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
|
/* @(#)e_sinh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
//#include <sys/cdefs.h>
//__FBSDID("$FreeBSD$");
/* __ieee754_sinh(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
* 2
*
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : sinh(x) := x*shuge (overflow)
*
* Special cases:
* sinh(x) is |x| if x is +INF, -INF, or NaN.
* only sinh(0)=0 is exact for finite x.
*/
#include <float.h>
#include "math_private.h"
static const double one = 1.0, shuge = 1.0e307;
double
__ieee754_sinh(double x)
{
double t,h;
int32_t ix,jx;
/* High word of |x|. */
GET_HIGH_WORD(jx,x);
ix = jx&0x7fffffff;
/* x is INF or NaN */
if(ix>=0x7ff00000) return x+x;
h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x40360000) { /* |x|<22 */
if (ix<0x3e300000) /* |x|<2**-28 */
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
t = expm1(fabs(x));
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
return h*(t+t/(t+one));
}
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix<=0x408633CE)
return h*2.0*__ldexp_exp(fabs(x), -1);
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}
|
