annotate CepstrumPitchTracker.cpp @ 16:63dde216ea37 track

Make compile; does not yet work
author Chris Cannam
date Fri, 29 Jun 2012 21:11:37 +0100
parents 9fa97de8692a
children edc7f59404da
rev   line source
Chris@8 1 /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */
Chris@8 2 /*
Chris@8 3 Permission is hereby granted, free of charge, to any person
Chris@8 4 obtaining a copy of this software and associated documentation
Chris@8 5 files (the "Software"), to deal in the Software without
Chris@8 6 restriction, including without limitation the rights to use, copy,
Chris@8 7 modify, merge, publish, distribute, sublicense, and/or sell copies
Chris@8 8 of the Software, and to permit persons to whom the Software is
Chris@8 9 furnished to do so, subject to the following conditions:
Chris@8 10
Chris@8 11 The above copyright notice and this permission notice shall be
Chris@8 12 included in all copies or substantial portions of the Software.
Chris@8 13
Chris@8 14 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
Chris@8 15 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
Chris@8 16 MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
Chris@8 17 NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR
Chris@8 18 ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
Chris@8 19 CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
Chris@8 20 WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Chris@8 21 */
Chris@8 22
Chris@8 23 #include "CepstrumPitchTracker.h"
Chris@8 24
Chris@8 25 #include <vector>
Chris@8 26 #include <algorithm>
Chris@8 27
Chris@8 28 #include <cstdio>
Chris@8 29 #include <cmath>
Chris@8 30 #include <complex>
Chris@8 31
Chris@8 32 using std::string;
Chris@12 33 using std::vector;
Chris@12 34
Chris@13 35 CepstrumPitchTracker::Hypothesis::Hypothesis()
Chris@12 36 {
Chris@13 37 m_state = New;
Chris@12 38 m_age = 0;
Chris@12 39 }
Chris@12 40
Chris@16 41 CepstrumPitchTracker::Hypothesis::~Hypothesis()
Chris@16 42 {
Chris@16 43 }
Chris@16 44
Chris@12 45 bool
Chris@12 46 CepstrumPitchTracker::Hypothesis::isWithinTolerance(Estimate s)
Chris@12 47 {
Chris@12 48 if (m_pending.empty()) {
Chris@12 49 return true;
Chris@12 50 }
Chris@12 51 Estimate last = m_pending[m_pending.size()-1];
Chris@12 52 double r = s.freq / last.freq;
Chris@12 53 int cents = lrint(1200.0 * (log(r) / log(2.0)));
Chris@12 54 return (cents > -200 && cents < 200);
Chris@12 55 }
Chris@12 56
Chris@12 57 bool
Chris@12 58 CepstrumPitchTracker::Hypothesis::isSatisfied()
Chris@12 59 {
Chris@12 60 return (m_pending.size() > 2);
Chris@12 61 }
Chris@12 62
Chris@13 63 void
Chris@13 64 CepstrumPitchTracker::Hypothesis::advanceTime()
Chris@13 65 {
Chris@13 66 ++m_age;
Chris@13 67 }
Chris@13 68
Chris@12 69 bool
Chris@12 70 CepstrumPitchTracker::Hypothesis::test(Estimate s)
Chris@12 71 {
Chris@13 72 bool accept = false;
Chris@13 73
Chris@13 74 switch (m_state) {
Chris@13 75
Chris@13 76 case New:
Chris@13 77 m_state = Provisional;
Chris@13 78 accept = true;
Chris@13 79 break;
Chris@13 80
Chris@13 81 case Provisional:
Chris@13 82 if (m_age > 3) {
Chris@13 83 m_state = Rejected;
Chris@13 84 } else if (isWithinTolerance(s)) {
Chris@13 85 accept = true;
Chris@13 86 }
Chris@13 87 break;
Chris@13 88
Chris@13 89 case Satisfied:
Chris@13 90 if (m_age > 3) {
Chris@13 91 m_state = Expired;
Chris@13 92 } else if (isWithinTolerance(s)) {
Chris@13 93 accept = true;
Chris@13 94 }
Chris@13 95 break;
Chris@13 96
Chris@13 97 case Rejected:
Chris@13 98 break;
Chris@13 99
Chris@13 100 case Expired:
Chris@13 101 break;
Chris@12 102 }
Chris@12 103
Chris@13 104 if (accept) {
Chris@13 105 m_pending.push_back(s);
Chris@13 106 m_age = 0;
Chris@13 107 if (m_state == Provisional && isSatisfied()) {
Chris@13 108 m_state = Satisfied;
Chris@12 109 }
Chris@12 110 }
Chris@12 111
Chris@13 112 return accept;
Chris@13 113 }
Chris@12 114
Chris@12 115 CepstrumPitchTracker::Hypothesis::State
Chris@12 116 CepstrumPitchTracker::Hypothesis::getState()
Chris@12 117 {
Chris@12 118 return m_state;
Chris@12 119 }
Chris@12 120
Chris@12 121 CepstrumPitchTracker::Hypothesis::Estimates
Chris@12 122 CepstrumPitchTracker::Hypothesis::getAcceptedEstimates()
Chris@12 123 {
Chris@12 124 if (m_state == Satisfied || m_state == Expired) {
Chris@12 125 return m_pending;
Chris@12 126 } else {
Chris@12 127 return Estimates();
Chris@12 128 }
Chris@12 129 }
Chris@12 130
Chris@16 131 void
Chris@16 132 CepstrumPitchTracker::Hypothesis::addFeatures(FeatureList &fl)
Chris@16 133 {
Chris@16 134 for (int i = 0; i < m_pending.size(); ++i) {
Chris@16 135 Feature f;
Chris@16 136 f.hasTimestamp = true;
Chris@16 137 f.timestamp = m_pending[i].time;
Chris@16 138 f.values.push_back(m_pending[i].freq);
Chris@16 139 fl.push_back(f);
Chris@16 140 }
Chris@16 141 }
Chris@8 142
Chris@8 143 CepstrumPitchTracker::CepstrumPitchTracker(float inputSampleRate) :
Chris@8 144 Plugin(inputSampleRate),
Chris@8 145 m_channels(0),
Chris@8 146 m_stepSize(256),
Chris@8 147 m_blockSize(1024),
Chris@8 148 m_fmin(50),
Chris@8 149 m_fmax(1000),
Chris@10 150 m_histlen(1),
Chris@10 151 m_vflen(3),
Chris@8 152 m_binFrom(0),
Chris@8 153 m_binTo(0),
Chris@8 154 m_bins(0),
Chris@11 155 m_history(0),
Chris@11 156 m_prevpeak(0),
Chris@11 157 m_prevprop(0)
Chris@8 158 {
Chris@8 159 }
Chris@8 160
Chris@8 161 CepstrumPitchTracker::~CepstrumPitchTracker()
Chris@8 162 {
Chris@8 163 if (m_history) {
Chris@8 164 for (int i = 0; i < m_histlen; ++i) {
Chris@8 165 delete[] m_history[i];
Chris@8 166 }
Chris@8 167 delete[] m_history;
Chris@8 168 }
Chris@8 169 }
Chris@8 170
Chris@8 171 string
Chris@8 172 CepstrumPitchTracker::getIdentifier() const
Chris@8 173 {
Chris@8 174 return "cepstrum-pitch";
Chris@8 175 }
Chris@8 176
Chris@8 177 string
Chris@8 178 CepstrumPitchTracker::getName() const
Chris@8 179 {
Chris@8 180 return "Cepstrum Pitch Tracker";
Chris@8 181 }
Chris@8 182
Chris@8 183 string
Chris@8 184 CepstrumPitchTracker::getDescription() const
Chris@8 185 {
Chris@8 186 return "Estimate f0 of monophonic material using a cepstrum method.";
Chris@8 187 }
Chris@8 188
Chris@8 189 string
Chris@8 190 CepstrumPitchTracker::getMaker() const
Chris@8 191 {
Chris@8 192 return "Chris Cannam";
Chris@8 193 }
Chris@8 194
Chris@8 195 int
Chris@8 196 CepstrumPitchTracker::getPluginVersion() const
Chris@8 197 {
Chris@8 198 // Increment this each time you release a version that behaves
Chris@8 199 // differently from the previous one
Chris@8 200 return 1;
Chris@8 201 }
Chris@8 202
Chris@8 203 string
Chris@8 204 CepstrumPitchTracker::getCopyright() const
Chris@8 205 {
Chris@8 206 return "Freely redistributable (BSD license)";
Chris@8 207 }
Chris@8 208
Chris@8 209 CepstrumPitchTracker::InputDomain
Chris@8 210 CepstrumPitchTracker::getInputDomain() const
Chris@8 211 {
Chris@8 212 return FrequencyDomain;
Chris@8 213 }
Chris@8 214
Chris@8 215 size_t
Chris@8 216 CepstrumPitchTracker::getPreferredBlockSize() const
Chris@8 217 {
Chris@8 218 return 1024;
Chris@8 219 }
Chris@8 220
Chris@8 221 size_t
Chris@8 222 CepstrumPitchTracker::getPreferredStepSize() const
Chris@8 223 {
Chris@8 224 return 256;
Chris@8 225 }
Chris@8 226
Chris@8 227 size_t
Chris@8 228 CepstrumPitchTracker::getMinChannelCount() const
Chris@8 229 {
Chris@8 230 return 1;
Chris@8 231 }
Chris@8 232
Chris@8 233 size_t
Chris@8 234 CepstrumPitchTracker::getMaxChannelCount() const
Chris@8 235 {
Chris@8 236 return 1;
Chris@8 237 }
Chris@8 238
Chris@8 239 CepstrumPitchTracker::ParameterList
Chris@8 240 CepstrumPitchTracker::getParameterDescriptors() const
Chris@8 241 {
Chris@8 242 ParameterList list;
Chris@8 243 return list;
Chris@8 244 }
Chris@8 245
Chris@8 246 float
Chris@8 247 CepstrumPitchTracker::getParameter(string identifier) const
Chris@8 248 {
Chris@8 249 return 0.f;
Chris@8 250 }
Chris@8 251
Chris@8 252 void
Chris@8 253 CepstrumPitchTracker::setParameter(string identifier, float value)
Chris@8 254 {
Chris@8 255 }
Chris@8 256
Chris@8 257 CepstrumPitchTracker::ProgramList
Chris@8 258 CepstrumPitchTracker::getPrograms() const
Chris@8 259 {
Chris@8 260 ProgramList list;
Chris@8 261 return list;
Chris@8 262 }
Chris@8 263
Chris@8 264 string
Chris@8 265 CepstrumPitchTracker::getCurrentProgram() const
Chris@8 266 {
Chris@8 267 return ""; // no programs
Chris@8 268 }
Chris@8 269
Chris@8 270 void
Chris@8 271 CepstrumPitchTracker::selectProgram(string name)
Chris@8 272 {
Chris@8 273 }
Chris@8 274
Chris@8 275 CepstrumPitchTracker::OutputList
Chris@8 276 CepstrumPitchTracker::getOutputDescriptors() const
Chris@8 277 {
Chris@8 278 OutputList outputs;
Chris@8 279
Chris@8 280 int n = 0;
Chris@8 281
Chris@8 282 OutputDescriptor d;
Chris@8 283
Chris@8 284 d.identifier = "f0";
Chris@8 285 d.name = "Estimated f0";
Chris@8 286 d.description = "Estimated fundamental frequency";
Chris@8 287 d.unit = "Hz";
Chris@8 288 d.hasFixedBinCount = true;
Chris@8 289 d.binCount = 1;
Chris@8 290 d.hasKnownExtents = true;
Chris@8 291 d.minValue = m_fmin;
Chris@8 292 d.maxValue = m_fmax;
Chris@8 293 d.isQuantized = false;
Chris@8 294 d.sampleType = OutputDescriptor::FixedSampleRate;
Chris@8 295 d.sampleRate = (m_inputSampleRate / m_stepSize);
Chris@8 296 d.hasDuration = false;
Chris@8 297 outputs.push_back(d);
Chris@8 298
Chris@8 299 return outputs;
Chris@8 300 }
Chris@8 301
Chris@8 302 bool
Chris@8 303 CepstrumPitchTracker::initialise(size_t channels, size_t stepSize, size_t blockSize)
Chris@8 304 {
Chris@8 305 if (channels < getMinChannelCount() ||
Chris@8 306 channels > getMaxChannelCount()) return false;
Chris@8 307
Chris@8 308 // std::cerr << "CepstrumPitchTracker::initialise: channels = " << channels
Chris@8 309 // << ", stepSize = " << stepSize << ", blockSize = " << blockSize
Chris@8 310 // << std::endl;
Chris@8 311
Chris@8 312 m_channels = channels;
Chris@8 313 m_stepSize = stepSize;
Chris@8 314 m_blockSize = blockSize;
Chris@8 315
Chris@8 316 m_binFrom = int(m_inputSampleRate / m_fmax);
Chris@8 317 m_binTo = int(m_inputSampleRate / m_fmin);
Chris@8 318
Chris@8 319 if (m_binTo >= (int)m_blockSize / 2) {
Chris@8 320 m_binTo = m_blockSize / 2 - 1;
Chris@8 321 }
Chris@8 322
Chris@8 323 m_bins = (m_binTo - m_binFrom) + 1;
Chris@8 324
Chris@8 325 m_history = new double *[m_histlen];
Chris@8 326 for (int i = 0; i < m_histlen; ++i) {
Chris@8 327 m_history[i] = new double[m_bins];
Chris@8 328 }
Chris@8 329
Chris@8 330 reset();
Chris@8 331
Chris@8 332 return true;
Chris@8 333 }
Chris@8 334
Chris@8 335 void
Chris@8 336 CepstrumPitchTracker::reset()
Chris@8 337 {
Chris@8 338 for (int i = 0; i < m_histlen; ++i) {
Chris@8 339 for (int j = 0; j < m_bins; ++j) {
Chris@8 340 m_history[i][j] = 0.0;
Chris@8 341 }
Chris@8 342 }
Chris@8 343 }
Chris@8 344
Chris@8 345 void
Chris@8 346 CepstrumPitchTracker::filter(const double *cep, double *result)
Chris@8 347 {
Chris@8 348 int hix = m_histlen - 1; // current history index
Chris@8 349
Chris@8 350 // roll back the history
Chris@8 351 if (m_histlen > 1) {
Chris@8 352 double *oldest = m_history[0];
Chris@8 353 for (int i = 1; i < m_histlen; ++i) {
Chris@8 354 m_history[i-1] = m_history[i];
Chris@8 355 }
Chris@8 356 // and stick this back in the newest spot, to recycle
Chris@8 357 m_history[hix] = oldest;
Chris@8 358 }
Chris@8 359
Chris@8 360 for (int i = 0; i < m_bins; ++i) {
Chris@10 361 double v = 0;
Chris@10 362 int n = 0;
Chris@10 363 // average according to the vertical filter length
Chris@10 364 for (int j = -m_vflen/2; j <= m_vflen/2; ++j) {
Chris@10 365 int ix = i + m_binFrom + j;
Chris@10 366 if (ix >= 0 && ix < m_blockSize) {
Chris@10 367 v += cep[ix];
Chris@10 368 ++n;
Chris@10 369 }
Chris@10 370 }
Chris@10 371 m_history[hix][i] = v / n;
Chris@8 372 }
Chris@8 373
Chris@8 374 for (int i = 0; i < m_bins; ++i) {
Chris@8 375 double mean = 0.0;
Chris@8 376 for (int j = 0; j < m_histlen; ++j) {
Chris@8 377 mean += m_history[j][i];
Chris@8 378 }
Chris@8 379 mean /= m_histlen;
Chris@8 380 result[i] = mean;
Chris@8 381 }
Chris@8 382 }
Chris@8 383
Chris@11 384 double
Chris@11 385 CepstrumPitchTracker::calculatePeakProportion(const double *data, double abstot, int n)
Chris@11 386 {
Chris@11 387 double aroundPeak = data[n];
Chris@11 388 double peakProportion = 0.0;
Chris@11 389
Chris@11 390 int i = n - 1;
Chris@11 391 while (i > 0 && data[i] <= data[i+1]) {
Chris@11 392 aroundPeak += fabs(data[i]);
Chris@11 393 --i;
Chris@11 394 }
Chris@11 395 i = n + 1;
Chris@11 396 while (i < m_bins && data[i] <= data[i-1]) {
Chris@11 397 aroundPeak += fabs(data[i]);
Chris@11 398 ++i;
Chris@11 399 }
Chris@11 400 peakProportion = aroundPeak / abstot;
Chris@11 401
Chris@11 402 return peakProportion;
Chris@11 403 }
Chris@11 404
Chris@11 405 bool
Chris@11 406 CepstrumPitchTracker::acceptPeak(int n, double peakProportion)
Chris@11 407 {
Chris@11 408 bool accept = false;
Chris@11 409
Chris@11 410 if (abs(n - m_prevpeak) < 10) { //!!! should depend on bin count
Chris@11 411 accept = true;
Chris@11 412 } else if (peakProportion > m_prevprop * 2) {
Chris@11 413 accept = true;
Chris@11 414 }
Chris@11 415
Chris@11 416 return accept;
Chris@11 417 }
Chris@11 418
Chris@8 419 CepstrumPitchTracker::FeatureSet
Chris@8 420 CepstrumPitchTracker::process(const float *const *inputBuffers, Vamp::RealTime timestamp)
Chris@8 421 {
Chris@8 422 FeatureSet fs;
Chris@8 423
Chris@8 424 int bs = m_blockSize;
Chris@8 425 int hs = m_blockSize/2 + 1;
Chris@8 426
Chris@8 427 double *rawcep = new double[bs];
Chris@8 428 double *io = new double[bs];
Chris@8 429 double *logmag = new double[bs];
Chris@8 430
Chris@9 431 // The "inverse symmetric" method. Seems to be the most reliable
Chris@8 432
Chris@8 433 for (int i = 0; i < hs; ++i) {
Chris@8 434
Chris@8 435 double power =
Chris@8 436 inputBuffers[0][i*2 ] * inputBuffers[0][i*2 ] +
Chris@8 437 inputBuffers[0][i*2+1] * inputBuffers[0][i*2+1];
Chris@8 438 double mag = sqrt(power);
Chris@8 439
Chris@8 440 double lm = log(mag + 0.00000001);
Chris@8 441
Chris@9 442 logmag[i] = lm;
Chris@9 443 if (i > 0) logmag[bs - i] = lm;
Chris@8 444 }
Chris@8 445
Chris@9 446 fft(bs, true, logmag, 0, rawcep, io);
Chris@8 447
Chris@8 448 delete[] logmag;
Chris@8 449 delete[] io;
Chris@8 450
Chris@8 451 int n = m_bins;
Chris@8 452 double *data = new double[n];
Chris@8 453 filter(rawcep, data);
Chris@8 454 delete[] rawcep;
Chris@8 455
Chris@11 456 double abstot = 0.0;
Chris@11 457
Chris@11 458 for (int i = 0; i < n; ++i) {
Chris@11 459 abstot += fabs(data[i]);
Chris@11 460 }
Chris@11 461
Chris@8 462 double maxval = 0.0;
Chris@11 463 int maxbin = -1;
Chris@8 464
Chris@8 465 for (int i = 0; i < n; ++i) {
Chris@8 466 if (data[i] > maxval) {
Chris@8 467 maxval = data[i];
Chris@8 468 maxbin = i;
Chris@8 469 }
Chris@8 470 }
Chris@8 471
Chris@13 472 if (maxbin < 0) return fs;
Chris@13 473
Chris@13 474 double peakfreq = m_inputSampleRate / (maxbin + m_binFrom);
Chris@13 475 Hypothesis::Estimate e;
Chris@13 476 e.freq = peakfreq;
Chris@13 477 e.time = timestamp;
Chris@13 478
Chris@13 479 m_accepted.advanceTime();
Chris@16 480
Chris@13 481 for (int i = 0; i < m_possible.size(); ++i) {
Chris@13 482 m_possible[i].advanceTime();
Chris@13 483 }
Chris@13 484
Chris@16 485 if (!m_accepted.test(e)) {
Chris@16 486 int candidate = -1;
Chris@16 487 for (int i = 0; i < m_possible.size(); ++i) {
Chris@16 488 if (m_possible[i].test(e)) {
Chris@16 489 if (m_possible[i].getState() == Hypothesis::Satisfied) {
Chris@16 490 candidate = i;
Chris@16 491 }
Chris@16 492 break;
Chris@16 493 }
Chris@16 494 }
Chris@16 495 if (m_accepted.getState() == Hypothesis::Expired) {
Chris@16 496 m_accepted.addFeatures(fs[0]);
Chris@16 497 if (candidate >= 0) {
Chris@16 498 m_accepted = m_possible[candidate];
Chris@16 499 } else {
Chris@16 500 m_accepted = Hypothesis();
Chris@16 501 }
Chris@16 502 }
Chris@13 503
Chris@16 504 //!!! and also need to reap rejected/expired hypotheses from the list
Chris@16 505 }
Chris@16 506
Chris@13 507
Chris@13 508 /*
Chris@11 509 bool accepted = false;
Chris@11 510
Chris@11 511 if (maxbin >= 0) {
Chris@11 512 double pp = calculatePeakProportion(data, abstot, maxbin);
Chris@11 513 if (acceptPeak(maxbin, pp)) {
Chris@11 514 accepted = true;
Chris@11 515 } else {
Chris@11 516 // try a secondary peak
Chris@11 517 maxval = 0.0;
Chris@11 518 int secondbin = 0;
Chris@11 519 for (int i = 1; i < n-1; ++i) {
Chris@11 520 if (i != maxbin &&
Chris@11 521 data[i] > data[i-1] &&
Chris@11 522 data[i] > data[i+1] &&
Chris@11 523 data[i] > maxval) {
Chris@11 524 maxval = data[i];
Chris@11 525 secondbin = i;
Chris@11 526 }
Chris@11 527 }
Chris@11 528 double spp = calculatePeakProportion(data, abstot, secondbin);
Chris@11 529 if (acceptPeak(secondbin, spp)) {
Chris@11 530 maxbin = secondbin;
Chris@11 531 pp = spp;
Chris@11 532 accepted = true;
Chris@11 533 }
Chris@8 534 }
Chris@11 535 if (accepted) {
Chris@11 536 m_prevpeak = maxbin;
Chris@11 537 m_prevprop = pp;
Chris@8 538 }
Chris@8 539 }
Chris@13 540 */
Chris@8 541 // std::cerr << "peakProportion = " << peakProportion << std::endl;
Chris@8 542 // std::cerr << "peak = " << m_inputSampleRate / (maxbin + m_binFrom) << std::endl;
Chris@9 543 // std::cerr << "bins = " << m_bins << std::endl;
Chris@8 544
Chris@11 545 // if (peakProportion >= (0.00006 * m_bins)) {
Chris@16 546 /*
Chris@11 547 if (accepted) {
Chris@8 548 Feature f;
Chris@8 549 f.hasTimestamp = true;
Chris@8 550 f.timestamp = timestamp;
Chris@8 551 f.values.push_back(m_inputSampleRate / (maxbin + m_binFrom));
Chris@8 552 fs[0].push_back(f);
Chris@8 553 }
Chris@16 554 */
Chris@8 555 delete[] data;
Chris@8 556 return fs;
Chris@8 557 }
Chris@8 558
Chris@8 559 CepstrumPitchTracker::FeatureSet
Chris@8 560 CepstrumPitchTracker::getRemainingFeatures()
Chris@8 561 {
Chris@8 562 FeatureSet fs;
Chris@16 563 if (m_accepted.getState() != Hypothesis::New) {
Chris@16 564 m_accepted.addFeatures(fs[0]);
Chris@16 565 }
Chris@8 566 return fs;
Chris@8 567 }
Chris@8 568
Chris@8 569 void
Chris@8 570 CepstrumPitchTracker::fft(unsigned int n, bool inverse,
Chris@8 571 double *ri, double *ii, double *ro, double *io)
Chris@8 572 {
Chris@8 573 if (!ri || !ro || !io) return;
Chris@8 574
Chris@8 575 unsigned int bits;
Chris@8 576 unsigned int i, j, k, m;
Chris@8 577 unsigned int blockSize, blockEnd;
Chris@8 578
Chris@8 579 double tr, ti;
Chris@8 580
Chris@8 581 if (n < 2) return;
Chris@8 582 if (n & (n-1)) return;
Chris@8 583
Chris@8 584 double angle = 2.0 * M_PI;
Chris@8 585 if (inverse) angle = -angle;
Chris@8 586
Chris@8 587 for (i = 0; ; ++i) {
Chris@8 588 if (n & (1 << i)) {
Chris@8 589 bits = i;
Chris@8 590 break;
Chris@8 591 }
Chris@8 592 }
Chris@8 593
Chris@8 594 static unsigned int tableSize = 0;
Chris@8 595 static int *table = 0;
Chris@8 596
Chris@8 597 if (tableSize != n) {
Chris@8 598
Chris@8 599 delete[] table;
Chris@8 600
Chris@8 601 table = new int[n];
Chris@8 602
Chris@8 603 for (i = 0; i < n; ++i) {
Chris@8 604
Chris@8 605 m = i;
Chris@8 606
Chris@8 607 for (j = k = 0; j < bits; ++j) {
Chris@8 608 k = (k << 1) | (m & 1);
Chris@8 609 m >>= 1;
Chris@8 610 }
Chris@8 611
Chris@8 612 table[i] = k;
Chris@8 613 }
Chris@8 614
Chris@8 615 tableSize = n;
Chris@8 616 }
Chris@8 617
Chris@8 618 if (ii) {
Chris@8 619 for (i = 0; i < n; ++i) {
Chris@8 620 ro[table[i]] = ri[i];
Chris@8 621 io[table[i]] = ii[i];
Chris@8 622 }
Chris@8 623 } else {
Chris@8 624 for (i = 0; i < n; ++i) {
Chris@8 625 ro[table[i]] = ri[i];
Chris@8 626 io[table[i]] = 0.0;
Chris@8 627 }
Chris@8 628 }
Chris@8 629
Chris@8 630 blockEnd = 1;
Chris@8 631
Chris@8 632 for (blockSize = 2; blockSize <= n; blockSize <<= 1) {
Chris@8 633
Chris@8 634 double delta = angle / (double)blockSize;
Chris@8 635 double sm2 = -sin(-2 * delta);
Chris@8 636 double sm1 = -sin(-delta);
Chris@8 637 double cm2 = cos(-2 * delta);
Chris@8 638 double cm1 = cos(-delta);
Chris@8 639 double w = 2 * cm1;
Chris@8 640 double ar[3], ai[3];
Chris@8 641
Chris@8 642 for (i = 0; i < n; i += blockSize) {
Chris@8 643
Chris@8 644 ar[2] = cm2;
Chris@8 645 ar[1] = cm1;
Chris@8 646
Chris@8 647 ai[2] = sm2;
Chris@8 648 ai[1] = sm1;
Chris@8 649
Chris@8 650 for (j = i, m = 0; m < blockEnd; j++, m++) {
Chris@8 651
Chris@8 652 ar[0] = w * ar[1] - ar[2];
Chris@8 653 ar[2] = ar[1];
Chris@8 654 ar[1] = ar[0];
Chris@8 655
Chris@8 656 ai[0] = w * ai[1] - ai[2];
Chris@8 657 ai[2] = ai[1];
Chris@8 658 ai[1] = ai[0];
Chris@8 659
Chris@8 660 k = j + blockEnd;
Chris@8 661 tr = ar[0] * ro[k] - ai[0] * io[k];
Chris@8 662 ti = ar[0] * io[k] + ai[0] * ro[k];
Chris@8 663
Chris@8 664 ro[k] = ro[j] - tr;
Chris@8 665 io[k] = io[j] - ti;
Chris@8 666
Chris@8 667 ro[j] += tr;
Chris@8 668 io[j] += ti;
Chris@8 669 }
Chris@8 670 }
Chris@8 671
Chris@8 672 blockEnd = blockSize;
Chris@8 673 }
Chris@8 674 }
Chris@8 675
Chris@8 676