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 /* 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) := 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 "fdlibm.h"
36
37 #ifdef _NEED_FLOAT64
38
39 static const __float64 one = _F_64(1.0), half = _F_64(0.5);
40
41 __float64
cosh64(__float64 x)42 cosh64(__float64 x)
43 {
44 __float64 t, w;
45 __int32_t ix;
46 __uint32_t lx;
47
48 x = fabs64(x);
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)
56 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(x);
61 w = one + t;
62 if (ix < 0x3c800000)
63 return w; /* cosh(tiny) = 1 */
64 return one + (t * t) / (w + w);
65 }
66
67 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
68 if (ix < 0x40360000) {
69 t = exp(x);
70 return half * t + half / t;
71 }
72
73 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
74 if (ix < 0x40862E42)
75 return half * exp(x);
76
77 /* |x| in [log(maxdouble), overflowthresold] */
78 GET_LOW_WORD(lx, x);
79 if (ix < 0x408633CE || (ix == 0x408633ce && lx <= (__uint32_t)0x8fb9f87d)) {
80 w = exp(half * x);
81 t = half * w;
82 return t * w;
83 }
84
85 /* |x| > overflowthresold, cosh(x) overflow */
86 return __math_oflow(0);
87 }
88
89 _MATH_ALIAS_d_d(cosh)
90
91 #endif /* _NEED_FLOAT64 */
92
