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