1 /* $NetBSD: casinl.c,v 1.1 2014/10/10 00:48:18 christos 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 <complex.h>
33 #include <math.h>
34
35 #ifdef _HAVE_LONG_DOUBLE_MATH
36
37 #ifdef __weak_alias
__weak_alias(casinl,_casinl)38 __weak_alias(casinl, _casinl)
39 #endif
40
41 long double complex
42 casinl(long double complex z)
43 {
44 long double complex w;
45 long double complex ca, ct, zz, z2;
46 long double x, y;
47
48 x = creall(z);
49 y = cimagl(z);
50
51 #if 0 /* MD: test is incorrect, casin(>1) is defined */
52 if (y == 0.0L) {
53 if (fabsl(x) > 1.0L) {
54 w = M_PI_2L + 0.0L * (double complex) I;
55 #if 0
56 mtherr ("casinl", DOMAIN);
57 #endif
58 } else {
59 w = asinl(x) + 0.0L * (double complex) I;
60 }
61 return w;
62 }
63 #endif
64
65 /* Power series expansion */
66 /*
67 b = cabsl(z);
68 if( b < 0.125L )
69 {
70 z2.r = (x - y) * (x + y);
71 z2.i = 2.0L * x * y;
72
73 cn = 1.0L;
74 n = 1.0L;
75 ca.r = x;
76 ca.i = y;
77 sum.r = x;
78 sum.i = y;
79 do
80 {
81 ct.r = z2.r * ca.r - z2.i * ca.i;
82 ct.i = z2.r * ca.i + z2.i * ca.r;
83 ca.r = ct.r;
84 ca.i = ct.i;
85
86 cn *= n;
87 n += 1.0;
88 cn /= n;
89 n += 1.0;
90 b = cn/n;
91
92 ct.r *= b;
93 ct.i *= b;
94 sum.r += ct.r;
95 sum.i += ct.i;
96 b = fabsl(ct.r) + fabsl(ct.i);
97 }
98 while( b > MACHEPL );
99 w->r = sum.r;
100 w->i = sum.i;
101 return;
102 }
103 */
104
105
106 ca = x + y * (long double complex) I;
107 ct = ca * (long double complex) I;
108 /* sqrtl( 1 - z*z) */
109 /* cmull( &ca, &ca, &zz ) */
110 /*x * x - y * y */
111 zz = (x - y) * (x + y) + (2.0L * x * y) * (long double complex) I;
112
113 zz = 1.0L - creall(zz) - cimagl(zz) * (long double complex) I;
114 z2 = csqrtl(zz);
115
116 zz = ct + z2;
117 zz = clogl(zz);
118 /* multiply by 1/i = -i */
119 w = zz * (-1.0L * (long double complex) I);
120 return w;
121 }
122
123 #endif
124
