1 /* $NetBSD: n_cosh.c,v 1.9 2014/10/10 20:58:09 martin 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
33 static 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
94 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB)
95 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
96 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA)
97
98 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF)
99 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
100 ic(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
114 double
cosh(double x)115 cosh(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
143 float
coshf(float x)144 coshf(float x)
145 {
146 return(cosh((double)x));
147 }
148