
88  return huge*huge;
89 }