1*05a0b428SJohn Marino /* $OpenBSD: s_catanf.c,v 1.2 2010/07/18 18:42:26 guenther 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 /* catanf()
19*05a0b428SJohn Marino *
20*05a0b428SJohn Marino * Complex circular arc tangent
21*05a0b428SJohn Marino *
22*05a0b428SJohn Marino *
23*05a0b428SJohn Marino *
24*05a0b428SJohn Marino * SYNOPSIS:
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * float complex catanf();
27*05a0b428SJohn Marino * float complex z, w;
28*05a0b428SJohn Marino *
29*05a0b428SJohn Marino * w = catanf( z );
30*05a0b428SJohn Marino *
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino *
33*05a0b428SJohn Marino * DESCRIPTION:
34*05a0b428SJohn Marino *
35*05a0b428SJohn Marino * If
36*05a0b428SJohn Marino * z = x + iy,
37*05a0b428SJohn Marino *
38*05a0b428SJohn Marino * then
39*05a0b428SJohn Marino * 1 ( 2x )
40*05a0b428SJohn Marino * Re w = - arctan(-----------) + k PI
41*05a0b428SJohn Marino * 2 ( 2 2)
42*05a0b428SJohn Marino * (1 - x - y )
43*05a0b428SJohn Marino *
44*05a0b428SJohn Marino * ( 2 2)
45*05a0b428SJohn Marino * 1 (x + (y+1) )
46*05a0b428SJohn Marino * Im w = - log(------------)
47*05a0b428SJohn Marino * 4 ( 2 2)
48*05a0b428SJohn Marino * (x + (y-1) )
49*05a0b428SJohn Marino *
50*05a0b428SJohn Marino * Where k is an arbitrary integer.
51*05a0b428SJohn Marino *
52*05a0b428SJohn Marino *
53*05a0b428SJohn Marino *
54*05a0b428SJohn Marino * ACCURACY:
55*05a0b428SJohn Marino *
56*05a0b428SJohn Marino * Relative error:
57*05a0b428SJohn Marino * arithmetic domain # trials peak rms
58*05a0b428SJohn Marino * IEEE -10,+10 30000 2.3e-6 5.2e-8
59*05a0b428SJohn Marino *
60*05a0b428SJohn Marino */
61*05a0b428SJohn Marino
62*05a0b428SJohn Marino #include <complex.h>
63*05a0b428SJohn Marino #include <math.h>
64*05a0b428SJohn Marino
65*05a0b428SJohn Marino #define MAXNUMF 1.0e38F
66*05a0b428SJohn Marino
67*05a0b428SJohn Marino static const double DP1 = 3.140625;
68*05a0b428SJohn Marino static const double DP2 = 9.67502593994140625E-4;
69*05a0b428SJohn Marino static const double DP3 = 1.509957990978376432E-7;
70*05a0b428SJohn Marino
71*05a0b428SJohn Marino static float
_redupif(float xx)72*05a0b428SJohn Marino _redupif(float xx)
73*05a0b428SJohn Marino {
74*05a0b428SJohn Marino float x, t;
75*05a0b428SJohn Marino long i;
76*05a0b428SJohn Marino
77*05a0b428SJohn Marino x = xx;
78*05a0b428SJohn Marino t = x/(float)M_PI;
79*05a0b428SJohn Marino if(t >= 0.0)
80*05a0b428SJohn Marino t += 0.5;
81*05a0b428SJohn Marino else
82*05a0b428SJohn Marino t -= 0.5;
83*05a0b428SJohn Marino
84*05a0b428SJohn Marino i = t; /* the multiple */
85*05a0b428SJohn Marino t = i;
86*05a0b428SJohn Marino t = ((x - t * DP1) - t * DP2) - t * DP3;
87*05a0b428SJohn Marino return(t);
88*05a0b428SJohn Marino }
89*05a0b428SJohn Marino
90*05a0b428SJohn Marino float complex
catanf(float complex z)91*05a0b428SJohn Marino catanf(float complex z)
92*05a0b428SJohn Marino {
93*05a0b428SJohn Marino float complex w;
94*05a0b428SJohn Marino float a, t, x, x2, y;
95*05a0b428SJohn Marino
96*05a0b428SJohn Marino x = crealf(z);
97*05a0b428SJohn Marino y = cimagf(z);
98*05a0b428SJohn Marino
99*05a0b428SJohn Marino if((x == 0.0f) && (y > 1.0f))
100*05a0b428SJohn Marino goto ovrf;
101*05a0b428SJohn Marino
102*05a0b428SJohn Marino x2 = x * x;
103*05a0b428SJohn Marino a = 1.0f - x2 - (y * y);
104*05a0b428SJohn Marino if (a == 0.0f)
105*05a0b428SJohn Marino goto ovrf;
106*05a0b428SJohn Marino
107*05a0b428SJohn Marino t = 0.5f * atan2f(2.0f * x, a);
108*05a0b428SJohn Marino w = _redupif(t);
109*05a0b428SJohn Marino
110*05a0b428SJohn Marino t = y - 1.0f;
111*05a0b428SJohn Marino a = x2 + (t * t);
112*05a0b428SJohn Marino if(a == 0.0f)
113*05a0b428SJohn Marino goto ovrf;
114*05a0b428SJohn Marino
115*05a0b428SJohn Marino t = y + 1.0f;
116*05a0b428SJohn Marino a = (x2 + (t * t))/a;
117*05a0b428SJohn Marino w = w + (0.25f * logf (a)) * I;
118*05a0b428SJohn Marino return (w);
119*05a0b428SJohn Marino
120*05a0b428SJohn Marino ovrf:
121*05a0b428SJohn Marino /*mtherr( "catanf", OVERFLOW );*/
122*05a0b428SJohn Marino w = MAXNUMF + MAXNUMF * I;
123*05a0b428SJohn Marino return (w);
124*05a0b428SJohn Marino }
125