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 /* __ieee754_cosh(x)
14 * Method :
15 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
16 * 1. Replace x by |x| (cosh(x) = cosh(-x)).
17 * 2.
18 * [ exp(x) - 1 ]^2
19 * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
20 * 2*exp(x)
21 *
22 * exp(x) + 1/exp(x)
23 * ln2/2 <= x <= 40 : cosh(x) := -------------------
24 * 2
25 * 40 <= x <= lnovft : cosh(x) := exp(x)/2
26 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
27 * ln2ovft < x : cosh(x) := huge*huge (overflow)
28 *
29 * Special cases:
30 * cosh(x) is |x| if x is +INF, -INF, or NaN.
31 * only cosh(0)=1 is exact for finite x.
32 */
33
34 #include <math.h>
35 #include <math_private.h>
36 #include <libm-alias-finite.h>
37
38 static const long double one = 1.0L, half=0.5L, huge = 1.0e300L;
39
40 long double
__ieee754_coshl(long double x)41 __ieee754_coshl (long double x)
42 {
43 long double t,w;
44 int64_t ix;
45 double xhi;
46
47 /* High word of |x|. */
48 xhi = ldbl_high (x);
49 EXTRACT_WORDS64 (ix, xhi);
50 ix &= 0x7fffffffffffffffLL;
51
52 /* x is INF or NaN */
53 if(ix>=0x7ff0000000000000LL) return x*x;
54
55 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
56 if(ix<0x3fd62e42fefa39efLL) {
57 if (ix<0x3c80000000000000LL) return one; /* cosh(tiny) = 1 */
58 t = __expm1l(fabsl(x));
59 w = one+t;
60 return one+(t*t)/(w+w);
61 }
62
63 /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
64 if (ix < 0x4044000000000000LL) {
65 t = __ieee754_expl(fabsl(x));
66 return half*t+half/t;
67 }
68
69 /* |x| in [40, log(maxdouble)] return half*exp(|x|) */
70 if (ix < 0x40862e42fefa39efLL) return half*__ieee754_expl(fabsl(x));
71
72 /* |x| in [log(maxdouble), overflowthresold] */
73 if (ix < 0x408633ce8fb9f87fLL) {
74 w = __ieee754_expl(half*fabsl(x));
75 t = half*w;
76 return t*w;
77 }
78
79 /* |x| > overflowthresold, cosh(x) overflow */
80 return huge*huge;
81 }
82 libm_alias_finite (__ieee754_coshl, __coshl)
83