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 #include "math.h"
35 #include "math_private.h"
36 
37 static const long double one = 1.0, half=0.5, huge = 1.0e4900L;
38 
39 long double
40 coshl(long double x)
41 {
42 	long double t,w;
43 	int32_t ex;
44 	u_int32_t mx,lx;
45 
46     /* High word of |x|. */
47 	GET_LDOUBLE_WORDS(ex,mx,lx,x);
48 	ex &= 0x7fff;
49 
50     /* x is INF or NaN */
51 	if(ex==0x7fff) return x*x;
52 
53     /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
54 	if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
55 	    t = expm1l(fabsl(x));
56 	    w = one+t;
57 	    if (ex<0x3fbc) return w;	/* cosh(tiny) = 1 */
58 	    return one+(t*t)/(w+w);
59 	}
60 
61     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
62 	if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
63 		t = expl(fabsl(x));
64 		return half*t+half/t;
65 	}
66 
67     /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
68 	if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
69 		return half*expl(fabsl(x));
70 
71     /* |x| in [log(maxdouble), log(2*maxdouble)) */
72 	if (ex == 0x400c && (mx < 0xb174ddc0u
73 			     || (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
74 	{
75 	    w = expl(half*fabsl(x));
76 	    t = half*w;
77 	    return t*w;
78 	}
79 
80     /* |x| >= log(2*maxdouble), cosh(x) overflow */
81 	return huge*huge;
82 }
83