e_cosh.c revision 176451 
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: head/lib/msun/src/e_cosh.c 176451 2008-02-22 02:30:36Z das $");
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 "math.h"
39#include "math_private.h"
40
41static const double one = 1.0, half=0.5, huge = 1.0e300;
42
43double
44__ieee754_cosh(double x)
45{
46	double t,w;
47	int32_t ix;
48	u_int32_t lx;
49
50    /* High word of |x|. */
51	GET_HIGH_WORD(ix,x);
52	ix &= 0x7fffffff;
53
54    /* x is INF or NaN */
55	if(ix>=0x7ff00000) return x*x;
56
57    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
58	if(ix<0x3fd62e43) {
59	    t = expm1(fabs(x));
60	    w = one+t;
61	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
62	    return one+(t*t)/(w+w);
63	}
64
65    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
66	if (ix < 0x40360000) {
67		t = __ieee754_exp(fabs(x));
68		return half*t+half/t;
69	}
70
71    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
72	if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
73
74    /* |x| in [log(maxdouble), overflowthresold] */
75	GET_LOW_WORD(lx,x);
76	if (ix<0x408633CE ||
77	      ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
78	    w = __ieee754_exp(half*fabs(x));
79	    t = half*w;
80	    return t*w;
81	}
82
83    /* |x| > overflowthresold, cosh(x) overflow */
84	return huge*huge;
85}
86