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 /* sinh(x)
14 * Method :
15 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
16 * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
17 * 2.
18 * E + E/(E+1)
19 * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
20 * 2
21 *
22 * 22 <= x <= lnovft : sinh(x) := exp(x)/2
23 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
24 * ln2ovft < x : sinh(x) := x*shuge (overflow)
25 *
26 * Special cases:
27 * sinh(x) is |x| if x is +INF, -INF, or NaN.
28 * only sinh(0)=0 is exact for finite x.
29 */
30
31 #include <float.h>
32 #include <math.h>
33
34 #include "math_private.h"
35
36 static const double one = 1.0, shuge = 1.0e307;
37
38 double
sinh(double x)39 sinh(double x)
40 {
41 double t,w,h;
42 int32_t ix,jx;
43 u_int32_t lx;
44
45 /* High word of |x|. */
46 GET_HIGH_WORD(jx,x);
47 ix = jx&0x7fffffff;
48
49 /* x is INF or NaN */
50 if(ix>=0x7ff00000) return x+x;
51
52 h = 0.5;
53 if (jx<0) h = -h;
54 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
55 if (ix < 0x40360000) { /* |x|<22 */
56 if (ix<0x3e300000) /* |x|<2**-28 */
57 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
58 t = expm1(fabs(x));
59 if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
60 return h*(t+t/(t+one));
61 }
62
63 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
64 if (ix < 0x40862E42) return h*exp(fabs(x));
65
66 /* |x| in [log(maxdouble), overflowthresold] */
67 GET_LOW_WORD(lx,x);
68 if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
69 w = exp(0.5*fabs(x));
70 t = h*w;
71 return t*w;
72 }
73
74 /* |x| > overflowthresold, sinh(x) overflow */
75 return x*shuge;
76 }
77 DEF_STD(sinh);
78 LDBL_MAYBE_CLONE(sinh);
79