annotate CepstrumPitchTracker.cpp @ 13:9fa97de8692a track

Partial updates to new method (but this doesn't currently build)
author Chris Cannam
date Fri, 29 Jun 2012 10:09:19 +0100
parents cb88b9954eec
children 63dde216ea37
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@12 41 bool
Chris@12 42 CepstrumPitchTracker::Hypothesis::isWithinTolerance(Estimate s)
Chris@12 43 {
Chris@12 44 if (m_pending.empty()) {
Chris@12 45 return true;
Chris@12 46 }
Chris@12 47 Estimate last = m_pending[m_pending.size()-1];
Chris@12 48 double r = s.freq / last.freq;
Chris@12 49 int cents = lrint(1200.0 * (log(r) / log(2.0)));
Chris@12 50 return (cents > -200 && cents < 200);
Chris@12 51 }
Chris@12 52
Chris@12 53 bool
Chris@12 54 CepstrumPitchTracker::Hypothesis::isSatisfied()
Chris@12 55 {
Chris@12 56 return (m_pending.size() > 2);
Chris@12 57 }
Chris@12 58
Chris@13 59 void
Chris@13 60 CepstrumPitchTracker::Hypothesis::advanceTime()
Chris@13 61 {
Chris@13 62 ++m_age;
Chris@13 63 }
Chris@13 64
Chris@12 65 bool
Chris@12 66 CepstrumPitchTracker::Hypothesis::test(Estimate s)
Chris@12 67 {
Chris@13 68 bool accept = false;
Chris@13 69
Chris@13 70 switch (m_state) {
Chris@13 71
Chris@13 72 case New:
Chris@13 73 m_state = Provisional;
Chris@13 74 accept = true;
Chris@13 75 break;
Chris@13 76
Chris@13 77 case Provisional:
Chris@13 78 if (m_age > 3) {
Chris@13 79 m_state = Rejected;
Chris@13 80 } else if (isWithinTolerance(s)) {
Chris@13 81 accept = true;
Chris@13 82 }
Chris@13 83 break;
Chris@13 84
Chris@13 85 case Satisfied:
Chris@13 86 if (m_age > 3) {
Chris@13 87 m_state = Expired;
Chris@13 88 } else if (isWithinTolerance(s)) {
Chris@13 89 accept = true;
Chris@13 90 }
Chris@13 91 break;
Chris@13 92
Chris@13 93 case Rejected:
Chris@13 94 break;
Chris@13 95
Chris@13 96 case Expired:
Chris@13 97 break;
Chris@12 98 }
Chris@12 99
Chris@13 100 if (accept) {
Chris@13 101 m_pending.push_back(s);
Chris@13 102 m_age = 0;
Chris@13 103 if (m_state == Provisional && isSatisfied()) {
Chris@13 104 m_state = Satisfied;
Chris@12 105 }
Chris@12 106 }
Chris@12 107
Chris@13 108 return accept;
Chris@13 109 }
Chris@12 110
Chris@12 111 CepstrumPitchTracker::Hypothesis::State
Chris@12 112 CepstrumPitchTracker::Hypothesis::getState()
Chris@12 113 {
Chris@12 114 return m_state;
Chris@12 115 }
Chris@12 116
Chris@12 117 CepstrumPitchTracker::Hypothesis::Estimates
Chris@12 118 CepstrumPitchTracker::Hypothesis::getAcceptedEstimates()
Chris@12 119 {
Chris@12 120 if (m_state == Satisfied || m_state == Expired) {
Chris@12 121 return m_pending;
Chris@12 122 } else {
Chris@12 123 return Estimates();
Chris@12 124 }
Chris@12 125 }
Chris@12 126
Chris@8 127
Chris@8 128 CepstrumPitchTracker::CepstrumPitchTracker(float inputSampleRate) :
Chris@8 129 Plugin(inputSampleRate),
Chris@8 130 m_channels(0),
Chris@8 131 m_stepSize(256),
Chris@8 132 m_blockSize(1024),
Chris@8 133 m_fmin(50),
Chris@8 134 m_fmax(1000),
Chris@10 135 m_histlen(1),
Chris@10 136 m_vflen(3),
Chris@8 137 m_binFrom(0),
Chris@8 138 m_binTo(0),
Chris@8 139 m_bins(0),
Chris@11 140 m_history(0),
Chris@11 141 m_prevpeak(0),
Chris@11 142 m_prevprop(0)
Chris@8 143 {
Chris@8 144 }
Chris@8 145
Chris@8 146 CepstrumPitchTracker::~CepstrumPitchTracker()
Chris@8 147 {
Chris@8 148 if (m_history) {
Chris@8 149 for (int i = 0; i < m_histlen; ++i) {
Chris@8 150 delete[] m_history[i];
Chris@8 151 }
Chris@8 152 delete[] m_history;
Chris@8 153 }
Chris@8 154 }
Chris@8 155
Chris@8 156 string
Chris@8 157 CepstrumPitchTracker::getIdentifier() const
Chris@8 158 {
Chris@8 159 return "cepstrum-pitch";
Chris@8 160 }
Chris@8 161
Chris@8 162 string
Chris@8 163 CepstrumPitchTracker::getName() const
Chris@8 164 {
Chris@8 165 return "Cepstrum Pitch Tracker";
Chris@8 166 }
Chris@8 167
Chris@8 168 string
Chris@8 169 CepstrumPitchTracker::getDescription() const
Chris@8 170 {
Chris@8 171 return "Estimate f0 of monophonic material using a cepstrum method.";
Chris@8 172 }
Chris@8 173
Chris@8 174 string
Chris@8 175 CepstrumPitchTracker::getMaker() const
Chris@8 176 {
Chris@8 177 return "Chris Cannam";
Chris@8 178 }
Chris@8 179
Chris@8 180 int
Chris@8 181 CepstrumPitchTracker::getPluginVersion() const
Chris@8 182 {
Chris@8 183 // Increment this each time you release a version that behaves
Chris@8 184 // differently from the previous one
Chris@8 185 return 1;
Chris@8 186 }
Chris@8 187
Chris@8 188 string
Chris@8 189 CepstrumPitchTracker::getCopyright() const
Chris@8 190 {
Chris@8 191 return "Freely redistributable (BSD license)";
Chris@8 192 }
Chris@8 193
Chris@8 194 CepstrumPitchTracker::InputDomain
Chris@8 195 CepstrumPitchTracker::getInputDomain() const
Chris@8 196 {
Chris@8 197 return FrequencyDomain;
Chris@8 198 }
Chris@8 199
Chris@8 200 size_t
Chris@8 201 CepstrumPitchTracker::getPreferredBlockSize() const
Chris@8 202 {
Chris@8 203 return 1024;
Chris@8 204 }
Chris@8 205
Chris@8 206 size_t
Chris@8 207 CepstrumPitchTracker::getPreferredStepSize() const
Chris@8 208 {
Chris@8 209 return 256;
Chris@8 210 }
Chris@8 211
Chris@8 212 size_t
Chris@8 213 CepstrumPitchTracker::getMinChannelCount() const
Chris@8 214 {
Chris@8 215 return 1;
Chris@8 216 }
Chris@8 217
Chris@8 218 size_t
Chris@8 219 CepstrumPitchTracker::getMaxChannelCount() const
Chris@8 220 {
Chris@8 221 return 1;
Chris@8 222 }
Chris@8 223
Chris@8 224 CepstrumPitchTracker::ParameterList
Chris@8 225 CepstrumPitchTracker::getParameterDescriptors() const
Chris@8 226 {
Chris@8 227 ParameterList list;
Chris@8 228 return list;
Chris@8 229 }
Chris@8 230
Chris@8 231 float
Chris@8 232 CepstrumPitchTracker::getParameter(string identifier) const
Chris@8 233 {
Chris@8 234 return 0.f;
Chris@8 235 }
Chris@8 236
Chris@8 237 void
Chris@8 238 CepstrumPitchTracker::setParameter(string identifier, float value)
Chris@8 239 {
Chris@8 240 }
Chris@8 241
Chris@8 242 CepstrumPitchTracker::ProgramList
Chris@8 243 CepstrumPitchTracker::getPrograms() const
Chris@8 244 {
Chris@8 245 ProgramList list;
Chris@8 246 return list;
Chris@8 247 }
Chris@8 248
Chris@8 249 string
Chris@8 250 CepstrumPitchTracker::getCurrentProgram() const
Chris@8 251 {
Chris@8 252 return ""; // no programs
Chris@8 253 }
Chris@8 254
Chris@8 255 void
Chris@8 256 CepstrumPitchTracker::selectProgram(string name)
Chris@8 257 {
Chris@8 258 }
Chris@8 259
Chris@8 260 CepstrumPitchTracker::OutputList
Chris@8 261 CepstrumPitchTracker::getOutputDescriptors() const
Chris@8 262 {
Chris@8 263 OutputList outputs;
Chris@8 264
Chris@8 265 int n = 0;
Chris@8 266
Chris@8 267 OutputDescriptor d;
Chris@8 268
Chris@8 269 d.identifier = "f0";
Chris@8 270 d.name = "Estimated f0";
Chris@8 271 d.description = "Estimated fundamental frequency";
Chris@8 272 d.unit = "Hz";
Chris@8 273 d.hasFixedBinCount = true;
Chris@8 274 d.binCount = 1;
Chris@8 275 d.hasKnownExtents = true;
Chris@8 276 d.minValue = m_fmin;
Chris@8 277 d.maxValue = m_fmax;
Chris@8 278 d.isQuantized = false;
Chris@8 279 d.sampleType = OutputDescriptor::FixedSampleRate;
Chris@8 280 d.sampleRate = (m_inputSampleRate / m_stepSize);
Chris@8 281 d.hasDuration = false;
Chris@8 282 outputs.push_back(d);
Chris@8 283
Chris@8 284 return outputs;
Chris@8 285 }
Chris@8 286
Chris@8 287 bool
Chris@8 288 CepstrumPitchTracker::initialise(size_t channels, size_t stepSize, size_t blockSize)
Chris@8 289 {
Chris@8 290 if (channels < getMinChannelCount() ||
Chris@8 291 channels > getMaxChannelCount()) return false;
Chris@8 292
Chris@8 293 // std::cerr << "CepstrumPitchTracker::initialise: channels = " << channels
Chris@8 294 // << ", stepSize = " << stepSize << ", blockSize = " << blockSize
Chris@8 295 // << std::endl;
Chris@8 296
Chris@8 297 m_channels = channels;
Chris@8 298 m_stepSize = stepSize;
Chris@8 299 m_blockSize = blockSize;
Chris@8 300
Chris@8 301 m_binFrom = int(m_inputSampleRate / m_fmax);
Chris@8 302 m_binTo = int(m_inputSampleRate / m_fmin);
Chris@8 303
Chris@8 304 if (m_binTo >= (int)m_blockSize / 2) {
Chris@8 305 m_binTo = m_blockSize / 2 - 1;
Chris@8 306 }
Chris@8 307
Chris@8 308 m_bins = (m_binTo - m_binFrom) + 1;
Chris@8 309
Chris@8 310 m_history = new double *[m_histlen];
Chris@8 311 for (int i = 0; i < m_histlen; ++i) {
Chris@8 312 m_history[i] = new double[m_bins];
Chris@8 313 }
Chris@8 314
Chris@8 315 reset();
Chris@8 316
Chris@8 317 return true;
Chris@8 318 }
Chris@8 319
Chris@8 320 void
Chris@8 321 CepstrumPitchTracker::reset()
Chris@8 322 {
Chris@8 323 for (int i = 0; i < m_histlen; ++i) {
Chris@8 324 for (int j = 0; j < m_bins; ++j) {
Chris@8 325 m_history[i][j] = 0.0;
Chris@8 326 }
Chris@8 327 }
Chris@8 328 }
Chris@8 329
Chris@8 330 void
Chris@8 331 CepstrumPitchTracker::filter(const double *cep, double *result)
Chris@8 332 {
Chris@8 333 int hix = m_histlen - 1; // current history index
Chris@8 334
Chris@8 335 // roll back the history
Chris@8 336 if (m_histlen > 1) {
Chris@8 337 double *oldest = m_history[0];
Chris@8 338 for (int i = 1; i < m_histlen; ++i) {
Chris@8 339 m_history[i-1] = m_history[i];
Chris@8 340 }
Chris@8 341 // and stick this back in the newest spot, to recycle
Chris@8 342 m_history[hix] = oldest;
Chris@8 343 }
Chris@8 344
Chris@8 345 for (int i = 0; i < m_bins; ++i) {
Chris@10 346 double v = 0;
Chris@10 347 int n = 0;
Chris@10 348 // average according to the vertical filter length
Chris@10 349 for (int j = -m_vflen/2; j <= m_vflen/2; ++j) {
Chris@10 350 int ix = i + m_binFrom + j;
Chris@10 351 if (ix >= 0 && ix < m_blockSize) {
Chris@10 352 v += cep[ix];
Chris@10 353 ++n;
Chris@10 354 }
Chris@10 355 }
Chris@10 356 m_history[hix][i] = v / n;
Chris@8 357 }
Chris@8 358
Chris@8 359 for (int i = 0; i < m_bins; ++i) {
Chris@8 360 double mean = 0.0;
Chris@8 361 for (int j = 0; j < m_histlen; ++j) {
Chris@8 362 mean += m_history[j][i];
Chris@8 363 }
Chris@8 364 mean /= m_histlen;
Chris@8 365 result[i] = mean;
Chris@8 366 }
Chris@8 367 }
Chris@8 368
Chris@11 369 double
Chris@11 370 CepstrumPitchTracker::calculatePeakProportion(const double *data, double abstot, int n)
Chris@11 371 {
Chris@11 372 double aroundPeak = data[n];
Chris@11 373 double peakProportion = 0.0;
Chris@11 374
Chris@11 375 int i = n - 1;
Chris@11 376 while (i > 0 && data[i] <= data[i+1]) {
Chris@11 377 aroundPeak += fabs(data[i]);
Chris@11 378 --i;
Chris@11 379 }
Chris@11 380 i = n + 1;
Chris@11 381 while (i < m_bins && data[i] <= data[i-1]) {
Chris@11 382 aroundPeak += fabs(data[i]);
Chris@11 383 ++i;
Chris@11 384 }
Chris@11 385 peakProportion = aroundPeak / abstot;
Chris@11 386
Chris@11 387 return peakProportion;
Chris@11 388 }
Chris@11 389
Chris@11 390 bool
Chris@11 391 CepstrumPitchTracker::acceptPeak(int n, double peakProportion)
Chris@11 392 {
Chris@11 393 bool accept = false;
Chris@11 394
Chris@11 395 if (abs(n - m_prevpeak) < 10) { //!!! should depend on bin count
Chris@11 396 accept = true;
Chris@11 397 } else if (peakProportion > m_prevprop * 2) {
Chris@11 398 accept = true;
Chris@11 399 }
Chris@11 400
Chris@11 401 return accept;
Chris@11 402 }
Chris@11 403
Chris@8 404 CepstrumPitchTracker::FeatureSet
Chris@8 405 CepstrumPitchTracker::process(const float *const *inputBuffers, Vamp::RealTime timestamp)
Chris@8 406 {
Chris@8 407 FeatureSet fs;
Chris@8 408
Chris@8 409 int bs = m_blockSize;
Chris@8 410 int hs = m_blockSize/2 + 1;
Chris@8 411
Chris@8 412 double *rawcep = new double[bs];
Chris@8 413 double *io = new double[bs];
Chris@8 414 double *logmag = new double[bs];
Chris@8 415
Chris@9 416 // The "inverse symmetric" method. Seems to be the most reliable
Chris@8 417
Chris@8 418 for (int i = 0; i < hs; ++i) {
Chris@8 419
Chris@8 420 double power =
Chris@8 421 inputBuffers[0][i*2 ] * inputBuffers[0][i*2 ] +
Chris@8 422 inputBuffers[0][i*2+1] * inputBuffers[0][i*2+1];
Chris@8 423 double mag = sqrt(power);
Chris@8 424
Chris@8 425 double lm = log(mag + 0.00000001);
Chris@8 426
Chris@9 427 logmag[i] = lm;
Chris@9 428 if (i > 0) logmag[bs - i] = lm;
Chris@8 429 }
Chris@8 430
Chris@9 431 fft(bs, true, logmag, 0, rawcep, io);
Chris@8 432
Chris@8 433 delete[] logmag;
Chris@8 434 delete[] io;
Chris@8 435
Chris@8 436 int n = m_bins;
Chris@8 437 double *data = new double[n];
Chris@8 438 filter(rawcep, data);
Chris@8 439 delete[] rawcep;
Chris@8 440
Chris@11 441 double abstot = 0.0;
Chris@11 442
Chris@11 443 for (int i = 0; i < n; ++i) {
Chris@11 444 abstot += fabs(data[i]);
Chris@11 445 }
Chris@11 446
Chris@8 447 double maxval = 0.0;
Chris@11 448 int maxbin = -1;
Chris@8 449
Chris@8 450 for (int i = 0; i < n; ++i) {
Chris@8 451 if (data[i] > maxval) {
Chris@8 452 maxval = data[i];
Chris@8 453 maxbin = i;
Chris@8 454 }
Chris@8 455 }
Chris@8 456
Chris@13 457 if (maxbin < 0) return fs;
Chris@13 458
Chris@13 459 double peakfreq = m_inputSampleRate / (maxbin + m_binFrom);
Chris@13 460 Hypothesis::Estimate e;
Chris@13 461 e.freq = peakfreq;
Chris@13 462 e.time = timestamp;
Chris@13 463
Chris@13 464 m_accepted.advanceTime();
Chris@13 465 for (int i = 0; i < m_possible.size(); ++i) {
Chris@13 466 m_possible[i].advanceTime();
Chris@13 467 }
Chris@13 468
Chris@13 469 if (m_accepted.test(e)) {
Chris@13 470 return fs;
Chris@13 471 }
Chris@13 472
Chris@13 473 //...
Chris@13 474
Chris@13 475 /*
Chris@11 476 bool accepted = false;
Chris@11 477
Chris@11 478 if (maxbin >= 0) {
Chris@11 479 double pp = calculatePeakProportion(data, abstot, maxbin);
Chris@11 480 if (acceptPeak(maxbin, pp)) {
Chris@11 481 accepted = true;
Chris@11 482 } else {
Chris@11 483 // try a secondary peak
Chris@11 484 maxval = 0.0;
Chris@11 485 int secondbin = 0;
Chris@11 486 for (int i = 1; i < n-1; ++i) {
Chris@11 487 if (i != maxbin &&
Chris@11 488 data[i] > data[i-1] &&
Chris@11 489 data[i] > data[i+1] &&
Chris@11 490 data[i] > maxval) {
Chris@11 491 maxval = data[i];
Chris@11 492 secondbin = i;
Chris@11 493 }
Chris@11 494 }
Chris@11 495 double spp = calculatePeakProportion(data, abstot, secondbin);
Chris@11 496 if (acceptPeak(secondbin, spp)) {
Chris@11 497 maxbin = secondbin;
Chris@11 498 pp = spp;
Chris@11 499 accepted = true;
Chris@11 500 }
Chris@8 501 }
Chris@11 502 if (accepted) {
Chris@11 503 m_prevpeak = maxbin;
Chris@11 504 m_prevprop = pp;
Chris@8 505 }
Chris@8 506 }
Chris@13 507 */
Chris@8 508 // std::cerr << "peakProportion = " << peakProportion << std::endl;
Chris@8 509 // std::cerr << "peak = " << m_inputSampleRate / (maxbin + m_binFrom) << std::endl;
Chris@9 510 // std::cerr << "bins = " << m_bins << std::endl;
Chris@8 511
Chris@11 512 // if (peakProportion >= (0.00006 * m_bins)) {
Chris@11 513 if (accepted) {
Chris@8 514 Feature f;
Chris@8 515 f.hasTimestamp = true;
Chris@8 516 f.timestamp = timestamp;
Chris@8 517 f.values.push_back(m_inputSampleRate / (maxbin + m_binFrom));
Chris@8 518 fs[0].push_back(f);
Chris@8 519 }
Chris@8 520
Chris@8 521 delete[] data;
Chris@8 522 return fs;
Chris@8 523 }
Chris@8 524
Chris@8 525 CepstrumPitchTracker::FeatureSet
Chris@8 526 CepstrumPitchTracker::getRemainingFeatures()
Chris@8 527 {
Chris@8 528 FeatureSet fs;
Chris@8 529 return fs;
Chris@8 530 }
Chris@8 531
Chris@8 532 void
Chris@8 533 CepstrumPitchTracker::fft(unsigned int n, bool inverse,
Chris@8 534 double *ri, double *ii, double *ro, double *io)
Chris@8 535 {
Chris@8 536 if (!ri || !ro || !io) return;
Chris@8 537
Chris@8 538 unsigned int bits;
Chris@8 539 unsigned int i, j, k, m;
Chris@8 540 unsigned int blockSize, blockEnd;
Chris@8 541
Chris@8 542 double tr, ti;
Chris@8 543
Chris@8 544 if (n < 2) return;
Chris@8 545 if (n & (n-1)) return;
Chris@8 546
Chris@8 547 double angle = 2.0 * M_PI;
Chris@8 548 if (inverse) angle = -angle;
Chris@8 549
Chris@8 550 for (i = 0; ; ++i) {
Chris@8 551 if (n & (1 << i)) {
Chris@8 552 bits = i;
Chris@8 553 break;
Chris@8 554 }
Chris@8 555 }
Chris@8 556
Chris@8 557 static unsigned int tableSize = 0;
Chris@8 558 static int *table = 0;
Chris@8 559
Chris@8 560 if (tableSize != n) {
Chris@8 561
Chris@8 562 delete[] table;
Chris@8 563
Chris@8 564 table = new int[n];
Chris@8 565
Chris@8 566 for (i = 0; i < n; ++i) {
Chris@8 567
Chris@8 568 m = i;
Chris@8 569
Chris@8 570 for (j = k = 0; j < bits; ++j) {
Chris@8 571 k = (k << 1) | (m & 1);
Chris@8 572 m >>= 1;
Chris@8 573 }
Chris@8 574
Chris@8 575 table[i] = k;
Chris@8 576 }
Chris@8 577
Chris@8 578 tableSize = n;
Chris@8 579 }
Chris@8 580
Chris@8 581 if (ii) {
Chris@8 582 for (i = 0; i < n; ++i) {
Chris@8 583 ro[table[i]] = ri[i];
Chris@8 584 io[table[i]] = ii[i];
Chris@8 585 }
Chris@8 586 } else {
Chris@8 587 for (i = 0; i < n; ++i) {
Chris@8 588 ro[table[i]] = ri[i];
Chris@8 589 io[table[i]] = 0.0;
Chris@8 590 }
Chris@8 591 }
Chris@8 592
Chris@8 593 blockEnd = 1;
Chris@8 594
Chris@8 595 for (blockSize = 2; blockSize <= n; blockSize <<= 1) {
Chris@8 596
Chris@8 597 double delta = angle / (double)blockSize;
Chris@8 598 double sm2 = -sin(-2 * delta);
Chris@8 599 double sm1 = -sin(-delta);
Chris@8 600 double cm2 = cos(-2 * delta);
Chris@8 601 double cm1 = cos(-delta);
Chris@8 602 double w = 2 * cm1;
Chris@8 603 double ar[3], ai[3];
Chris@8 604
Chris@8 605 for (i = 0; i < n; i += blockSize) {
Chris@8 606
Chris@8 607 ar[2] = cm2;
Chris@8 608 ar[1] = cm1;
Chris@8 609
Chris@8 610 ai[2] = sm2;
Chris@8 611 ai[1] = sm1;
Chris@8 612
Chris@8 613 for (j = i, m = 0; m < blockEnd; j++, m++) {
Chris@8 614
Chris@8 615 ar[0] = w * ar[1] - ar[2];
Chris@8 616 ar[2] = ar[1];
Chris@8 617 ar[1] = ar[0];
Chris@8 618
Chris@8 619 ai[0] = w * ai[1] - ai[2];
Chris@8 620 ai[2] = ai[1];
Chris@8 621 ai[1] = ai[0];
Chris@8 622
Chris@8 623 k = j + blockEnd;
Chris@8 624 tr = ar[0] * ro[k] - ai[0] * io[k];
Chris@8 625 ti = ar[0] * io[k] + ai[0] * ro[k];
Chris@8 626
Chris@8 627 ro[k] = ro[j] - tr;
Chris@8 628 io[k] = io[j] - ti;
Chris@8 629
Chris@8 630 ro[j] += tr;
Chris@8 631 io[j] += ti;
Chris@8 632 }
Chris@8 633 }
Chris@8 634
Chris@8 635 blockEnd = blockSize;
Chris@8 636 }
Chris@8 637 }
Chris@8 638
Chris@8 639