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