1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
|
/* -*- c++ -*- */
/*
* Copyright 2005,2013 Free Software Foundation, Inc.
*
* This file is part of GNU Radio
*
* SPDX-License-Identifier: GPL-3.0-or-later
*
*/
#include <gnuradio/math.h> // declaration is in here
#include <cmath>
namespace gr {
/***************************************************************************/
/* Constant definitions */
/***************************************************************************/
#define TAN_MAP_RES 0.003921569 /* (smallest non-zero value in table) */
#define RAD_PER_DEG 0.017453293
#define TAN_MAP_SIZE 255
/* arctangents from 0 to pi/4 radians */
static float fast_atan_table[257] = {
0.000000e+00, 3.921549e-03, 7.842976e-03, 1.176416e-02, 1.568499e-02, 1.960533e-02,
2.352507e-02, 2.744409e-02, 3.136226e-02, 3.527947e-02, 3.919560e-02, 4.311053e-02,
4.702413e-02, 5.093629e-02, 5.484690e-02, 5.875582e-02, 6.266295e-02, 6.656816e-02,
7.047134e-02, 7.437238e-02, 7.827114e-02, 8.216752e-02, 8.606141e-02, 8.995267e-02,
9.384121e-02, 9.772691e-02, 1.016096e-01, 1.054893e-01, 1.093658e-01, 1.132390e-01,
1.171087e-01, 1.209750e-01, 1.248376e-01, 1.286965e-01, 1.325515e-01, 1.364026e-01,
1.402496e-01, 1.440924e-01, 1.479310e-01, 1.517652e-01, 1.555948e-01, 1.594199e-01,
1.632403e-01, 1.670559e-01, 1.708665e-01, 1.746722e-01, 1.784728e-01, 1.822681e-01,
1.860582e-01, 1.898428e-01, 1.936220e-01, 1.973956e-01, 2.011634e-01, 2.049255e-01,
2.086818e-01, 2.124320e-01, 2.161762e-01, 2.199143e-01, 2.236461e-01, 2.273716e-01,
2.310907e-01, 2.348033e-01, 2.385093e-01, 2.422086e-01, 2.459012e-01, 2.495869e-01,
2.532658e-01, 2.569376e-01, 2.606024e-01, 2.642600e-01, 2.679104e-01, 2.715535e-01,
2.751892e-01, 2.788175e-01, 2.824383e-01, 2.860514e-01, 2.896569e-01, 2.932547e-01,
2.968447e-01, 3.004268e-01, 3.040009e-01, 3.075671e-01, 3.111252e-01, 3.146752e-01,
3.182170e-01, 3.217506e-01, 3.252758e-01, 3.287927e-01, 3.323012e-01, 3.358012e-01,
3.392926e-01, 3.427755e-01, 3.462497e-01, 3.497153e-01, 3.531721e-01, 3.566201e-01,
3.600593e-01, 3.634896e-01, 3.669110e-01, 3.703234e-01, 3.737268e-01, 3.771211e-01,
3.805064e-01, 3.838825e-01, 3.872494e-01, 3.906070e-01, 3.939555e-01, 3.972946e-01,
4.006244e-01, 4.039448e-01, 4.072558e-01, 4.105574e-01, 4.138496e-01, 4.171322e-01,
4.204054e-01, 4.236689e-01, 4.269229e-01, 4.301673e-01, 4.334021e-01, 4.366272e-01,
4.398426e-01, 4.430483e-01, 4.462443e-01, 4.494306e-01, 4.526070e-01, 4.557738e-01,
4.589307e-01, 4.620778e-01, 4.652150e-01, 4.683424e-01, 4.714600e-01, 4.745676e-01,
4.776654e-01, 4.807532e-01, 4.838312e-01, 4.868992e-01, 4.899573e-01, 4.930055e-01,
4.960437e-01, 4.990719e-01, 5.020902e-01, 5.050985e-01, 5.080968e-01, 5.110852e-01,
5.140636e-01, 5.170320e-01, 5.199904e-01, 5.229388e-01, 5.258772e-01, 5.288056e-01,
5.317241e-01, 5.346325e-01, 5.375310e-01, 5.404195e-01, 5.432980e-01, 5.461666e-01,
5.490251e-01, 5.518738e-01, 5.547124e-01, 5.575411e-01, 5.603599e-01, 5.631687e-01,
5.659676e-01, 5.687566e-01, 5.715357e-01, 5.743048e-01, 5.770641e-01, 5.798135e-01,
5.825531e-01, 5.852828e-01, 5.880026e-01, 5.907126e-01, 5.934128e-01, 5.961032e-01,
5.987839e-01, 6.014547e-01, 6.041158e-01, 6.067672e-01, 6.094088e-01, 6.120407e-01,
6.146630e-01, 6.172755e-01, 6.198784e-01, 6.224717e-01, 6.250554e-01, 6.276294e-01,
6.301939e-01, 6.327488e-01, 6.352942e-01, 6.378301e-01, 6.403565e-01, 6.428734e-01,
6.453808e-01, 6.478788e-01, 6.503674e-01, 6.528466e-01, 6.553165e-01, 6.577770e-01,
6.602282e-01, 6.626701e-01, 6.651027e-01, 6.675261e-01, 6.699402e-01, 6.723452e-01,
6.747409e-01, 6.771276e-01, 6.795051e-01, 6.818735e-01, 6.842328e-01, 6.865831e-01,
6.889244e-01, 6.912567e-01, 6.935800e-01, 6.958943e-01, 6.981998e-01, 7.004964e-01,
7.027841e-01, 7.050630e-01, 7.073330e-01, 7.095943e-01, 7.118469e-01, 7.140907e-01,
7.163258e-01, 7.185523e-01, 7.207701e-01, 7.229794e-01, 7.251800e-01, 7.273721e-01,
7.295557e-01, 7.317307e-01, 7.338974e-01, 7.360555e-01, 7.382053e-01, 7.403467e-01,
7.424797e-01, 7.446045e-01, 7.467209e-01, 7.488291e-01, 7.509291e-01, 7.530208e-01,
7.551044e-01, 7.571798e-01, 7.592472e-01, 7.613064e-01, 7.633576e-01, 7.654008e-01,
7.674360e-01, 7.694633e-01, 7.714826e-01, 7.734940e-01, 7.754975e-01, 7.774932e-01,
7.794811e-01, 7.814612e-01, 7.834335e-01, 7.853982e-01, 7.853982e-01
};
/*****************************************************************************
Function: Arc tangent
Syntax: angle = fast_atan2(y, x);
float y y component of input vector
float x x component of input vector
float angle angle of vector (x, y) in radians
Description: This function calculates the angle of the vector (x,y)
based on a table lookup and linear interpolation. The table uses a
256 point table covering -45 to +45 degrees and uses symmetry to
determine the final angle value in the range of -180 to 180
degrees. Note that this function uses the small angle approximation
for values close to zero. This routine calculates the arc tangent
with an average error of +/- 3.56e-5 degrees (6.21e-7 radians).
*****************************************************************************/
float fast_atan2f(float y, float x)
{
float x_abs, y_abs, z;
float alpha, angle, base_angle;
int index;
/* normalize to +/- 45 degree range */
y_abs = fabsf(y);
x_abs = fabsf(x);
/* don't divide by zero! */
if (!((y_abs > 0.0f) || (x_abs > 0.0f)))
return 0.0;
if (y_abs < x_abs)
z = y_abs / x_abs;
else
z = x_abs / y_abs;
/* when ratio approaches the table resolution, the angle is */
/* best approximated with the argument itself... */
if (z < TAN_MAP_RES)
base_angle = z;
else {
/* find index and interpolation value */
alpha = z * (float)TAN_MAP_SIZE;
index = ((int)alpha) & 0xff;
alpha -= (float)index;
/* determine base angle based on quadrant and */
/* add or subtract table value from base angle based on quadrant */
base_angle = fast_atan_table[index];
base_angle += (fast_atan_table[index + 1] - fast_atan_table[index]) * alpha;
}
if (x_abs > y_abs) { /* -45 -> 45 or 135 -> 225 */
if (x >= 0.0) { /* -45 -> 45 */
if (y >= 0.0)
angle = base_angle; /* 0 -> 45, angle OK */
else
angle = -base_angle; /* -45 -> 0, angle = -angle */
} else { /* 135 -> 180 or 180 -> -135 */
angle = 3.14159265358979323846;
if (y >= 0.0)
angle -= base_angle; /* 135 -> 180, angle = 180 - angle */
else
angle = base_angle - angle; /* 180 -> -135, angle = angle - 180 */
}
} else { /* 45 -> 135 or -135 -> -45 */
if (y >= 0.0) { /* 45 -> 135 */
angle = 1.57079632679489661923;
if (x >= 0.0)
angle -= base_angle; /* 45 -> 90, angle = 90 - angle */
else
angle += base_angle; /* 90 -> 135, angle = 90 + angle */
} else { /* -135 -> -45 */
angle = -1.57079632679489661923;
if (x >= 0.0)
angle += base_angle; /* -90 -> -45, angle = -90 + angle */
else
angle -= base_angle; /* -135 -> -90, angle = -90 - angle */
}
}
#ifdef ZERO_TO_TWOPI
if (angle < 0)
return (angle + TWOPI);
else
return (angle);
#else
return (angle);
#endif
}
} /* namespace gr */
|
