1 /* $NetBSD: cephes_subrf.c,v 1.1 2007/08/20 16:01:34 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_subrf.h"
39
40 /* calculate cosh and sinh */
41
42 void
_cchshf(float x,float * c,float * s)43 _cchshf(float x, float *c, float *s)
44 {
45 float e, ei;
46
47 if (fabsf(x) <= 0.5f) {
48 *c = coshf(x);
49 *s = sinhf(x);
50 } else {
51 e = expf(x);
52 ei = 0.5f / e;
53 e = 0.5f * 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 = 3.140625;
63 static const double DP2 = 9.67502593994140625E-4;
64 static const double DP3 = 1.509957990978376432E-7;
65 #define MACHEPF 3.0e-8f
66
67 float
_redupif(float x)68 _redupif(float x)
69 {
70 float t;
71 long i;
72
73 t = x / (float)M_PI;
74 if (t >= 0.0f)
75 t += 0.5f;
76 else
77 t -= 0.5f;
78
79 i = t; /* the multiple */
80 t = i;
81 t = (((double) x - (double) t * DP1) - (double) t * DP2) - (double) t * DP3;
82 return t;
83 }
84
85 /* Taylor series expansion for cosh(2y) - cos(2x) */
86
87 float
_ctansf(float complex z)88 _ctansf(float complex z)
89 {
90 float f, x, x2, y, y2, rn, t, d;
91
92 x = fabsf(2.0f * crealf(z));
93 y = fabsf(2.0f * cimagf(z));
94
95 x = _redupif(x);
96
97 x = x * x;
98 y = y * y;
99 x2 = 1.0f;
100 y2 = 1.0f;
101 f = 1.0f;
102 rn = 0.0f;
103 d = 0.0f;
104 do {
105 rn += 1.0f;
106 f *= rn;
107 rn += 1.0f;
108 f *= rn;
109 x2 *= x;
110 y2 *= y;
111 t = y2 + x2;
112 t /= f;
113 d += t;
114
115 rn += 1.0f;
116 f *= rn;
117 rn += 1.0f;
118 f *= rn;
119 x2 *= x;
120 y2 *= y;
121 t = y2 - x2;
122 t /= f;
123 d += t;
124 } while (fabsf(t/d) > MACHEPF);
125 return d;
126 }
127
