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
56 double complex
casin(double complex z)57 casin(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 }
133 DEF_STD(casin);
134 LDBL_MAYBE_CLONE(casin);
135