webaudio/blink/IIRFilter.cpp

// Copyright 2016 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

#include "IIRFilter.h"

#include "DenormalDisabler.h"

#include <mozilla/Assertions.h>

#include <complex>

namespace blink {

// The length of the memory buffers for the IIR filter.  This MUST be a power of
// two and must be greater than the possible length of the filter coefficients.
const int kBufferLength = 32;
static_assert(kBufferLength >= IIRFilter::kMaxOrder + 1,
              "Internal IIR buffer length must be greater than maximum IIR "
              "Filter order.");

IIRFilter::IIRFilter(const AudioDoubleArray* feedforwardCoef,
                     const AudioDoubleArray* feedbackCoef)
    : m_bufferIndex(0),
      m_feedback(feedbackCoef),
      m_feedforward(feedforwardCoef) {
  m_xBuffer.SetLength(kBufferLength);
  m_yBuffer.SetLength(kBufferLength);
  reset();
}

IIRFilter::~IIRFilter() = default;

void IIRFilter::reset() {
  memset(m_xBuffer.Elements(), 0, m_xBuffer.Length() * sizeof(double));
  memset(m_yBuffer.Elements(), 0, m_yBuffer.Length() * sizeof(double));
}

static std::complex<double> evaluatePolynomial(const double* coef,
                                               std::complex<double> z,
                                               int order) {
  // Use Horner's method to evaluate the polynomial P(z) = sum(coef[k]*z^k, k,
  // 0, order);
  std::complex<double> result = 0;

  for (int k = order; k >= 0; --k)
    result = result * z + std::complex<double>(coef[k]);

  return result;
}

void IIRFilter::process(const float* sourceP, float* destP,
                        size_t framesToProcess) {
  // Compute
  //
  //   y[n] = sum(b[k] * x[n - k], k = 0, M) - sum(a[k] * y[n - k], k = 1, N)
  //
  // where b[k] are the feedforward coefficients and a[k] are the feedback
  // coefficients of the filter.

  // This is a Direct Form I implementation of an IIR Filter.  Should we
  // consider doing a different implementation such as Transposed Direct Form
  // II?
  const double* feedback = m_feedback->Elements();
  const double* feedforward = m_feedforward->Elements();

  MOZ_ASSERT(feedback);
  MOZ_ASSERT(feedforward);

  // Sanity check to see if the feedback coefficients have been scaled
  // appropriately. It must be EXACTLY 1!
  MOZ_ASSERT(feedback[0] == 1);

  int feedbackLength = m_feedback->Length();
  int feedforwardLength = m_feedforward->Length();
  int minLength = std::min(feedbackLength, feedforwardLength);

  double* xBuffer = m_xBuffer.Elements();
  double* yBuffer = m_yBuffer.Elements();

  for (size_t n = 0; n < framesToProcess; ++n) {
    // To help minimize roundoff, we compute using double's, even though the
    // filter coefficients only have single precision values.
    double yn = feedforward[0] * sourceP[n];

    // Run both the feedforward and feedback terms together, when possible.
    for (int k = 1; k < minLength; ++k) {
      int n = (m_bufferIndex - k) & (kBufferLength - 1);
      yn += feedforward[k] * xBuffer[n];
      yn -= feedback[k] * yBuffer[n];
    }

    // Handle any remaining feedforward or feedback terms.
    for (int k = minLength; k < feedforwardLength; ++k)
      yn += feedforward[k] * xBuffer[(m_bufferIndex - k) & (kBufferLength - 1)];

    for (int k = minLength; k < feedbackLength; ++k)
      yn -= feedback[k] * yBuffer[(m_bufferIndex - k) & (kBufferLength - 1)];

    // Save the current input and output values in the memory buffers for the
    // next output.
    m_xBuffer[m_bufferIndex] = sourceP[n];
    m_yBuffer[m_bufferIndex] = yn;

    m_bufferIndex = (m_bufferIndex + 1) & (kBufferLength - 1);

    // Avoid introducing a stream of subnormals
    destP[n] = WebCore::DenormalDisabler::flushDenormalFloatToZero(yn);
    MOZ_ASSERT(destP[n] == 0.0 || fabs(destP[n]) > FLT_MIN || IsNaN(destP[n]),
               "output should not be subnormal, but can be NaN");
  }
}

void IIRFilter::getFrequencyResponse(int nFrequencies, const float* frequency,
                                     float* magResponse, float* phaseResponse) {
  // Evaluate the z-transform of the filter at the given normalized frequencies
  // from 0 to 1. (One corresponds to the Nyquist frequency.)
  //
  // The z-tranform of the filter is
  //
  // H(z) = sum(b[k]*z^(-k), k, 0, M) / sum(a[k]*z^(-k), k, 0, N);
  //
  // The desired frequency response is H(exp(j*omega)), where omega is in
  // [0, 1).
  //
  // Let P(x) = sum(c[k]*x^k, k, 0, P) be a polynomial of order P.  Then each of
  // the sums in H(z) is equivalent to evaluating a polynomial at the point 1/z.

  for (int k = 0; k < nFrequencies; ++k) {
    // zRecip = 1/z = exp(-j*frequency)
    double omega = -M_PI * frequency[k];
    std::complex<double> zRecip = std::complex<double>(cos(omega), sin(omega));

    std::complex<double> numerator = evaluatePolynomial(
        m_feedforward->Elements(), zRecip, m_feedforward->Length() - 1);
    std::complex<double> denominator = evaluatePolynomial(
        m_feedback->Elements(), zRecip, m_feedback->Length() - 1);
    // Strangely enough, using complex division:
    // e.g. Complex response = numerator / denominator;
    // fails on our test machines, yielding infinities and NaNs, so we do
    // things the long way here.
    double n = norm(denominator);
    double r = (real(numerator) * real(denominator) +
                imag(numerator) * imag(denominator)) /
               n;
    double i = (imag(numerator) * real(denominator) -
                real(numerator) * imag(denominator)) /
               n;
    std::complex<double> response = std::complex<double>(r, i);

    magResponse[k] = static_cast<float>(abs(response));
    phaseResponse[k] =
        static_cast<float>(atan2(imag(response), real(response)));
  }
}

bool IIRFilter::buffersAreZero() {
  double* xBuffer = m_xBuffer.Elements();
  double* yBuffer = m_yBuffer.Elements();

  for (size_t k = 0; k < m_feedforward->Length(); ++k) {
    if (xBuffer[(m_bufferIndex - k) & (kBufferLength - 1)] != 0.0) {
      return false;
    }
  }

  for (size_t k = 0; k < m_feedback->Length(); ++k) {
    if (fabs(yBuffer[(m_bufferIndex - k) & (kBufferLength - 1)]) >= FLT_MIN) {
      return false;
    }
  }

  return true;
}

}  // namespace blink