1*2fe8fb19SBen Gras /* $NetBSD: casinf.c,v 1.1 2007/08/20 16:01:31 drochner Exp $ */
2*2fe8fb19SBen Gras
3*2fe8fb19SBen Gras /*-
4*2fe8fb19SBen Gras * Copyright (c) 2007 The NetBSD Foundation, Inc.
5*2fe8fb19SBen Gras * All rights reserved.
6*2fe8fb19SBen Gras *
7*2fe8fb19SBen Gras * This code is derived from software written by Stephen L. Moshier.
8*2fe8fb19SBen Gras * It is redistributed by the NetBSD Foundation by permission of the author.
9*2fe8fb19SBen Gras *
10*2fe8fb19SBen Gras * Redistribution and use in source and binary forms, with or without
11*2fe8fb19SBen Gras * modification, are permitted provided that the following conditions
12*2fe8fb19SBen Gras * are met:
13*2fe8fb19SBen Gras * 1. Redistributions of source code must retain the above copyright
14*2fe8fb19SBen Gras * notice, this list of conditions and the following disclaimer.
15*2fe8fb19SBen Gras * 2. Redistributions in binary form must reproduce the above copyright
16*2fe8fb19SBen Gras * notice, this list of conditions and the following disclaimer in the
17*2fe8fb19SBen Gras * documentation and/or other materials provided with the distribution.
18*2fe8fb19SBen Gras *
19*2fe8fb19SBen Gras * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
20*2fe8fb19SBen Gras * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
21*2fe8fb19SBen Gras * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22*2fe8fb19SBen Gras * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
23*2fe8fb19SBen Gras * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
24*2fe8fb19SBen Gras * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
25*2fe8fb19SBen Gras * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
26*2fe8fb19SBen Gras * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
27*2fe8fb19SBen Gras * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
28*2fe8fb19SBen Gras * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
29*2fe8fb19SBen Gras * POSSIBILITY OF SUCH DAMAGE.
30*2fe8fb19SBen Gras */
31*2fe8fb19SBen Gras
32*2fe8fb19SBen Gras #include "../src/namespace.h"
33*2fe8fb19SBen Gras #include <complex.h>
34*2fe8fb19SBen Gras #include <math.h>
35*2fe8fb19SBen Gras
36*2fe8fb19SBen Gras #ifdef __weak_alias
__weak_alias(casinf,_casinf)37*2fe8fb19SBen Gras __weak_alias(casinf, _casinf)
38*2fe8fb19SBen Gras #endif
39*2fe8fb19SBen Gras
40*2fe8fb19SBen Gras float complex
41*2fe8fb19SBen Gras casinf(float complex z)
42*2fe8fb19SBen Gras {
43*2fe8fb19SBen Gras float complex w;
44*2fe8fb19SBen Gras float complex ca, ct, zz, z2;
45*2fe8fb19SBen Gras float x, y;
46*2fe8fb19SBen Gras
47*2fe8fb19SBen Gras x = crealf(z);
48*2fe8fb19SBen Gras y = cimagf(z);
49*2fe8fb19SBen Gras
50*2fe8fb19SBen Gras #if 0 /* MD: test is incorrect, casin(>1) is defined */
51*2fe8fb19SBen Gras if (y == 0.0f) {
52*2fe8fb19SBen Gras if (fabsf(x) > 1.0) {
53*2fe8fb19SBen Gras w = M_PI_2 + 0.0f * I;
54*2fe8fb19SBen Gras #if 0
55*2fe8fb19SBen Gras mtherr ("casin", DOMAIN);
56*2fe8fb19SBen Gras #endif
57*2fe8fb19SBen Gras } else {
58*2fe8fb19SBen Gras w = asinf(x) + 0.0f * I;
59*2fe8fb19SBen Gras }
60*2fe8fb19SBen Gras return w;
61*2fe8fb19SBen Gras }
62*2fe8fb19SBen Gras #endif
63*2fe8fb19SBen Gras
64*2fe8fb19SBen Gras /* Power series expansion */
65*2fe8fb19SBen Gras /*
66*2fe8fb19SBen Gras b = cabsf(z);
67*2fe8fb19SBen Gras if( b < 0.125 )
68*2fe8fb19SBen Gras {
69*2fe8fb19SBen Gras z2.r = (x - y) * (x + y);
70*2fe8fb19SBen Gras z2.i = 2.0 * x * y;
71*2fe8fb19SBen Gras
72*2fe8fb19SBen Gras cn = 1.0;
73*2fe8fb19SBen Gras n = 1.0;
74*2fe8fb19SBen Gras ca.r = x;
75*2fe8fb19SBen Gras ca.i = y;
76*2fe8fb19SBen Gras sum.r = x;
77*2fe8fb19SBen Gras sum.i = y;
78*2fe8fb19SBen Gras do
79*2fe8fb19SBen Gras {
80*2fe8fb19SBen Gras ct.r = z2.r * ca.r - z2.i * ca.i;
81*2fe8fb19SBen Gras ct.i = z2.r * ca.i + z2.i * ca.r;
82*2fe8fb19SBen Gras ca.r = ct.r;
83*2fe8fb19SBen Gras ca.i = ct.i;
84*2fe8fb19SBen Gras
85*2fe8fb19SBen Gras cn *= n;
86*2fe8fb19SBen Gras n += 1.0;
87*2fe8fb19SBen Gras cn /= n;
88*2fe8fb19SBen Gras n += 1.0;
89*2fe8fb19SBen Gras b = cn/n;
90*2fe8fb19SBen Gras
91*2fe8fb19SBen Gras ct.r *= b;
92*2fe8fb19SBen Gras ct.i *= b;
93*2fe8fb19SBen Gras sum.r += ct.r;
94*2fe8fb19SBen Gras sum.i += ct.i;
95*2fe8fb19SBen Gras b = fabsf(ct.r) + fabsf(ct.i);
96*2fe8fb19SBen Gras }
97*2fe8fb19SBen Gras while( b > MACHEP );
98*2fe8fb19SBen Gras w->r = sum.r;
99*2fe8fb19SBen Gras w->i = sum.i;
100*2fe8fb19SBen Gras return;
101*2fe8fb19SBen Gras }
102*2fe8fb19SBen Gras */
103*2fe8fb19SBen Gras
104*2fe8fb19SBen Gras
105*2fe8fb19SBen Gras ca = x + y * I;
106*2fe8fb19SBen Gras ct = ca * I;
107*2fe8fb19SBen Gras /* sqrt( 1 - z*z) */
108*2fe8fb19SBen Gras /* cmul( &ca, &ca, &zz ) */
109*2fe8fb19SBen Gras /*x * x - y * y */
110*2fe8fb19SBen Gras zz = (x - y) * (x + y) + (2.0f * x * y) * I;
111*2fe8fb19SBen Gras
112*2fe8fb19SBen Gras zz = 1.0f - crealf(zz) - cimagf(zz) * I;
113*2fe8fb19SBen Gras z2 = csqrtf(zz);
114*2fe8fb19SBen Gras
115*2fe8fb19SBen Gras zz = ct + z2;
116*2fe8fb19SBen Gras zz = clogf(zz);
117*2fe8fb19SBen Gras /* multiply by 1/i = -i */
118*2fe8fb19SBen Gras w = zz * (-1.0f * I);
119*2fe8fb19SBen Gras return w;
120*2fe8fb19SBen Gras }
121