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 "libm.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 |
|
---|
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 |
|
---|
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 | if ((x == 0.0f) && (y > 1.0f))
|
---|
91 | goto ovrf;
|
---|
92 |
|
---|
93 | x2 = x * x;
|
---|
94 | a = 1.0f - x2 - (y * y);
|
---|
95 | if (a == 0.0f)
|
---|
96 | goto ovrf;
|
---|
97 |
|
---|
98 | t = 0.5f * atan2f(2.0f * x, a);
|
---|
99 | w = _redupif(t);
|
---|
100 |
|
---|
101 | t = y - 1.0f;
|
---|
102 | a = x2 + (t * t);
|
---|
103 | if (a == 0.0f)
|
---|
104 | goto ovrf;
|
---|
105 |
|
---|
106 | t = y + 1.0f;
|
---|
107 | a = (x2 + (t * t))/a;
|
---|
108 | w = w + (0.25f * logf (a)) * I;
|
---|
109 | return w;
|
---|
110 |
|
---|
111 | ovrf:
|
---|
112 | // FIXME
|
---|
113 | w = MAXNUMF + MAXNUMF * I;
|
---|
114 | return w;
|
---|
115 | }
|
---|