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 /* 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 <float.h>
33
34 #include "math.h"
35 #include "math_private.h"
36
37 static const double one = 1.0, shuge = 1.0e307;
38
39 double
sinh(double x)40 sinh(double x)
41 {
42 double t,h;
43 int32_t ix,jx;
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 if (ix<=0x408633CE)
68 return h*2.0*__ldexp_exp(fabs(x), -1);
69
70 /* |x| > overflowthresold, sinh(x) overflow */
71 return x*shuge;
72 }
73
74 #if (LDBL_MANT_DIG == 53)
75 __weak_reference(sinh, sinhl);
76 #endif
77