1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
|
/* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_cosh(x)
* Method :
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* ln2/2 <= x <= 22 : cosh(x) := -------------------
* 2
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : cosh(x) := huge*huge (overflow)
*
* Special cases:
* cosh(x) is |x| if x is +INF, -INF, or NaN.
* only cosh(0)=1 is exact for finite x.
*/
#include <math.h>
#include <math_private.h>
static const double one = 1.0, half = 0.5, huge = 1.0e300;
double
__ieee754_cosh (double x)
{
double t, w;
int32_t ix;
u_int32_t lx;
/* High word of |x|. */
GET_HIGH_WORD (ix, x);
ix &= 0x7fffffff;
/* |x| in [0,22] */
if (ix < 0x40360000)
{
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if (ix < 0x3fd62e43)
{
if (ix < 0x3c800000)
return one; /* cosh(tiny) = 1 */
t = __expm1 (fabs (x));
w = one + t;
return one + (t * t) / (w + w);
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
t = __ieee754_exp (fabs (x));
return half * t + half / t;
}
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862e42)
return half * __ieee754_exp (fabs (x));
/* |x| in [log(maxdouble), overflowthresold] */
GET_LOW_WORD (lx, x);
if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (u_int32_t) 0x8fb9f87d)))
{
w = __ieee754_exp (half * fabs (x));
t = half * w;
return t * w;
}
/* x is INF or NaN */
if (ix >= 0x7ff00000)
return x * x;
/* |x| > overflowthresold, cosh(x) overflow */
return huge * huge;
}
strong_alias (__ieee754_cosh, __cosh_finite)
|
