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 /* 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 <float.h>
36
37 #include "math.h"
38 #include "math_private.h"
39
40 static const double one = 1.0, half=0.5, huge = 1.0e300;
41
42 double
cosh(double x)43 cosh(double x)
44 {
45 double t,w;
46 int32_t ix;
47
48 /* High word of |x|. */
49 GET_HIGH_WORD(ix,x);
50 ix &= 0x7fffffff;
51
52 /* x is INF or NaN */
53 if(ix>=0x7ff00000) return x*x;
54
55 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
56 if(ix<0x3fd62e43) {
57 t = expm1(fabs(x));
58 w = one+t;
59 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
60 return one+(t*t)/(w+w);
61 }
62
63 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
64 if (ix < 0x40360000) {
65 t = exp(fabs(x));
66 return half*t+half/t;
67 }
68
69 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
70 if (ix < 0x40862E42) return half*exp(fabs(x));
71
72 /* |x| in [log(maxdouble), overflowthresold] */
73 if (ix<=0x408633CE)
74 return __ldexp_exp(fabs(x), -1);
75
76 /* |x| > overflowthresold, cosh(x) overflow */
77 return huge*huge;
78 }
79
80 #if (LDBL_MANT_DIG == 53)
81 __weak_reference(cosh, coshl);
82 #endif
83