1/* @(#)e_sinh.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13#ifndef lint
14static char rcsid[] = "$Id: e_sinh.c,v 1.1.1.1 1994/08/19 09:39:44 jkh Exp $";
15#endif
16
17/* __ieee754_sinh(x)
18 * Method :
19 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
20 * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
21 * 2.
22 * E + E/(E+1)
23 * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
24 * 2
25 *
26 * 22 <= x <= lnovft : sinh(x) := exp(x)/2
27 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
28 * ln2ovft < x : sinh(x) := x*shuge (overflow)
29 *
30 * Special cases:
31 * sinh(x) is |x| if x is +INF, -INF, or NaN.
32 * only sinh(0)=0 is exact for finite x.
33 */
34
35#include "math.h"
36#include "math_private.h"
37
38#ifdef __STDC__
39static const double one = 1.0, shuge = 1.0e307;
40#else
41static double one = 1.0, shuge = 1.0e307;
42#endif
43
44#ifdef __STDC__
45 double __ieee754_sinh(double x)
46#else
47 double __ieee754_sinh(x)
48 double x;
49#endif
50{
51 double t,w,h;
52 int32_t ix,jx;
53 u_int32_t lx;
54
55 /* High word of |x|. */
56 GET_HIGH_WORD(jx,x);
57 ix = jx&0x7fffffff;
58
59 /* x is INF or NaN */
60 if(ix>=0x7ff00000) return x+x;
61
62 h = 0.5;
63 if (jx<0) h = -h;
64 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
65 if (ix < 0x40360000) { /* |x|<22 */
66 if (ix<0x3e300000) /* |x|<2**-28 */
67 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
68 t = expm1(fabs(x));
69 if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
70 return h*(t+t/(t+one));
71 }
72
73 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
74 if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
75
76 /* |x| in [log(maxdouble), overflowthresold] */
77 GET_LOW_WORD(lx,x);
78 if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d)) {
79 w = __ieee754_exp(0.5*fabs(x));
80 t = h*w;
81 return t*w;
82 }
83
84 /* |x| > overflowthresold, sinh(x) overflow */
85 return x*shuge;
86}