1/*	$OpenBSD: s_casin.c,v 1.8 2016/09/12 19:47:02 guenther Exp $	*/
2/*
3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4 *
5 * Permission to use, copy, modify, and distribute this software for any
6 * purpose with or without fee is hereby granted, provided that the above
7 * copyright notice and this permission notice appear in all copies.
8 *
9 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
16 */
17
18/*							casin()
19 *
20 *	Complex circular arc sine
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * double complex casin();
27 * double complex z, w;
28 *
29 * w = casin (z);
30 *
31 *
32 *
33 * DESCRIPTION:
34 *
35 * Inverse complex sine:
36 *
37 *                               2
38 * w = -i clog( iz + csqrt( 1 - z ) ).
39 *
40 * casin(z) = -i casinh(iz)
41 *
42 * ACCURACY:
43 *
44 *                      Relative error:
45 * arithmetic   domain     # trials      peak         rms
46 *    DEC       -10,+10     10100       2.1e-15     3.4e-16
47 *    IEEE      -10,+10     30000       2.2e-14     2.7e-15
48 * Larger relative error can be observed for z near zero.
49 * Also tested by csin(casin(z)) = z.
50 */
51
52#include <complex.h>
53#include <float.h>
54#include <math.h>
55
56double complex
57casin(double complex z)
58{
59	double complex w;
60	static double complex ca, ct, zz, z2;
61	double x, y;
62
63	x = creal (z);
64	y = cimag (z);
65
66#if 0
67	if (y == 0.0) {
68		if (fabs(x) > 1.0) {
69			w = M_PI_2 + 0.0 * I;
70			/*mtherr ("casin", DOMAIN);*/
71		}
72		else {
73			w = asin (x) + 0.0 * I;
74		}
75		return (w);
76	}
77#endif
78
79	/* Power series expansion */
80	/*
81	b = cabs(z);
82	if( b < 0.125 ) {
83		z2.r = (x - y) * (x + y);
84		z2.i = 2.0 * x * y;
85
86		cn = 1.0;
87		n = 1.0;
88		ca.r = x;
89		ca.i = y;
90		sum.r = x;
91		sum.i = y;
92		do {
93			ct.r = z2.r * ca.r  -  z2.i * ca.i;
94			ct.i = z2.r * ca.i  +  z2.i * ca.r;
95			ca.r = ct.r;
96			ca.i = ct.i;
97
98			cn *= n;
99			n += 1.0;
100			cn /= n;
101			n += 1.0;
102			b = cn/n;
103
104			ct.r *= b;
105			ct.i *= b;
106			sum.r += ct.r;
107			sum.i += ct.i;
108			b = fabs(ct.r) + fabs(ct.i);
109		}
110		while( b > MACHEP );
111		w->r = sum.r;
112		w->i = sum.i;
113		return;
114	}
115	*/
116
117	ca = x + y * I;
118	ct = ca * I;
119	/* sqrt( 1 - z*z) */
120	/* cmul( &ca, &ca, &zz ) */
121	/*x * x  -  y * y */
122	zz = (x - y) * (x + y) + (2.0 * x * y) * I;
123
124	zz = 1.0 - creal(zz) - cimag(zz) * I;
125	z2 = csqrt (zz);
126
127	zz = ct + z2;
128	zz = clog (zz);
129	/* multiply by 1/i = -i */
130	w = zz * (-1.0 * I);
131	return (w);
132}
133DEF_STD(casin);
134LDBL_MAYBE_CLONE(casin);
135