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dennis.sheirer
262
src/util/ArcTangent.java
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262
src/util/ArcTangent.java
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/*******************************************************************************
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* SDR Trunk
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* Copyright (C) 2014 Dennis Sheirer
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>
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*
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* ----------------------------------------------
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* Adapted from GNU Radio's gr_fast_atan2f() method, retrieved Jan 2013 from
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* https://raw.github.com/gnuradio/gnuradio/master/gnuradio-core/src/lib/general/gr_fast_atan2f.cc
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*
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* Copyright 2005 Free Software Foundation, Inc.
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*
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* This file is part of GNU Radio
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*
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* GNU Radio is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3, or (at your option)
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* any later version.
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*
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* GNU Radio is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with GNU Radio; see the file COPYING. If not, write to
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* the Free Software Foundation, Inc., 51 Franklin Street,
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* Boston, MA 02110-1301, USA.
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*/
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package util;
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import sample.complex.ComplexSample;
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public class ArcTangent
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{
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public static final double sTANGENT_MAP_RESOLUTION = 0.003921549;
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public static final double sRADIANS_PER_DEGREE = 0.017453293;
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public static final int sTANGENT_MAP_SIZE = 256;
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public static final double sHALF_PI = Math.PI / 2;
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//ArcTangents from 0 to pi/4 radians
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private static double[] sLOOKUP_TABLE = new double[] {
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0.000000e+00, 3.921549e-03, 7.842976e-03, 1.176416e-02,
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1.568499e-02, 1.960533e-02, 2.352507e-02, 2.744409e-02,
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3.136226e-02, 3.527947e-02, 3.919560e-02, 4.311053e-02,
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4.702413e-02, 5.093629e-02, 5.484690e-02, 5.875582e-02,
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6.266295e-02, 6.656816e-02, 7.047134e-02, 7.437238e-02,
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7.827114e-02, 8.216752e-02, 8.606141e-02, 8.995267e-02,
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9.384121e-02, 9.772691e-02, 1.016096e-01, 1.054893e-01,
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1.093658e-01, 1.132390e-01, 1.171087e-01, 1.209750e-01,
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1.248376e-01, 1.286965e-01, 1.325515e-01, 1.364026e-01,
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1.402496e-01, 1.440924e-01, 1.479310e-01, 1.517652e-01,
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1.555948e-01, 1.594199e-01, 1.632403e-01, 1.670559e-01,
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1.708665e-01, 1.746722e-01, 1.784728e-01, 1.822681e-01,
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1.860582e-01, 1.898428e-01, 1.936220e-01, 1.973956e-01,
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2.011634e-01, 2.049255e-01, 2.086818e-01, 2.124320e-01,
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2.161762e-01, 2.199143e-01, 2.236461e-01, 2.273716e-01,
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2.310907e-01, 2.348033e-01, 2.385093e-01, 2.422086e-01,
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2.459012e-01, 2.495869e-01, 2.532658e-01, 2.569376e-01,
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2.606024e-01, 2.642600e-01, 2.679104e-01, 2.715535e-01,
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2.751892e-01, 2.788175e-01, 2.824383e-01, 2.860514e-01,
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2.896569e-01, 2.932547e-01, 2.968447e-01, 3.004268e-01,
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3.040009e-01, 3.075671e-01, 3.111252e-01, 3.146752e-01,
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3.182170e-01, 3.217506e-01, 3.252758e-01, 3.287927e-01,
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3.323012e-01, 3.358012e-01, 3.392926e-01, 3.427755e-01,
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3.462497e-01, 3.497153e-01, 3.531721e-01, 3.566201e-01,
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3.600593e-01, 3.634896e-01, 3.669110e-01, 3.703234e-01,
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3.737268e-01, 3.771211e-01, 3.805064e-01, 3.838825e-01,
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3.872494e-01, 3.906070e-01, 3.939555e-01, 3.972946e-01,
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4.006244e-01, 4.039448e-01, 4.072558e-01, 4.105574e-01,
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4.138496e-01, 4.171322e-01, 4.204054e-01, 4.236689e-01,
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4.269229e-01, 4.301673e-01, 4.334021e-01, 4.366272e-01,
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4.398426e-01, 4.430483e-01, 4.462443e-01, 4.494306e-01,
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4.526070e-01, 4.557738e-01, 4.589307e-01, 4.620778e-01,
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4.652150e-01, 4.683424e-01, 4.714600e-01, 4.745676e-01,
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4.776654e-01, 4.807532e-01, 4.838312e-01, 4.868992e-01,
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4.899573e-01, 4.930055e-01, 4.960437e-01, 4.990719e-01,
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5.020902e-01, 5.050985e-01, 5.080968e-01, 5.110852e-01,
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5.140636e-01, 5.170320e-01, 5.199904e-01, 5.229388e-01,
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5.258772e-01, 5.288056e-01, 5.317241e-01, 5.346325e-01,
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5.375310e-01, 5.404195e-01, 5.432980e-01, 5.461666e-01,
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5.490251e-01, 5.518738e-01, 5.547124e-01, 5.575411e-01,
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5.603599e-01, 5.631687e-01, 5.659676e-01, 5.687566e-01,
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5.715357e-01, 5.743048e-01, 5.770641e-01, 5.798135e-01,
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5.825531e-01, 5.852828e-01, 5.880026e-01, 5.907126e-01,
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5.934128e-01, 5.961032e-01, 5.987839e-01, 6.014547e-01,
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6.041158e-01, 6.067672e-01, 6.094088e-01, 6.120407e-01,
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6.146630e-01, 6.172755e-01, 6.198784e-01, 6.224717e-01,
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6.250554e-01, 6.276294e-01, 6.301939e-01, 6.327488e-01,
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6.352942e-01, 6.378301e-01, 6.403565e-01, 6.428734e-01,
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6.453808e-01, 6.478788e-01, 6.503674e-01, 6.528466e-01,
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6.553165e-01, 6.577770e-01, 6.602282e-01, 6.626701e-01,
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6.651027e-01, 6.675261e-01, 6.699402e-01, 6.723452e-01,
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6.747409e-01, 6.771276e-01, 6.795051e-01, 6.818735e-01,
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6.842328e-01, 6.865831e-01, 6.889244e-01, 6.912567e-01,
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6.935800e-01, 6.958943e-01, 6.981998e-01, 7.004964e-01,
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7.027841e-01, 7.050630e-01, 7.073330e-01, 7.095943e-01,
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7.118469e-01, 7.140907e-01, 7.163258e-01, 7.185523e-01,
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7.207701e-01, 7.229794e-01, 7.251800e-01, 7.273721e-01,
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7.295557e-01, 7.317307e-01, 7.338974e-01, 7.360555e-01,
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7.382053e-01, 7.403467e-01, 7.424797e-01, 7.446045e-01,
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7.467209e-01, 7.488291e-01, 7.509291e-01, 7.530208e-01,
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7.551044e-01, 7.571798e-01, 7.592472e-01, 7.613064e-01,
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7.633576e-01, 7.654008e-01, 7.674360e-01, 7.694633e-01,
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7.714826e-01, 7.734940e-01, 7.754975e-01, 7.774932e-01,
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7.794811e-01, 7.814612e-01, 7.834335e-01, 7.853983e-01,
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7.853983e-01 };
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/**
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* Lookup radian angle from polar coordinates represented by the
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* ComplexSample
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*
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* @param sample representing polar coordinates
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* @return - angle in radians
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*/
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public static double getAngle( ComplexSample sample )
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{
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return getAngle( ( (double) sample.inphase() ),
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( (double) sample.quadrature() ) );
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}
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/**
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* Lookup radian angle from polar coordinates x and y
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* @param x - x polar coordinate
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* @param y - y polar coordinate
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* @return - angle in radians
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*/
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public static double getAngle( double x, double y )
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{
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/**
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* Calculates the angle of the vector (x,y) based on a table lookup and
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* linear interpolation. The table uses a 256 point table covering
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* -45 to +45 degrees and uses symmetry to determine the final angle
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* value in the range of -180 to 180 degrees. Note that this function
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* uses the small angle approximation for values close to zero. This
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* routine calculates the arc tangent with an average error of
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* +/- 0.045 degrees.
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*/
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double alpha;
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double angle;
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double base_angle;
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int index;
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//Check for divide by zero
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if( x == 0.0 && y == 0.0 )
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{
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return 0.0;
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}
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//Normalize to +/- 45 degree range
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double x_abs = Math.abs( x );
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double y_abs = Math.abs( y );
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//Calculate the ratio ( opposite/adjacent )
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double z;
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if( x_abs < y_abs )
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{
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z = x_abs / y_abs;
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}
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else
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{
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z = y_abs / x_abs;
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}
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//When the ratio approaches table resolution, the angle is best
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//approximated with the argument itself
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if( z < sTANGENT_MAP_RESOLUTION )
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{
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base_angle = z;
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}
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else
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{
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alpha = z * (double)( sTANGENT_MAP_SIZE - .5 );
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index = (int)alpha;
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alpha -= (double)index;
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//Determine base angle based on quadrant and add or subtract table
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//value from base angle, based on quadrant
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base_angle = sLOOKUP_TABLE[ index ];
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base_angle += ( sLOOKUP_TABLE[ index + 1 ] -
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sLOOKUP_TABLE[ index ] ) * alpha;
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}
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//Map the angle to the correct quadrant
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if( x_abs > y_abs ) // -45 to 45, or 135 to -135
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{
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if( x >= 0.0 ) // -45 to 45
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{
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if( y >= 0.0 )
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{
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angle = base_angle; // 0 to 45
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}
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else
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{
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angle = -base_angle; // -45 to 0
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}
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}
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else // 135 to 180 or -180 to -135
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{
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angle = Math.PI;
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if( y >= 0.0 )
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{
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angle -= base_angle; // 135 to 180
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}
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else
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{
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angle = base_angle - angle; // 180 to -135
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}
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}
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}
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else // 45 to 135, or -135 to -45
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{
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if( y >= 0.0 ) //45 to 135
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{
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angle = sHALF_PI;
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if( x >= 0.0 )
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{
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angle -= base_angle; // 45 to 90
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}
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else
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{
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angle += base_angle; // 90 to 135
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}
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}
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else
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{
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angle = -sHALF_PI;
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if( x >= 0.0 )
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{
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angle += base_angle; //-90 to -45
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}
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else
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{
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angle -= base_angle; //-135 to -90
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}
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}
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}
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// //Check for negative radian angle value
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//
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// if( angle < 0 )
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// {
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// angle += 2 * Math.PI;
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// }
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return angle;
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}
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}
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