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