source: trunk/sys/libm/e_cosh.c @ 1

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1
2/* @(#)e_cosh.c 5.1 93/09/24 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, 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/* __ieee754_cosh(x)
15 * Method :
16 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
17 *      1. Replace x by |x| (cosh(x) = cosh(-x)).
18 *      2.
19 *                                                      [ exp(x) - 1 ]^2
20 *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
21 *                                                         2*exp(x)
22 *
23 *                                                exp(x) +  1/exp(x)
24 *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
25 *                                                        2
26 *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
27 *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
28 *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
29 *
30 * Special cases:
31 *      cosh(x) is |x| if x is +INF, -INF, or NaN.
32 *      only cosh(0)=1 is exact for finite x.
33 */
34
35#include <libm/fdlibm.h>
36
37#ifdef __STDC__
38static const double one = 1.0, half=0.5, huge = 1.0e300;
39#else
40static double one = 1.0, half=0.5, huge = 1.0e300;
41#endif
42
43#ifdef __STDC__
44        double __ieee754_cosh(double x)
45#else
46        double __ieee754_cosh(x)
47        double x;
48#endif
49{       
50        double t,w;
51        int ix;
52        unsigned lx;
53
54    /* High word of |x|. */
55        ix = *( (((*(int*)&one)>>29)^1) + (int*)&x);
56        ix &= 0x7fffffff;
57
58    /* x is INF or NaN */
59        if(ix>=0x7ff00000) return x*x; 
60
61    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
62        if(ix<0x3fd62e43) {
63            t = expm1(fabs(x));
64            w = one+t;
65            if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */
66            return one+(t*t)/(w+w);
67        }
68
69    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
70        if (ix < 0x40360000) {
71                t = __ieee754_exp(fabs(x));
72                return half*t+half/t;
73        }
74
75    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
76        if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
77
78    /* |x| in [log(maxdouble), overflowthresold] */
79        lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
80        if (((ix<0x408633CE) || 
81            (ix==0x408633ce))&&(lx<=(unsigned)0x8fb9f87d)) {
82            w = __ieee754_exp(half*fabs(x));
83            t = half*w;
84            return t*w;
85        }
86
87    /* |x| > overflowthresold, cosh(x) overflow */
88        return huge*huge;
89}
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