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 * imported and modified include for newlib 2010/10/03
32 * Marco Atzeri <marco_atzeri@yahoo.it>
33 */
34
35 /*
36 FUNCTION
37 <<casin>>, <<casinf>>---complex arc sine
38
39 INDEX
40 casin
41 INDEX
42 casinf
43
44 SYNOPSIS
45 #include <complex.h>
46 double complex casin(double complex <[z]>);
47 float complex casinf(float complex <[z]>);
48
49
50 DESCRIPTION
51 These functions compute the complex arc sine of <[z]>,
52 with branch cuts outside the interval [-1, +1] along the real axis.
53
54 <<casinf>> is identical to <<casin>>, except that it performs
55 its calculations on <<floats complex>>.
56
57 RETURNS
58 @ifnottex
59 These functions return the complex arc sine value, in the range
60 of a strip mathematically unbounded along the imaginary axis
61 and in the interval [-pi/2, +pi/2] along the real axis.
62 @end ifnottex
63 @tex
64 These functions return the complex arc sine value, in the range
65 of a strip mathematically unbounded along the imaginary axis
66 and in the interval [$-\pi/2$, $+\pi/2$] along the real axis.
67 @end tex
68
69 PORTABILITY
70 <<casin>> and <<casinf>> are ISO C99
71
72 QUICKREF
73 <<casin>> and <<casinf>> are ISO C99
74
75 */
76
77
78 #include <complex.h>
79 #include <math.h>
80
81 #ifdef __weak_alias
__weak_alias(casin,_casin)82 __weak_alias(casin, _casin)
83 #endif
84
85 double complex
86 casin(double complex z)
87 {
88 double complex w;
89 double complex ca, ct, zz, z2;
90 double x, y;
91
92 x = creal(z);
93 y = cimag(z);
94
95 #if 0 /* MD: test is incorrect, casin(>1) is defined */
96 if (y == 0.0) {
97 if (fabs(x) > 1.0) {
98 w = M_PI_2 + 0.0 * (double complex) I;
99 #if 0
100 mtherr ("casin", DOMAIN);
101 #endif
102 } else {
103 w = asin(x) + 0.0 * (double complex) I;
104 }
105 return w;
106 }
107 #endif
108
109 /* Power series expansion */
110 /*
111 b = cabs(z);
112 if( b < 0.125 )
113 {
114 z2.r = (x - y) * (x + y);
115 z2.i = 2.0 * x * y;
116
117 cn = 1.0;
118 n = 1.0;
119 ca.r = x;
120 ca.i = y;
121 sum.r = x;
122 sum.i = y;
123 do
124 {
125 ct.r = z2.r * ca.r - z2.i * ca.i;
126 ct.i = z2.r * ca.i + z2.i * ca.r;
127 ca.r = ct.r;
128 ca.i = ct.i;
129
130 cn *= n;
131 n += 1.0;
132 cn /= n;
133 n += 1.0;
134 b = cn/n;
135
136 ct.r *= b;
137 ct.i *= b;
138 sum.r += ct.r;
139 sum.i += ct.i;
140 b = fabs(ct.r) + fabs(ct.i);
141 }
142 while( b > MACHEP );
143 w->r = sum.r;
144 w->i = sum.i;
145 return;
146 }
147 */
148
149
150 ca = x + y * (double complex) I;
151 ct = ca * (double complex) I;
152 /* sqrt( 1 - z*z) */
153 /* cmul( &ca, &ca, &zz ) */
154 /*x * x - y * y */
155 zz = (x - y) * (x + y) + (2.0 * x * y) * (double complex) I;
156
157 zz = 1.0 - creal(zz) - cimag(zz) * (double complex) I;
158 z2 = csqrt(zz);
159
160 zz = ct + z2;
161 zz = clog(zz);
162 /* multiply by 1/i = -i */
163 w = zz * (-1.0 * (double complex) I);
164 return w;
165 }
166
