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 #include <LibConfig.h>
13 #include <sys/EfiCdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: e_cosh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
16 #endif
17
18 #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
19 // C4756: overflow in constant arithmetic
20 #pragma warning ( disable : 4756 )
21 #endif
22
23 /* __ieee754_cosh(x)
24 * Method :
25 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
26 * 1. Replace x by |x| (cosh(x) = cosh(-x)).
27 * 2.
28 * [ exp(x) - 1 ]^2
29 * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
30 * 2*exp(x)
31 *
32 * exp(x) + 1/exp(x)
33 * ln2/2 <= x <= 22 : cosh(x) := -------------------
34 * 2
35 * 22 <= x <= lnovft : cosh(x) := exp(x)/2
36 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
37 * ln2ovft < x : cosh(x) := huge*huge (overflow)
38 *
39 * Special cases:
40 * cosh(x) is |x| if x is +INF, -INF, or NaN.
41 * only cosh(0)=1 is exact for finite x.
42 */
43
44 #include "math.h"
45 #include "math_private.h"
46
47 static const double one = 1.0, half=0.5, huge = 1.0e300;
48
49 double
__ieee754_cosh(double x)50 __ieee754_cosh(double x)
51 {
52 double t,w;
53 int32_t ix;
54 u_int32_t lx;
55
56 /* High word of |x|. */
57 GET_HIGH_WORD(ix,x);
58 ix &= 0x7fffffff;
59
60 /* x is INF or NaN */
61 if(ix>=0x7ff00000) return x*x;
62
63 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
64 if(ix<0x3fd62e43) {
65 t = expm1(fabs(x));
66 w = one+t;
67 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
68 return one+(t*t)/(w+w);
69 }
70
71 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
72 if (ix < 0x40360000) {
73 t = __ieee754_exp(fabs(x));
74 return half*t+half/t;
75 }
76
77 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
78 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
79
80 /* |x| in [log(maxdouble), overflowthresold] */
81 GET_LOW_WORD(lx,x);
82 if (ix<0x408633CE ||
83 ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
84 w = __ieee754_exp(half*fabs(x));
85 t = half*w;
86 return t*w;
87 }
88
89 /* |x| > overflowthresold, cosh(x) overflow */
90 return huge*huge;
91 }
92