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e_cosh.c (2378B)
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1 /* @(#)e_cosh.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, 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 #ifndef lint
14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_cosh.c,v 1.7 2002/05/28 17:03:12 alfred Exp $";
15 #endif
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
41 static const double one = 1.0, half=0.5, huge = 1.0e300;
42
43 double
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 }