1 /* $NetBSD: casin.c,v 1.1 2007/08/20 16:01:31 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
36 #ifdef __weak_alias
__weak_alias(casin,_casin)37 __weak_alias(casin, _casin)
38 #endif
39
40 double complex
41 casin(double complex z)
42 {
43 double complex w;
44 double complex ca, ct, zz, z2;
45 double x, y;
46
47 x = creal(z);
48 y = cimag(z);
49
50 #if 0 /* MD: test is incorrect, casin(>1) is defined */
51 if (y == 0.0) {
52 if (fabs(x) > 1.0) {
53 w = M_PI_2 + 0.0 * I;
54 #if 0
55 mtherr ("casin", DOMAIN);
56 #endif
57 } else {
58 w = asin(x) + 0.0 * I;
59 }
60 return w;
61 }
62 #endif
63
64 /* Power series expansion */
65 /*
66 b = cabs(z);
67 if( b < 0.125 )
68 {
69 z2.r = (x - y) * (x + y);
70 z2.i = 2.0 * x * y;
71
72 cn = 1.0;
73 n = 1.0;
74 ca.r = x;
75 ca.i = y;
76 sum.r = x;
77 sum.i = y;
78 do
79 {
80 ct.r = z2.r * ca.r - z2.i * ca.i;
81 ct.i = z2.r * ca.i + z2.i * ca.r;
82 ca.r = ct.r;
83 ca.i = ct.i;
84
85 cn *= n;
86 n += 1.0;
87 cn /= n;
88 n += 1.0;
89 b = cn/n;
90
91 ct.r *= b;
92 ct.i *= b;
93 sum.r += ct.r;
94 sum.i += ct.i;
95 b = fabs(ct.r) + fabs(ct.i);
96 }
97 while( b > MACHEP );
98 w->r = sum.r;
99 w->i = sum.i;
100 return;
101 }
102 */
103
104
105 ca = x + y * I;
106 ct = ca * I;
107 /* sqrt( 1 - z*z) */
108 /* cmul( &ca, &ca, &zz ) */
109 /*x * x - y * y */
110 zz = (x - y) * (x + y) + (2.0 * x * y) * I;
111
112 zz = 1.0 - creal(zz) - cimag(zz) * I;
113 z2 = csqrt(zz);
114
115 zz = ct + z2;
116 zz = clog(zz);
117 /* multiply by 1/i = -i */
118 w = zz * (-1.0 * I);
119 return w;
120 }
121