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e_sinh.c
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1 
2 /* @(#)e_sinh.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_sinh(x)
15  * Method :
16  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
17  * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
18  * 2.
19  * E + E/(E+1)
20  * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
21  * 2
22  *
23  * 22 <= x <= lnovft : sinh(x) := exp(x)/2
24  * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
25  * ln2ovft < x : sinh(x) := x*shuge (overflow)
26  *
27  * Special cases:
28  * sinh(x) is |x| if x is +INF, -INF, or NaN.
29  * only sinh(0)=0 is exact for finite x.
30  */
31 
32 #include "fdlibm.h"
33 
34 #ifdef __STDC__
35 static const double one = 1.0, shuge = 1.0e307;
36 #else
37 static double one = 1.0, shuge = 1.0e307;
38 #endif
39 
40 #ifdef __STDC__
41  double __ieee754_sinh(double x)
42 #else
43  double __ieee754_sinh(x)
44  double x;
45 #endif
46 {
47  double t,w,h;
48  int ix,jx;
49  unsigned lx;
50 
51  /* High word of |x|. */
52  jx = __HI(x);
53  ix = jx&0x7fffffff;
54 
55  /* x is INF or NaN */
56  if(ix>=0x7ff00000) return x+x;
57 
58  h = 0.5;
59  if (jx<0) h = -h;
60  /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
61  if (ix < 0x40360000) { /* |x|<22 */
62  if (ix<0x3e300000) /* |x|<2**-28 */
63  if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
64  t = expm1(fabs(x));
65  if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
66  return h*(t+t/(t+one));
67  }
68 
69  /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
70  if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
71 
72  /* |x| in [log(maxdouble), overflowthresold] */
73  lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
74  if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
75  w = __ieee754_exp(0.5*fabs(x));
76  t = h*w;
77  return t*w;
78  }
79 
80  /* |x| > overflowthresold, sinh(x) overflow */
81  return x*shuge;
82 }