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 #include <LibConfig.h>
13 #include <sys/EfiCdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: e_sinh.c,v 1.11 2002/05/26 22:01:52 wiz Exp $");
16 #endif
17
18 #include "math.h"
19 #include "math_private.h"
20
21 /* __ieee754_sinh(x)
22 * Method :
23 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
24 * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
25 * 2.
26 * E + E/(E+1)
27 * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
28 * 2
29 *
30 * 22 <= x <= lnovft : sinh(x) := exp(x)/2
31 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
32 * ln2ovft < x : sinh(x) := x*shuge (overflow)
33 *
34 * Special cases:
35 * sinh(x) is |x| if x is +INF, -INF, or NaN.
36 * only sinh(0)=0 is exact for finite x.
37 */
38
39 static const double one = 1.0, shuge = 1.0e307;
40
41 double
__ieee754_sinh(double x)42 __ieee754_sinh(double x)
43 {
44 double t,w,h;
45 int32_t ix,jx;
46 u_int32_t lx;
47
48 /* High word of |x|. */
49 GET_HIGH_WORD(jx,x);
50 ix = jx&0x7fffffff;
51
52 /* x is INF or NaN */
53 if(ix>=0x7ff00000) return x+x;
54
55 h = 0.5;
56 if (jx<0) h = -h;
57 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
58 if (ix < 0x40360000) { /* |x|<22 */
59 if (ix<0x3e300000) /* |x|<2**-28 */
60 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
61 t = expm1(fabs(x));
62 if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
63 return h*(t+t/(t+one));
64 }
65
66 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
67 if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
68
69 /* |x| in [log(maxdouble), overflowthresold] */
70 GET_LOW_WORD(lx,x);
71 if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
72 w = __ieee754_exp(0.5*fabs(x));
73 t = h*w;
74 return t*w;
75 }
76
77 /* |x| > overflowthresold, sinh(x) overflow */
78 return x*shuge;
79 }
80