1 /*
2 * Copyright (c) 1985 Regents of the University of California.
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 * 3. All advertising materials mentioning features or use of this software
14 * must display the following acknowledgement:
15 * This product includes software developed by the University of
16 * California, Berkeley and its contributors.
17 * 4. Neither the name of the University nor the names of its contributors
18 * may be used to endorse or promote products derived from this software
19 * without specific prior written permission.
20 *
21 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
22 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
23 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
24 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
25 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
26 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
27 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
28 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
29 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
30 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
31 * SUCH DAMAGE.
32 */
33
34 #ifndef lint
35 static char sccsid[] = "@(#)cosh.c 5.6 (Berkeley) 10/9/90";
36 #endif /* not lint */
37
38 /* COSH(X)
39 * RETURN THE HYPERBOLIC COSINE OF X
40 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
41 * CODED IN C BY K.C. NG, 1/8/85;
42 * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
43 *
44 * Required system supported functions :
45 * copysign(x,y)
46 * scalb(x,N)
47 *
48 * Required kernel function:
49 * exp(x)
50 * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465
51 *
52 * Method :
53 * 1. Replace x by |x|.
54 * 2.
55 * [ exp(x) - 1 ]^2
56 * 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
57 * 2*exp(x)
58 *
59 * exp(x) + 1/exp(x)
60 * 0.3465 <= x <= 22 : cosh(x) := -------------------
61 * 2
62 * 22 <= x <= lnovfl : cosh(x) := exp(x)/2
63 * lnovfl <= x <= lnovfl+log(2)
64 * : cosh(x) := exp(x)/2 (avoid overflow)
65 * log(2)+lnovfl < x < INF: overflow to INF
66 *
67 * Note: .3465 is a number near one half of ln2.
68 *
69 * Special cases:
70 * cosh(x) is x if x is +INF, -INF, or NaN.
71 * only cosh(0)=1 is exact for finite x.
72 *
73 * Accuracy:
74 * cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
75 * In a test run with 768,000 random arguments on a VAX, the maximum
76 * observed error was 1.23 ulps (units in the last place).
77 *
78 * Constants:
79 * The hexadecimal values are the intended ones for the following constants.
80 * The decimal values may be used, provided that the compiler will convert
81 * from decimal to binary accurately enough to produce the hexadecimal values
82 * shown.
83 */
84
85 #include "mathimpl.h"
86
87 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB)
88 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
89 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA)
90
91 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF)
92 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
93 ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF)
94
95 #ifdef vccast
96 #define mln2hi vccast(mln2hi)
97 #define mln2lo vccast(mln2lo)
98 #define lnovfl vccast(lnovfl)
99 #endif
100
101 #if defined(vax)||defined(tahoe)
102 static max = 126 ;
103 #else /* defined(vax)||defined(tahoe) */
104 static max = 1023 ;
105 #endif /* defined(vax)||defined(tahoe) */
106
cosh(x)107 double cosh(x)
108 double x;
109 {
110 static const double half=1.0/2.0,
111 one=1.0, small=1.0E-18; /* fl(1+small)==1 */
112 double t;
113
114 #if !defined(vax)&&!defined(tahoe)
115 if(x!=x) return(x); /* x is NaN */
116 #endif /* !defined(vax)&&!defined(tahoe) */
117 if((x=copysign(x,one)) <= 22)
118 if(x<0.3465)
119 if(x<small) return(one+x);
120 else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
121
122 else /* for x lies in [0.3465,22] */
123 { t=exp(x); return((t+one/t)*half); }
124
125 if( lnovfl <= x && x <= (lnovfl+0.7))
126 /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
127 * and return 2^max*exp(x) to avoid unnecessary overflow
128 */
129 return(scalb(exp((x-mln2hi)-mln2lo), max));
130
131 else
132 return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */
133 }
134