xref: /netbsd/lib/libm/complex/cephes_subrf.c (revision 6550d01e)
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
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
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
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