annotate CepstrumPitchTracker.cpp @ 7:32defdb2f9d9 track

Start an alternative idea
author Chris Cannam
date Thu, 28 Jun 2012 12:17:18 +0100
parents 291c75f6e837
children e9d86e129467 83603936e4d2
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@3 116 m_binFrom(0),
Chris@3 117 m_binTo(0),
Chris@3 118 m_bins(0),
Chris@7 119 m_accepted(0),
Chris@6 120 m_history(0),
Chris@6 121 m_prevpeak(0),
Chris@6 122 m_prevprop(0)
Chris@3 123 {
Chris@3 124 }
Chris@3 125
Chris@3 126 CepstrumPitchTracker::~CepstrumPitchTracker()
Chris@3 127 {
Chris@3 128 if (m_history) {
Chris@3 129 for (int i = 0; i < m_histlen; ++i) {
Chris@3 130 delete[] m_history[i];
Chris@3 131 }
Chris@3 132 delete[] m_history;
Chris@3 133 }
Chris@3 134 }
Chris@3 135
Chris@3 136 string
Chris@3 137 CepstrumPitchTracker::getIdentifier() const
Chris@3 138 {
Chris@3 139 return "cepstrum-pitch";
Chris@3 140 }
Chris@3 141
Chris@3 142 string
Chris@3 143 CepstrumPitchTracker::getName() const
Chris@3 144 {
Chris@3 145 return "Cepstrum Pitch Tracker";
Chris@3 146 }
Chris@3 147
Chris@3 148 string
Chris@3 149 CepstrumPitchTracker::getDescription() const
Chris@3 150 {
Chris@3 151 return "Estimate f0 of monophonic material using a cepstrum method.";
Chris@3 152 }
Chris@3 153
Chris@3 154 string
Chris@3 155 CepstrumPitchTracker::getMaker() const
Chris@3 156 {
Chris@3 157 return "Chris Cannam";
Chris@3 158 }
Chris@3 159
Chris@3 160 int
Chris@3 161 CepstrumPitchTracker::getPluginVersion() const
Chris@3 162 {
Chris@3 163 // Increment this each time you release a version that behaves
Chris@3 164 // differently from the previous one
Chris@3 165 return 1;
Chris@3 166 }
Chris@3 167
Chris@3 168 string
Chris@3 169 CepstrumPitchTracker::getCopyright() const
Chris@3 170 {
Chris@3 171 return "Freely redistributable (BSD license)";
Chris@3 172 }
Chris@3 173
Chris@3 174 CepstrumPitchTracker::InputDomain
Chris@3 175 CepstrumPitchTracker::getInputDomain() const
Chris@3 176 {
Chris@3 177 return FrequencyDomain;
Chris@3 178 }
Chris@3 179
Chris@3 180 size_t
Chris@3 181 CepstrumPitchTracker::getPreferredBlockSize() const
Chris@3 182 {
Chris@3 183 return 1024;
Chris@3 184 }
Chris@3 185
Chris@3 186 size_t
Chris@3 187 CepstrumPitchTracker::getPreferredStepSize() const
Chris@3 188 {
Chris@3 189 return 256;
Chris@3 190 }
Chris@3 191
Chris@3 192 size_t
Chris@3 193 CepstrumPitchTracker::getMinChannelCount() const
Chris@3 194 {
Chris@3 195 return 1;
Chris@3 196 }
Chris@3 197
Chris@3 198 size_t
Chris@3 199 CepstrumPitchTracker::getMaxChannelCount() const
Chris@3 200 {
Chris@3 201 return 1;
Chris@3 202 }
Chris@3 203
Chris@3 204 CepstrumPitchTracker::ParameterList
Chris@3 205 CepstrumPitchTracker::getParameterDescriptors() const
Chris@3 206 {
Chris@3 207 ParameterList list;
Chris@3 208 return list;
Chris@3 209 }
Chris@3 210
Chris@3 211 float
Chris@3 212 CepstrumPitchTracker::getParameter(string identifier) const
Chris@3 213 {
Chris@3 214 return 0.f;
Chris@3 215 }
Chris@3 216
Chris@3 217 void
Chris@3 218 CepstrumPitchTracker::setParameter(string identifier, float value)
Chris@3 219 {
Chris@3 220 }
Chris@3 221
Chris@3 222 CepstrumPitchTracker::ProgramList
Chris@3 223 CepstrumPitchTracker::getPrograms() const
Chris@3 224 {
Chris@3 225 ProgramList list;
Chris@3 226 return list;
Chris@3 227 }
Chris@3 228
Chris@3 229 string
Chris@3 230 CepstrumPitchTracker::getCurrentProgram() const
Chris@3 231 {
Chris@3 232 return ""; // no programs
Chris@3 233 }
Chris@3 234
Chris@3 235 void
Chris@3 236 CepstrumPitchTracker::selectProgram(string name)
Chris@3 237 {
Chris@3 238 }
Chris@3 239
Chris@3 240 CepstrumPitchTracker::OutputList
Chris@3 241 CepstrumPitchTracker::getOutputDescriptors() const
Chris@3 242 {
Chris@3 243 OutputList outputs;
Chris@3 244
Chris@3 245 int n = 0;
Chris@3 246
Chris@3 247 OutputDescriptor d;
Chris@3 248
Chris@3 249 d.identifier = "f0";
Chris@3 250 d.name = "Estimated f0";
Chris@3 251 d.description = "Estimated fundamental frequency";
Chris@3 252 d.unit = "Hz";
Chris@3 253 d.hasFixedBinCount = true;
Chris@3 254 d.binCount = 1;
Chris@3 255 d.hasKnownExtents = true;
Chris@3 256 d.minValue = m_fmin;
Chris@3 257 d.maxValue = m_fmax;
Chris@3 258 d.isQuantized = false;
Chris@3 259 d.sampleType = OutputDescriptor::FixedSampleRate;
Chris@3 260 d.sampleRate = (m_inputSampleRate / m_stepSize);
Chris@3 261 d.hasDuration = false;
Chris@3 262 outputs.push_back(d);
Chris@3 263
Chris@3 264 return outputs;
Chris@3 265 }
Chris@3 266
Chris@3 267 bool
Chris@3 268 CepstrumPitchTracker::initialise(size_t channels, size_t stepSize, size_t blockSize)
Chris@3 269 {
Chris@3 270 if (channels < getMinChannelCount() ||
Chris@3 271 channels > getMaxChannelCount()) return false;
Chris@3 272
Chris@3 273 // std::cerr << "CepstrumPitchTracker::initialise: channels = " << channels
Chris@3 274 // << ", stepSize = " << stepSize << ", blockSize = " << blockSize
Chris@3 275 // << std::endl;
Chris@3 276
Chris@3 277 m_channels = channels;
Chris@3 278 m_stepSize = stepSize;
Chris@3 279 m_blockSize = blockSize;
Chris@3 280
Chris@3 281 m_binFrom = int(m_inputSampleRate / m_fmax);
Chris@3 282 m_binTo = int(m_inputSampleRate / m_fmin);
Chris@3 283
Chris@3 284 if (m_binTo >= (int)m_blockSize / 2) {
Chris@3 285 m_binTo = m_blockSize / 2 - 1;
Chris@3 286 }
Chris@3 287
Chris@3 288 m_bins = (m_binTo - m_binFrom) + 1;
Chris@3 289
Chris@3 290 m_history = new double *[m_histlen];
Chris@3 291 for (int i = 0; i < m_histlen; ++i) {
Chris@3 292 m_history[i] = new double[m_bins];
Chris@3 293 }
Chris@3 294
Chris@3 295 reset();
Chris@3 296
Chris@3 297 return true;
Chris@3 298 }
Chris@3 299
Chris@3 300 void
Chris@3 301 CepstrumPitchTracker::reset()
Chris@3 302 {
Chris@3 303 for (int i = 0; i < m_histlen; ++i) {
Chris@3 304 for (int j = 0; j < m_bins; ++j) {
Chris@3 305 m_history[i][j] = 0.0;
Chris@3 306 }
Chris@3 307 }
Chris@3 308 }
Chris@3 309
Chris@3 310 void
Chris@3 311 CepstrumPitchTracker::filter(const double *cep, double *result)
Chris@3 312 {
Chris@3 313 int hix = m_histlen - 1; // current history index
Chris@3 314
Chris@3 315 // roll back the history
Chris@3 316 if (m_histlen > 1) {
Chris@3 317 double *oldest = m_history[0];
Chris@3 318 for (int i = 1; i < m_histlen; ++i) {
Chris@3 319 m_history[i-1] = m_history[i];
Chris@3 320 }
Chris@3 321 // and stick this back in the newest spot, to recycle
Chris@3 322 m_history[hix] = oldest;
Chris@3 323 }
Chris@3 324
Chris@3 325 for (int i = 0; i < m_bins; ++i) {
Chris@5 326 double v = 0;
Chris@5 327 int n = 0;
Chris@5 328 // average according to the vertical filter length
Chris@5 329 for (int j = -m_vflen/2; j <= m_vflen/2; ++j) {
Chris@5 330 int ix = i + m_binFrom + j;
Chris@5 331 if (ix >= 0 && ix < m_blockSize) {
Chris@5 332 v += cep[ix];
Chris@5 333 ++n;
Chris@5 334 }
Chris@5 335 }
Chris@5 336 m_history[hix][i] = v / n;
Chris@3 337 }
Chris@3 338
Chris@3 339 for (int i = 0; i < m_bins; ++i) {
Chris@3 340 double mean = 0.0;
Chris@3 341 for (int j = 0; j < m_histlen; ++j) {
Chris@3 342 mean += m_history[j][i];
Chris@3 343 }
Chris@3 344 mean /= m_histlen;
Chris@3 345 result[i] = mean;
Chris@3 346 }
Chris@3 347 }
Chris@3 348
Chris@6 349 double
Chris@6 350 CepstrumPitchTracker::calculatePeakProportion(const double *data, double abstot, int n)
Chris@6 351 {
Chris@6 352 double aroundPeak = data[n];
Chris@6 353 double peakProportion = 0.0;
Chris@6 354
Chris@6 355 int i = n - 1;
Chris@6 356 while (i > 0 && data[i] <= data[i+1]) {
Chris@6 357 aroundPeak += fabs(data[i]);
Chris@6 358 --i;
Chris@6 359 }
Chris@6 360 i = n + 1;
Chris@6 361 while (i < m_bins && data[i] <= data[i-1]) {
Chris@6 362 aroundPeak += fabs(data[i]);
Chris@6 363 ++i;
Chris@6 364 }
Chris@6 365 peakProportion = aroundPeak / abstot;
Chris@6 366
Chris@6 367 return peakProportion;
Chris@6 368 }
Chris@6 369
Chris@6 370 bool
Chris@6 371 CepstrumPitchTracker::acceptPeak(int n, double peakProportion)
Chris@6 372 {
Chris@6 373 bool accept = false;
Chris@6 374
Chris@6 375 if (abs(n - m_prevpeak) < 10) { //!!! should depend on bin count
Chris@6 376 accept = true;
Chris@6 377 } else if (peakProportion > m_prevprop * 2) {
Chris@6 378 accept = true;
Chris@6 379 }
Chris@6 380
Chris@6 381 return accept;
Chris@6 382 }
Chris@6 383
Chris@3 384 CepstrumPitchTracker::FeatureSet
Chris@3 385 CepstrumPitchTracker::process(const float *const *inputBuffers, Vamp::RealTime timestamp)
Chris@3 386 {
Chris@3 387 FeatureSet fs;
Chris@3 388
Chris@3 389 int bs = m_blockSize;
Chris@3 390 int hs = m_blockSize/2 + 1;
Chris@3 391
Chris@3 392 double *rawcep = new double[bs];
Chris@3 393 double *io = new double[bs];
Chris@3 394 double *logmag = new double[bs];
Chris@3 395
Chris@4 396 // The "inverse symmetric" method. Seems to be the most reliable
Chris@3 397
Chris@3 398 for (int i = 0; i < hs; ++i) {
Chris@3 399
Chris@3 400 double power =
Chris@3 401 inputBuffers[0][i*2 ] * inputBuffers[0][i*2 ] +
Chris@3 402 inputBuffers[0][i*2+1] * inputBuffers[0][i*2+1];
Chris@3 403 double mag = sqrt(power);
Chris@3 404
Chris@3 405 double lm = log(mag + 0.00000001);
Chris@3 406
Chris@4 407 logmag[i] = lm;
Chris@4 408 if (i > 0) logmag[bs - i] = lm;
Chris@3 409 }
Chris@3 410
Chris@4 411 fft(bs, true, logmag, 0, rawcep, io);
Chris@3 412
Chris@3 413 delete[] logmag;
Chris@3 414 delete[] io;
Chris@3 415
Chris@3 416 int n = m_bins;
Chris@3 417 double *data = new double[n];
Chris@3 418 filter(rawcep, data);
Chris@3 419 delete[] rawcep;
Chris@3 420
Chris@6 421 double abstot = 0.0;
Chris@6 422
Chris@6 423 for (int i = 0; i < n; ++i) {
Chris@6 424 abstot += fabs(data[i]);
Chris@6 425 }
Chris@6 426
Chris@3 427 double maxval = 0.0;
Chris@6 428 int maxbin = -1;
Chris@3 429
Chris@3 430 for (int i = 0; i < n; ++i) {
Chris@3 431 if (data[i] > maxval) {
Chris@3 432 maxval = data[i];
Chris@3 433 maxbin = i;
Chris@3 434 }
Chris@3 435 }
Chris@3 436
Chris@6 437 bool accepted = false;
Chris@6 438
Chris@6 439 if (maxbin >= 0) {
Chris@6 440 double pp = calculatePeakProportion(data, abstot, maxbin);
Chris@6 441 if (acceptPeak(maxbin, pp)) {
Chris@6 442 accepted = true;
Chris@6 443 } else {
Chris@6 444 // try a secondary peak
Chris@6 445 maxval = 0.0;
Chris@6 446 int secondbin = 0;
Chris@6 447 for (int i = 1; i < n-1; ++i) {
Chris@6 448 if (i != maxbin &&
Chris@6 449 data[i] > data[i-1] &&
Chris@6 450 data[i] > data[i+1] &&
Chris@6 451 data[i] > maxval) {
Chris@6 452 maxval = data[i];
Chris@6 453 secondbin = i;
Chris@6 454 }
Chris@6 455 }
Chris@6 456 double spp = calculatePeakProportion(data, abstot, secondbin);
Chris@6 457 if (acceptPeak(secondbin, spp)) {
Chris@6 458 maxbin = secondbin;
Chris@6 459 pp = spp;
Chris@6 460 accepted = true;
Chris@6 461 }
Chris@3 462 }
Chris@6 463 if (accepted) {
Chris@6 464 m_prevpeak = maxbin;
Chris@6 465 m_prevprop = pp;
Chris@3 466 }
Chris@3 467 }
Chris@6 468
Chris@3 469 // std::cerr << "peakProportion = " << peakProportion << std::endl;
Chris@3 470 // std::cerr << "peak = " << m_inputSampleRate / (maxbin + m_binFrom) << std::endl;
Chris@4 471 // std::cerr << "bins = " << m_bins << std::endl;
Chris@3 472
Chris@6 473 // if (peakProportion >= (0.00006 * m_bins)) {
Chris@6 474 if (accepted) {
Chris@3 475 Feature f;
Chris@3 476 f.hasTimestamp = true;
Chris@3 477 f.timestamp = timestamp;
Chris@3 478 f.values.push_back(m_inputSampleRate / (maxbin + m_binFrom));
Chris@3 479 fs[0].push_back(f);
Chris@3 480 }
Chris@3 481
Chris@3 482 delete[] data;
Chris@3 483 return fs;
Chris@3 484 }
Chris@3 485
Chris@3 486 CepstrumPitchTracker::FeatureSet
Chris@3 487 CepstrumPitchTracker::getRemainingFeatures()
Chris@3 488 {
Chris@3 489 FeatureSet fs;
Chris@3 490 return fs;
Chris@3 491 }
Chris@3 492
Chris@3 493 void
Chris@3 494 CepstrumPitchTracker::fft(unsigned int n, bool inverse,
Chris@3 495 double *ri, double *ii, double *ro, double *io)
Chris@3 496 {
Chris@3 497 if (!ri || !ro || !io) return;
Chris@3 498
Chris@3 499 unsigned int bits;
Chris@3 500 unsigned int i, j, k, m;
Chris@3 501 unsigned int blockSize, blockEnd;
Chris@3 502
Chris@3 503 double tr, ti;
Chris@3 504
Chris@3 505 if (n < 2) return;
Chris@3 506 if (n & (n-1)) return;
Chris@3 507
Chris@3 508 double angle = 2.0 * M_PI;
Chris@3 509 if (inverse) angle = -angle;
Chris@3 510
Chris@3 511 for (i = 0; ; ++i) {
Chris@3 512 if (n & (1 << i)) {
Chris@3 513 bits = i;
Chris@3 514 break;
Chris@3 515 }
Chris@3 516 }
Chris@3 517
Chris@3 518 static unsigned int tableSize = 0;
Chris@3 519 static int *table = 0;
Chris@3 520
Chris@3 521 if (tableSize != n) {
Chris@3 522
Chris@3 523 delete[] table;
Chris@3 524
Chris@3 525 table = new int[n];
Chris@3 526
Chris@3 527 for (i = 0; i < n; ++i) {
Chris@3 528
Chris@3 529 m = i;
Chris@3 530
Chris@3 531 for (j = k = 0; j < bits; ++j) {
Chris@3 532 k = (k << 1) | (m & 1);
Chris@3 533 m >>= 1;
Chris@3 534 }
Chris@3 535
Chris@3 536 table[i] = k;
Chris@3 537 }
Chris@3 538
Chris@3 539 tableSize = n;
Chris@3 540 }
Chris@3 541
Chris@3 542 if (ii) {
Chris@3 543 for (i = 0; i < n; ++i) {
Chris@3 544 ro[table[i]] = ri[i];
Chris@3 545 io[table[i]] = ii[i];
Chris@3 546 }
Chris@3 547 } else {
Chris@3 548 for (i = 0; i < n; ++i) {
Chris@3 549 ro[table[i]] = ri[i];
Chris@3 550 io[table[i]] = 0.0;
Chris@3 551 }
Chris@3 552 }
Chris@3 553
Chris@3 554 blockEnd = 1;
Chris@3 555
Chris@3 556 for (blockSize = 2; blockSize <= n; blockSize <<= 1) {
Chris@3 557
Chris@3 558 double delta = angle / (double)blockSize;
Chris@3 559 double sm2 = -sin(-2 * delta);
Chris@3 560 double sm1 = -sin(-delta);
Chris@3 561 double cm2 = cos(-2 * delta);
Chris@3 562 double cm1 = cos(-delta);
Chris@3 563 double w = 2 * cm1;
Chris@3 564 double ar[3], ai[3];
Chris@3 565
Chris@3 566 for (i = 0; i < n; i += blockSize) {
Chris@3 567
Chris@3 568 ar[2] = cm2;
Chris@3 569 ar[1] = cm1;
Chris@3 570
Chris@3 571 ai[2] = sm2;
Chris@3 572 ai[1] = sm1;
Chris@3 573
Chris@3 574 for (j = i, m = 0; m < blockEnd; j++, m++) {
Chris@3 575
Chris@3 576 ar[0] = w * ar[1] - ar[2];
Chris@3 577 ar[2] = ar[1];
Chris@3 578 ar[1] = ar[0];
Chris@3 579
Chris@3 580 ai[0] = w * ai[1] - ai[2];
Chris@3 581 ai[2] = ai[1];
Chris@3 582 ai[1] = ai[0];
Chris@3 583
Chris@3 584 k = j + blockEnd;
Chris@3 585 tr = ar[0] * ro[k] - ai[0] * io[k];
Chris@3 586 ti = ar[0] * io[k] + ai[0] * ro[k];
Chris@3 587
Chris@3 588 ro[k] = ro[j] - tr;
Chris@3 589 io[k] = io[j] - ti;
Chris@3 590
Chris@3 591 ro[j] += tr;
Chris@3 592 io[j] += ti;
Chris@3 593 }
Chris@3 594 }
Chris@3 595
Chris@3 596 blockEnd = blockSize;
Chris@3 597 }
Chris@3 598 }
Chris@3 599
Chris@3 600