1 | /* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */ |
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 <= 22 : cosh(x) := ------------------- |
24 | * 2 |
25 | * 22 <= 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 | |
37 | static const double one = 1.0, half=0.5, huge = 1.0e300; |
38 | |
39 | double |
40 | __ieee754_cosh (double x) |
41 | { |
42 | double t,w; |
43 | int32_t ix; |
44 | |
45 | /* High word of |x|. */ |
46 | GET_HIGH_WORD(ix,x); |
47 | ix &= 0x7fffffff; |
48 | |
49 | /* |x| in [0,22] */ |
50 | if (ix < 0x40360000) { |
51 | /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ |
52 | if(ix<0x3fd62e43) { |
53 | if (ix<0x3c800000) /* cosh(tiny) = 1 */ |
54 | return one; |
55 | t = __expm1(fabs(x)); |
56 | w = one+t; |
57 | return one+(t*t)/(w+w); |
58 | } |
59 | |
60 | /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ |
61 | t = __ieee754_exp(fabs(x)); |
62 | return half*t+half/t; |
63 | } |
64 | |
65 | /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ |
66 | if (ix < 0x40862e42) return half*__ieee754_exp(fabs(x)); |
67 | |
68 | /* |x| in [log(maxdouble), overflowthresold] */ |
69 | int64_t fix; |
70 | EXTRACT_WORDS64(fix, x); |
71 | fix &= UINT64_C(0x7fffffffffffffff); |
72 | if (fix <= UINT64_C(0x408633ce8fb9f87d)) { |
73 | w = __ieee754_exp(half*fabs(x)); |
74 | t = half*w; |
75 | return t*w; |
76 | } |
77 | |
78 | /* x is INF or NaN */ |
79 | if(ix>=0x7ff00000) return x*x; |
80 | |
81 | /* |x| > overflowthresold, cosh(x) overflow */ |
82 | return huge*huge; |
83 | } |
84 | strong_alias (__ieee754_cosh, __cosh_finite) |
85 | |