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)
13static 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#ifdef __STDC__
41static const long double one = 1.0, half=0.5, huge = 1.0e4900L;
42#else
43static long double one = 1.0, half=0.5, huge = 1.0e4900L;
44#endif
45
46#ifdef __STDC__
47	long double __ieee754_coshl(long double x)
48#else
49	long double __ieee754_coshl(x)
50	long double x;
51#endif
52{
53	long double t,w;
54	int32_t ex;
55	u_int32_t mx,lx;
56
57    /* High word of |x|. */
58	GET_LDOUBLE_WORDS(ex,mx,lx,x);
59	ex &= 0x7fff;
60
61    /* x is INF or NaN */
62	if(ex==0x7fff) return x*x;
63
64    /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
65	if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
66	    t = __expm1l(fabsl(x));
67	    w = one+t;
68	    if (ex<0x3fbc) return w;	/* cosh(tiny) = 1 */
69	    return one+(t*t)/(w+w);
70	}
71
72    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
73	if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
74		t = __ieee754_expl(fabsl(x));
75		return half*t+half/t;
76	}
77
78    /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
79	if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
80		return half*__ieee754_expl(fabsl(x));
81
82    /* |x| in [log(maxdouble), log(2*maxdouble)) */
83	if (ex == 0x400c && (mx < 0xb174ddc0u
84			     || (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
85	{
86	    w = __ieee754_expl(half*fabsl(x));
87	    t = half*w;
88	    return t*w;
89	}
90
91    /* |x| >= log(2*maxdouble), cosh(x) overflow */
92	return huge*huge;
93}
94