annotate CepstrumPitchTracker.cpp @ 9:83603936e4d2 track

An experiment in mean-filtering proportion values -- not very successful
author Chris Cannam
date Fri, 29 Jun 2012 11:25:05 +0100
parents 32defdb2f9d9
children
rev   line source
Chris@3 1 /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */
Chris@3 2 /*
Chris@3 3 Permission is hereby granted, free of charge, to any person
Chris@3 4 obtaining a copy of this software and associated documentation
Chris@3 5 files (the "Software"), to deal in the Software without
Chris@3 6 restriction, including without limitation the rights to use, copy,
Chris@3 7 modify, merge, publish, distribute, sublicense, and/or sell copies
Chris@3 8 of the Software, and to permit persons to whom the Software is
Chris@3 9 furnished to do so, subject to the following conditions:
Chris@3 10
Chris@3 11 The above copyright notice and this permission notice shall be
Chris@3 12 included in all copies or substantial portions of the Software.
Chris@3 13
Chris@3 14 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
Chris@3 15 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
Chris@3 16 MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
Chris@3 17 NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR
Chris@3 18 ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
Chris@3 19 CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
Chris@3 20 WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Chris@3 21 */
Chris@3 22
Chris@3 23 #include "CepstrumPitchTracker.h"
Chris@3 24
Chris@3 25 #include <vector>
Chris@3 26 #include <algorithm>
Chris@3 27
Chris@3 28 #include <cstdio>
Chris@3 29 #include <cmath>
Chris@3 30 #include <complex>
Chris@3 31
Chris@3 32 using std::string;
Chris@7 33 using std::vector;
Chris@7 34
Chris@7 35 CepstrumPitchTracker::Hypothesis::Hypothesis(Estimate s)
Chris@7 36 {
Chris@7 37 m_state = Provisional;
Chris@7 38 m_pending.push_back(s);
Chris@7 39 m_age = 0;
Chris@7 40 }
Chris@7 41
Chris@7 42 bool
Chris@7 43 CepstrumPitchTracker::Hypothesis::isWithinTolerance(Estimate s)
Chris@7 44 {
Chris@7 45 if (m_pending.empty()) {
Chris@7 46 return true;
Chris@7 47 }
Chris@7 48 Estimate last = m_pending[m_pending.size()-1];
Chris@7 49 double r = s.freq / last.freq;
Chris@7 50 int cents = lrint(1200.0 * (log(r) / log(2.0)));
Chris@7 51 return (cents > -200 && cents < 200);
Chris@7 52 }
Chris@7 53
Chris@7 54 bool
Chris@7 55 CepstrumPitchTracker::Hypothesis::isSatisfied()
Chris@7 56 {
Chris@7 57 return (m_pending.size() > 2);
Chris@7 58 }
Chris@7 59
Chris@7 60 bool
Chris@7 61 CepstrumPitchTracker::Hypothesis::test(Estimate s)
Chris@7 62 {
Chris@7 63 if (m_state == Rejected || m_state == Expired) {
Chris@7 64 return false;
Chris@7 65 }
Chris@7 66
Chris@7 67 if (++m_age > 3) {
Chris@7 68 if (m_state == Satisfied) {
Chris@7 69 m_state = Expired;
Chris@7 70 } else {
Chris@7 71 m_state = Rejected;
Chris@7 72 }
Chris@7 73 return false;
Chris@7 74 }
Chris@7 75
Chris@7 76 if (isWithinTolerance(s)) {
Chris@7 77 m_pending.push_back(s);
Chris@7 78 if (m_state == Provisional) {
Chris@7 79 if (isSatisfied()) {
Chris@7 80 m_state == Satisfied;
Chris@7 81 }
Chris@7 82 }
Chris@7 83 m_age = 0;
Chris@7 84 return true;
Chris@7 85 }
Chris@7 86
Chris@7 87 return false;
Chris@7 88 }
Chris@7 89
Chris@7 90 CepstrumPitchTracker::Hypothesis::State
Chris@7 91 CepstrumPitchTracker::Hypothesis::getState()
Chris@7 92 {
Chris@7 93 return m_state;
Chris@7 94 }
Chris@7 95
Chris@7 96 CepstrumPitchTracker::Hypothesis::Estimates
Chris@7 97 CepstrumPitchTracker::Hypothesis::getAcceptedEstimates()
Chris@7 98 {
Chris@7 99 if (m_state == Satisfied || m_state == Expired) {
Chris@7 100 return m_pending;
Chris@7 101 } else {
Chris@7 102 return Estimates();
Chris@7 103 }
Chris@7 104 }
Chris@7 105
Chris@3 106
Chris@3 107 CepstrumPitchTracker::CepstrumPitchTracker(float inputSampleRate) :
Chris@3 108 Plugin(inputSampleRate),
Chris@3 109 m_channels(0),
Chris@3 110 m_stepSize(256),
Chris@3 111 m_blockSize(1024),
Chris@3 112 m_fmin(50),
Chris@3 113 m_fmax(1000),
Chris@5 114 m_histlen(1),
Chris@5 115 m_vflen(3),
Chris@9 116 m_ppflen(4),
Chris@3 117 m_binFrom(0),
Chris@3 118 m_binTo(0),
Chris@3 119 m_bins(0),
Chris@7 120 m_accepted(0),
Chris@6 121 m_history(0),
Chris@9 122 m_ppfilter(0),
Chris@6 123 m_prevpeak(0),
Chris@6 124 m_prevprop(0)
Chris@3 125 {
Chris@3 126 }
Chris@3 127
Chris@3 128 CepstrumPitchTracker::~CepstrumPitchTracker()
Chris@3 129 {
Chris@3 130 if (m_history) {
Chris@3 131 for (int i = 0; i < m_histlen; ++i) {
Chris@3 132 delete[] m_history[i];
Chris@3 133 }
Chris@3 134 delete[] m_history;
Chris@3 135 }
Chris@9 136 delete[] m_ppfilter;
Chris@3 137 }
Chris@3 138
Chris@3 139 string
Chris@3 140 CepstrumPitchTracker::getIdentifier() const
Chris@3 141 {
Chris@3 142 return "cepstrum-pitch";
Chris@3 143 }
Chris@3 144
Chris@3 145 string
Chris@3 146 CepstrumPitchTracker::getName() const
Chris@3 147 {
Chris@3 148 return "Cepstrum Pitch Tracker";
Chris@3 149 }
Chris@3 150
Chris@3 151 string
Chris@3 152 CepstrumPitchTracker::getDescription() const
Chris@3 153 {
Chris@3 154 return "Estimate f0 of monophonic material using a cepstrum method.";
Chris@3 155 }
Chris@3 156
Chris@3 157 string
Chris@3 158 CepstrumPitchTracker::getMaker() const
Chris@3 159 {
Chris@3 160 return "Chris Cannam";
Chris@3 161 }
Chris@3 162
Chris@3 163 int
Chris@3 164 CepstrumPitchTracker::getPluginVersion() const
Chris@3 165 {
Chris@3 166 // Increment this each time you release a version that behaves
Chris@3 167 // differently from the previous one
Chris@3 168 return 1;
Chris@3 169 }
Chris@3 170
Chris@3 171 string
Chris@3 172 CepstrumPitchTracker::getCopyright() const
Chris@3 173 {
Chris@3 174 return "Freely redistributable (BSD license)";
Chris@3 175 }
Chris@3 176
Chris@3 177 CepstrumPitchTracker::InputDomain
Chris@3 178 CepstrumPitchTracker::getInputDomain() const
Chris@3 179 {
Chris@3 180 return FrequencyDomain;
Chris@3 181 }
Chris@3 182
Chris@3 183 size_t
Chris@3 184 CepstrumPitchTracker::getPreferredBlockSize() const
Chris@3 185 {
Chris@3 186 return 1024;
Chris@3 187 }
Chris@3 188
Chris@3 189 size_t
Chris@3 190 CepstrumPitchTracker::getPreferredStepSize() const
Chris@3 191 {
Chris@3 192 return 256;
Chris@3 193 }
Chris@3 194
Chris@3 195 size_t
Chris@3 196 CepstrumPitchTracker::getMinChannelCount() const
Chris@3 197 {
Chris@3 198 return 1;
Chris@3 199 }
Chris@3 200
Chris@3 201 size_t
Chris@3 202 CepstrumPitchTracker::getMaxChannelCount() const
Chris@3 203 {
Chris@3 204 return 1;
Chris@3 205 }
Chris@3 206
Chris@3 207 CepstrumPitchTracker::ParameterList
Chris@3 208 CepstrumPitchTracker::getParameterDescriptors() const
Chris@3 209 {
Chris@3 210 ParameterList list;
Chris@3 211 return list;
Chris@3 212 }
Chris@3 213
Chris@3 214 float
Chris@3 215 CepstrumPitchTracker::getParameter(string identifier) const
Chris@3 216 {
Chris@3 217 return 0.f;
Chris@3 218 }
Chris@3 219
Chris@3 220 void
Chris@3 221 CepstrumPitchTracker::setParameter(string identifier, float value)
Chris@3 222 {
Chris@3 223 }
Chris@3 224
Chris@3 225 CepstrumPitchTracker::ProgramList
Chris@3 226 CepstrumPitchTracker::getPrograms() const
Chris@3 227 {
Chris@3 228 ProgramList list;
Chris@3 229 return list;
Chris@3 230 }
Chris@3 231
Chris@3 232 string
Chris@3 233 CepstrumPitchTracker::getCurrentProgram() const
Chris@3 234 {
Chris@3 235 return ""; // no programs
Chris@3 236 }
Chris@3 237
Chris@3 238 void
Chris@3 239 CepstrumPitchTracker::selectProgram(string name)
Chris@3 240 {
Chris@3 241 }
Chris@3 242
Chris@3 243 CepstrumPitchTracker::OutputList
Chris@3 244 CepstrumPitchTracker::getOutputDescriptors() const
Chris@3 245 {
Chris@3 246 OutputList outputs;
Chris@3 247
Chris@3 248 int n = 0;
Chris@3 249
Chris@3 250 OutputDescriptor d;
Chris@3 251
Chris@3 252 d.identifier = "f0";
Chris@3 253 d.name = "Estimated f0";
Chris@3 254 d.description = "Estimated fundamental frequency";
Chris@3 255 d.unit = "Hz";
Chris@3 256 d.hasFixedBinCount = true;
Chris@3 257 d.binCount = 1;
Chris@3 258 d.hasKnownExtents = true;
Chris@3 259 d.minValue = m_fmin;
Chris@3 260 d.maxValue = m_fmax;
Chris@3 261 d.isQuantized = false;
Chris@3 262 d.sampleType = OutputDescriptor::FixedSampleRate;
Chris@3 263 d.sampleRate = (m_inputSampleRate / m_stepSize);
Chris@3 264 d.hasDuration = false;
Chris@3 265 outputs.push_back(d);
Chris@3 266
Chris@3 267 return outputs;
Chris@3 268 }
Chris@3 269
Chris@3 270 bool
Chris@3 271 CepstrumPitchTracker::initialise(size_t channels, size_t stepSize, size_t blockSize)
Chris@3 272 {
Chris@3 273 if (channels < getMinChannelCount() ||
Chris@3 274 channels > getMaxChannelCount()) return false;
Chris@3 275
Chris@3 276 // std::cerr << "CepstrumPitchTracker::initialise: channels = " << channels
Chris@3 277 // << ", stepSize = " << stepSize << ", blockSize = " << blockSize
Chris@3 278 // << std::endl;
Chris@3 279
Chris@3 280 m_channels = channels;
Chris@3 281 m_stepSize = stepSize;
Chris@3 282 m_blockSize = blockSize;
Chris@3 283
Chris@3 284 m_binFrom = int(m_inputSampleRate / m_fmax);
Chris@3 285 m_binTo = int(m_inputSampleRate / m_fmin);
Chris@3 286
Chris@3 287 if (m_binTo >= (int)m_blockSize / 2) {
Chris@3 288 m_binTo = m_blockSize / 2 - 1;
Chris@3 289 }
Chris@3 290
Chris@3 291 m_bins = (m_binTo - m_binFrom) + 1;
Chris@3 292
Chris@3 293 m_history = new double *[m_histlen];
Chris@3 294 for (int i = 0; i < m_histlen; ++i) {
Chris@3 295 m_history[i] = new double[m_bins];
Chris@3 296 }
Chris@3 297
Chris@9 298 m_ppfilter = new double[m_ppflen];
Chris@9 299
Chris@3 300 reset();
Chris@3 301
Chris@3 302 return true;
Chris@3 303 }
Chris@3 304
Chris@3 305 void
Chris@3 306 CepstrumPitchTracker::reset()
Chris@3 307 {
Chris@3 308 for (int i = 0; i < m_histlen; ++i) {
Chris@3 309 for (int j = 0; j < m_bins; ++j) {
Chris@3 310 m_history[i][j] = 0.0;
Chris@3 311 }
Chris@3 312 }
Chris@9 313 for (int i = 0; i < m_ppflen; ++i) {
Chris@9 314 m_ppfilter[i] = 0.0;
Chris@9 315 }
Chris@3 316 }
Chris@3 317
Chris@3 318 void
Chris@3 319 CepstrumPitchTracker::filter(const double *cep, double *result)
Chris@3 320 {
Chris@3 321 int hix = m_histlen - 1; // current history index
Chris@3 322
Chris@3 323 // roll back the history
Chris@3 324 if (m_histlen > 1) {
Chris@3 325 double *oldest = m_history[0];
Chris@3 326 for (int i = 1; i < m_histlen; ++i) {
Chris@3 327 m_history[i-1] = m_history[i];
Chris@3 328 }
Chris@3 329 // and stick this back in the newest spot, to recycle
Chris@3 330 m_history[hix] = oldest;
Chris@3 331 }
Chris@3 332
Chris@3 333 for (int i = 0; i < m_bins; ++i) {
Chris@5 334 double v = 0;
Chris@5 335 int n = 0;
Chris@5 336 // average according to the vertical filter length
Chris@5 337 for (int j = -m_vflen/2; j <= m_vflen/2; ++j) {
Chris@5 338 int ix = i + m_binFrom + j;
Chris@5 339 if (ix >= 0 && ix < m_blockSize) {
Chris@5 340 v += cep[ix];
Chris@5 341 ++n;
Chris@5 342 }
Chris@5 343 }
Chris@5 344 m_history[hix][i] = v / n;
Chris@3 345 }
Chris@3 346
Chris@3 347 for (int i = 0; i < m_bins; ++i) {
Chris@3 348 double mean = 0.0;
Chris@3 349 for (int j = 0; j < m_histlen; ++j) {
Chris@3 350 mean += m_history[j][i];
Chris@3 351 }
Chris@3 352 mean /= m_histlen;
Chris@3 353 result[i] = mean;
Chris@3 354 }
Chris@3 355 }
Chris@3 356
Chris@6 357 double
Chris@6 358 CepstrumPitchTracker::calculatePeakProportion(const double *data, double abstot, int n)
Chris@6 359 {
Chris@6 360 double aroundPeak = data[n];
Chris@6 361 double peakProportion = 0.0;
Chris@6 362
Chris@6 363 int i = n - 1;
Chris@6 364 while (i > 0 && data[i] <= data[i+1]) {
Chris@6 365 aroundPeak += fabs(data[i]);
Chris@6 366 --i;
Chris@6 367 }
Chris@6 368 i = n + 1;
Chris@6 369 while (i < m_bins && data[i] <= data[i-1]) {
Chris@6 370 aroundPeak += fabs(data[i]);
Chris@6 371 ++i;
Chris@6 372 }
Chris@6 373 peakProportion = aroundPeak / abstot;
Chris@6 374
Chris@6 375 return peakProportion;
Chris@6 376 }
Chris@6 377
Chris@6 378 bool
Chris@6 379 CepstrumPitchTracker::acceptPeak(int n, double peakProportion)
Chris@6 380 {
Chris@6 381 bool accept = false;
Chris@6 382
Chris@6 383 if (abs(n - m_prevpeak) < 10) { //!!! should depend on bin count
Chris@9 384 std::cerr << "accepting " << n << " [as prevpeak was " << m_prevpeak
Chris@9 385 << "]" << std::endl;
Chris@6 386 accept = true;
Chris@6 387 } else if (peakProportion > m_prevprop * 2) {
Chris@9 388 std::cerr << "accepting " << n << " [as peakProportion " << peakProportion << " much higher than prev " << m_prevprop << "]" << std::endl;
Chris@6 389 accept = true;
Chris@9 390 } else {
Chris@9 391 std::cerr << "rejecting " << n << " with " << peakProportion
Chris@9 392 << " [prevpeak " << m_prevpeak
Chris@9 393 << ", prevprop " << m_prevprop << "]" << std::endl;
Chris@6 394 }
Chris@6 395
Chris@6 396 return accept;
Chris@6 397 }
Chris@6 398
Chris@9 399 void
Chris@9 400 CepstrumPitchTracker::updatePropFilter(double prop)
Chris@9 401 {
Chris@9 402 double tot = 0.0;
Chris@9 403 for (int i = 1; i < m_ppflen; ++i) {
Chris@9 404 double val = m_ppfilter[i];
Chris@9 405 m_ppfilter[i-1] = val;
Chris@9 406 tot += val;
Chris@9 407 }
Chris@9 408 double mean = tot / (m_ppflen - 1);
Chris@9 409 m_ppfilter[m_ppflen-1] = prop;
Chris@9 410 m_prevprop = mean;
Chris@9 411 }
Chris@9 412
Chris@3 413 CepstrumPitchTracker::FeatureSet
Chris@3 414 CepstrumPitchTracker::process(const float *const *inputBuffers, Vamp::RealTime timestamp)
Chris@3 415 {
Chris@3 416 FeatureSet fs;
Chris@3 417
Chris@3 418 int bs = m_blockSize;
Chris@3 419 int hs = m_blockSize/2 + 1;
Chris@3 420
Chris@3 421 double *rawcep = new double[bs];
Chris@3 422 double *io = new double[bs];
Chris@3 423 double *logmag = new double[bs];
Chris@3 424
Chris@4 425 // The "inverse symmetric" method. Seems to be the most reliable
Chris@3 426
Chris@3 427 for (int i = 0; i < hs; ++i) {
Chris@3 428
Chris@3 429 double power =
Chris@3 430 inputBuffers[0][i*2 ] * inputBuffers[0][i*2 ] +
Chris@3 431 inputBuffers[0][i*2+1] * inputBuffers[0][i*2+1];
Chris@3 432 double mag = sqrt(power);
Chris@3 433
Chris@3 434 double lm = log(mag + 0.00000001);
Chris@3 435
Chris@4 436 logmag[i] = lm;
Chris@4 437 if (i > 0) logmag[bs - i] = lm;
Chris@3 438 }
Chris@3 439
Chris@4 440 fft(bs, true, logmag, 0, rawcep, io);
Chris@3 441
Chris@3 442 delete[] logmag;
Chris@3 443 delete[] io;
Chris@3 444
Chris@3 445 int n = m_bins;
Chris@3 446 double *data = new double[n];
Chris@3 447 filter(rawcep, data);
Chris@3 448 delete[] rawcep;
Chris@3 449
Chris@6 450 double abstot = 0.0;
Chris@6 451
Chris@6 452 for (int i = 0; i < n; ++i) {
Chris@6 453 abstot += fabs(data[i]);
Chris@6 454 }
Chris@6 455
Chris@3 456 double maxval = 0.0;
Chris@6 457 int maxbin = -1;
Chris@3 458
Chris@3 459 for (int i = 0; i < n; ++i) {
Chris@3 460 if (data[i] > maxval) {
Chris@3 461 maxval = data[i];
Chris@3 462 maxbin = i;
Chris@3 463 }
Chris@3 464 }
Chris@3 465
Chris@6 466 bool accepted = false;
Chris@6 467
Chris@6 468 if (maxbin >= 0) {
Chris@6 469 double pp = calculatePeakProportion(data, abstot, maxbin);
Chris@6 470 if (acceptPeak(maxbin, pp)) {
Chris@6 471 accepted = true;
Chris@6 472 } else {
Chris@6 473 // try a secondary peak
Chris@6 474 maxval = 0.0;
Chris@6 475 int secondbin = 0;
Chris@6 476 for (int i = 1; i < n-1; ++i) {
Chris@6 477 if (i != maxbin &&
Chris@6 478 data[i] > data[i-1] &&
Chris@6 479 data[i] > data[i+1] &&
Chris@6 480 data[i] > maxval) {
Chris@6 481 maxval = data[i];
Chris@6 482 secondbin = i;
Chris@6 483 }
Chris@6 484 }
Chris@6 485 double spp = calculatePeakProportion(data, abstot, secondbin);
Chris@6 486 if (acceptPeak(secondbin, spp)) {
Chris@6 487 maxbin = secondbin;
Chris@6 488 pp = spp;
Chris@6 489 accepted = true;
Chris@6 490 }
Chris@3 491 }
Chris@6 492 if (accepted) {
Chris@6 493 m_prevpeak = maxbin;
Chris@3 494 }
Chris@9 495 updatePropFilter(pp);
Chris@3 496 }
Chris@6 497
Chris@3 498 // std::cerr << "peakProportion = " << peakProportion << std::endl;
Chris@3 499 // std::cerr << "peak = " << m_inputSampleRate / (maxbin + m_binFrom) << std::endl;
Chris@4 500 // std::cerr << "bins = " << m_bins << std::endl;
Chris@3 501
Chris@6 502 // if (peakProportion >= (0.00006 * m_bins)) {
Chris@6 503 if (accepted) {
Chris@3 504 Feature f;
Chris@3 505 f.hasTimestamp = true;
Chris@3 506 f.timestamp = timestamp;
Chris@3 507 f.values.push_back(m_inputSampleRate / (maxbin + m_binFrom));
Chris@3 508 fs[0].push_back(f);
Chris@3 509 }
Chris@3 510
Chris@3 511 delete[] data;
Chris@3 512 return fs;
Chris@3 513 }
Chris@3 514
Chris@3 515 CepstrumPitchTracker::FeatureSet
Chris@3 516 CepstrumPitchTracker::getRemainingFeatures()
Chris@3 517 {
Chris@3 518 FeatureSet fs;
Chris@3 519 return fs;
Chris@3 520 }
Chris@3 521
Chris@3 522 void
Chris@3 523 CepstrumPitchTracker::fft(unsigned int n, bool inverse,
Chris@3 524 double *ri, double *ii, double *ro, double *io)
Chris@3 525 {
Chris@3 526 if (!ri || !ro || !io) return;
Chris@3 527
Chris@3 528 unsigned int bits;
Chris@3 529 unsigned int i, j, k, m;
Chris@3 530 unsigned int blockSize, blockEnd;
Chris@3 531
Chris@3 532 double tr, ti;
Chris@3 533
Chris@3 534 if (n < 2) return;
Chris@3 535 if (n & (n-1)) return;
Chris@3 536
Chris@3 537 double angle = 2.0 * M_PI;
Chris@3 538 if (inverse) angle = -angle;
Chris@3 539
Chris@3 540 for (i = 0; ; ++i) {
Chris@3 541 if (n & (1 << i)) {
Chris@3 542 bits = i;
Chris@3 543 break;
Chris@3 544 }
Chris@3 545 }
Chris@3 546
Chris@3 547 static unsigned int tableSize = 0;
Chris@3 548 static int *table = 0;
Chris@3 549
Chris@3 550 if (tableSize != n) {
Chris@3 551
Chris@3 552 delete[] table;
Chris@3 553
Chris@3 554 table = new int[n];
Chris@3 555
Chris@3 556 for (i = 0; i < n; ++i) {
Chris@3 557
Chris@3 558 m = i;
Chris@3 559
Chris@3 560 for (j = k = 0; j < bits; ++j) {
Chris@3 561 k = (k << 1) | (m & 1);
Chris@3 562 m >>= 1;
Chris@3 563 }
Chris@3 564
Chris@3 565 table[i] = k;
Chris@3 566 }
Chris@3 567
Chris@3 568 tableSize = n;
Chris@3 569 }
Chris@3 570
Chris@3 571 if (ii) {
Chris@3 572 for (i = 0; i < n; ++i) {
Chris@3 573 ro[table[i]] = ri[i];
Chris@3 574 io[table[i]] = ii[i];
Chris@3 575 }
Chris@3 576 } else {
Chris@3 577 for (i = 0; i < n; ++i) {
Chris@3 578 ro[table[i]] = ri[i];
Chris@3 579 io[table[i]] = 0.0;
Chris@3 580 }
Chris@3 581 }
Chris@3 582
Chris@3 583 blockEnd = 1;
Chris@3 584
Chris@3 585 for (blockSize = 2; blockSize <= n; blockSize <<= 1) {
Chris@3 586
Chris@3 587 double delta = angle / (double)blockSize;
Chris@3 588 double sm2 = -sin(-2 * delta);
Chris@3 589 double sm1 = -sin(-delta);
Chris@3 590 double cm2 = cos(-2 * delta);
Chris@3 591 double cm1 = cos(-delta);
Chris@3 592 double w = 2 * cm1;
Chris@3 593 double ar[3], ai[3];
Chris@3 594
Chris@3 595 for (i = 0; i < n; i += blockSize) {
Chris@3 596
Chris@3 597 ar[2] = cm2;
Chris@3 598 ar[1] = cm1;
Chris@3 599
Chris@3 600 ai[2] = sm2;
Chris@3 601 ai[1] = sm1;
Chris@3 602
Chris@3 603 for (j = i, m = 0; m < blockEnd; j++, m++) {
Chris@3 604
Chris@3 605 ar[0] = w * ar[1] - ar[2];
Chris@3 606 ar[2] = ar[1];
Chris@3 607 ar[1] = ar[0];
Chris@3 608
Chris@3 609 ai[0] = w * ai[1] - ai[2];
Chris@3 610 ai[2] = ai[1];
Chris@3 611 ai[1] = ai[0];
Chris@3 612
Chris@3 613 k = j + blockEnd;
Chris@3 614 tr = ar[0] * ro[k] - ai[0] * io[k];
Chris@3 615 ti = ar[0] * io[k] + ai[0] * ro[k];
Chris@3 616
Chris@3 617 ro[k] = ro[j] - tr;
Chris@3 618 io[k] = io[j] - ti;
Chris@3 619
Chris@3 620 ro[j] += tr;
Chris@3 621 io[j] += ti;
Chris@3 622 }
Chris@3 623 }
Chris@3 624
Chris@3 625 blockEnd = blockSize;
Chris@3 626 }
Chris@3 627 }
Chris@3 628
Chris@3 629