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/*
* Copyright (C) 2010 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 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
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* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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*/
#include "config.h"
#if ENABLE(WEB_AUDIO)
#include "Biquad.h"
#include "DenormalDisabler.h"
#include <algorithm>
#include <stdio.h>
#include <wtf/MathExtras.h>
#if USE(ACCELERATE)
// Work around a bug where VForce.h forward declares std::complex in a way that's incompatible with libc++ complex.
#define __VFORCE_H
#include <Accelerate/Accelerate.h>
#endif
namespace WebCore {
#if USE(ACCELERATE)
const int kBufferSize = 1024;
#endif
Biquad::Biquad()
{
#if USE(ACCELERATE)
// Allocate two samples more for filter history
m_inputBuffer.allocate(kBufferSize + 2);
m_outputBuffer.allocate(kBufferSize + 2);
#endif
// Initialize as pass-thru (straight-wire, no filter effect)
setNormalizedCoefficients(1, 0, 0, 1, 0, 0);
reset(); // clear filter memory
}
Biquad::~Biquad() = default;
void Biquad::process(const float* sourceP, float* destP, size_t framesToProcess)
{
#if USE(ACCELERATE)
// Use vecLib if available
processFast(sourceP, destP, framesToProcess);
#else
int n = framesToProcess;
// Create local copies of member variables
double x1 = m_x1;
double x2 = m_x2;
double y1 = m_y1;
double y2 = m_y2;
double b0 = m_b0;
double b1 = m_b1;
double b2 = m_b2;
double a1 = m_a1;
double a2 = m_a2;
while (n--) {
// FIXME: this can be optimized by pipelining the multiply adds...
float x = *sourceP++;
float y = b0*x + b1*x1 + b2*x2 - a1*y1 - a2*y2;
*destP++ = y;
// Update state variables
x2 = x1;
x1 = x;
y2 = y1;
y1 = y;
}
// Local variables back to member. Flush denormals here so we
// don't slow down the inner loop above.
m_x1 = DenormalDisabler::flushDenormalFloatToZero(x1);
m_x2 = DenormalDisabler::flushDenormalFloatToZero(x2);
m_y1 = DenormalDisabler::flushDenormalFloatToZero(y1);
m_y2 = DenormalDisabler::flushDenormalFloatToZero(y2);
m_b0 = b0;
m_b1 = b1;
m_b2 = b2;
m_a1 = a1;
m_a2 = a2;
#endif
}
#if USE(ACCELERATE)
// Here we have optimized version using Accelerate.framework
void Biquad::processFast(const float* sourceP, float* destP, size_t framesToProcess)
{
double filterCoefficients[5];
filterCoefficients[0] = m_b0;
filterCoefficients[1] = m_b1;
filterCoefficients[2] = m_b2;
filterCoefficients[3] = m_a1;
filterCoefficients[4] = m_a2;
double* inputP = m_inputBuffer.data();
double* outputP = m_outputBuffer.data();
double* input2P = inputP + 2;
double* output2P = outputP + 2;
// Break up processing into smaller slices (kBufferSize) if necessary.
int n = framesToProcess;
while (n > 0) {
int framesThisTime = n < kBufferSize ? n : kBufferSize;
// Copy input to input buffer
for (int i = 0; i < framesThisTime; ++i)
input2P[i] = *sourceP++;
processSliceFast(inputP, outputP, filterCoefficients, framesThisTime);
// Copy output buffer to output (converts float -> double).
for (int i = 0; i < framesThisTime; ++i)
*destP++ = static_cast<float>(output2P[i]);
n -= framesThisTime;
}
}
void Biquad::processSliceFast(double* sourceP, double* destP, double* coefficientsP, size_t framesToProcess)
{
// Use double-precision for filter stability
vDSP_deq22D(sourceP, 1, coefficientsP, destP, 1, framesToProcess);
// Save history. Note that sourceP and destP reference m_inputBuffer and m_outputBuffer respectively.
// These buffers are allocated (in the constructor) with space for two extra samples so it's OK to access
// array values two beyond framesToProcess.
sourceP[0] = sourceP[framesToProcess - 2 + 2];
sourceP[1] = sourceP[framesToProcess - 1 + 2];
destP[0] = destP[framesToProcess - 2 + 2];
destP[1] = destP[framesToProcess - 1 + 2];
}
#endif // USE(ACCELERATE)
void Biquad::reset()
{
#if USE(ACCELERATE)
// Two extra samples for filter history
double* inputP = m_inputBuffer.data();
inputP[0] = 0;
inputP[1] = 0;
double* outputP = m_outputBuffer.data();
outputP[0] = 0;
outputP[1] = 0;
#else
m_x1 = m_x2 = m_y1 = m_y2 = 0;
#endif
}
void Biquad::setLowpassParams(double cutoff, double resonance)
{
// Limit cutoff to 0 to 1.
cutoff = std::max(0.0, std::min(cutoff, 1.0));
if (cutoff == 1) {
// When cutoff is 1, the z-transform is 1.
setNormalizedCoefficients(1, 0, 0,
1, 0, 0);
} else if (cutoff > 0) {
// Compute biquad coefficients for lowpass filter
resonance = std::max(0.0, resonance); // can't go negative
double g = pow(10.0, 0.05 * resonance);
double d = sqrt((4 - sqrt(16 - 16 / (g * g))) / 2);
double theta = piDouble * cutoff;
double sn = 0.5 * d * sin(theta);
double beta = 0.5 * (1 - sn) / (1 + sn);
double gamma = (0.5 + beta) * cos(theta);
double alpha = 0.25 * (0.5 + beta - gamma);
double b0 = 2 * alpha;
double b1 = 2 * 2 * alpha;
double b2 = 2 * alpha;
double a1 = 2 * -gamma;
double a2 = 2 * beta;
setNormalizedCoefficients(b0, b1, b2, 1, a1, a2);
} else {
// When cutoff is zero, nothing gets through the filter, so set
// coefficients up correctly.
setNormalizedCoefficients(0, 0, 0,
1, 0, 0);
}
}
void Biquad::setHighpassParams(double cutoff, double resonance)
{
// Limit cutoff to 0 to 1.
cutoff = std::max(0.0, std::min(cutoff, 1.0));
if (cutoff == 1) {
// The z-transform is 0.
setNormalizedCoefficients(0, 0, 0,
1, 0, 0);
} else if (cutoff > 0) {
// Compute biquad coefficients for highpass filter
resonance = std::max(0.0, resonance); // can't go negative
double g = pow(10.0, 0.05 * resonance);
double d = sqrt((4 - sqrt(16 - 16 / (g * g))) / 2);
double theta = piDouble * cutoff;
double sn = 0.5 * d * sin(theta);
double beta = 0.5 * (1 - sn) / (1 + sn);
double gamma = (0.5 + beta) * cos(theta);
double alpha = 0.25 * (0.5 + beta + gamma);
double b0 = 2 * alpha;
double b1 = 2 * -2 * alpha;
double b2 = 2 * alpha;
double a1 = 2 * -gamma;
double a2 = 2 * beta;
setNormalizedCoefficients(b0, b1, b2, 1, a1, a2);
} else {
// When cutoff is zero, we need to be careful because the above
// gives a quadratic divided by the same quadratic, with poles
// and zeros on the unit circle in the same place. When cutoff
// is zero, the z-transform is 1.
setNormalizedCoefficients(1, 0, 0,
1, 0, 0);
}
}
void Biquad::setNormalizedCoefficients(double b0, double b1, double b2, double a0, double a1, double a2)
{
double a0Inverse = 1 / a0;
m_b0 = b0 * a0Inverse;
m_b1 = b1 * a0Inverse;
m_b2 = b2 * a0Inverse;
m_a1 = a1 * a0Inverse;
m_a2 = a2 * a0Inverse;
}
void Biquad::setLowShelfParams(double frequency, double dbGain)
{
// Clip frequencies to between 0 and 1, inclusive.
frequency = std::max(0.0, std::min(frequency, 1.0));
double A = pow(10.0, dbGain / 40);
if (frequency == 1) {
// The z-transform is a constant gain.
setNormalizedCoefficients(A * A, 0, 0,
1, 0, 0);
} else if (frequency > 0) {
double w0 = piDouble * frequency;
double S = 1; // filter slope (1 is max value)
double alpha = 0.5 * sin(w0) * sqrt((A + 1 / A) * (1 / S - 1) + 2);
double k = cos(w0);
double k2 = 2 * sqrt(A) * alpha;
double aPlusOne = A + 1;
double aMinusOne = A - 1;
double b0 = A * (aPlusOne - aMinusOne * k + k2);
double b1 = 2 * A * (aMinusOne - aPlusOne * k);
double b2 = A * (aPlusOne - aMinusOne * k - k2);
double a0 = aPlusOne + aMinusOne * k + k2;
double a1 = -2 * (aMinusOne + aPlusOne * k);
double a2 = aPlusOne + aMinusOne * k - k2;
setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
} else {
// When frequency is 0, the z-transform is 1.
setNormalizedCoefficients(1, 0, 0,
1, 0, 0);
}
}
void Biquad::setHighShelfParams(double frequency, double dbGain)
{
// Clip frequencies to between 0 and 1, inclusive.
frequency = std::max(0.0, std::min(frequency, 1.0));
double A = pow(10.0, dbGain / 40);
if (frequency == 1) {
// The z-transform is 1.
setNormalizedCoefficients(1, 0, 0,
1, 0, 0);
} else if (frequency > 0) {
double w0 = piDouble * frequency;
double S = 1; // filter slope (1 is max value)
double alpha = 0.5 * sin(w0) * sqrt((A + 1 / A) * (1 / S - 1) + 2);
double k = cos(w0);
double k2 = 2 * sqrt(A) * alpha;
double aPlusOne = A + 1;
double aMinusOne = A - 1;
double b0 = A * (aPlusOne + aMinusOne * k + k2);
double b1 = -2 * A * (aMinusOne + aPlusOne * k);
double b2 = A * (aPlusOne + aMinusOne * k - k2);
double a0 = aPlusOne - aMinusOne * k + k2;
double a1 = 2 * (aMinusOne - aPlusOne * k);
double a2 = aPlusOne - aMinusOne * k - k2;
setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
} else {
// When frequency = 0, the filter is just a gain, A^2.
setNormalizedCoefficients(A * A, 0, 0,
1, 0, 0);
}
}
void Biquad::setPeakingParams(double frequency, double Q, double dbGain)
{
// Clip frequencies to between 0 and 1, inclusive.
frequency = std::max(0.0, std::min(frequency, 1.0));
// Don't let Q go negative, which causes an unstable filter.
Q = std::max(0.0, Q);
double A = pow(10.0, dbGain / 40);
if (frequency > 0 && frequency < 1) {
if (Q > 0) {
double w0 = piDouble * frequency;
double alpha = sin(w0) / (2 * Q);
double k = cos(w0);
double b0 = 1 + alpha * A;
double b1 = -2 * k;
double b2 = 1 - alpha * A;
double a0 = 1 + alpha / A;
double a1 = -2 * k;
double a2 = 1 - alpha / A;
setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
} else {
// When Q = 0, the above formulas have problems. If we look at
// the z-transform, we can see that the limit as Q->0 is A^2, so
// set the filter that way.
setNormalizedCoefficients(A * A, 0, 0,
1, 0, 0);
}
} else {
// When frequency is 0 or 1, the z-transform is 1.
setNormalizedCoefficients(1, 0, 0,
1, 0, 0);
}
}
void Biquad::setAllpassParams(double frequency, double Q)
{
// Clip frequencies to between 0 and 1, inclusive.
frequency = std::max(0.0, std::min(frequency, 1.0));
// Don't let Q go negative, which causes an unstable filter.
Q = std::max(0.0, Q);
if (frequency > 0 && frequency < 1) {
if (Q > 0) {
double w0 = piDouble * frequency;
double alpha = sin(w0) / (2 * Q);
double k = cos(w0);
double b0 = 1 - alpha;
double b1 = -2 * k;
double b2 = 1 + alpha;
double a0 = 1 + alpha;
double a1 = -2 * k;
double a2 = 1 - alpha;
setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
} else {
// When Q = 0, the above formulas have problems. If we look at
// the z-transform, we can see that the limit as Q->0 is -1, so
// set the filter that way.
setNormalizedCoefficients(-1, 0, 0,
1, 0, 0);
}
} else {
// When frequency is 0 or 1, the z-transform is 1.
setNormalizedCoefficients(1, 0, 0,
1, 0, 0);
}
}
void Biquad::setNotchParams(double frequency, double Q)
{
// Clip frequencies to between 0 and 1, inclusive.
frequency = std::max(0.0, std::min(frequency, 1.0));
// Don't let Q go negative, which causes an unstable filter.
Q = std::max(0.0, Q);
if (frequency > 0 && frequency < 1) {
if (Q > 0) {
double w0 = piDouble * frequency;
double alpha = sin(w0) / (2 * Q);
double k = cos(w0);
double b0 = 1;
double b1 = -2 * k;
double b2 = 1;
double a0 = 1 + alpha;
double a1 = -2 * k;
double a2 = 1 - alpha;
setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
} else {
// When Q = 0, the above formulas have problems. If we look at
// the z-transform, we can see that the limit as Q->0 is 0, so
// set the filter that way.
setNormalizedCoefficients(0, 0, 0,
1, 0, 0);
}
} else {
// When frequency is 0 or 1, the z-transform is 1.
setNormalizedCoefficients(1, 0, 0,
1, 0, 0);
}
}
void Biquad::setBandpassParams(double frequency, double Q)
{
// No negative frequencies allowed.
frequency = std::max(0.0, frequency);
// Don't let Q go negative, which causes an unstable filter.
Q = std::max(0.0, Q);
if (frequency > 0 && frequency < 1) {
double w0 = piDouble * frequency;
if (Q > 0) {
double alpha = sin(w0) / (2 * Q);
double k = cos(w0);
double b0 = alpha;
double b1 = 0;
double b2 = -alpha;
double a0 = 1 + alpha;
double a1 = -2 * k;
double a2 = 1 - alpha;
setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
} else {
// When Q = 0, the above formulas have problems. If we look at
// the z-transform, we can see that the limit as Q->0 is 1, so
// set the filter that way.
setNormalizedCoefficients(1, 0, 0,
1, 0, 0);
}
} else {
// When the cutoff is zero, the z-transform approaches 0, if Q
// > 0. When both Q and cutoff are zero, the z-transform is
// pretty much undefined. What should we do in this case?
// For now, just make the filter 0. When the cutoff is 1, the
// z-transform also approaches 0.
setNormalizedCoefficients(0, 0, 0,
1, 0, 0);
}
}
void Biquad::setZeroPolePairs(std::complex<double> zero, std::complex<double> pole)
{
double b0 = 1;
double b1 = -2 * zero.real();
double zeroMag = abs(zero);
double b2 = zeroMag * zeroMag;
double a1 = -2 * pole.real();
double poleMag = abs(pole);
double a2 = poleMag * poleMag;
setNormalizedCoefficients(b0, b1, b2, 1, a1, a2);
}
void Biquad::setAllpassPole(std::complex<double> pole)
{
std::complex<double> zero = std::complex<double>(1, 0) / pole;
setZeroPolePairs(zero, pole);
}
void Biquad::getFrequencyResponse(int nFrequencies,
const float* frequency,
float* magResponse,
float* phaseResponse)
{
// Evaluate the Z-transform of the filter at given normalized
// frequency from 0 to 1. (1 corresponds to the Nyquist
// frequency.)
//
// The z-transform of the filter is
//
// H(z) = (b0 + b1*z^(-1) + b2*z^(-2))/(1 + a1*z^(-1) + a2*z^(-2))
//
// Evaluate as
//
// b0 + (b1 + b2*z1)*z1
// --------------------
// 1 + (a1 + a2*z1)*z1
//
// with z1 = 1/z and z = exp(j*pi*frequency). Hence z1 = exp(-j*pi*frequency)
// Make local copies of the coefficients as a micro-optimization.
double b0 = m_b0;
double b1 = m_b1;
double b2 = m_b2;
double a1 = m_a1;
double a2 = m_a2;
for (int k = 0; k < nFrequencies; ++k) {
double omega = -piDouble * frequency[k];
std::complex<double> z = std::complex<double>(cos(omega), sin(omega));
std::complex<double> numerator = b0 + (b1 + b2 * z) * z;
std::complex<double> denominator = std::complex<double>(1, 0) + (a1 + a2 * z) * z;
std::complex<double> response = numerator / denominator;
magResponse[k] = static_cast<float>(abs(response));
phaseResponse[k] = static_cast<float>(atan2(imag(response), real(response)));
}
}
} // namespace WebCore
#endif // ENABLE(WEB_AUDIO)