1/*      $NetBSD: n_cosh.c,v 1.8 2008/03/20 16:41:26 mhitch Exp $ */
2/*
3 * Copyright (c) 1985, 1993
4 *	The Regents of the University of California.  All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 * 3. Neither the name of the University nor the names of its contributors
15 *    may be used to endorse or promote products derived from this software
16 *    without specific prior written permission.
17 *
18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28 * SUCH DAMAGE.
29 */
30
31#ifndef lint
32#if 0
33static char sccsid[] = "@(#)cosh.c	8.1 (Berkeley) 6/4/93";
34#endif
35#endif /* not lint */
36
37/* COSH(X)
38 * RETURN THE HYPERBOLIC COSINE OF X
39 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
40 * CODED IN C BY K.C. NG, 1/8/85;
41 * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
42 *
43 * Required system supported functions :
44 *	copysign(x,y)
45 *	scalb(x,N)
46 *
47 * Required kernel function:
48 *	exp(x)
49 *	exp__E(x,c)	...return exp(x+c)-1-x for |x|<0.3465
50 *
51 * Method :
52 *	1. Replace x by |x|.
53 *	2.
54 *		                                        [ exp(x) - 1 ]^2
55 *	    0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
56 *			       			           2*exp(x)
57 *
58 *		                                   exp(x) +  1/exp(x)
59 *	    0.3465   <= x <= 22      :  cosh(x) := -------------------
60 *			       			           2
61 *	    22       <= x <= lnovfl  :  cosh(x) := exp(x)/2
62 *	    lnovfl   <= x <= lnovfl+log(2)
63 *				     :  cosh(x) := exp(x)/2 (avoid overflow)
64 *	    log(2)+lnovfl <  x <  INF:  overflow to INF
65 *
66 *	Note: .3465 is a number near one half of ln2.
67 *
68 * Special cases:
69 *	cosh(x) is x if x is +INF, -INF, or NaN.
70 *	only cosh(0)=1 is exact for finite x.
71 *
72 * Accuracy:
73 *	cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
74 *	In a test run with 768,000 random arguments on a VAX, the maximum
75 *	observed error was 1.23 ulps (units in the last place).
76 *
77 * Constants:
78 * The hexadecimal values are the intended ones for the following constants.
79 * The decimal values may be used, provided that the compiler will convert
80 * from decimal to binary accurately enough to produce the hexadecimal values
81 * shown.
82 */
83
84#define _LIBM_STATIC
85#include "../src/namespace.h"
86#include "mathimpl.h"
87
88#ifdef __weak_alias
89__weak_alias(cosh, _cosh);
90__weak_alias(_coshl, _cosh);
91__weak_alias(coshf, _coshf);
92#endif
93
94vc(mln2hi, 8.8029691931113054792E1   ,0f33,43b0,2bdb,c7e2,   7, .B00F33C7E22BDB)
95vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
96vc(lnovfl, 8.8029691931113053016E1   ,0f33,43b0,2bda,c7e2,   7, .B00F33C7E22BDA)
97
98ic(mln2hi, 7.0978271289338397310E2,    10, 1.62E42FEFA39EF)
99ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
100ic(lnovfl, 7.0978271289338397310E2,     9, 1.62E42FEFA39EF)
101
102#ifdef vccast
103#define   mln2hi    vccast(mln2hi)
104#define   mln2lo    vccast(mln2lo)
105#define   lnovfl    vccast(lnovfl)
106#endif
107
108#if defined(__vax__)||defined(tahoe)
109#define EXPMAX 126
110#else
111#define EXPMAX 1023
112#endif	/* defined(__vax__)||defined(tahoe) */
113
114double
115cosh(double x)
116{
117	static const double half=1.0/2.0,
118		one=1.0, small=1.0E-18; /* fl(1+small)==1 */
119	double t;
120
121#if !defined(__vax__)&&!defined(tahoe)
122	if(x!=x) return(x);	/* x is NaN */
123#endif	/* !defined(__vax__)&&!defined(tahoe) */
124	if((x=copysign(x,one)) <= 22) {
125	    if(x<0.3465) {
126		if(x<small) { return(one+x); }
127		else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
128
129	    } else /* for x lies in [0.3465,22] */
130	        { t=exp(x); return((t+one/t)*half); }
131	}
132
133	if( lnovfl <= x && x <= (lnovfl+0.7))
134        /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(EXPMAX+1))
135         * and return 2^EXPMAX*exp(x) to avoid unnecessary overflow
136         */
137	    return(scalb(exp((x-mln2hi)-mln2lo), EXPMAX));
138
139	else
140	    return(exp(x)*half);	/* for large x,  cosh(x)=exp(x)/2 */
141}
142
143float
144coshf(float x)
145{
146	return(cosh((double)x));
147}
148