annotate CepstrumPitchTracker.cpp @ 8:e9d86e129467 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 32defdb2f9d9
children c938c60de2de
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@8 35 CepstrumPitchTracker::Hypothesis::Hypothesis()
Chris@7 36 {
Chris@8 37 m_state = New;
Chris@7 38 m_age = 0;
Chris@7 39 }
Chris@7 40
Chris@7 41 bool
Chris@7 42 CepstrumPitchTracker::Hypothesis::isWithinTolerance(Estimate s)
Chris@7 43 {
Chris@7 44 if (m_pending.empty()) {
Chris@7 45 return true;
Chris@7 46 }
Chris@7 47 Estimate last = m_pending[m_pending.size()-1];
Chris@7 48 double r = s.freq / last.freq;
Chris@7 49 int cents = lrint(1200.0 * (log(r) / log(2.0)));
Chris@7 50 return (cents > -200 && cents < 200);
Chris@7 51 }
Chris@7 52
Chris@7 53 bool
Chris@7 54 CepstrumPitchTracker::Hypothesis::isSatisfied()
Chris@7 55 {
Chris@7 56 return (m_pending.size() > 2);
Chris@7 57 }
Chris@7 58
Chris@8 59 void
Chris@8 60 CepstrumPitchTracker::Hypothesis::advanceTime()
Chris@8 61 {
Chris@8 62 ++m_age;
Chris@8 63 }
Chris@8 64
Chris@7 65 bool
Chris@7 66 CepstrumPitchTracker::Hypothesis::test(Estimate s)
Chris@7 67 {
Chris@8 68 bool accept = false;
Chris@8 69
Chris@8 70 switch (m_state) {
Chris@8 71
Chris@8 72 case New:
Chris@8 73 m_state = Provisional;
Chris@8 74 accept = true;
Chris@8 75 break;
Chris@8 76
Chris@8 77 case Provisional:
Chris@8 78 if (m_age > 3) {
Chris@8 79 m_state = Rejected;
Chris@8 80 } else if (isWithinTolerance(s)) {
Chris@8 81 accept = true;
Chris@8 82 }
Chris@8 83 break;
Chris@8 84
Chris@8 85 case Satisfied:
Chris@8 86 if (m_age > 3) {
Chris@8 87 m_state = Expired;
Chris@8 88 } else if (isWithinTolerance(s)) {
Chris@8 89 accept = true;
Chris@8 90 }
Chris@8 91 break;
Chris@8 92
Chris@8 93 case Rejected:
Chris@8 94 break;
Chris@8 95
Chris@8 96 case Expired:
Chris@8 97 break;
Chris@7 98 }
Chris@7 99
Chris@8 100 if (accept) {
Chris@8 101 m_pending.push_back(s);
Chris@8 102 m_age = 0;
Chris@8 103 if (m_state == Provisional && isSatisfied()) {
Chris@8 104 m_state = Satisfied;
Chris@7 105 }
Chris@7 106 }
Chris@7 107
Chris@8 108 return accept;
Chris@8 109 }
Chris@7 110
Chris@7 111 CepstrumPitchTracker::Hypothesis::State
Chris@7 112 CepstrumPitchTracker::Hypothesis::getState()
Chris@7 113 {
Chris@7 114 return m_state;
Chris@7 115 }
Chris@7 116
Chris@7 117 CepstrumPitchTracker::Hypothesis::Estimates
Chris@7 118 CepstrumPitchTracker::Hypothesis::getAcceptedEstimates()
Chris@7 119 {
Chris@7 120 if (m_state == Satisfied || m_state == Expired) {
Chris@7 121 return m_pending;
Chris@7 122 } else {
Chris@7 123 return Estimates();
Chris@7 124 }
Chris@7 125 }
Chris@7 126
Chris@3 127
Chris@3 128 CepstrumPitchTracker::CepstrumPitchTracker(float inputSampleRate) :
Chris@3 129 Plugin(inputSampleRate),
Chris@3 130 m_channels(0),
Chris@3 131 m_stepSize(256),
Chris@3 132 m_blockSize(1024),
Chris@3 133 m_fmin(50),
Chris@3 134 m_fmax(1000),
Chris@5 135 m_histlen(1),
Chris@5 136 m_vflen(3),
Chris@3 137 m_binFrom(0),
Chris@3 138 m_binTo(0),
Chris@3 139 m_bins(0),
Chris@6 140 m_history(0),
Chris@6 141 m_prevpeak(0),
Chris@6 142 m_prevprop(0)
Chris@3 143 {
Chris@3 144 }
Chris@3 145
Chris@3 146 CepstrumPitchTracker::~CepstrumPitchTracker()
Chris@3 147 {
Chris@3 148 if (m_history) {
Chris@3 149 for (int i = 0; i < m_histlen; ++i) {
Chris@3 150 delete[] m_history[i];
Chris@3 151 }
Chris@3 152 delete[] m_history;
Chris@3 153 }
Chris@3 154 }
Chris@3 155
Chris@3 156 string
Chris@3 157 CepstrumPitchTracker::getIdentifier() const
Chris@3 158 {
Chris@3 159 return "cepstrum-pitch";
Chris@3 160 }
Chris@3 161
Chris@3 162 string
Chris@3 163 CepstrumPitchTracker::getName() const
Chris@3 164 {
Chris@3 165 return "Cepstrum Pitch Tracker";
Chris@3 166 }
Chris@3 167
Chris@3 168 string
Chris@3 169 CepstrumPitchTracker::getDescription() const
Chris@3 170 {
Chris@3 171 return "Estimate f0 of monophonic material using a cepstrum method.";
Chris@3 172 }
Chris@3 173
Chris@3 174 string
Chris@3 175 CepstrumPitchTracker::getMaker() const
Chris@3 176 {
Chris@3 177 return "Chris Cannam";
Chris@3 178 }
Chris@3 179
Chris@3 180 int
Chris@3 181 CepstrumPitchTracker::getPluginVersion() const
Chris@3 182 {
Chris@3 183 // Increment this each time you release a version that behaves
Chris@3 184 // differently from the previous one
Chris@3 185 return 1;
Chris@3 186 }
Chris@3 187
Chris@3 188 string
Chris@3 189 CepstrumPitchTracker::getCopyright() const
Chris@3 190 {
Chris@3 191 return "Freely redistributable (BSD license)";
Chris@3 192 }
Chris@3 193
Chris@3 194 CepstrumPitchTracker::InputDomain
Chris@3 195 CepstrumPitchTracker::getInputDomain() const
Chris@3 196 {
Chris@3 197 return FrequencyDomain;
Chris@3 198 }
Chris@3 199
Chris@3 200 size_t
Chris@3 201 CepstrumPitchTracker::getPreferredBlockSize() const
Chris@3 202 {
Chris@3 203 return 1024;
Chris@3 204 }
Chris@3 205
Chris@3 206 size_t
Chris@3 207 CepstrumPitchTracker::getPreferredStepSize() const
Chris@3 208 {
Chris@3 209 return 256;
Chris@3 210 }
Chris@3 211
Chris@3 212 size_t
Chris@3 213 CepstrumPitchTracker::getMinChannelCount() const
Chris@3 214 {
Chris@3 215 return 1;
Chris@3 216 }
Chris@3 217
Chris@3 218 size_t
Chris@3 219 CepstrumPitchTracker::getMaxChannelCount() const
Chris@3 220 {
Chris@3 221 return 1;
Chris@3 222 }
Chris@3 223
Chris@3 224 CepstrumPitchTracker::ParameterList
Chris@3 225 CepstrumPitchTracker::getParameterDescriptors() const
Chris@3 226 {
Chris@3 227 ParameterList list;
Chris@3 228 return list;
Chris@3 229 }
Chris@3 230
Chris@3 231 float
Chris@3 232 CepstrumPitchTracker::getParameter(string identifier) const
Chris@3 233 {
Chris@3 234 return 0.f;
Chris@3 235 }
Chris@3 236
Chris@3 237 void
Chris@3 238 CepstrumPitchTracker::setParameter(string identifier, float value)
Chris@3 239 {
Chris@3 240 }
Chris@3 241
Chris@3 242 CepstrumPitchTracker::ProgramList
Chris@3 243 CepstrumPitchTracker::getPrograms() const
Chris@3 244 {
Chris@3 245 ProgramList list;
Chris@3 246 return list;
Chris@3 247 }
Chris@3 248
Chris@3 249 string
Chris@3 250 CepstrumPitchTracker::getCurrentProgram() const
Chris@3 251 {
Chris@3 252 return ""; // no programs
Chris@3 253 }
Chris@3 254
Chris@3 255 void
Chris@3 256 CepstrumPitchTracker::selectProgram(string name)
Chris@3 257 {
Chris@3 258 }
Chris@3 259
Chris@3 260 CepstrumPitchTracker::OutputList
Chris@3 261 CepstrumPitchTracker::getOutputDescriptors() const
Chris@3 262 {
Chris@3 263 OutputList outputs;
Chris@3 264
Chris@3 265 int n = 0;
Chris@3 266
Chris@3 267 OutputDescriptor d;
Chris@3 268
Chris@3 269 d.identifier = "f0";
Chris@3 270 d.name = "Estimated f0";
Chris@3 271 d.description = "Estimated fundamental frequency";
Chris@3 272 d.unit = "Hz";
Chris@3 273 d.hasFixedBinCount = true;
Chris@3 274 d.binCount = 1;
Chris@3 275 d.hasKnownExtents = true;
Chris@3 276 d.minValue = m_fmin;
Chris@3 277 d.maxValue = m_fmax;
Chris@3 278 d.isQuantized = false;
Chris@3 279 d.sampleType = OutputDescriptor::FixedSampleRate;
Chris@3 280 d.sampleRate = (m_inputSampleRate / m_stepSize);
Chris@3 281 d.hasDuration = false;
Chris@3 282 outputs.push_back(d);
Chris@3 283
Chris@3 284 return outputs;
Chris@3 285 }
Chris@3 286
Chris@3 287 bool
Chris@3 288 CepstrumPitchTracker::initialise(size_t channels, size_t stepSize, size_t blockSize)
Chris@3 289 {
Chris@3 290 if (channels < getMinChannelCount() ||
Chris@3 291 channels > getMaxChannelCount()) return false;
Chris@3 292
Chris@3 293 // std::cerr << "CepstrumPitchTracker::initialise: channels = " << channels
Chris@3 294 // << ", stepSize = " << stepSize << ", blockSize = " << blockSize
Chris@3 295 // << std::endl;
Chris@3 296
Chris@3 297 m_channels = channels;
Chris@3 298 m_stepSize = stepSize;
Chris@3 299 m_blockSize = blockSize;
Chris@3 300
Chris@3 301 m_binFrom = int(m_inputSampleRate / m_fmax);
Chris@3 302 m_binTo = int(m_inputSampleRate / m_fmin);
Chris@3 303
Chris@3 304 if (m_binTo >= (int)m_blockSize / 2) {
Chris@3 305 m_binTo = m_blockSize / 2 - 1;
Chris@3 306 }
Chris@3 307
Chris@3 308 m_bins = (m_binTo - m_binFrom) + 1;
Chris@3 309
Chris@3 310 m_history = new double *[m_histlen];
Chris@3 311 for (int i = 0; i < m_histlen; ++i) {
Chris@3 312 m_history[i] = new double[m_bins];
Chris@3 313 }
Chris@3 314
Chris@3 315 reset();
Chris@3 316
Chris@3 317 return true;
Chris@3 318 }
Chris@3 319
Chris@3 320 void
Chris@3 321 CepstrumPitchTracker::reset()
Chris@3 322 {
Chris@3 323 for (int i = 0; i < m_histlen; ++i) {
Chris@3 324 for (int j = 0; j < m_bins; ++j) {
Chris@3 325 m_history[i][j] = 0.0;
Chris@3 326 }
Chris@3 327 }
Chris@3 328 }
Chris@3 329
Chris@3 330 void
Chris@3 331 CepstrumPitchTracker::filter(const double *cep, double *result)
Chris@3 332 {
Chris@3 333 int hix = m_histlen - 1; // current history index
Chris@3 334
Chris@3 335 // roll back the history
Chris@3 336 if (m_histlen > 1) {
Chris@3 337 double *oldest = m_history[0];
Chris@3 338 for (int i = 1; i < m_histlen; ++i) {
Chris@3 339 m_history[i-1] = m_history[i];
Chris@3 340 }
Chris@3 341 // and stick this back in the newest spot, to recycle
Chris@3 342 m_history[hix] = oldest;
Chris@3 343 }
Chris@3 344
Chris@3 345 for (int i = 0; i < m_bins; ++i) {
Chris@5 346 double v = 0;
Chris@5 347 int n = 0;
Chris@5 348 // average according to the vertical filter length
Chris@5 349 for (int j = -m_vflen/2; j <= m_vflen/2; ++j) {
Chris@5 350 int ix = i + m_binFrom + j;
Chris@5 351 if (ix >= 0 && ix < m_blockSize) {
Chris@5 352 v += cep[ix];
Chris@5 353 ++n;
Chris@5 354 }
Chris@5 355 }
Chris@5 356 m_history[hix][i] = v / n;
Chris@3 357 }
Chris@3 358
Chris@3 359 for (int i = 0; i < m_bins; ++i) {
Chris@3 360 double mean = 0.0;
Chris@3 361 for (int j = 0; j < m_histlen; ++j) {
Chris@3 362 mean += m_history[j][i];
Chris@3 363 }
Chris@3 364 mean /= m_histlen;
Chris@3 365 result[i] = mean;
Chris@3 366 }
Chris@3 367 }
Chris@3 368
Chris@6 369 double
Chris@6 370 CepstrumPitchTracker::calculatePeakProportion(const double *data, double abstot, int n)
Chris@6 371 {
Chris@6 372 double aroundPeak = data[n];
Chris@6 373 double peakProportion = 0.0;
Chris@6 374
Chris@6 375 int i = n - 1;
Chris@6 376 while (i > 0 && data[i] <= data[i+1]) {
Chris@6 377 aroundPeak += fabs(data[i]);
Chris@6 378 --i;
Chris@6 379 }
Chris@6 380 i = n + 1;
Chris@6 381 while (i < m_bins && data[i] <= data[i-1]) {
Chris@6 382 aroundPeak += fabs(data[i]);
Chris@6 383 ++i;
Chris@6 384 }
Chris@6 385 peakProportion = aroundPeak / abstot;
Chris@6 386
Chris@6 387 return peakProportion;
Chris@6 388 }
Chris@6 389
Chris@6 390 bool
Chris@6 391 CepstrumPitchTracker::acceptPeak(int n, double peakProportion)
Chris@6 392 {
Chris@6 393 bool accept = false;
Chris@6 394
Chris@6 395 if (abs(n - m_prevpeak) < 10) { //!!! should depend on bin count
Chris@6 396 accept = true;
Chris@6 397 } else if (peakProportion > m_prevprop * 2) {
Chris@6 398 accept = true;
Chris@6 399 }
Chris@6 400
Chris@6 401 return accept;
Chris@6 402 }
Chris@6 403
Chris@3 404 CepstrumPitchTracker::FeatureSet
Chris@3 405 CepstrumPitchTracker::process(const float *const *inputBuffers, Vamp::RealTime timestamp)
Chris@3 406 {
Chris@3 407 FeatureSet fs;
Chris@3 408
Chris@3 409 int bs = m_blockSize;
Chris@3 410 int hs = m_blockSize/2 + 1;
Chris@3 411
Chris@3 412 double *rawcep = new double[bs];
Chris@3 413 double *io = new double[bs];
Chris@3 414 double *logmag = new double[bs];
Chris@3 415
Chris@4 416 // The "inverse symmetric" method. Seems to be the most reliable
Chris@3 417
Chris@3 418 for (int i = 0; i < hs; ++i) {
Chris@3 419
Chris@3 420 double power =
Chris@3 421 inputBuffers[0][i*2 ] * inputBuffers[0][i*2 ] +
Chris@3 422 inputBuffers[0][i*2+1] * inputBuffers[0][i*2+1];
Chris@3 423 double mag = sqrt(power);
Chris@3 424
Chris@3 425 double lm = log(mag + 0.00000001);
Chris@3 426
Chris@4 427 logmag[i] = lm;
Chris@4 428 if (i > 0) logmag[bs - i] = lm;
Chris@3 429 }
Chris@3 430
Chris@4 431 fft(bs, true, logmag, 0, rawcep, io);
Chris@3 432
Chris@3 433 delete[] logmag;
Chris@3 434 delete[] io;
Chris@3 435
Chris@3 436 int n = m_bins;
Chris@3 437 double *data = new double[n];
Chris@3 438 filter(rawcep, data);
Chris@3 439 delete[] rawcep;
Chris@3 440
Chris@6 441 double abstot = 0.0;
Chris@6 442
Chris@6 443 for (int i = 0; i < n; ++i) {
Chris@6 444 abstot += fabs(data[i]);
Chris@6 445 }
Chris@6 446
Chris@3 447 double maxval = 0.0;
Chris@6 448 int maxbin = -1;
Chris@3 449
Chris@3 450 for (int i = 0; i < n; ++i) {
Chris@3 451 if (data[i] > maxval) {
Chris@3 452 maxval = data[i];
Chris@3 453 maxbin = i;
Chris@3 454 }
Chris@3 455 }
Chris@3 456
Chris@8 457 if (maxbin < 0) return fs;
Chris@8 458
Chris@8 459 double peakfreq = m_inputSampleRate / (maxbin + m_binFrom);
Chris@8 460 Hypothesis::Estimate e;
Chris@8 461 e.freq = peakfreq;
Chris@8 462 e.time = timestamp;
Chris@8 463
Chris@8 464 m_accepted.advanceTime();
Chris@8 465 for (int i = 0; i < m_possible.size(); ++i) {
Chris@8 466 m_possible[i].advanceTime();
Chris@8 467 }
Chris@8 468
Chris@8 469 if (m_accepted.test(e)) {
Chris@8 470 return fs;
Chris@8 471 }
Chris@8 472
Chris@8 473 //...
Chris@8 474
Chris@8 475 /*
Chris@6 476 bool accepted = false;
Chris@6 477
Chris@6 478 if (maxbin >= 0) {
Chris@6 479 double pp = calculatePeakProportion(data, abstot, maxbin);
Chris@6 480 if (acceptPeak(maxbin, pp)) {
Chris@6 481 accepted = true;
Chris@6 482 } else {
Chris@6 483 // try a secondary peak
Chris@6 484 maxval = 0.0;
Chris@6 485 int secondbin = 0;
Chris@6 486 for (int i = 1; i < n-1; ++i) {
Chris@6 487 if (i != maxbin &&
Chris@6 488 data[i] > data[i-1] &&
Chris@6 489 data[i] > data[i+1] &&
Chris@6 490 data[i] > maxval) {
Chris@6 491 maxval = data[i];
Chris@6 492 secondbin = i;
Chris@6 493 }
Chris@6 494 }
Chris@6 495 double spp = calculatePeakProportion(data, abstot, secondbin);
Chris@6 496 if (acceptPeak(secondbin, spp)) {
Chris@6 497 maxbin = secondbin;
Chris@6 498 pp = spp;
Chris@6 499 accepted = true;
Chris@6 500 }
Chris@3 501 }
Chris@6 502 if (accepted) {
Chris@6 503 m_prevpeak = maxbin;
Chris@6 504 m_prevprop = pp;
Chris@3 505 }
Chris@3 506 }
Chris@8 507 */
Chris@3 508 // std::cerr << "peakProportion = " << peakProportion << std::endl;
Chris@3 509 // std::cerr << "peak = " << m_inputSampleRate / (maxbin + m_binFrom) << std::endl;
Chris@4 510 // std::cerr << "bins = " << m_bins << std::endl;
Chris@3 511
Chris@6 512 // if (peakProportion >= (0.00006 * m_bins)) {
Chris@6 513 if (accepted) {
Chris@3 514 Feature f;
Chris@3 515 f.hasTimestamp = true;
Chris@3 516 f.timestamp = timestamp;
Chris@3 517 f.values.push_back(m_inputSampleRate / (maxbin + m_binFrom));
Chris@3 518 fs[0].push_back(f);
Chris@3 519 }
Chris@3 520
Chris@3 521 delete[] data;
Chris@3 522 return fs;
Chris@3 523 }
Chris@3 524
Chris@3 525 CepstrumPitchTracker::FeatureSet
Chris@3 526 CepstrumPitchTracker::getRemainingFeatures()
Chris@3 527 {
Chris@3 528 FeatureSet fs;
Chris@3 529 return fs;
Chris@3 530 }
Chris@3 531
Chris@3 532 void
Chris@3 533 CepstrumPitchTracker::fft(unsigned int n, bool inverse,
Chris@3 534 double *ri, double *ii, double *ro, double *io)
Chris@3 535 {
Chris@3 536 if (!ri || !ro || !io) return;
Chris@3 537
Chris@3 538 unsigned int bits;
Chris@3 539 unsigned int i, j, k, m;
Chris@3 540 unsigned int blockSize, blockEnd;
Chris@3 541
Chris@3 542 double tr, ti;
Chris@3 543
Chris@3 544 if (n < 2) return;
Chris@3 545 if (n & (n-1)) return;
Chris@3 546
Chris@3 547 double angle = 2.0 * M_PI;
Chris@3 548 if (inverse) angle = -angle;
Chris@3 549
Chris@3 550 for (i = 0; ; ++i) {
Chris@3 551 if (n & (1 << i)) {
Chris@3 552 bits = i;
Chris@3 553 break;
Chris@3 554 }
Chris@3 555 }
Chris@3 556
Chris@3 557 static unsigned int tableSize = 0;
Chris@3 558 static int *table = 0;
Chris@3 559
Chris@3 560 if (tableSize != n) {
Chris@3 561
Chris@3 562 delete[] table;
Chris@3 563
Chris@3 564 table = new int[n];
Chris@3 565
Chris@3 566 for (i = 0; i < n; ++i) {
Chris@3 567
Chris@3 568 m = i;
Chris@3 569
Chris@3 570 for (j = k = 0; j < bits; ++j) {
Chris@3 571 k = (k << 1) | (m & 1);
Chris@3 572 m >>= 1;
Chris@3 573 }
Chris@3 574
Chris@3 575 table[i] = k;
Chris@3 576 }
Chris@3 577
Chris@3 578 tableSize = n;
Chris@3 579 }
Chris@3 580
Chris@3 581 if (ii) {
Chris@3 582 for (i = 0; i < n; ++i) {
Chris@3 583 ro[table[i]] = ri[i];
Chris@3 584 io[table[i]] = ii[i];
Chris@3 585 }
Chris@3 586 } else {
Chris@3 587 for (i = 0; i < n; ++i) {
Chris@3 588 ro[table[i]] = ri[i];
Chris@3 589 io[table[i]] = 0.0;
Chris@3 590 }
Chris@3 591 }
Chris@3 592
Chris@3 593 blockEnd = 1;
Chris@3 594
Chris@3 595 for (blockSize = 2; blockSize <= n; blockSize <<= 1) {
Chris@3 596
Chris@3 597 double delta = angle / (double)blockSize;
Chris@3 598 double sm2 = -sin(-2 * delta);
Chris@3 599 double sm1 = -sin(-delta);
Chris@3 600 double cm2 = cos(-2 * delta);
Chris@3 601 double cm1 = cos(-delta);
Chris@3 602 double w = 2 * cm1;
Chris@3 603 double ar[3], ai[3];
Chris@3 604
Chris@3 605 for (i = 0; i < n; i += blockSize) {
Chris@3 606
Chris@3 607 ar[2] = cm2;
Chris@3 608 ar[1] = cm1;
Chris@3 609
Chris@3 610 ai[2] = sm2;
Chris@3 611 ai[1] = sm1;
Chris@3 612
Chris@3 613 for (j = i, m = 0; m < blockEnd; j++, m++) {
Chris@3 614
Chris@3 615 ar[0] = w * ar[1] - ar[2];
Chris@3 616 ar[2] = ar[1];
Chris@3 617 ar[1] = ar[0];
Chris@3 618
Chris@3 619 ai[0] = w * ai[1] - ai[2];
Chris@3 620 ai[2] = ai[1];
Chris@3 621 ai[1] = ai[0];
Chris@3 622
Chris@3 623 k = j + blockEnd;
Chris@3 624 tr = ar[0] * ro[k] - ai[0] * io[k];
Chris@3 625 ti = ar[0] * io[k] + ai[0] * ro[k];
Chris@3 626
Chris@3 627 ro[k] = ro[j] - tr;
Chris@3 628 io[k] = io[j] - ti;
Chris@3 629
Chris@3 630 ro[j] += tr;
Chris@3 631 io[j] += ti;
Chris@3 632 }
Chris@3 633 }
Chris@3 634
Chris@3 635 blockEnd = blockSize;
Chris@3 636 }
Chris@3 637 }
Chris@3 638
Chris@3 639