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 /* coshl(x)
14 * Method :
15 * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
16 * 1. Replace x by |x| (coshl(x) = coshl(-x)).
17 * 2.
18 * [ exp(x) - 1 ]^2
19 * 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
20 * 2*exp(x)
21 *
22 * exp(x) + 1/exp(x)
23 * ln2/2 <= x <= 22 : coshl(x) := -------------------
24 * 2
25 * 22 <= x <= lnovft : coshl(x) := expl(x)/2
26 * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2)
27 * ln2ovft < x : coshl(x) := huge*huge (overflow)
28 *
29 * Special cases:
30 * coshl(x) is |x| if x is +INF, -INF, or NaN.
31 * only coshl(0)=1 is exact for finite x.
32 */
33
34 static const long double one = 1.0l, half=0.5l, huge = 1.0e4900L;
35
36 long double
coshl(long double x)37 coshl(long double x)
38 {
39 long double t,w;
40 int32_t ex;
41 u_int32_t mx,lx;
42
43 /* High word of |x|. */
44 GET_LDOUBLE_WORDS(ex,mx,lx,x);
45 ex &= 0x7fff;
46
47 /* x is INF or NaN */
48 if(ex==0x7fff) return x*x;
49
50 /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
51 if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
52 if (ex<0x3fbc) return one; /* cosh(tiny) = 1 */
53 t = expm1l(fabsl(x));
54 w = one+t;
55 return one+(t*t)/(w+w);
56 }
57
58 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
59 if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
60 t = expl(fabsl(x));
61 return half*t+half/t;
62 }
63
64 /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
65 if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
66 return half*expl(fabsl(x));
67
68 /* |x| in [log(maxdouble), log(2*maxdouble)) */
69 if (ex == 0x400c && (mx < 0xb174ddc0u
70 || (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
71 {
72 w = expl(half*fabsl(x));
73 t = half*w;
74 return t*w;
75 }
76
77 /* |x| >= log(2*maxdouble), cosh(x) overflow */
78 return __math_oflowl(0);
79 }
80
