1*05a0b428SJohn Marino /* $OpenBSD: s_casinf.c,v 1.3 2011/07/20 19:28:33 martynas Exp $ */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
4*05a0b428SJohn Marino *
5*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this software for any
6*05a0b428SJohn Marino * purpose with or without fee is hereby granted, provided that the above
7*05a0b428SJohn Marino * copyright notice and this permission notice appear in all copies.
8*05a0b428SJohn Marino *
9*05a0b428SJohn Marino * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
10*05a0b428SJohn Marino * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
11*05a0b428SJohn Marino * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
12*05a0b428SJohn Marino * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
13*05a0b428SJohn Marino * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
14*05a0b428SJohn Marino * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
15*05a0b428SJohn Marino * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
16*05a0b428SJohn Marino */
17*05a0b428SJohn Marino
18*05a0b428SJohn Marino /* casinf()
19*05a0b428SJohn Marino *
20*05a0b428SJohn Marino * Complex circular arc sine
21*05a0b428SJohn Marino *
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino * SYNOPSIS:
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * void casinf();
27*05a0b428SJohn Marino * cmplxf z, w;
28*05a0b428SJohn Marino *
29*05a0b428SJohn Marino * casinf( &z, &w );
30*05a0b428SJohn Marino *
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino *
33*05a0b428SJohn Marino * DESCRIPTION:
34*05a0b428SJohn Marino *
35*05a0b428SJohn Marino * Inverse complex sine:
36*05a0b428SJohn Marino *
37*05a0b428SJohn Marino * 2
38*05a0b428SJohn Marino * w = -i clog( iz + csqrt( 1 - z ) ).
39*05a0b428SJohn Marino *
40*05a0b428SJohn Marino *
41*05a0b428SJohn Marino * ACCURACY:
42*05a0b428SJohn Marino *
43*05a0b428SJohn Marino * Relative error:
44*05a0b428SJohn Marino * arithmetic domain # trials peak rms
45*05a0b428SJohn Marino * IEEE -10,+10 30000 1.1e-5 1.5e-6
46*05a0b428SJohn Marino * Larger relative error can be observed for z near zero.
47*05a0b428SJohn Marino *
48*05a0b428SJohn Marino */
49*05a0b428SJohn Marino
50*05a0b428SJohn Marino #include <complex.h>
51*05a0b428SJohn Marino #include <math.h>
52*05a0b428SJohn Marino
53*05a0b428SJohn Marino float complex
casinf(float complex z)54*05a0b428SJohn Marino casinf(float complex z)
55*05a0b428SJohn Marino {
56*05a0b428SJohn Marino float complex w;
57*05a0b428SJohn Marino float x, y;
58*05a0b428SJohn Marino static float complex ca, ct, zz, z2;
59*05a0b428SJohn Marino /*
60*05a0b428SJohn Marino float cn, n;
61*05a0b428SJohn Marino static float a, b, s, t, u, v, y2;
62*05a0b428SJohn Marino static cmplxf sum;
63*05a0b428SJohn Marino */
64*05a0b428SJohn Marino
65*05a0b428SJohn Marino x = crealf(z);
66*05a0b428SJohn Marino y = cimagf(z);
67*05a0b428SJohn Marino
68*05a0b428SJohn Marino if(y == 0.0f) {
69*05a0b428SJohn Marino if(fabsf(x) > 1.0f) {
70*05a0b428SJohn Marino w = (float)M_PI_2 + 0.0f * I;
71*05a0b428SJohn Marino /*mtherr( "casinf", DOMAIN );*/
72*05a0b428SJohn Marino }
73*05a0b428SJohn Marino else {
74*05a0b428SJohn Marino w = asinf (x) + 0.0f * I;
75*05a0b428SJohn Marino }
76*05a0b428SJohn Marino return (w);
77*05a0b428SJohn Marino }
78*05a0b428SJohn Marino
79*05a0b428SJohn Marino /* Power series expansion */
80*05a0b428SJohn Marino /*
81*05a0b428SJohn Marino b = cabsf(z);
82*05a0b428SJohn Marino if(b < 0.125) {
83*05a0b428SJohn Marino z2.r = (x - y) * (x + y);
84*05a0b428SJohn Marino z2.i = 2.0 * x * y;
85*05a0b428SJohn Marino
86*05a0b428SJohn Marino cn = 1.0;
87*05a0b428SJohn Marino n = 1.0;
88*05a0b428SJohn Marino ca.r = x;
89*05a0b428SJohn Marino ca.i = y;
90*05a0b428SJohn Marino sum.r = x;
91*05a0b428SJohn Marino sum.i = y;
92*05a0b428SJohn Marino do {
93*05a0b428SJohn Marino ct.r = z2.r * ca.r - z2.i * ca.i;
94*05a0b428SJohn Marino ct.i = z2.r * ca.i + z2.i * ca.r;
95*05a0b428SJohn Marino ca.r = ct.r;
96*05a0b428SJohn Marino ca.i = ct.i;
97*05a0b428SJohn Marino
98*05a0b428SJohn Marino cn *= n;
99*05a0b428SJohn Marino n += 1.0;
100*05a0b428SJohn Marino cn /= n;
101*05a0b428SJohn Marino n += 1.0;
102*05a0b428SJohn Marino b = cn/n;
103*05a0b428SJohn Marino
104*05a0b428SJohn Marino ct.r *= b;
105*05a0b428SJohn Marino ct.i *= b;
106*05a0b428SJohn Marino sum.r += ct.r;
107*05a0b428SJohn Marino sum.i += ct.i;
108*05a0b428SJohn Marino b = fabsf(ct.r) + fabsf(ct.i);
109*05a0b428SJohn Marino }
110*05a0b428SJohn Marino while(b > MACHEPF);
111*05a0b428SJohn Marino w->r = sum.r;
112*05a0b428SJohn Marino w->i = sum.i;
113*05a0b428SJohn Marino return;
114*05a0b428SJohn Marino }
115*05a0b428SJohn Marino */
116*05a0b428SJohn Marino
117*05a0b428SJohn Marino
118*05a0b428SJohn Marino ca = x + y * I;
119*05a0b428SJohn Marino ct = ca * I; /* iz */
120*05a0b428SJohn Marino /* sqrt( 1 - z*z) */
121*05a0b428SJohn Marino /* cmul( &ca, &ca, &zz ) */
122*05a0b428SJohn Marino /*x * x - y * y */
123*05a0b428SJohn Marino zz = (x - y) * (x + y) + (2.0f * x * y) * I;
124*05a0b428SJohn Marino zz = 1.0f - crealf(zz) - cimagf(zz) * I;
125*05a0b428SJohn Marino z2 = csqrtf (zz);
126*05a0b428SJohn Marino
127*05a0b428SJohn Marino zz = ct + z2;
128*05a0b428SJohn Marino zz = clogf (zz);
129*05a0b428SJohn Marino /* multiply by 1/i = -i */
130*05a0b428SJohn Marino w = zz * (-1.0f * I);
131*05a0b428SJohn Marino return (w);
132*05a0b428SJohn Marino }
133