1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
|
/* $OpenBSD: n_cosh.c,v 1.10 2009/10/27 23:59:29 deraadt Exp $ */
/* $NetBSD: n_cosh.c,v 1.1 1995/10/10 23:36:42 ragge Exp $ */
/*
* Copyright (c) 1985, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
/* COSH(X)
* RETURN THE HYPERBOLIC COSINE OF X
* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
* CODED IN C BY K.C. NG, 1/8/85;
* REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
*
* Required system supported functions :
* copysign(x,y)
* scalbn(x,N)
*
* Required kernel function:
* exp(x)
* exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465
*
* Method :
* 1. Replace x by |x|.
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* 0.3465 <= x <= 22 : cosh(x) := -------------------
* 2
* 22 <= x <= lnovfl : cosh(x) := exp(x)/2
* lnovfl <= x <= lnovfl+log(2)
* : cosh(x) := exp(x)/2 (avoid overflow)
* log(2)+lnovfl < x < INF: overflow to INF
*
* Note: .3465 is a number near one half of ln2.
*
* Special cases:
* cosh(x) is x if x is +INF, -INF, or NaN.
* only cosh(0)=1 is exact for finite x.
*
* Accuracy:
* cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
* In a test run with 768,000 random arguments on a VAX, the maximum
* observed error was 1.23 ulps (units in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
*/
#include "math.h"
#include "mathimpl.h"
static const double mln2hi = 8.8029691931113054792E1;
static const double mln2lo = -4.9650192275318476525E-16;
static const double lnovfl = 8.8029691931113053016E1;
#if defined(__vax__)
static max = 126 ;
#else /* defined(__vax__) */
static max = 1023 ;
#endif /* defined(__vax__) */
double
cosh(double x)
{
static const double half=1.0/2.0,
one=1.0, small=1.0E-18; /* fl(1+small)==1 */
double t;
if (isnan(x))
return (x);
if((x=copysign(x,one)) <= 22)
if(x<0.3465)
if(x<small) return(one+x);
else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
else /* for x lies in [0.3465,22] */
{ t=exp(x); return((t+one/t)*half); }
if( lnovfl <= x && x <= (lnovfl+0.7))
/* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
* and return 2^max*exp(x) to avoid unnecessary overflow
*/
return(scalbn(exp((x-mln2hi)-mln2lo), max));
else
return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */
}
|
