e_sinh.c revision 141296 
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#ifndef lint
15static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_sinh.c 141296 2005-02-04 18:26:06Z das $";
16#endif
17
18/* __ieee754_sinh(x)
19 * Method :
20 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
21 *	1. Replace x by |x| (sinh(-x) = -sinh(x)).
22 *	2.
23 *		                                    E + E/(E+1)
24 *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
25 *			       			        2
26 *
27 *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2
28 *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
29 *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
30 *
31 * Special cases:
32 *	sinh(x) is |x| if x is +INF, -INF, or NaN.
33 *	only sinh(0)=0 is exact for finite x.
34 */
35
36#include "math.h"
37#include "math_private.h"
38
39static const double one = 1.0, shuge = 1.0e307;
40
41double
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