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 |
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(x: fabsl(x: 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: 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: x)); |
71 | |
72 | /* |x| in [log(maxdouble), overflowthresold] */ |
73 | if (ix < 0x408633ce8fb9f87fLL) { |
74 | w = __ieee754_expl(half*fabsl(x: 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 | |