cephes_subr.c revision 1.1 1 1.1 drochner /* $NetBSD: cephes_subr.c,v 1.1 2007/08/20 16:01:33 drochner Exp $ */
2 1.1 drochner
3 1.1 drochner /*-
4 1.1 drochner * Copyright (c) 2007 The NetBSD Foundation, Inc.
5 1.1 drochner * All rights reserved.
6 1.1 drochner *
7 1.1 drochner * This code is derived from software written by Stephen L. Moshier.
8 1.1 drochner * It is redistributed by the NetBSD Foundation by permission of the author.
9 1.1 drochner *
10 1.1 drochner * Redistribution and use in source and binary forms, with or without
11 1.1 drochner * modification, are permitted provided that the following conditions
12 1.1 drochner * are met:
13 1.1 drochner * 1. Redistributions of source code must retain the above copyright
14 1.1 drochner * notice, this list of conditions and the following disclaimer.
15 1.1 drochner * 2. Redistributions in binary form must reproduce the above copyright
16 1.1 drochner * notice, this list of conditions and the following disclaimer in the
17 1.1 drochner * documentation and/or other materials provided with the distribution.
18 1.1 drochner *
19 1.1 drochner * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
20 1.1 drochner * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
21 1.1 drochner * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22 1.1 drochner * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
23 1.1 drochner * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
24 1.1 drochner * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
25 1.1 drochner * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
26 1.1 drochner * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
27 1.1 drochner * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
28 1.1 drochner * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
29 1.1 drochner * POSSIBILITY OF SUCH DAMAGE.
30 1.1 drochner */
31 1.1 drochner
32 1.1 drochner #include "../src/namespace.h"
33 1.1 drochner #include <complex.h>
34 1.1 drochner #include <math.h>
35 1.1 drochner #include "cephes_subr.h"
36 1.1 drochner
37 1.1 drochner /* calculate cosh and sinh */
38 1.1 drochner
39 1.1 drochner void
40 1.1 drochner _cchsh(double x, double *c, double *s)
41 1.1 drochner {
42 1.1 drochner double e, ei;
43 1.1 drochner
44 1.1 drochner if (fabs(x) <= 0.5) {
45 1.1 drochner *c = cosh(x);
46 1.1 drochner *s = sinh(x);
47 1.1 drochner } else {
48 1.1 drochner e = exp(x);
49 1.1 drochner ei = 0.5 / e;
50 1.1 drochner e = 0.5 * e;
51 1.1 drochner *s = e - ei;
52 1.1 drochner *c = e + ei;
53 1.1 drochner }
54 1.1 drochner }
55 1.1 drochner
56 1.1 drochner /* Program to subtract nearest integer multiple of PI */
57 1.1 drochner
58 1.1 drochner /* extended precision value of PI: */
59 1.1 drochner static const double DP1 = 3.14159265160560607910E0;
60 1.1 drochner static const double DP2 = 1.98418714791870343106E-9;
61 1.1 drochner static const double DP3 = 1.14423774522196636802E-17;
62 1.1 drochner #define MACHEP 1.1e-16
63 1.1 drochner
64 1.1 drochner double
65 1.1 drochner _redupi(double x)
66 1.1 drochner {
67 1.1 drochner double t;
68 1.1 drochner long i;
69 1.1 drochner
70 1.1 drochner t = x / M_PI;
71 1.1 drochner if (t >= 0.0)
72 1.1 drochner t += 0.5;
73 1.1 drochner else
74 1.1 drochner t -= 0.5;
75 1.1 drochner
76 1.1 drochner i = t; /* the multiple */
77 1.1 drochner t = i;
78 1.1 drochner t = ((x - t * DP1) - t * DP2) - t * DP3;
79 1.1 drochner return t;
80 1.1 drochner }
81 1.1 drochner
82 1.1 drochner /* Taylor series expansion for cosh(2y) - cos(2x) */
83 1.1 drochner
84 1.1 drochner double
85 1.1 drochner _ctans(double complex z)
86 1.1 drochner {
87 1.1 drochner double f, x, x2, y, y2, rn, t;
88 1.1 drochner double d;
89 1.1 drochner
90 1.1 drochner x = fabs(2.0 * creal(z));
91 1.1 drochner y = fabs(2.0 * cimag(z));
92 1.1 drochner
93 1.1 drochner x = _redupi(x);
94 1.1 drochner
95 1.1 drochner x = x * x;
96 1.1 drochner y = y * y;
97 1.1 drochner x2 = 1.0;
98 1.1 drochner y2 = 1.0;
99 1.1 drochner f = 1.0;
100 1.1 drochner rn = 0.0;
101 1.1 drochner d = 0.0;
102 1.1 drochner do {
103 1.1 drochner rn += 1.0;
104 1.1 drochner f *= rn;
105 1.1 drochner rn += 1.0;
106 1.1 drochner f *= rn;
107 1.1 drochner x2 *= x;
108 1.1 drochner y2 *= y;
109 1.1 drochner t = y2 + x2;
110 1.1 drochner t /= f;
111 1.1 drochner d += t;
112 1.1 drochner
113 1.1 drochner rn += 1.0;
114 1.1 drochner f *= rn;
115 1.1 drochner rn += 1.0;
116 1.1 drochner f *= rn;
117 1.1 drochner x2 *= x;
118 1.1 drochner y2 *= y;
119 1.1 drochner t = y2 - x2;
120 1.1 drochner t /= f;
121 1.1 drochner d += t;
122 1.1 drochner } while (fabs(t/d) > MACHEP);
123 1.1 drochner return d;
124 1.1 drochner }
125