1*9d8b5fa7Sdrochner /* $NetBSD: casinf.c,v 1.1 2007/08/20 16:01:31 drochner Exp $ */
2*9d8b5fa7Sdrochner
3*9d8b5fa7Sdrochner /*-
4*9d8b5fa7Sdrochner * Copyright (c) 2007 The NetBSD Foundation, Inc.
5*9d8b5fa7Sdrochner * All rights reserved.
6*9d8b5fa7Sdrochner *
7*9d8b5fa7Sdrochner * This code is derived from software written by Stephen L. Moshier.
8*9d8b5fa7Sdrochner * It is redistributed by the NetBSD Foundation by permission of the author.
9*9d8b5fa7Sdrochner *
10*9d8b5fa7Sdrochner * Redistribution and use in source and binary forms, with or without
11*9d8b5fa7Sdrochner * modification, are permitted provided that the following conditions
12*9d8b5fa7Sdrochner * are met:
13*9d8b5fa7Sdrochner * 1. Redistributions of source code must retain the above copyright
14*9d8b5fa7Sdrochner * notice, this list of conditions and the following disclaimer.
15*9d8b5fa7Sdrochner * 2. Redistributions in binary form must reproduce the above copyright
16*9d8b5fa7Sdrochner * notice, this list of conditions and the following disclaimer in the
17*9d8b5fa7Sdrochner * documentation and/or other materials provided with the distribution.
18*9d8b5fa7Sdrochner *
19*9d8b5fa7Sdrochner * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
20*9d8b5fa7Sdrochner * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
21*9d8b5fa7Sdrochner * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22*9d8b5fa7Sdrochner * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
23*9d8b5fa7Sdrochner * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
24*9d8b5fa7Sdrochner * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
25*9d8b5fa7Sdrochner * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
26*9d8b5fa7Sdrochner * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
27*9d8b5fa7Sdrochner * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
28*9d8b5fa7Sdrochner * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
29*9d8b5fa7Sdrochner * POSSIBILITY OF SUCH DAMAGE.
30*9d8b5fa7Sdrochner */
31*9d8b5fa7Sdrochner
32*9d8b5fa7Sdrochner #include "../src/namespace.h"
33*9d8b5fa7Sdrochner #include <complex.h>
34*9d8b5fa7Sdrochner #include <math.h>
35*9d8b5fa7Sdrochner
36*9d8b5fa7Sdrochner #ifdef __weak_alias
__weak_alias(casinf,_casinf)37*9d8b5fa7Sdrochner __weak_alias(casinf, _casinf)
38*9d8b5fa7Sdrochner #endif
39*9d8b5fa7Sdrochner
40*9d8b5fa7Sdrochner float complex
41*9d8b5fa7Sdrochner casinf(float complex z)
42*9d8b5fa7Sdrochner {
43*9d8b5fa7Sdrochner float complex w;
44*9d8b5fa7Sdrochner float complex ca, ct, zz, z2;
45*9d8b5fa7Sdrochner float x, y;
46*9d8b5fa7Sdrochner
47*9d8b5fa7Sdrochner x = crealf(z);
48*9d8b5fa7Sdrochner y = cimagf(z);
49*9d8b5fa7Sdrochner
50*9d8b5fa7Sdrochner #if 0 /* MD: test is incorrect, casin(>1) is defined */
51*9d8b5fa7Sdrochner if (y == 0.0f) {
52*9d8b5fa7Sdrochner if (fabsf(x) > 1.0) {
53*9d8b5fa7Sdrochner w = M_PI_2 + 0.0f * I;
54*9d8b5fa7Sdrochner #if 0
55*9d8b5fa7Sdrochner mtherr ("casin", DOMAIN);
56*9d8b5fa7Sdrochner #endif
57*9d8b5fa7Sdrochner } else {
58*9d8b5fa7Sdrochner w = asinf(x) + 0.0f * I;
59*9d8b5fa7Sdrochner }
60*9d8b5fa7Sdrochner return w;
61*9d8b5fa7Sdrochner }
62*9d8b5fa7Sdrochner #endif
63*9d8b5fa7Sdrochner
64*9d8b5fa7Sdrochner /* Power series expansion */
65*9d8b5fa7Sdrochner /*
66*9d8b5fa7Sdrochner b = cabsf(z);
67*9d8b5fa7Sdrochner if( b < 0.125 )
68*9d8b5fa7Sdrochner {
69*9d8b5fa7Sdrochner z2.r = (x - y) * (x + y);
70*9d8b5fa7Sdrochner z2.i = 2.0 * x * y;
71*9d8b5fa7Sdrochner
72*9d8b5fa7Sdrochner cn = 1.0;
73*9d8b5fa7Sdrochner n = 1.0;
74*9d8b5fa7Sdrochner ca.r = x;
75*9d8b5fa7Sdrochner ca.i = y;
76*9d8b5fa7Sdrochner sum.r = x;
77*9d8b5fa7Sdrochner sum.i = y;
78*9d8b5fa7Sdrochner do
79*9d8b5fa7Sdrochner {
80*9d8b5fa7Sdrochner ct.r = z2.r * ca.r - z2.i * ca.i;
81*9d8b5fa7Sdrochner ct.i = z2.r * ca.i + z2.i * ca.r;
82*9d8b5fa7Sdrochner ca.r = ct.r;
83*9d8b5fa7Sdrochner ca.i = ct.i;
84*9d8b5fa7Sdrochner
85*9d8b5fa7Sdrochner cn *= n;
86*9d8b5fa7Sdrochner n += 1.0;
87*9d8b5fa7Sdrochner cn /= n;
88*9d8b5fa7Sdrochner n += 1.0;
89*9d8b5fa7Sdrochner b = cn/n;
90*9d8b5fa7Sdrochner
91*9d8b5fa7Sdrochner ct.r *= b;
92*9d8b5fa7Sdrochner ct.i *= b;
93*9d8b5fa7Sdrochner sum.r += ct.r;
94*9d8b5fa7Sdrochner sum.i += ct.i;
95*9d8b5fa7Sdrochner b = fabsf(ct.r) + fabsf(ct.i);
96*9d8b5fa7Sdrochner }
97*9d8b5fa7Sdrochner while( b > MACHEP );
98*9d8b5fa7Sdrochner w->r = sum.r;
99*9d8b5fa7Sdrochner w->i = sum.i;
100*9d8b5fa7Sdrochner return;
101*9d8b5fa7Sdrochner }
102*9d8b5fa7Sdrochner */
103*9d8b5fa7Sdrochner
104*9d8b5fa7Sdrochner
105*9d8b5fa7Sdrochner ca = x + y * I;
106*9d8b5fa7Sdrochner ct = ca * I;
107*9d8b5fa7Sdrochner /* sqrt( 1 - z*z) */
108*9d8b5fa7Sdrochner /* cmul( &ca, &ca, &zz ) */
109*9d8b5fa7Sdrochner /*x * x - y * y */
110*9d8b5fa7Sdrochner zz = (x - y) * (x + y) + (2.0f * x * y) * I;
111*9d8b5fa7Sdrochner
112*9d8b5fa7Sdrochner zz = 1.0f - crealf(zz) - cimagf(zz) * I;
113*9d8b5fa7Sdrochner z2 = csqrtf(zz);
114*9d8b5fa7Sdrochner
115*9d8b5fa7Sdrochner zz = ct + z2;
116*9d8b5fa7Sdrochner zz = clogf(zz);
117*9d8b5fa7Sdrochner /* multiply by 1/i = -i */
118*9d8b5fa7Sdrochner w = zz * (-1.0f * I);
119*9d8b5fa7Sdrochner return w;
120*9d8b5fa7Sdrochner }
121