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/* cosh(x)
14 * Method :
15 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
16 *	1. Replace x by |x| (cosh(x) = cosh(-x)).
17 *	2.
18 *		                                        [ exp(x) - 1 ]^2
19 *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
20 *			       			           2*exp(x)
21 *
22 *		                                  exp(x) +  1/exp(x)
23 *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
24 *			       			          2
25 *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2
26 *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
27 *	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)
28 *
29 * Special cases:
30 *	cosh(x) is |x| if x is +INF, -INF, or NaN.
31 *	only cosh(0)=1 is exact for finite x.
32 */
33
34#include <float.h>
35
36#include "math.h"
37#include "math_private.h"
38
39static const double one = 1.0, half=0.5, huge = 1.0e300;
40
41double
42cosh(double x)
43{
44	double t,w;
45	int32_t ix;
46
47    /* High word of |x|. */
48	GET_HIGH_WORD(ix,x);
49	ix &= 0x7fffffff;
50
51    /* x is INF or NaN */
52	if(ix>=0x7ff00000) return x*x;
53
54    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
55	if(ix<0x3fd62e43) {
56	    t = expm1(fabs(x));
57	    w = one+t;
58	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
59	    return one+(t*t)/(w+w);
60	}
61
62    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
63	if (ix < 0x40360000) {
64		t = exp(fabs(x));
65		return half*t+half/t;
66	}
67
68    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
69	if (ix < 0x40862E42)  return half*exp(fabs(x));
70
71    /* |x| in [log(maxdouble), overflowthresold] */
72	if (ix<=0x408633CE)
73	    return __ldexp_exp(fabs(x), -1);
74
75    /* |x| > overflowthresold, cosh(x) overflow */
76	return huge*huge;
77}
78
79#if (LDBL_MANT_DIG == 53)
80__weak_reference(cosh, coshl);
81#endif
82