1 /* $NetBSD: cephes_subr.c,v 1.1 2007/08/20 16:01:33 drochner Exp $ */
2
3 /*-
4 * Copyright (c) 2007 The NetBSD Foundation, Inc.
5 * All rights reserved.
6 *
7 * This code is derived from software written by Stephen L. Moshier.
8 * It is redistributed by the NetBSD Foundation by permission of the author.
9 *
10 * Redistribution and use in source and binary forms, with or without
11 * modification, are permitted provided that the following conditions
12 * are met:
13 * 1. Redistributions of source code must retain the above copyright
14 * notice, this list of conditions and the following disclaimer.
15 * 2. Redistributions in binary form must reproduce the above copyright
16 * notice, this list of conditions and the following disclaimer in the
17 * documentation and/or other materials provided with the distribution.
18 *
19 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
20 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
21 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
23 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
24 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
25 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
26 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
27 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
28 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
29 * POSSIBILITY OF SUCH DAMAGE.
30 *
31 * imported and modified include for newlib 2010/10/03
32 * Marco Atzeri <marco_atzeri@yahoo.it>
33 */
34
35 #define _DEFAULT_SOURCE
36 #include <complex.h>
37 #include <math.h>
38 #include "cephes_subr.h"
39
40 /* calculate cosh and sinh */
41
42 void
_cchsh(double x,double * c,double * s)43 _cchsh(double x, double *c, double *s)
44 {
45 double e, ei;
46
47 if (fabs(x) <= 0.5) {
48 *c = cosh(x);
49 *s = sinh(x);
50 } else {
51 e = exp(x);
52 ei = 0.5 / e;
53 e = 0.5 * e;
54 *s = e - ei;
55 *c = e + ei;
56 }
57 }
58
59 /* Program to subtract nearest integer multiple of PI */
60
61 /* extended precision value of PI: */
62 static const double DP1 = 3.14159265160560607910E0;
63 static const double DP2 = 1.98418714791870343106E-9;
64 static const double DP3 = 1.14423774522196636802E-17;
65 #define MACHEP 1.1e-16
66
67 double
_redupi(double x)68 _redupi(double x)
69 {
70 double t;
71 long i;
72
73 t = x / M_PI;
74 if (t >= 0.0)
75 t += 0.5;
76 else
77 t -= 0.5;
78
79 i = t; /* the multiple */
80 t = i;
81 t = ((x - t * DP1) - t * DP2) - t * DP3;
82 return t;
83 }
84
85 /* Taylor series expansion for cosh(2y) - cos(2x) */
86
87 double
_ctans(double complex z)88 _ctans(double complex z)
89 {
90 double f, x, x2, y, y2, rn, t;
91 double d;
92
93 x = fabs(2.0 * creal(z));
94 y = fabs(2.0 * cimag(z));
95
96 x = _redupi(x);
97
98 x = x * x;
99 y = y * y;
100 x2 = 1.0;
101 y2 = 1.0;
102 f = 1.0;
103 rn = 0.0;
104 d = 0.0;
105 do {
106 rn += 1.0;
107 f *= rn;
108 rn += 1.0;
109 f *= rn;
110 x2 *= x;
111 y2 *= y;
112 t = y2 + x2;
113 t /= f;
114 d += t;
115
116 rn += 1.0;
117 f *= rn;
118 rn += 1.0;
119 f *= rn;
120 x2 *= x;
121 y2 *= y;
122 t = y2 - x2;
123 t /= f;
124 d += t;
125 } while (fabs(t/d) > MACHEP);
126 return d;
127 }
128
