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
32 #include "../src/namespace.h"
33 #include <complex.h>
34 #include <math.h>
35 #include "cephes_subrf.h"
36
37 /* calculate cosh and sinh */
38
39 void
_cchshf(float x,float * c,float * s)40 _cchshf(float x, float *c, float *s)
41 {
42 float e, ei;
43
44 if (fabsf(x) <= 0.5f) {
45 *c = coshf(x);
46 *s = sinhf(x);
47 } else {
48 e = expf(x);
49 ei = 0.5f / e;
50 e = 0.5f * e;
51 *s = e - ei;
52 *c = e + ei;
53 }
54 }
55
56 /* Program to subtract nearest integer multiple of PI */
57
58 /* extended precision value of PI: */
59 static const double DP1 = 3.140625;
60 static const double DP2 = 9.67502593994140625E-4;
61 static const double DP3 = 1.509957990978376432E-7;
62 #define MACHEPF 3.0e-8
63
64 float
_redupif(float x)65 _redupif(float x)
66 {
67 float t;
68 long i;
69
70 t = x / (float)M_PI;
71 if (t >= 0.0f)
72 t += 0.5f;
73 else
74 t -= 0.5f;
75
76 i = t; /* the multiple */
77 t = i;
78 t = ((x - t * DP1) - t * DP2) - t * DP3;
79 return t;
80 }
81
82 /* Taylor series expansion for cosh(2y) - cos(2x) */
83
84 float
_ctansf(float complex z)85 _ctansf(float complex z)
86 {
87 float f, x, x2, y, y2, rn, t, d;
88
89 x = fabsf(2.0f * crealf(z));
90 y = fabsf(2.0f * cimagf(z));
91
92 x = _redupif(x);
93
94 x = x * x;
95 y = y * y;
96 x2 = 1.0f;
97 y2 = 1.0f;
98 f = 1.0f;
99 rn = 0.0f;
100 d = 0.0f;
101 do {
102 rn += 1.0f;
103 f *= rn;
104 rn += 1.0f;
105 f *= rn;
106 x2 *= x;
107 y2 *= y;
108 t = y2 + x2;
109 t /= f;
110 d += t;
111
112 rn += 1.0f;
113 f *= rn;
114 rn += 1.0f;
115 f *= rn;
116 x2 *= x;
117 y2 *= y;
118 t = y2 - x2;
119 t /= f;
120 d += t;
121 } while (fabsf(t/d) > MACHEPF);
122 return d;
123 }
124