1 /* $OpenBSD: s_casinf.c,v 1.5 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 /* casinf()
19 *
20 * Complex circular arc sine
21 *
22 *
23 *
24 * SYNOPSIS:
25 *
26 * void casinf();
27 * cmplxf z, w;
28 *
29 * casinf( &z, &w );
30 *
31 *
32 *
33 * DESCRIPTION:
34 *
35 * Inverse complex sine:
36 *
37 * 2
38 * w = -i clog( iz + csqrt( 1 - z ) ).
39 *
40 *
41 * ACCURACY:
42 *
43 * Relative error:
44 * arithmetic domain # trials peak rms
45 * IEEE -10,+10 30000 1.1e-5 1.5e-6
46 * Larger relative error can be observed for z near zero.
47 *
48 */
49
50 #include <complex.h>
51 #include <math.h>
52
53 float complex
casinf(float complex z)54 casinf(float complex z)
55 {
56 float complex w;
57 float x, y;
58 static float complex ca, ct, zz, z2;
59 /*
60 float cn, n;
61 static float a, b, s, t, u, v, y2;
62 static cmplxf sum;
63 */
64
65 x = crealf(z);
66 y = cimagf(z);
67
68 #if 0
69 if(y == 0.0f) {
70 if(fabsf(x) > 1.0f) {
71 w = (float)M_PI_2 + 0.0f * I;
72 /*mtherr( "casinf", DOMAIN );*/
73 }
74 else {
75 w = asinf (x) + 0.0f * I;
76 }
77 return (w);
78 }
79 #endif
80
81 /* Power series expansion */
82 /*
83 b = cabsf(z);
84 if(b < 0.125) {
85 z2.r = (x - y) * (x + y);
86 z2.i = 2.0 * x * y;
87
88 cn = 1.0;
89 n = 1.0;
90 ca.r = x;
91 ca.i = y;
92 sum.r = x;
93 sum.i = y;
94 do {
95 ct.r = z2.r * ca.r - z2.i * ca.i;
96 ct.i = z2.r * ca.i + z2.i * ca.r;
97 ca.r = ct.r;
98 ca.i = ct.i;
99
100 cn *= n;
101 n += 1.0;
102 cn /= n;
103 n += 1.0;
104 b = cn/n;
105
106 ct.r *= b;
107 ct.i *= b;
108 sum.r += ct.r;
109 sum.i += ct.i;
110 b = fabsf(ct.r) + fabsf(ct.i);
111 }
112 while(b > MACHEPF);
113 w->r = sum.r;
114 w->i = sum.i;
115 return;
116 }
117 */
118
119
120 ca = x + y * I;
121 ct = ca * I; /* iz */
122 /* sqrt( 1 - z*z) */
123 /* cmul( &ca, &ca, &zz ) */
124 /*x * x - y * y */
125 zz = (x - y) * (x + y) + (2.0f * x * y) * I;
126 zz = 1.0f - crealf(zz) - cimagf(zz) * I;
127 z2 = csqrtf (zz);
128
129 zz = ct + z2;
130 zz = clogf (zz);
131 /* multiply by 1/i = -i */
132 w = zz * (-1.0f * I);
133 return (w);
134 }
135 DEF_STD(casinf);
136