1 | /* |
2 | * ==================================================== |
3 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
4 | * |
5 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
6 | * Permission to use, copy, modify, and distribute this |
7 | * software is freely granted, provided that this notice |
8 | * is preserved. |
9 | * ==================================================== |
10 | */ |
11 | |
12 | #if defined(LIBM_SCCS) && !defined(lint) |
13 | static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $" ; |
14 | #endif |
15 | |
16 | /* __ieee754_coshl(x) |
17 | * Method : |
18 | * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 |
19 | * 1. Replace x by |x| (coshl(x) = coshl(-x)). |
20 | * 2. |
21 | * [ exp(x) - 1 ]^2 |
22 | * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- |
23 | * 2*exp(x) |
24 | * |
25 | * exp(x) + 1/exp(x) |
26 | * ln2/2 <= x <= 22 : coshl(x) := ------------------- |
27 | * 2 |
28 | * 22 <= x <= lnovft : coshl(x) := expl(x)/2 |
29 | * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) |
30 | * ln2ovft < x : coshl(x) := huge*huge (overflow) |
31 | * |
32 | * Special cases: |
33 | * coshl(x) is |x| if x is +INF, -INF, or NaN. |
34 | * only coshl(0)=1 is exact for finite x. |
35 | */ |
36 | |
37 | #include <math.h> |
38 | #include <math_private.h> |
39 | |
40 | static const long double one = 1.0, half=0.5, huge = 1.0e4900L; |
41 | |
42 | long double |
43 | __ieee754_coshl (long double x) |
44 | { |
45 | long double t,w; |
46 | int32_t ex; |
47 | uint32_t mx,lx; |
48 | |
49 | /* High word of |x|. */ |
50 | GET_LDOUBLE_WORDS(ex,mx,lx,x); |
51 | ex &= 0x7fff; |
52 | |
53 | /* |x| in [0,22] */ |
54 | if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { |
55 | /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ |
56 | if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { |
57 | if (ex<0x3fbc) 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*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ |
64 | t = __ieee754_expl(fabsl(x)); |
65 | return half*t+half/t; |
66 | } |
67 | |
68 | /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ |
69 | if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) |
70 | return half*__ieee754_expl(fabsl(x)); |
71 | |
72 | /* |x| in [log(maxdouble), log(2*maxdouble)) */ |
73 | if (ex == 0x400c && (mx < 0xb174ddc0u |
74 | || (mx == 0xb174ddc0u && lx < 0x31aec0ebu))) |
75 | { |
76 | w = __ieee754_expl(half*fabsl(x)); |
77 | t = half*w; |
78 | return t*w; |
79 | } |
80 | |
81 | /* x is INF or NaN */ |
82 | if(ex==0x7fff) return x*x; |
83 | |
84 | /* |x| >= log(2*maxdouble), cosh(x) overflow */ |
85 | return huge*huge; |
86 | } |
87 | strong_alias (__ieee754_coshl, __coshl_finite) |
88 | |