e_cosh.c revision 271779 
1
2/* @(#)e_cosh.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#include <sys/cdefs.h>
15__FBSDID("$FreeBSD: stable/10/lib/msun/src/e_cosh.c 271779 2014-09-18 15:10:22Z tijl $");
16
17/* __ieee754_cosh(x)
18 * Method :
19 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
20 *	1. Replace x by |x| (cosh(x) = cosh(-x)).
21 *	2.
22 *		                                        [ exp(x) - 1 ]^2
23 *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
24 *			       			           2*exp(x)
25 *
26 *		                                  exp(x) +  1/exp(x)
27 *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
28 *			       			          2
29 *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2
30 *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
31 *	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)
32 *
33 * Special cases:
34 *	cosh(x) is |x| if x is +INF, -INF, or NaN.
35 *	only cosh(0)=1 is exact for finite x.
36 */
37
38#include <float.h>
39
40#include "math.h"
41#include "math_private.h"
42
43static const double one = 1.0, half=0.5, huge = 1.0e300;
44
45double
46__ieee754_cosh(double x)
47{
48	double t,w;
49	int32_t ix;
50
51    /* High word of |x|. */
52	GET_HIGH_WORD(ix,x);
53	ix &= 0x7fffffff;
54
55    /* x is INF or NaN */
56	if(ix>=0x7ff00000) return x*x;
57
58    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
59	if(ix<0x3fd62e43) {
60	    t = expm1(fabs(x));
61	    w = one+t;
62	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
63	    return one+(t*t)/(w+w);
64	}
65
66    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
67	if (ix < 0x40360000) {
68		t = __ieee754_exp(fabs(x));
69		return half*t+half/t;
70	}
71
72    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
73	if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
74
75    /* |x| in [log(maxdouble), overflowthresold] */
76	if (ix<=0x408633CE)
77	    return __ldexp_exp(fabs(x), -1);
78
79    /* |x| > overflowthresold, cosh(x) overflow */
80	return huge*huge;
81}
82
83#if (LDBL_MANT_DIG == 53)
84__weak_reference(cosh, coshl);
85#endif
86