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 #include <sys/cdefs.h>
15 __FBSDID("$FreeBSD$");
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 static const double one = 1.0, shuge = 1.0e307;
39
40 double
__ieee754_sinh(double x)41 __ieee754_sinh(double x)
42 {
43 double t,h;
44 int32_t ix,jx;
45
46 /* High word of |x|. */
47 GET_HIGH_WORD(jx,x);
48 ix = jx&0x7fffffff;
49
50 /* x is INF or NaN */
51 if(ix>=0x7ff00000) return x+x;
52
53 h = 0.5;
54 if (jx<0) h = -h;
55 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
56 if (ix < 0x40360000) { /* |x|<22 */
57 if (ix<0x3e300000) /* |x|<2**-28 */
58 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
59 t = expm1(fabs(x));
60 if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
61 return h*(t+t/(t+one));
62 }
63
64 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
65 if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
66
67 /* |x| in [log(maxdouble), overflowthresold] */
68 if (ix<=0x408633CE)
69 return h*2.0*__ldexp_exp(fabs(x), -1);
70
71 /* |x| > overflowthresold, sinh(x) overflow */
72 return x*shuge;
73 }
74