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 #include <libm-alias-finite.h>
40
41 static const long double one = 1.0, half=0.5, huge = 1.0e4900L;
42
43 long double
__ieee754_coshl(long double x)44 __ieee754_coshl (long double x)
45 {
46 long double t,w;
47 int32_t ex;
48 uint32_t mx,lx;
49
50 /* High word of |x|. */
51 GET_LDOUBLE_WORDS(ex,mx,lx,x);
52 ex &= 0x7fff;
53
54 /* |x| in [0,22] */
55 if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
56 /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
57 if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
58 if (ex<0x3fbc) return one; /* cosh(tiny) = 1 */
59 t = __expm1l(fabsl(x));
60 w = one+t;
61 return one+(t*t)/(w+w);
62 }
63
64 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
65 t = __ieee754_expl(fabsl(x));
66 return half*t+half/t;
67 }
68
69 /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
70 if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
71 return half*__ieee754_expl(fabsl(x));
72
73 /* |x| in [log(maxdouble), log(2*maxdouble)) */
74 if (ex == 0x400c && (mx < 0xb174ddc0u
75 || (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
76 {
77 w = __ieee754_expl(half*fabsl(x));
78 t = half*w;
79 return t*w;
80 }
81
82 /* x is INF or NaN */
83 if(ex==0x7fff) return x*x;
84
85 /* |x| >= log(2*maxdouble), cosh(x) overflow */
86 return huge*huge;
87 }
88 libm_alias_finite (__ieee754_coshl, __coshl)
89