AudioFFT.cpp

// ==================================================================================
// Copyright (c) 2017 HiFi-LoFi
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is furnished
// to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
// FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
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// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
// ==================================================================================

#include "AudioFFT.h"

#include <cassert>
#include <cmath>
#include <cstring>


#if defined(AUDIOFFT_APPLE_ACCELERATE)
  #define AUDIOFFT_APPLE_ACCELERATE_USED
  #include <Accelerate/Accelerate.h>
  #include <vector>
#elif defined (AUDIOFFT_FFTW3)
  #define AUDIOFFT_FFTW3_USED
  #include <fftw3.h>
#else
  #if !defined(AUDIOFFT_OOURA)
    #define AUDIOFFT_OOURA
  #endif
  #define AUDIOFFT_OOURA_USED
  #include <vector>
#endif


namespace audiofft
{

  namespace detail
  {

    class AudioFFTImpl
    {
    public:
      AudioFFTImpl() = default;
      AudioFFTImpl(const AudioFFTImpl&) = delete;
      AudioFFTImpl& operator=(const AudioFFTImpl&) = delete;
      virtual ~AudioFFTImpl() = default;
      virtual void init(size_t size) = 0;
      virtual void fft(const float* data, float* re, float* im) = 0;
      virtual void ifft(float* data, const float* re, const float* im) = 0;
    };


    constexpr bool IsPowerOf2(size_t val)
    {
      return (val == 1 || (val & (val-1)) == 0);
    }


    template<typename TypeDest, typename TypeSrc>
    void ConvertBuffer(TypeDest* dest, const TypeSrc* src, size_t len)
    {
      for (size_t i=0; i<len; ++i)
      {
        dest[i] = static_cast<TypeDest>(src[i]);
      }
    }


    template<typename TypeDest, typename TypeSrc, typename TypeFactor>
    void ScaleBuffer(TypeDest* dest, const TypeSrc* src, const TypeFactor factor, size_t len)
    {
      for (size_t i=0; i<len; ++i)
      {
        dest[i] = static_cast<TypeDest>(static_cast<TypeFactor>(src[i]) * factor);
      }
    }

  } // End of namespace detail


  // ================================================================


#ifdef AUDIOFFT_OOURA_USED

  /**
   * @internal
   * @class OouraFFT
   * @brief FFT implementation based on the great radix-4 routines by Takuya Ooura
   */
  class OouraFFT : public detail::AudioFFTImpl
  {
  public:
    OouraFFT() :
      detail::AudioFFTImpl(),
      _size(0),
      _ip(),
      _w(),
      _buffer()
    {
    }

    OouraFFT(const OouraFFT&) = delete;
    OouraFFT& operator=(const OouraFFT&) = delete;

    virtual void init(size_t size) override
    {
      if (_size != size)
      {
        _ip.resize(2 + static_cast<int>(std::sqrt(static_cast<double>(size))));
        _w.resize(size / 2);
        _buffer.resize(size);
        _size = size;

        const int size4 = static_cast<int>(_size) / 4;
        makewt(size4, _ip.data(), _w.data());
        makect(size4, _ip.data(), _w.data() + size4);
      }
    }

    virtual void fft(const float* data, float* re, float* im) override
    {
      // Convert into the format as required by the Ooura FFT
      detail::ConvertBuffer(_buffer.data(), data, _size);

      rdft(static_cast<int>(_size), +1, _buffer.data(), _ip.data(), _w.data());

      // Convert back to split-complex
      {
        double* b = _buffer.data();
        double* bEnd = b + _size;
        float *r = re;
        float *i = im;
        while (b != bEnd)
        {
          *(r++) = static_cast<float>(*(b++));
          *(i++) = static_cast<float>(-(*(b++)));
        }
      }
      const size_t size2 = _size / 2;
      re[size2] = -im[0];
      im[0] = 0.0;
      im[size2] = 0.0;
    }

    virtual void ifft(float* data, const float* re, const float* im) override
    {
      // Convert into the format as required by the Ooura FFT
      {
        double* b = _buffer.data();
        double* bEnd = b + _size;
        const float *r = re;
        const float *i = im;
        while (b != bEnd)
        {
          *(b++) = static_cast<double>(*(r++));
          *(b++) = -static_cast<double>(*(i++));
        }
        _buffer[1] = re[_size / 2];
      }

      rdft(static_cast<int>(_size), -1, _buffer.data(), _ip.data(), _w.data());

      // Convert back to split-complex
      detail::ScaleBuffer(data, _buffer.data(), 2.0 / static_cast<double>(_size), _size);
    }

  private:
    size_t _size;
    std::vector<int> _ip;
    std::vector<double> _w;
    std::vector<double> _buffer;

    void rdft(int n, int isgn, double *a, int *ip, double *w)
    {
      int nw = ip[0];
      int nc = ip[1];

      if (isgn >= 0)
      {
        if (n > 4)
        {
          bitrv2(n, ip + 2, a);
          cftfsub(n, a, w);
          rftfsub(n, a, nc, w + nw);
        }
        else if (n == 4)
        {
          cftfsub(n, a, w);
        }
        double xi = a[0] - a[1];
        a[0] += a[1];
        a[1] = xi;
      }
      else
      {
        a[1] = 0.5 * (a[0] - a[1]);
        a[0] -= a[1];
        if (n > 4)
        {
          rftbsub(n, a, nc, w + nw);
          bitrv2(n, ip + 2, a);
          cftbsub(n, a, w);
        }
        else if (n == 4)
        {
          cftfsub(n, a, w);
        }
      }
    }


    /* -------- initializing routines -------- */

    void makewt(int nw, int *ip, double *w)
    {
      int j, nwh;
      double delta, x, y;

      ip[0] = nw;
      ip[1] = 1;
      if (nw > 2) {
        nwh = nw >> 1;
        delta = atan(1.0) / nwh;
        w[0] = 1;
        w[1] = 0;
        w[nwh] = cos(delta * nwh);
        w[nwh + 1] = w[nwh];
        if (nwh > 2) {
          for (j = 2; j < nwh; j += 2) {
            x = cos(delta * j);
            y = sin(delta * j);
            w[j] = x;
            w[j + 1] = y;
            w[nw - j] = y;
            w[nw - j + 1] = x;
          }
          bitrv2(nw, ip + 2, w);
        }
      }
    }


    void makect(int nc, int *ip, double *c)
    {
      int j, nch;
      double delta;

      ip[1] = nc;
      if (nc > 1) {
        nch = nc >> 1;
        delta = atan(1.0) / nch;
        c[0] = cos(delta * nch);
        c[nch] = 0.5 * c[0];
        for (j = 1; j < nch; j++) {
          c[j] = 0.5 * cos(delta * j);
          c[nc - j] = 0.5 * sin(delta * j);
        }
      }
    }


    /* -------- child routines -------- */


    void bitrv2(int n, int *ip, double *a)
    {
      int j, j1, k, k1, l, m, m2;
      double xr, xi, yr, yi;

      ip[0] = 0;
      l = n;
      m = 1;
      while ((m << 3) < l) {
        l >>= 1;
        for (j = 0; j < m; j++) {
          ip[m + j] = ip[j] + l;
        }
        m <<= 1;
      }
      m2 = 2 * m;
      if ((m << 3) == l) {
        for (k = 0; k < m; k++) {
          for (j = 0; j < k; j++) {
            j1 = 2 * j + ip[k];
            k1 = 2 * k + ip[j];
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 += m2;
            k1 += 2 * m2;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 += m2;
            k1 -= m2;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 += m2;
            k1 += 2 * m2;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
          }
          j1 = 2 * k + m2 + ip[k];
          k1 = j1 + m2;
          xr = a[j1];
          xi = a[j1 + 1];
          yr = a[k1];
          yi = a[k1 + 1];
          a[j1] = yr;
          a[j1 + 1] = yi;
          a[k1] = xr;
          a[k1 + 1] = xi;
        }
      } else {
        for (k = 1; k < m; k++) {
          for (j = 0; j < k; j++) {
            j1 = 2 * j + ip[k];
            k1 = 2 * k + ip[j];
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 += m2;
            k1 += m2;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
          }
        }
      }
    }


    void cftfsub(int n, double *a, double *w)
    {
      int j, j1, j2, j3, l;
      double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

      l = 2;
      if (n > 8) {
        cft1st(n, a, w);
        l = 8;
        while ((l << 2) < n) {
          cftmdl(n, l, a, w);
          l <<= 2;
        }
      }
      if ((l << 2) == n) {
        for (j = 0; j < l; j += 2) {
          j1 = j + l;
          j2 = j1 + l;
          j3 = j2 + l;
          x0r = a[j] + a[j1];
          x0i = a[j + 1] + a[j1 + 1];
          x1r = a[j] - a[j1];
          x1i = a[j + 1] - a[j1 + 1];
          x2r = a[j2] + a[j3];
          x2i = a[j2 + 1] + a[j3 + 1];
          x3r = a[j2] - a[j3];
          x3i = a[j2 + 1] - a[j3 + 1];
          a[j] = x0r + x2r;
          a[j + 1] = x0i + x2i;
          a[j2] = x0r - x2r;
          a[j2 + 1] = x0i - x2i;
          a[j1] = x1r - x3i;
          a[j1 + 1] = x1i + x3r;
          a[j3] = x1r + x3i;
          a[j3 + 1] = x1i - x3r;
        }
      } else {
        for (j = 0; j < l; j += 2) {
          j1 = j + l;
          x0r = a[j] - a[j1];
          x0i = a[j + 1] - a[j1 + 1];
          a[j] += a[j1];
          a[j + 1] += a[j1 + 1];
          a[j1] = x0r;
          a[j1 + 1] = x0i;
        }
      }
    }


    void cftbsub(int n, double *a, double *w)
    {
      int j, j1, j2, j3, l;
      double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

      l = 2;
      if (n > 8) {
        cft1st(n, a, w);
        l = 8;
        while ((l << 2) < n) {
          cftmdl(n, l, a, w);
          l <<= 2;
        }
      }
      if ((l << 2) == n) {
        for (j = 0; j < l; j += 2) {
          j1 = j + l;
          j2 = j1 + l;
          j3 = j2 + l;
          x0r = a[j] + a[j1];
          x0i = -a[j + 1] - a[j1 + 1];
          x1r = a[j] - a[j1];
          x1i = -a[j + 1] + a[j1 + 1];
          x2r = a[j2] + a[j3];
          x2i = a[j2 + 1] + a[j3 + 1];
          x3r = a[j2] - a[j3];
          x3i = a[j2 + 1] - a[j3 + 1];
          a[j] = x0r + x2r;
          a[j + 1] = x0i - x2i;
          a[j2] = x0r - x2r;
          a[j2 + 1] = x0i + x2i;
          a[j1] = x1r - x3i;
          a[j1 + 1] = x1i - x3r;
          a[j3] = x1r + x3i;
          a[j3 + 1] = x1i + x3r;
        }
      } else {
        for (j = 0; j < l; j += 2) {
          j1 = j + l;
          x0r = a[j] - a[j1];
          x0i = -a[j + 1] + a[j1 + 1];
          a[j] += a[j1];
          a[j + 1] = -a[j + 1] - a[j1 + 1];
          a[j1] = x0r;
          a[j1 + 1] = x0i;
        }
      }
    }


    void cft1st(int n, double *a, double *w)
    {
      int j, k1, k2;
      double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
      double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

      x0r = a[0] + a[2];
      x0i = a[1] + a[3];
      x1r = a[0] - a[2];
      x1i = a[1] - a[3];
      x2r = a[4] + a[6];
      x2i = a[5] + a[7];
      x3r = a[4] - a[6];
      x3i = a[5] - a[7];
      a[0] = x0r + x2r;
      a[1] = x0i + x2i;
      a[4] = x0r - x2r;
      a[5] = x0i - x2i;
      a[2] = x1r - x3i;
      a[3] = x1i + x3r;
      a[6] = x1r + x3i;
      a[7] = x1i - x3r;
      wk1r = w[2];
      x0r = a[8] + a[10];
      x0i = a[9] + a[11];
      x1r = a[8] - a[10];
      x1i = a[9] - a[11];
      x2r = a[12] + a[14];
      x2i = a[13] + a[15];
      x3r = a[12] - a[14];
      x3i = a[13] - a[15];
      a[8] = x0r + x2r;
      a[9] = x0i + x2i;
      a[12] = x2i - x0i;
      a[13] = x0r - x2r;
      x0r = x1r - x3i;
      x0i = x1i + x3r;
      a[10] = wk1r * (x0r - x0i);
      a[11] = wk1r * (x0r + x0i);
      x0r = x3i + x1r;
      x0i = x3r - x1i;
      a[14] = wk1r * (x0i - x0r);
      a[15] = wk1r * (x0i + x0r);
      k1 = 0;
      for (j = 16; j < n; j += 16) {
        k1 += 2;
        k2 = 2 * k1;
        wk2r = w[k1];
        wk2i = w[k1 + 1];
        wk1r = w[k2];
        wk1i = w[k2 + 1];
        wk3r = wk1r - 2 * wk2i * wk1i;
        wk3i = 2 * wk2i * wk1r - wk1i;
        x0r = a[j] + a[j + 2];
        x0i = a[j + 1] + a[j + 3];
        x1r = a[j] - a[j + 2];
        x1i = a[j + 1] - a[j + 3];
        x2r = a[j + 4] + a[j + 6];
        x2i = a[j + 5] + a[j + 7];
        x3r = a[j + 4] - a[j + 6];
        x3i = a[j + 5] - a[j + 7];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        x0r -= x2r;
        x0i -= x2i;
        a[j + 4] = wk2r * x0r - wk2i * x0i;
        a[j + 5] = wk2r * x0i + wk2i * x0r;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j + 2] = wk1r * x0r - wk1i * x0i;
        a[j + 3] = wk1r * x0i + wk1i * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j + 6] = wk3r * x0r - wk3i * x0i;
        a[j + 7] = wk3r * x0i + wk3i * x0r;
        wk1r = w[k2 + 2];
        wk1i = w[k2 + 3];
        wk3r = wk1r - 2 * wk2r * wk1i;
        wk3i = 2 * wk2r * wk1r - wk1i;
        x0r = a[j + 8] + a[j + 10];
        x0i = a[j + 9] + a[j + 11];
        x1r = a[j + 8] - a[j + 10];
        x1i = a[j + 9] - a[j + 11];
        x2r = a[j + 12] + a[j + 14];
        x2i = a[j + 13] + a[j + 15];
        x3r = a[j + 12] - a[j + 14];
        x3i = a[j + 13] - a[j + 15];
        a[j + 8] = x0r + x2r;
        a[j + 9] = x0i + x2i;
        x0r -= x2r;
        x0i -= x2i;
        a[j + 12] = -wk2i * x0r - wk2r * x0i;
        a[j + 13] = -wk2i * x0i + wk2r * x0r;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j + 10] = wk1r * x0r - wk1i * x0i;
        a[j + 11] = wk1r * x0i + wk1i * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j + 14] = wk3r * x0r - wk3i * x0i;
        a[j + 15] = wk3r * x0i + wk3i * x0r;
      }
    }


    void cftmdl(int n, int l, double *a, double *w)
    {
      int j, j1, j2, j3, k, k1, k2, m, m2;
      double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
      double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

      m = l << 2;
      for (j = 0; j < l; j += 2) {
        j1 = j + l;
        j2 = j1 + l;
        j3 = j2 + l;
        x0r = a[j] + a[j1];
        x0i = a[j + 1] + a[j1 + 1];
        x1r = a[j] - a[j1];
        x1i = a[j + 1] - a[j1 + 1];
        x2r = a[j2] + a[j3];
        x2i = a[j2 + 1] + a[j3 + 1];
        x3r = a[j2] - a[j3];
        x3i = a[j2 + 1] - a[j3 + 1];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        a[j2] = x0r - x2r;
        a[j2 + 1] = x0i - x2i;
        a[j1] = x1r - x3i;
        a[j1 + 1] = x1i + x3r;
        a[j3] = x1r + x3i;
        a[j3 + 1] = x1i - x3r;
      }
      wk1r = w[2];
      for (j = m; j < l + m; j += 2) {
        j1 = j + l;
        j2 = j1 + l;
        j3 = j2 + l;
        x0r = a[j] + a[j1];
        x0i = a[j + 1] + a[j1 + 1];
        x1r = a[j] - a[j1];
        x1i = a[j + 1] - a[j1 + 1];
        x2r = a[j2] + a[j3];
        x2i = a[j2 + 1] + a[j3 + 1];
        x3r = a[j2] - a[j3];
        x3i = a[j2 + 1] - a[j3 + 1];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        a[j2] = x2i - x0i;
        a[j2 + 1] = x0r - x2r;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j1] = wk1r * (x0r - x0i);
        a[j1 + 1] = wk1r * (x0r + x0i);
        x0r = x3i + x1r;
        x0i = x3r - x1i;
        a[j3] = wk1r * (x0i - x0r);
        a[j3 + 1] = wk1r * (x0i + x0r);
      }
      k1 = 0;
      m2 = 2 * m;
      for (k = m2; k < n; k += m2) {
        k1 += 2;
        k2 = 2 * k1;
        wk2r = w[k1];
        wk2i = w[k1 + 1];
        wk1r = w[k2];
        wk1i = w[k2 + 1];
        wk3r = wk1r - 2 * wk2i * wk1i;
        wk3i = 2 * wk2i * wk1r - wk1i;
        for (j = k; j < l + k; j += 2) {
          j1 = j + l;
          j2 = j1 + l;
          j3 = j2 + l;
          x0r = a[j] + a[j1];
          x0i = a[j + 1] + a[j1 + 1];
          x1r = a[j] - a[j1];
          x1i = a[j + 1] - a[j1 + 1];
          x2r = a[j2] + a[j3];
          x2i = a[j2 + 1] + a[j3 + 1];
          x3r = a[j2] - a[j3];
          x3i = a[j2 + 1] - a[j3 + 1];
          a[j] = x0r + x2r;
          a[j + 1] = x0i + x2i;
          x0r -= x2r;
          x0i -= x2i;
          a[j2] = wk2r * x0r - wk2i * x0i;
          a[j2 + 1] = wk2r * x0i + wk2i * x0r;
          x0r = x1r - x3i;
          x0i = x1i + x3r;
          a[j1] = wk1r * x0r - wk1i * x0i;
          a[j1 + 1] = wk1r * x0i + wk1i * x0r;
          x0r = x1r + x3i;
          x0i = x1i - x3r;
          a[j3] = wk3r * x0r - wk3i * x0i;
          a[j3 + 1] = wk3r * x0i + wk3i * x0r;
        }
        wk1r = w[k2 + 2];
        wk1i = w[k2 + 3];
        wk3r = wk1r - 2 * wk2r * wk1i;
        wk3i = 2 * wk2r * wk1r - wk1i;
        for (j = k + m; j < l + (k + m); j += 2) {
          j1 = j + l;
          j2 = j1 + l;
          j3 = j2 + l;
          x0r = a[j] + a[j1];
          x0i = a[j + 1] + a[j1 + 1];
          x1r = a[j] - a[j1];
          x1i = a[j + 1] - a[j1 + 1];
          x2r = a[j2] + a[j3];
          x2i = a[j2 + 1] + a[j3 + 1];
          x3r = a[j2] - a[j3];
          x3i = a[j2 + 1] - a[j3 + 1];
          a[j] = x0r + x2r;
          a[j + 1] = x0i + x2i;
          x0r -= x2r;
          x0i -= x2i;
          a[j2] = -wk2i * x0r - wk2r * x0i;
          a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
          x0r = x1r - x3i;
          x0i = x1i + x3r;
          a[j1] = wk1r * x0r - wk1i * x0i;
          a[j1 + 1] = wk1r * x0i + wk1i * x0r;
          x0r = x1r + x3i;
          x0i = x1i - x3r;
          a[j3] = wk3r * x0r - wk3i * x0i;
          a[j3 + 1] = wk3r * x0i + wk3i * x0r;
        }
      }
    }


    void rftfsub(int n, double *a, int nc, double *c)
    {
      int j, k, kk, ks, m;
      double wkr, wki, xr, xi, yr, yi;

      m = n >> 1;
      ks = 2 * nc / m;
      kk = 0;
      for (j = 2; j < m; j += 2) {
        k = n - j;
        kk += ks;
        wkr = 0.5 - c[nc - kk];
        wki = c[kk];
        xr = a[j] - a[k];
        xi = a[j + 1] + a[k + 1];
        yr = wkr * xr - wki * xi;
        yi = wkr * xi + wki * xr;
        a[j] -= yr;
        a[j + 1] -= yi;
        a[k] += yr;
        a[k + 1] -= yi;
      }
    }


    void rftbsub(int n, double *a, int nc, double *c)
    {
      int j, k, kk, ks, m;
      double wkr, wki, xr, xi, yr, yi;

      a[1] = -a[1];
      m = n >> 1;
      ks = 2 * nc / m;
      kk = 0;
      for (j = 2; j < m; j += 2) {
        k = n - j;
        kk += ks;
        wkr = 0.5 - c[nc - kk];
        wki = c[kk];
        xr = a[j] - a[k];
        xi = a[j + 1] + a[k + 1];
        yr = wkr * xr + wki * xi;
        yi = wkr * xi - wki * xr;
        a[j] -= yr;
        a[j + 1] = yi - a[j + 1];
        a[k] += yr;
        a[k + 1] = yi - a[k + 1];
      }
      a[m + 1] = -a[m + 1];
    }
  };


  /**
   * @internal
   * @brief Concrete FFT implementation
   */
  typedef OouraFFT AudioFFTImplementation;


#endif // AUDIOFFT_OOURA_USED


  // ================================================================


#ifdef AUDIOFFT_APPLE_ACCELERATE_USED


  /**
   * @internal
   * @class AppleAccelerateFFT
   * @brief FFT implementation using the Apple Accelerate framework internally
   */
  class AppleAccelerateFFT : public detail::AudioFFTImpl
  {
  public:
    AppleAccelerateFFT() :
      detail::AudioFFTImpl(),
      _size(0),
      _powerOf2(0),
      _fftSetup(0),
      _re(),
      _im()
    {
    }

    AppleAccelerateFFT(const AppleAccelerateFFT&) = delete;
    AppleAccelerateFFT& operator=(const AppleAccelerateFFT&) = delete;

    virtual ~AppleAccelerateFFT()
    {
      init(0);
    }

    virtual void init(size_t size) override
    {
      if (_fftSetup)
      {
        vDSP_destroy_fftsetup(_fftSetup);
        _size = 0;
        _powerOf2 = 0;
        _fftSetup = 0;
        _re.clear();
        _im.clear();
      }

      if (size > 0)
      {
        _size = size;
        _powerOf2 = 0;
        while ((1 << _powerOf2) < _size)
        {
          ++_powerOf2;
        }
        _fftSetup = vDSP_create_fftsetup(_powerOf2, FFT_RADIX2);
        _re.resize(_size / 2);
        _im.resize(_size / 2);
      }
    }

    virtual void fft(const float* data, float* re, float* im) override
    {
      const size_t size2 = _size / 2;
      DSPSplitComplex splitComplex;
      splitComplex.realp = re;
      splitComplex.imagp = im;
      vDSP_ctoz(reinterpret_cast<const COMPLEX*>(data), 2, &splitComplex, 1, size2);
      vDSP_fft_zrip(_fftSetup, &splitComplex, 1, _powerOf2, FFT_FORWARD);
      const float factor = 0.5f;
      vDSP_vsmul(re, 1, &factor, re, 1, size2);
      vDSP_vsmul(im, 1, &factor, im, 1, size2);
      re[size2] = im[0];
      im[0] = 0.0f;
      im[size2] = 0.0f;
    }

    virtual void ifft(float* data, const float* re, const float* im) override
    {
      const size_t size2 = _size / 2;
      ::memcpy(_re.data(), re, size2 * sizeof(float));
      ::memcpy(_im.data(), im, size2 * sizeof(float));
      _im[0] = re[size2];
      DSPSplitComplex splitComplex;
      splitComplex.realp = _re.data();
      splitComplex.imagp = _im.data();
      vDSP_fft_zrip(_fftSetup, &splitComplex, 1, _powerOf2, FFT_INVERSE);
      vDSP_ztoc(&splitComplex, 1, reinterpret_cast<COMPLEX*>(data), 2, size2);
      const float factor = 1.0f / static_cast<float>(_size);
      vDSP_vsmul(data, 1, &factor, data, 1, _size);
    }

  private:
    size_t _size;
    size_t _powerOf2;
    FFTSetup _fftSetup;
    std::vector<float> _re;
    std::vector<float> _im;
  };


  /**
   * @internal
   * @brief Concrete FFT implementation
   */
  typedef AppleAccelerateFFT AudioFFTImplementation;


#endif // AUDIOFFT_APPLE_ACCELERATE_USED


  // ================================================================


#ifdef AUDIOFFT_FFTW3_USED


  /**
   * @internal
   * @class FFTW3FFT
   * @brief FFT implementation using FFTW3 internally (see fftw.org)
   */
  class FFTW3FFT : public detail::AudioFFTImpl
  {
  public:
    FFTW3FFT() :
      detail::AudioFFTImpl(),
      _size(0),
      _complexSize(0),
      _planForward(0),
      _planBackward(0),
      _data(0),
      _re(0),
      _im(0)
    {
    }

    FFTW3FFT(const FFTW3FFT&) = delete;
    FFTW3FFT& operator=(const FFTW3FFT&) = delete;

    virtual ~FFTW3FFT()
    {
      init(0);
    }

    virtual void init(size_t size) override
    {
      if (_size != size)
      {
        if (_size > 0)
        {
          fftwf_destroy_plan(_planForward);
          fftwf_destroy_plan(_planBackward);
          _planForward = 0;
          _planBackward = 0;
          _size = 0;
          _complexSize = 0;

          if (_data)
          {
            fftwf_free(_data);
            _data = 0;
          }

          if (_re)
          {
            fftwf_free(_re);
            _re = 0;
          }

          if (_im)
          {
            fftwf_free(_im);
            _im = 0;
          }
        }

        if (size > 0)
        {
          _size = size;
          _complexSize = AudioFFT::ComplexSize(_size);
          const size_t complexSize = AudioFFT::ComplexSize(_size);
          _data = reinterpret_cast<float*>(fftwf_malloc(_size * sizeof(float)));
          _re = reinterpret_cast<float*>(fftwf_malloc(complexSize * sizeof(float)));
          _im = reinterpret_cast<float*>(fftwf_malloc(complexSize * sizeof(float)));

          fftw_iodim dim;
          dim.n = static_cast<int>(size);
          dim.is = 1;
          dim.os = 1;
          _planForward = fftwf_plan_guru_split_dft_r2c(1, &dim, 0, 0, _data, _re, _im, FFTW_MEASURE);
          _planBackward = fftwf_plan_guru_split_dft_c2r(1, &dim, 0, 0, _re, _im, _data, FFTW_MEASURE);
        }
      }
    }

    virtual void fft(const float* data, float* re, float* im) override
    {
      ::memcpy(_data, data, _size * sizeof(float));
      fftwf_execute_split_dft_r2c(_planForward, _data, _re, _im);
      ::memcpy(re, _re, _complexSize * sizeof(float));
      ::memcpy(im, _im, _complexSize * sizeof(float));
    }

    virtual void ifft(float* data, const float* re, const float* im) override
    {
      ::memcpy(_re, re, _complexSize * sizeof(float));
      ::memcpy(_im, im, _complexSize * sizeof(float));
      fftwf_execute_split_dft_c2r(_planBackward, _re, _im, _data);
      detail::ScaleBuffer(data, _data, 1.0f / static_cast<float>(_size), _size);
    }

  private:
    size_t _size;
    size_t _complexSize;
    fftwf_plan _planForward;
    fftwf_plan _planBackward;
    float* _data;
    float* _re;
    float* _im;
  };


  /**
   * @internal
   * @brief Concrete FFT implementation
   */
  typedef FFTW3FFT AudioFFTImplementation;


#endif // AUDIOFFT_FFTW3_USED


  // =============================================================


  AudioFFT::AudioFFT() :
    _impl(new AudioFFTImplementation())
  {
  }


  AudioFFT::~AudioFFT()
  {
  }


  void AudioFFT::init(size_t size)
  {
    assert(detail::IsPowerOf2(size));
    _impl->init(size);
  }


  void AudioFFT::fft(const float* data, float* re, float* im)
  {
    _impl->fft(data, re, im);
  }


  void AudioFFT::ifft(float* data, const float* re, const float* im)
  {
    _impl->ifft(data, re, im);
  }


  size_t AudioFFT::ComplexSize(size_t size)
  {
    return (size / 2) + 1;
  }

} // End of namespace