Chris@3: /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */
Chris@3: /*
Chris@3:     Permission is hereby granted, free of charge, to any person
Chris@3:     obtaining a copy of this software and associated documentation
Chris@3:     files (the "Software"), to deal in the Software without
Chris@3:     restriction, including without limitation the rights to use, copy,
Chris@3:     modify, merge, publish, distribute, sublicense, and/or sell copies
Chris@3:     of the Software, and to permit persons to whom the Software is
Chris@3:     furnished to do so, subject to the following conditions:
Chris@3: 
Chris@3:     The above copyright notice and this permission notice shall be
Chris@3:     included in all copies or substantial portions of the Software.
Chris@3: 
Chris@3:     THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
Chris@3:     EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
Chris@3:     MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
Chris@3:     NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR
Chris@3:     ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
Chris@3:     CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
Chris@3:     WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Chris@3: */
Chris@3: 
Chris@3: #include "CepstrumPitchTracker.h"
Chris@3: 
Chris@3: #include <vector>
Chris@3: #include <algorithm>
Chris@3: 
Chris@3: #include <cstdio>
Chris@3: #include <cmath>
Chris@3: #include <complex>
Chris@3: 
Chris@3: using std::string;
Chris@7: using std::vector;
Chris@7: 
Chris@8: CepstrumPitchTracker::Hypothesis::Hypothesis()
Chris@7: {
Chris@8:     m_state = New;
Chris@7:     m_age = 0;
Chris@7: }
Chris@7: 
Chris@11: CepstrumPitchTracker::Hypothesis::~Hypothesis()
Chris@11: {
Chris@11: }
Chris@11: 
Chris@7: bool
Chris@7: CepstrumPitchTracker::Hypothesis::isWithinTolerance(Estimate s)
Chris@7: {
Chris@7:     if (m_pending.empty()) {
Chris@7:         return true;
Chris@7:     }
Chris@7:     Estimate last = m_pending[m_pending.size()-1];
Chris@7:     double r = s.freq / last.freq;
Chris@7:     int cents = lrint(1200.0 * (log(r) / log(2.0)));
Chris@7:     return (cents > -200 && cents < 200);
Chris@7: }
Chris@7: 
Chris@7: bool 
Chris@7: CepstrumPitchTracker::Hypothesis::isSatisfied()
Chris@7: {
Chris@7:     return (m_pending.size() > 2);
Chris@7: }
Chris@7: 
Chris@8: void
Chris@8: CepstrumPitchTracker::Hypothesis::advanceTime()
Chris@8: {
Chris@8:     ++m_age;
Chris@8: }
Chris@8: 
Chris@7: bool
Chris@7: CepstrumPitchTracker::Hypothesis::test(Estimate s)
Chris@7: {
Chris@8:     bool accept = false;
Chris@8: 
Chris@8:     switch (m_state) {
Chris@8: 
Chris@8:     case New:
Chris@8:         m_state = Provisional;
Chris@8:         accept = true;
Chris@8:         break;
Chris@8: 
Chris@8:     case Provisional:
Chris@8:         if (m_age > 3) {
Chris@8:             m_state = Rejected;
Chris@8:         } else if (isWithinTolerance(s)) {
Chris@8:             accept = true;
Chris@8:         }
Chris@8:         break;
Chris@8:         
Chris@8:     case Satisfied:
Chris@8:         if (m_age > 3) {
Chris@8:             m_state = Expired;
Chris@8:         } else if (isWithinTolerance(s)) {
Chris@8:             accept = true;
Chris@8:         }
Chris@8:         break;
Chris@8: 
Chris@8:     case Rejected:
Chris@8:         break;
Chris@8: 
Chris@8:     case Expired:
Chris@8:         break;
Chris@7:     }
Chris@7: 
Chris@8:     if (accept) {
Chris@8:         m_pending.push_back(s);
Chris@8:         m_age = 0;
Chris@8:         if (m_state == Provisional && isSatisfied()) {
Chris@8:             m_state = Satisfied;
Chris@7:         }
Chris@7:     }
Chris@7: 
Chris@8:     return accept;
Chris@8: }        
Chris@7: 
Chris@7: CepstrumPitchTracker::Hypothesis::State
Chris@7: CepstrumPitchTracker::Hypothesis::getState()
Chris@7: {
Chris@7:     return m_state;
Chris@7: }
Chris@7: 
Chris@12: int
Chris@12: CepstrumPitchTracker::Hypothesis::getPendingLength()
Chris@12: {
Chris@12:     return m_pending.size();
Chris@12: }
Chris@12: 
Chris@7: CepstrumPitchTracker::Hypothesis::Estimates
Chris@7: CepstrumPitchTracker::Hypothesis::getAcceptedEstimates()
Chris@7: {
Chris@7:     if (m_state == Satisfied || m_state == Expired) {
Chris@7:         return m_pending;
Chris@7:     } else {
Chris@7:         return Estimates();
Chris@7:     }
Chris@7: }
Chris@7: 
Chris@11: void
Chris@11: CepstrumPitchTracker::Hypothesis::addFeatures(FeatureList &fl)
Chris@11: {
Chris@11:     for (int i = 0; i < m_pending.size(); ++i) {
Chris@11: 	Feature f;
Chris@11: 	f.hasTimestamp = true;
Chris@11: 	f.timestamp = m_pending[i].time;
Chris@11: 	f.values.push_back(m_pending[i].freq);
Chris@11: 	fl.push_back(f);
Chris@11:     }
Chris@11: }
Chris@3: 
Chris@3: CepstrumPitchTracker::CepstrumPitchTracker(float inputSampleRate) :
Chris@3:     Plugin(inputSampleRate),
Chris@3:     m_channels(0),
Chris@3:     m_stepSize(256),
Chris@3:     m_blockSize(1024),
Chris@3:     m_fmin(50),
Chris@3:     m_fmax(1000),
Chris@5:     m_histlen(1),
Chris@5:     m_vflen(3),
Chris@3:     m_binFrom(0),
Chris@3:     m_binTo(0),
Chris@3:     m_bins(0),
Chris@6:     m_history(0),
Chris@6:     m_prevpeak(0),
Chris@6:     m_prevprop(0)
Chris@3: {
Chris@3: }
Chris@3: 
Chris@3: CepstrumPitchTracker::~CepstrumPitchTracker()
Chris@3: {
Chris@3:     if (m_history) {
Chris@3:         for (int i = 0; i < m_histlen; ++i) {
Chris@3:             delete[] m_history[i];
Chris@3:         }
Chris@3:         delete[] m_history;
Chris@3:     }
Chris@3: }
Chris@3: 
Chris@3: string
Chris@3: CepstrumPitchTracker::getIdentifier() const
Chris@3: {
Chris@3:     return "cepstrum-pitch";
Chris@3: }
Chris@3: 
Chris@3: string
Chris@3: CepstrumPitchTracker::getName() const
Chris@3: {
Chris@3:     return "Cepstrum Pitch Tracker";
Chris@3: }
Chris@3: 
Chris@3: string
Chris@3: CepstrumPitchTracker::getDescription() const
Chris@3: {
Chris@3:     return "Estimate f0 of monophonic material using a cepstrum method.";
Chris@3: }
Chris@3: 
Chris@3: string
Chris@3: CepstrumPitchTracker::getMaker() const
Chris@3: {
Chris@3:     return "Chris Cannam";
Chris@3: }
Chris@3: 
Chris@3: int
Chris@3: CepstrumPitchTracker::getPluginVersion() const
Chris@3: {
Chris@3:     // Increment this each time you release a version that behaves
Chris@3:     // differently from the previous one
Chris@3:     return 1;
Chris@3: }
Chris@3: 
Chris@3: string
Chris@3: CepstrumPitchTracker::getCopyright() const
Chris@3: {
Chris@3:     return "Freely redistributable (BSD license)";
Chris@3: }
Chris@3: 
Chris@3: CepstrumPitchTracker::InputDomain
Chris@3: CepstrumPitchTracker::getInputDomain() const
Chris@3: {
Chris@3:     return FrequencyDomain;
Chris@3: }
Chris@3: 
Chris@3: size_t
Chris@3: CepstrumPitchTracker::getPreferredBlockSize() const
Chris@3: {
Chris@3:     return 1024;
Chris@3: }
Chris@3: 
Chris@3: size_t 
Chris@3: CepstrumPitchTracker::getPreferredStepSize() const
Chris@3: {
Chris@3:     return 256;
Chris@3: }
Chris@3: 
Chris@3: size_t
Chris@3: CepstrumPitchTracker::getMinChannelCount() const
Chris@3: {
Chris@3:     return 1;
Chris@3: }
Chris@3: 
Chris@3: size_t
Chris@3: CepstrumPitchTracker::getMaxChannelCount() const
Chris@3: {
Chris@3:     return 1;
Chris@3: }
Chris@3: 
Chris@3: CepstrumPitchTracker::ParameterList
Chris@3: CepstrumPitchTracker::getParameterDescriptors() const
Chris@3: {
Chris@3:     ParameterList list;
Chris@3:     return list;
Chris@3: }
Chris@3: 
Chris@3: float
Chris@3: CepstrumPitchTracker::getParameter(string identifier) const
Chris@3: {
Chris@3:     return 0.f;
Chris@3: }
Chris@3: 
Chris@3: void
Chris@3: CepstrumPitchTracker::setParameter(string identifier, float value) 
Chris@3: {
Chris@3: }
Chris@3: 
Chris@3: CepstrumPitchTracker::ProgramList
Chris@3: CepstrumPitchTracker::getPrograms() const
Chris@3: {
Chris@3:     ProgramList list;
Chris@3:     return list;
Chris@3: }
Chris@3: 
Chris@3: string
Chris@3: CepstrumPitchTracker::getCurrentProgram() const
Chris@3: {
Chris@3:     return ""; // no programs
Chris@3: }
Chris@3: 
Chris@3: void
Chris@3: CepstrumPitchTracker::selectProgram(string name)
Chris@3: {
Chris@3: }
Chris@3: 
Chris@3: CepstrumPitchTracker::OutputList
Chris@3: CepstrumPitchTracker::getOutputDescriptors() const
Chris@3: {
Chris@3:     OutputList outputs;
Chris@3: 
Chris@3:     int n = 0;
Chris@3: 
Chris@3:     OutputDescriptor d;
Chris@3: 
Chris@3:     d.identifier = "f0";
Chris@3:     d.name = "Estimated f0";
Chris@3:     d.description = "Estimated fundamental frequency";
Chris@3:     d.unit = "Hz";
Chris@3:     d.hasFixedBinCount = true;
Chris@3:     d.binCount = 1;
Chris@3:     d.hasKnownExtents = true;
Chris@3:     d.minValue = m_fmin;
Chris@3:     d.maxValue = m_fmax;
Chris@3:     d.isQuantized = false;
Chris@3:     d.sampleType = OutputDescriptor::FixedSampleRate;
Chris@3:     d.sampleRate = (m_inputSampleRate / m_stepSize);
Chris@3:     d.hasDuration = false;
Chris@3:     outputs.push_back(d);
Chris@3: 
Chris@3:     return outputs;
Chris@3: }
Chris@3: 
Chris@3: bool
Chris@3: CepstrumPitchTracker::initialise(size_t channels, size_t stepSize, size_t blockSize)
Chris@3: {
Chris@3:     if (channels < getMinChannelCount() ||
Chris@3: 	channels > getMaxChannelCount()) return false;
Chris@3: 
Chris@3: //    std::cerr << "CepstrumPitchTracker::initialise: channels = " << channels
Chris@3: //	      << ", stepSize = " << stepSize << ", blockSize = " << blockSize
Chris@3: //	      << std::endl;
Chris@3: 
Chris@3:     m_channels = channels;
Chris@3:     m_stepSize = stepSize;
Chris@3:     m_blockSize = blockSize;
Chris@3: 
Chris@3:     m_binFrom = int(m_inputSampleRate / m_fmax);
Chris@3:     m_binTo = int(m_inputSampleRate / m_fmin); 
Chris@3: 
Chris@3:     if (m_binTo >= (int)m_blockSize / 2) {
Chris@3:         m_binTo = m_blockSize / 2 - 1;
Chris@3:     }
Chris@3: 
Chris@3:     m_bins = (m_binTo - m_binFrom) + 1;
Chris@3: 
Chris@3:     m_history = new double *[m_histlen];
Chris@3:     for (int i = 0; i < m_histlen; ++i) {
Chris@3:         m_history[i] = new double[m_bins];
Chris@3:     }
Chris@3: 
Chris@3:     reset();
Chris@3: 
Chris@3:     return true;
Chris@3: }
Chris@3: 
Chris@3: void
Chris@3: CepstrumPitchTracker::reset()
Chris@3: {
Chris@3:     for (int i = 0; i < m_histlen; ++i) {
Chris@3:         for (int j = 0; j < m_bins; ++j) {
Chris@3:             m_history[i][j] = 0.0;
Chris@3:         }
Chris@3:     }
Chris@3: }
Chris@3: 
Chris@3: void
Chris@3: CepstrumPitchTracker::filter(const double *cep, double *result)
Chris@3: {
Chris@3:     int hix = m_histlen - 1; // current history index
Chris@3: 
Chris@3:     // roll back the history
Chris@3:     if (m_histlen > 1) {
Chris@3:         double *oldest = m_history[0];
Chris@3:         for (int i = 1; i < m_histlen; ++i) {
Chris@3:             m_history[i-1] = m_history[i];
Chris@3:         }
Chris@3:         // and stick this back in the newest spot, to recycle
Chris@3:         m_history[hix] = oldest;
Chris@3:     }
Chris@3: 
Chris@3:     for (int i = 0; i < m_bins; ++i) {
Chris@5:         double v = 0;
Chris@5:         int n = 0;
Chris@5:         // average according to the vertical filter length
Chris@5:         for (int j = -m_vflen/2; j <= m_vflen/2; ++j) {
Chris@5:             int ix = i + m_binFrom + j;
Chris@5:             if (ix >= 0 && ix < m_blockSize) {
Chris@5:                 v += cep[ix];
Chris@5:                 ++n;
Chris@5:             }
Chris@5:         }
Chris@5:         m_history[hix][i] = v / n;
Chris@3:     }
Chris@3: 
Chris@3:     for (int i = 0; i < m_bins; ++i) {
Chris@3:         double mean = 0.0;
Chris@3:         for (int j = 0; j < m_histlen; ++j) {
Chris@3:             mean += m_history[j][i];
Chris@3:         }
Chris@3:         mean /= m_histlen;
Chris@3:         result[i] = mean;
Chris@3:     }
Chris@3: }
Chris@3: 
Chris@6: double
Chris@6: CepstrumPitchTracker::calculatePeakProportion(const double *data, double abstot, int n)
Chris@6: {
Chris@6:     double aroundPeak = data[n];
Chris@6:     double peakProportion = 0.0;
Chris@6: 
Chris@6:     int i = n - 1;
Chris@6:     while (i > 0 && data[i] <= data[i+1]) {
Chris@6:         aroundPeak += fabs(data[i]);
Chris@6:         --i;
Chris@6:     }
Chris@6:     i = n + 1;
Chris@6:     while (i < m_bins && data[i] <= data[i-1]) {
Chris@6:         aroundPeak += fabs(data[i]);
Chris@6:         ++i;
Chris@6:     }
Chris@6:     peakProportion = aroundPeak / abstot;
Chris@6: 
Chris@6:     return peakProportion;
Chris@6: }
Chris@6: 
Chris@6: bool
Chris@6: CepstrumPitchTracker::acceptPeak(int n, double peakProportion)
Chris@6: {
Chris@6:     bool accept = false;
Chris@6: 
Chris@6:     if (abs(n - m_prevpeak) < 10) { //!!! should depend on bin count
Chris@6:         accept = true;
Chris@6:     } else if (peakProportion > m_prevprop * 2) {
Chris@6:         accept = true;
Chris@6:     }
Chris@6: 
Chris@6:     return accept;
Chris@6: }
Chris@6: 
Chris@3: CepstrumPitchTracker::FeatureSet
Chris@3: CepstrumPitchTracker::process(const float *const *inputBuffers, Vamp::RealTime timestamp)
Chris@3: {
Chris@3:     FeatureSet fs;
Chris@3: 
Chris@3:     int bs = m_blockSize;
Chris@3:     int hs = m_blockSize/2 + 1;
Chris@3: 
Chris@3:     double *rawcep = new double[bs];
Chris@3:     double *io = new double[bs];
Chris@3:     double *logmag = new double[bs];
Chris@3: 
Chris@4:     // The "inverse symmetric" method. Seems to be the most reliable
Chris@3:         
Chris@3:     for (int i = 0; i < hs; ++i) {
Chris@3: 
Chris@3: 	double power =
Chris@3: 	    inputBuffers[0][i*2  ] * inputBuffers[0][i*2  ] +
Chris@3: 	    inputBuffers[0][i*2+1] * inputBuffers[0][i*2+1];
Chris@3: 	double mag = sqrt(power);
Chris@3: 	
Chris@3: 	double lm = log(mag + 0.00000001);
Chris@3: 	
Chris@4: 	logmag[i] = lm;
Chris@4: 	if (i > 0) logmag[bs - i] = lm;
Chris@3:     }
Chris@3: 
Chris@4:     fft(bs, true, logmag, 0, rawcep, io);
Chris@3:     
Chris@3:     delete[] logmag;
Chris@3:     delete[] io;
Chris@3: 
Chris@3:     int n = m_bins;
Chris@3:     double *data = new double[n];
Chris@3:     filter(rawcep, data);
Chris@3:     delete[] rawcep;
Chris@3: 
Chris@6:     double abstot = 0.0;
Chris@6: 
Chris@6:     for (int i = 0; i < n; ++i) {
Chris@6: 	abstot += fabs(data[i]);
Chris@6:     }
Chris@6: 
Chris@3:     double maxval = 0.0;
Chris@6:     int maxbin = -1;
Chris@3: 
Chris@3:     for (int i = 0; i < n; ++i) {
Chris@3:         if (data[i] > maxval) {
Chris@3:             maxval = data[i];
Chris@3:             maxbin = i;
Chris@3:         }
Chris@3:     }
Chris@3: 
Chris@8:     if (maxbin < 0) return fs;
Chris@8: 
Chris@8:     double peakfreq = m_inputSampleRate / (maxbin + m_binFrom);
Chris@8:     Hypothesis::Estimate e;
Chris@8:     e.freq = peakfreq;
Chris@8:     e.time = timestamp;
Chris@8: 
Chris@8:     m_accepted.advanceTime();
Chris@11: 
Chris@8:     for (int i = 0; i < m_possible.size(); ++i) {
Chris@8:         m_possible[i].advanceTime();
Chris@8:     }
Chris@8: 
Chris@11:     if (!m_accepted.test(e)) {
Chris@13: 
Chris@11:         int candidate = -1;
Chris@13:         bool accepted = false;
Chris@13: 
Chris@11:         for (int i = 0; i < m_possible.size(); ++i) {
Chris@11:             if (m_possible[i].test(e)) {
Chris@13:                 accepted = true;
Chris@11:                 if (m_possible[i].getState() == Hypothesis::Satisfied) {
Chris@11:                     candidate = i;
Chris@11:                 }
Chris@11:                 break;
Chris@11:             }
Chris@11:         }
Chris@12: 
Chris@13:         if (!accepted) {
Chris@13:             Hypothesis h;
Chris@13:             h.test(e); //!!! must succeed as h is new, so perhaps there should be a ctor for this
Chris@13:             m_possible.push_back(h);
Chris@13:         }
Chris@13: 
Chris@11:         if (m_accepted.getState() == Hypothesis::Expired) {
Chris@11:             m_accepted.addFeatures(fs[0]);
Chris@12:         }
Chris@12:         
Chris@12:         if (m_accepted.getState() == Hypothesis::Expired ||
Chris@12:             m_accepted.getState() == Hypothesis::Rejected) {
Chris@11:             if (candidate >= 0) {
Chris@11:                 m_accepted = m_possible[candidate];
Chris@11:             } else {
Chris@11:                 m_accepted = Hypothesis();
Chris@11:             }
Chris@11:         }
Chris@8: 
Chris@12:         std::cerr << "accepted length = " << m_accepted.getPendingLength()
Chris@12:                   << ", state = " << m_accepted.getState()
Chris@12:                   << ", hypothesis count = " << m_possible.size() << std::endl;
Chris@12: 
Chris@11:         //!!! and also need to reap rejected/expired hypotheses from the list
Chris@11:     }  
Chris@11:             
Chris@8: 
Chris@8: /*
Chris@6:     bool accepted = false;
Chris@6: 
Chris@6:     if (maxbin >= 0) {
Chris@6:         double pp = calculatePeakProportion(data, abstot, maxbin);
Chris@6:         if (acceptPeak(maxbin, pp)) {
Chris@6:             accepted = true;
Chris@6:         } else {
Chris@6:             // try a secondary peak
Chris@6:             maxval = 0.0;
Chris@6:             int secondbin = 0;
Chris@6:             for (int i = 1; i < n-1; ++i) {
Chris@6:                 if (i != maxbin &&
Chris@6:                     data[i] > data[i-1] &&
Chris@6:                     data[i] > data[i+1] &&
Chris@6:                     data[i] > maxval) {
Chris@6:                     maxval = data[i];
Chris@6:                     secondbin = i;
Chris@6:                 }
Chris@6:             }
Chris@6:             double spp = calculatePeakProportion(data, abstot, secondbin);
Chris@6:             if (acceptPeak(secondbin, spp)) {
Chris@6:                 maxbin = secondbin;
Chris@6:                 pp = spp;
Chris@6:                 accepted = true;
Chris@6:             }
Chris@3:         }
Chris@6:         if (accepted) {
Chris@6:             m_prevpeak = maxbin;
Chris@6:             m_prevprop = pp;
Chris@3:         }
Chris@3:     }
Chris@8: */
Chris@3: //    std::cerr << "peakProportion = " << peakProportion << std::endl;
Chris@3: //    std::cerr << "peak = " << m_inputSampleRate / (maxbin + m_binFrom) << std::endl;
Chris@4: //    std::cerr << "bins = " << m_bins << std::endl;
Chris@3: 
Chris@6: //    if (peakProportion >= (0.00006 * m_bins)) {
Chris@11: /*
Chris@6:     if (accepted) {
Chris@3: 	Feature f;
Chris@3: 	f.hasTimestamp = true;
Chris@3: 	f.timestamp = timestamp;
Chris@3: 	f.values.push_back(m_inputSampleRate / (maxbin + m_binFrom));
Chris@3: 	fs[0].push_back(f);
Chris@3:     }
Chris@11: */
Chris@3:     delete[] data;
Chris@3:     return fs;
Chris@3: }
Chris@3: 
Chris@3: CepstrumPitchTracker::FeatureSet
Chris@3: CepstrumPitchTracker::getRemainingFeatures()
Chris@3: {
Chris@3:     FeatureSet fs;
Chris@11:     if (m_accepted.getState() != Hypothesis::New) {
Chris@11:         m_accepted.addFeatures(fs[0]);
Chris@11:     }
Chris@3:     return fs;
Chris@3: }
Chris@3: 
Chris@3: void
Chris@3: CepstrumPitchTracker::fft(unsigned int n, bool inverse,
Chris@3:                     double *ri, double *ii, double *ro, double *io)
Chris@3: {
Chris@3:     if (!ri || !ro || !io) return;
Chris@3: 
Chris@3:     unsigned int bits;
Chris@3:     unsigned int i, j, k, m;
Chris@3:     unsigned int blockSize, blockEnd;
Chris@3: 
Chris@3:     double tr, ti;
Chris@3: 
Chris@3:     if (n < 2) return;
Chris@3:     if (n & (n-1)) return;
Chris@3: 
Chris@3:     double angle = 2.0 * M_PI;
Chris@3:     if (inverse) angle = -angle;
Chris@3: 
Chris@3:     for (i = 0; ; ++i) {
Chris@3: 	if (n & (1 << i)) {
Chris@3: 	    bits = i;
Chris@3: 	    break;
Chris@3: 	}
Chris@3:     }
Chris@3: 
Chris@3:     static unsigned int tableSize = 0;
Chris@3:     static int *table = 0;
Chris@3: 
Chris@3:     if (tableSize != n) {
Chris@3: 
Chris@3: 	delete[] table;
Chris@3: 
Chris@3: 	table = new int[n];
Chris@3: 
Chris@3: 	for (i = 0; i < n; ++i) {
Chris@3: 	
Chris@3: 	    m = i;
Chris@3: 
Chris@3: 	    for (j = k = 0; j < bits; ++j) {
Chris@3: 		k = (k << 1) | (m & 1);
Chris@3: 		m >>= 1;
Chris@3: 	    }
Chris@3: 
Chris@3: 	    table[i] = k;
Chris@3: 	}
Chris@3: 
Chris@3: 	tableSize = n;
Chris@3:     }
Chris@3: 
Chris@3:     if (ii) {
Chris@3: 	for (i = 0; i < n; ++i) {
Chris@3: 	    ro[table[i]] = ri[i];
Chris@3: 	    io[table[i]] = ii[i];
Chris@3: 	}
Chris@3:     } else {
Chris@3: 	for (i = 0; i < n; ++i) {
Chris@3: 	    ro[table[i]] = ri[i];
Chris@3: 	    io[table[i]] = 0.0;
Chris@3: 	}
Chris@3:     }
Chris@3: 
Chris@3:     blockEnd = 1;
Chris@3: 
Chris@3:     for (blockSize = 2; blockSize <= n; blockSize <<= 1) {
Chris@3: 
Chris@3: 	double delta = angle / (double)blockSize;
Chris@3: 	double sm2 = -sin(-2 * delta);
Chris@3: 	double sm1 = -sin(-delta);
Chris@3: 	double cm2 = cos(-2 * delta);
Chris@3: 	double cm1 = cos(-delta);
Chris@3: 	double w = 2 * cm1;
Chris@3: 	double ar[3], ai[3];
Chris@3: 
Chris@3: 	for (i = 0; i < n; i += blockSize) {
Chris@3: 
Chris@3: 	    ar[2] = cm2;
Chris@3: 	    ar[1] = cm1;
Chris@3: 
Chris@3: 	    ai[2] = sm2;
Chris@3: 	    ai[1] = sm1;
Chris@3: 
Chris@3: 	    for (j = i, m = 0; m < blockEnd; j++, m++) {
Chris@3: 
Chris@3: 		ar[0] = w * ar[1] - ar[2];
Chris@3: 		ar[2] = ar[1];
Chris@3: 		ar[1] = ar[0];
Chris@3: 
Chris@3: 		ai[0] = w * ai[1] - ai[2];
Chris@3: 		ai[2] = ai[1];
Chris@3: 		ai[1] = ai[0];
Chris@3: 
Chris@3: 		k = j + blockEnd;
Chris@3: 		tr = ar[0] * ro[k] - ai[0] * io[k];
Chris@3: 		ti = ar[0] * io[k] + ai[0] * ro[k];
Chris@3: 
Chris@3: 		ro[k] = ro[j] - tr;
Chris@3: 		io[k] = io[j] - ti;
Chris@3: 
Chris@3: 		ro[j] += tr;
Chris@3: 		io[j] += ti;
Chris@3: 	    }
Chris@3: 	}
Chris@3: 
Chris@3: 	blockEnd = blockSize;
Chris@3:     }
Chris@3: }
Chris@3: 
Chris@3: