1
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, 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/* sinh(x)
14 * Method :
15 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
16 *	1. Replace x by |x| (sinh(-x) = -sinh(x)).
17 *	2.
18 *		                                    E + E/(E+1)
19 *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
20 *			       			        2
21 *
22 *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2
23 *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
24 *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
25 *
26 * Special cases:
27 *	sinh(x) is |x| if x is +INF, -INF, or NaN.
28 *	only sinh(0)=0 is exact for finite x.
29 */
30
31#include <float.h>
32
33#include "math.h"
34#include "math_private.h"
35
36static const double one = 1.0, shuge = 1.0e307;
37
38double
39sinh(double x)
40{
41	double t,h;
42	int32_t ix,jx;
43
44    /* High word of |x|. */
45	GET_HIGH_WORD(jx,x);
46	ix = jx&0x7fffffff;
47
48    /* x is INF or NaN */
49	if(ix>=0x7ff00000) return x+x;
50
51	h = 0.5;
52	if (jx<0) h = -h;
53    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
54	if (ix < 0x40360000) {		/* |x|<22 */
55	    if (ix<0x3e300000) 		/* |x|<2**-28 */
56		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
57	    t = expm1(fabs(x));
58	    if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
59	    return h*(t+t/(t+one));
60	}
61
62    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
63	if (ix < 0x40862E42)  return h*exp(fabs(x));
64
65    /* |x| in [log(maxdouble), overflowthresold] */
66	if (ix<=0x408633CE)
67	    return h*2.0*__ldexp_exp(fabs(x), -1);
68
69    /* |x| > overflowthresold, sinh(x) overflow */
70	return x*shuge;
71}
72
73#if (LDBL_MANT_DIG == 53)
74__weak_reference(sinh, sinhl);
75#endif
76