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+/*
+ * Copyright (C) 2012 Google Inc. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. Neither the name of Apple Computer, Inc. ("Apple") nor the names of
+ * its contributors may be used to endorse or promote products derived
+ * from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY APPLE AND ITS CONTRIBUTORS "AS IS" AND ANY
+ * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL APPLE OR ITS CONTRIBUTORS BE LIABLE FOR ANY
+ * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#include "PeriodicWave.h"
+#include <algorithm>
+#include <cmath>
+#include <limits>
+#include "mozilla/FFTBlock.h"
+
+const unsigned MinPeriodicWaveSize = 4096; // This must be a power of two.
+const unsigned MaxPeriodicWaveSize = 8192; // This must be a power of two.
+const float CentsPerRange = 1200 / 3; // 1/3 Octave.
+
+using namespace mozilla;
+using mozilla::dom::OscillatorType;
+
+namespace WebCore {
+
+already_AddRefed<PeriodicWave> PeriodicWave::create(float sampleRate,
+ const float* real,
+ const float* imag,
+ size_t numberOfComponents,
+ bool disableNormalization) {
+ bool isGood = real && imag && numberOfComponents > 0;
+ MOZ_ASSERT(isGood);
+ if (isGood) {
+ RefPtr<PeriodicWave> periodicWave =
+ new PeriodicWave(sampleRate, numberOfComponents, disableNormalization);
+
+ // Limit the number of components used to those for frequencies below the
+ // Nyquist of the fixed length inverse FFT.
+ size_t halfSize = periodicWave->m_periodicWaveSize / 2;
+ numberOfComponents = std::min(numberOfComponents, halfSize);
+ periodicWave->m_numberOfComponents = numberOfComponents;
+ periodicWave->m_realComponents =
+ MakeUnique<AudioFloatArray>(numberOfComponents);
+ periodicWave->m_imagComponents =
+ MakeUnique<AudioFloatArray>(numberOfComponents);
+ memcpy(periodicWave->m_realComponents->Elements(), real,
+ numberOfComponents * sizeof(float));
+ memcpy(periodicWave->m_imagComponents->Elements(), imag,
+ numberOfComponents * sizeof(float));
+
+ return periodicWave.forget();
+ }
+ return nullptr;
+}
+
+already_AddRefed<PeriodicWave> PeriodicWave::createSine(float sampleRate) {
+ RefPtr<PeriodicWave> periodicWave =
+ new PeriodicWave(sampleRate, MinPeriodicWaveSize, false);
+ periodicWave->generateBasicWaveform(OscillatorType::Sine);
+ return periodicWave.forget();
+}
+
+already_AddRefed<PeriodicWave> PeriodicWave::createSquare(float sampleRate) {
+ RefPtr<PeriodicWave> periodicWave =
+ new PeriodicWave(sampleRate, MinPeriodicWaveSize, false);
+ periodicWave->generateBasicWaveform(OscillatorType::Square);
+ return periodicWave.forget();
+}
+
+already_AddRefed<PeriodicWave> PeriodicWave::createSawtooth(float sampleRate) {
+ RefPtr<PeriodicWave> periodicWave =
+ new PeriodicWave(sampleRate, MinPeriodicWaveSize, false);
+ periodicWave->generateBasicWaveform(OscillatorType::Sawtooth);
+ return periodicWave.forget();
+}
+
+already_AddRefed<PeriodicWave> PeriodicWave::createTriangle(float sampleRate) {
+ RefPtr<PeriodicWave> periodicWave =
+ new PeriodicWave(sampleRate, MinPeriodicWaveSize, false);
+ periodicWave->generateBasicWaveform(OscillatorType::Triangle);
+ return periodicWave.forget();
+}
+
+PeriodicWave::PeriodicWave(float sampleRate, size_t numberOfComponents,
+ bool disableNormalization)
+ : m_sampleRate(sampleRate),
+ m_centsPerRange(CentsPerRange),
+ m_maxPartialsInBandLimitedTable(0),
+ m_normalizationScale(1.0f),
+ m_disableNormalization(disableNormalization) {
+ float nyquist = 0.5 * m_sampleRate;
+
+ if (numberOfComponents <= MinPeriodicWaveSize) {
+ m_periodicWaveSize = MinPeriodicWaveSize;
+ } else {
+ unsigned npow2 =
+ exp2f(floorf(logf(numberOfComponents - 1.0) / logf(2.0f) + 1.0f));
+ m_periodicWaveSize = std::min(MaxPeriodicWaveSize, npow2);
+ }
+
+ m_numberOfRanges = (unsigned)(3.0f * logf(m_periodicWaveSize) / logf(2.0f));
+ m_bandLimitedTables.SetLength(m_numberOfRanges);
+ m_lowestFundamentalFrequency = nyquist / maxNumberOfPartials();
+ m_rateScale = m_periodicWaveSize / m_sampleRate;
+}
+
+size_t PeriodicWave::sizeOfIncludingThis(
+ mozilla::MallocSizeOf aMallocSizeOf) const {
+ size_t amount = aMallocSizeOf(this);
+
+ amount += m_bandLimitedTables.ShallowSizeOfExcludingThis(aMallocSizeOf);
+ for (size_t i = 0; i < m_bandLimitedTables.Length(); i++) {
+ if (m_bandLimitedTables[i]) {
+ amount +=
+ m_bandLimitedTables[i]->ShallowSizeOfIncludingThis(aMallocSizeOf);
+ }
+ }
+
+ return amount;
+}
+
+void PeriodicWave::waveDataForFundamentalFrequency(
+ float fundamentalFrequency, float*& lowerWaveData, float*& higherWaveData,
+ float& tableInterpolationFactor) {
+ // Negative frequencies are allowed, in which case we alias
+ // to the positive frequency.
+ fundamentalFrequency = fabsf(fundamentalFrequency);
+
+ // We only need to rebuild to the tables if the new fundamental
+ // frequency is low enough to allow for more partials below the
+ // Nyquist frequency.
+ unsigned numberOfPartials = numberOfPartialsForRange(0);
+ float nyquist = 0.5 * m_sampleRate;
+ if (fundamentalFrequency != 0.0) {
+ numberOfPartials =
+ std::min(numberOfPartials, (unsigned)(nyquist / fundamentalFrequency));
+ }
+ if (numberOfPartials > m_maxPartialsInBandLimitedTable) {
+ for (unsigned rangeIndex = 0; rangeIndex < m_numberOfRanges; ++rangeIndex) {
+ m_bandLimitedTables[rangeIndex] = 0;
+ }
+
+ // We need to create the first table to determine the normalization
+ // constant.
+ createBandLimitedTables(fundamentalFrequency, 0);
+ m_maxPartialsInBandLimitedTable = numberOfPartials;
+ }
+
+ // Calculate the pitch range.
+ float ratio = fundamentalFrequency > 0
+ ? fundamentalFrequency / m_lowestFundamentalFrequency
+ : 0.5;
+ float centsAboveLowestFrequency = logf(ratio) / logf(2.0f) * 1200;
+
+ // Add one to round-up to the next range just in time to truncate
+ // partials before aliasing occurs.
+ float pitchRange = 1 + centsAboveLowestFrequency / m_centsPerRange;
+
+ pitchRange = std::max(pitchRange, 0.0f);
+ pitchRange = std::min(pitchRange, static_cast<float>(m_numberOfRanges - 1));
+
+ // The words "lower" and "higher" refer to the table data having
+ // the lower and higher numbers of partials. It's a little confusing
+ // since the range index gets larger the more partials we cull out.
+ // So the lower table data will have a larger range index.
+ unsigned rangeIndex1 = static_cast<unsigned>(pitchRange);
+ unsigned rangeIndex2 =
+ rangeIndex1 < m_numberOfRanges - 1 ? rangeIndex1 + 1 : rangeIndex1;
+
+ if (!m_bandLimitedTables[rangeIndex1].get())
+ createBandLimitedTables(fundamentalFrequency, rangeIndex1);
+
+ if (!m_bandLimitedTables[rangeIndex2].get())
+ createBandLimitedTables(fundamentalFrequency, rangeIndex2);
+
+ lowerWaveData = m_bandLimitedTables[rangeIndex2]->Elements();
+ higherWaveData = m_bandLimitedTables[rangeIndex1]->Elements();
+
+ // Ranges from 0 -> 1 to interpolate between lower -> higher.
+ tableInterpolationFactor = rangeIndex2 - pitchRange;
+}
+
+unsigned PeriodicWave::maxNumberOfPartials() const {
+ return m_periodicWaveSize / 2;
+}
+
+unsigned PeriodicWave::numberOfPartialsForRange(unsigned rangeIndex) const {
+ // Number of cents below nyquist where we cull partials.
+ float centsToCull = rangeIndex * m_centsPerRange;
+
+ // A value from 0 -> 1 representing what fraction of the partials to keep.
+ float cullingScale = exp2(-centsToCull / 1200);
+
+ // The very top range will have all the partials culled.
+ unsigned numberOfPartials = cullingScale * maxNumberOfPartials();
+
+ return numberOfPartials;
+}
+
+// Convert into time-domain wave buffers.
+// One table is created for each range for non-aliasing playback
+// at different playback rates. Thus, higher ranges have more
+// high-frequency partials culled out.
+void PeriodicWave::createBandLimitedTables(float fundamentalFrequency,
+ unsigned rangeIndex) {
+ unsigned fftSize = m_periodicWaveSize;
+ unsigned i;
+
+ const float* realData = m_realComponents->Elements();
+ const float* imagData = m_imagComponents->Elements();
+
+ // This FFTBlock is used to cull partials (represented by frequency bins).
+ FFTBlock frame(fftSize);
+
+ // Find the starting bin where we should start culling the aliasing
+ // partials for this pitch range. We need to clear out the highest
+ // frequencies to band-limit the waveform.
+ unsigned numberOfPartials = numberOfPartialsForRange(rangeIndex);
+ // Also limit to the number of components that are provided.
+ numberOfPartials = std::min(numberOfPartials, m_numberOfComponents - 1);
+
+ // Limit number of partials to those below Nyquist frequency
+ float nyquist = 0.5 * m_sampleRate;
+ if (fundamentalFrequency != 0.0) {
+ numberOfPartials =
+ std::min(numberOfPartials, (unsigned)(nyquist / fundamentalFrequency));
+ }
+
+ // Copy from loaded frequency data and generate complex conjugate
+ // because of the way the inverse FFT is defined.
+ // The coefficients of higher partials remain zero, as initialized in
+ // the FFTBlock constructor.
+ for (i = 0; i < numberOfPartials + 1; ++i) {
+ frame.RealData(i) = realData[i];
+ frame.ImagData(i) = -imagData[i];
+ }
+
+ // Clear any DC-offset.
+ frame.RealData(0) = 0;
+ // Clear value which has no effect.
+ frame.ImagData(0) = 0;
+
+ // Create the band-limited table.
+ m_bandLimitedTables[rangeIndex] =
+ MakeUnique<AlignedAudioFloatArray>(m_periodicWaveSize);
+
+ // Apply an inverse FFT to generate the time-domain table data.
+ float* data = m_bandLimitedTables[rangeIndex]->Elements();
+ frame.GetInverseWithoutScaling(data);
+
+ // For the first range (which has the highest power), calculate
+ // its peak value then compute normalization scale.
+ if (m_disableNormalization) {
+ // See Bug 1424906, results need to be scaled by 0.5 even
+ // when normalization is disabled.
+ m_normalizationScale = 0.5;
+ } else if (!rangeIndex) {
+ float maxValue;
+ maxValue = AudioBufferPeakValue(data, m_periodicWaveSize);
+
+ if (maxValue) m_normalizationScale = 1.0f / maxValue;
+ }
+
+ // Apply normalization scale.
+ AudioBufferInPlaceScale(data, m_normalizationScale, m_periodicWaveSize);
+}
+
+void PeriodicWave::generateBasicWaveform(OscillatorType shape) {
+ const float piFloat = float(M_PI);
+ unsigned fftSize = periodicWaveSize();
+ unsigned halfSize = fftSize / 2;
+
+ m_numberOfComponents = halfSize;
+ m_realComponents = MakeUnique<AudioFloatArray>(halfSize);
+ m_imagComponents = MakeUnique<AudioFloatArray>(halfSize);
+ float* realP = m_realComponents->Elements();
+ float* imagP = m_imagComponents->Elements();
+
+ // Clear DC and imag value which is ignored.
+ realP[0] = 0;
+ imagP[0] = 0;
+
+ for (unsigned n = 1; n < halfSize; ++n) {
+ float omega = 2 * piFloat * n;
+ float invOmega = 1 / omega;
+
+ // Fourier coefficients according to standard definition.
+ float a; // Coefficient for cos().
+ float b; // Coefficient for sin().
+
+ // Calculate Fourier coefficients depending on the shape.
+ // Note that the overall scaling (magnitude) of the waveforms
+ // is normalized in createBandLimitedTables().
+ switch (shape) {
+ case OscillatorType::Sine:
+ // Standard sine wave function.
+ a = 0;
+ b = (n == 1) ? 1 : 0;
+ break;
+ case OscillatorType::Square:
+ // Square-shaped waveform with the first half its maximum value
+ // and the second half its minimum value.
+ a = 0;
+ b = invOmega * ((n & 1) ? 2 : 0);
+ break;
+ case OscillatorType::Sawtooth:
+ // Sawtooth-shaped waveform with the first half ramping from
+ // zero to maximum and the second half from minimum to zero.
+ a = 0;
+ b = -invOmega * cos(0.5 * omega);
+ break;
+ case OscillatorType::Triangle:
+ // Triangle-shaped waveform going from its maximum value to
+ // its minimum value then back to the maximum value.
+ a = 0;
+ if (n & 1) {
+ b = 2 * (2 / (n * piFloat) * 2 / (n * piFloat)) *
+ ((((n - 1) >> 1) & 1) ? -1 : 1);
+ } else {
+ b = 0;
+ }
+ break;
+ default:
+ MOZ_ASSERT_UNREACHABLE("invalid oscillator type");
+ a = 0;
+ b = 0;
+ break;
+ }
+
+ realP[n] = a;
+ imagP[n] = b;
+ }
+}
+
+} // namespace WebCore