e_sinh.c revision 97413 
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[] = "$FreeBSD: head/lib/msun/src/e_sinh.c 97413 2002-05-28 18:15:04Z alfred $";
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
38static const double one = 1.0, shuge = 1.0e307;
39
40double
41__ieee754_sinh(double x)
42{
43	double t,w,h;
44	int32_t ix,jx;
45	u_int32_t lx;
46
47    /* High word of |x|. */
48	GET_HIGH_WORD(jx,x);
49	ix = jx&0x7fffffff;
50
51    /* x is INF or NaN */
52	if(ix>=0x7ff00000) return x+x;
53
54	h = 0.5;
55	if (jx<0) h = -h;
56    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
57	if (ix < 0x40360000) {		/* |x|<22 */
58	    if (ix<0x3e300000) 		/* |x|<2**-28 */
59		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
60	    t = expm1(fabs(x));
61	    if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
62	    return h*(t+t/(t+one));
63	}
64
65    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
66	if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
67
68    /* |x| in [log(maxdouble), overflowthresold] */
69	GET_LOW_WORD(lx,x);
70	if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
71	    w = __ieee754_exp(0.5*fabs(x));
72	    t = h*w;
73	    return t*w;
74	}
75
76    /* |x| > overflowthresold, sinh(x) overflow */
77	return x*shuge;
78}
79