/*
 * http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html
 * Copyright Takuya OOURA, 1996-2001
 *
 * You may use, copy, modify and distribute this code for any purpose (include
 * commercial use) and without fee. Please refer to this package when you modify
 * this code.
 *
 * Changes:
 * Trivial type modifications by the WebRTC authors.
 */

/*
Fast Fourier/Cosine/Sine Transform
    dimension   :one
    data length :power of 2
    decimation  :frequency
    radix       :4, 2
    data        :inplace
    table       :use
functions
    cdft: Complex Discrete Fourier Transform
    rdft: Real Discrete Fourier Transform
    ddct: Discrete Cosine Transform
    ddst: Discrete Sine Transform
    dfct: Cosine Transform of RDFT (Real Symmetric DFT)
    dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
function prototypes
    void cdft(int, int, float *, int *, float *);
    void rdft(size_t, int, float *, size_t *, float *);
    void ddct(int, int, float *, int *, float *);
    void ddst(int, int, float *, int *, float *);
    void dfct(int, float *, float *, int *, float *);
    void dfst(int, float *, float *, int *, float *);


-------- Complex DFT (Discrete Fourier Transform) --------
    [definition]
        <case1>
            X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
        <case2>
            X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
        (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
    [usage]
        <case1>
            ip[0] = 0; // first time only
            cdft(2*n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            cdft(2*n, -1, a, ip, w);
    [parameters]
        2*n            :data length (int)
                        n >= 1, n = power of 2
        a[0...2*n-1]   :input/output data (float *)
                        input data
                            a[2*j] = Re(x[j]),
                            a[2*j+1] = Im(x[j]), 0<=j<n
                        output data
                            a[2*k] = Re(X[k]),
                            a[2*k+1] = Im(X[k]), 0<=k<n
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n/2-1]   :cos/sin table (float *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            cdft(2*n, -1, a, ip, w);
        is
            cdft(2*n, 1, a, ip, w);
            for (j = 0; j <= 2 * n - 1; j++) {
                a[j] *= 1.0 / n;
            }
        .


-------- Real DFT / Inverse of Real DFT --------
    [definition]
        <case1> RDFT
            R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
            I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
        <case2> IRDFT (excluding scale)
            a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
                   sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
                   sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            rdft(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            rdft(n, -1, a, ip, w);
    [parameters]
        n              :data length (size_t)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (float *)
                        <case1>
                            output data
                                a[2*k] = R[k], 0<=k<n/2
                                a[2*k+1] = I[k], 0<k<n/2
                                a[1] = R[n/2]
                        <case2>
                            input data
                                a[2*j] = R[j], 0<=j<n/2
                                a[2*j+1] = I[j], 0<j<n/2
                                a[1] = R[n/2]
        ip[0...*]      :work area for bit reversal (size_t *)
                        length of ip >= 2+sqrt(n/2)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n/2-1]   :cos/sin table (float *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            rdft(n, 1, a, ip, w);
        is
            rdft(n, -1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
    [definition]
        <case1> IDCT (excluding scale)
            C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DCT
            C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            ddct(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            ddct(n, -1, a, ip, w);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (float *)
                        output data
                            a[k] = C[k], 0<=k<n
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/2)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/4-1] :cos/sin table (float *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            ddct(n, -1, a, ip, w);
        is
            a[0] *= 0.5;
            ddct(n, 1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DST (Discrete Sine Transform) / Inverse of DST --------
    [definition]
        <case1> IDST (excluding scale)
            S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DST
            S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
    [usage]
        <case1>
            ip[0] = 0; // first time only
            ddst(n, 1, a, ip, w);
        <case2>
            ip[0] = 0; // first time only
            ddst(n, -1, a, ip, w);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (float *)
                        <case1>
                            input data
                                a[j] = A[j], 0<j<n
                                a[0] = A[n]
                            output data
                                a[k] = S[k], 0<=k<n
                        <case2>
                            output data
                                a[k] = S[k], 0<k<n
                                a[0] = S[n]
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/2)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/4-1] :cos/sin table (float *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            ddst(n, -1, a, ip, w);
        is
            a[0] *= 0.5;
            ddst(n, 1, a, ip, w);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
    [definition]
        C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
    [usage]
        ip[0] = 0; // first time only
        dfct(n, a, t, ip, w);
    [parameters]
        n              :data length - 1 (int)
                        n >= 2, n = power of 2
        a[0...n]       :input/output data (float *)
                        output data
                            a[k] = C[k], 0<=k<=n
        t[0...n/2]     :work area (float *)
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/4)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/4+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/8-1] :cos/sin table (float *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a, t, ip, w);
        is
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a, t, ip, w);
            for (j = 0; j <= n; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
    [definition]
        S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
    [usage]
        ip[0] = 0; // first time only
        dfst(n, a, t, ip, w);
    [parameters]
        n              :data length + 1 (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (float *)
                        output data
                            a[k] = S[k], 0<k<n
                        (a[0] is used for work area)
        t[0...n/2-1]   :work area (float *)
        ip[0...*]      :work area for bit reversal (int *)
                        length of ip >= 2+sqrt(n/4)
                        strictly,
                        length of ip >=
                            2+(1<<(int)(log(n/4+0.5)/log(2))/2).
                        ip[0],ip[1] are pointers of the cos/sin table.
        w[0...n*5/8-1] :cos/sin table (float *)
                        w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of
            dfst(n, a, t, ip, w);
        is
            dfst(n, a, t, ip, w);
            for (j = 1; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


Appendix :
    The cos/sin table is recalculated when the larger table required.
    w[] and ip[] are compatible with all routines.
*/

#include <math.h>
#include <stddef.h>

namespace webrtc {

namespace {

void makewt(size_t nw, size_t* ip, float* w);
void makect(size_t nc, size_t* ip, float* c);
void bitrv2(size_t n, size_t* ip, float* a);
void cftfsub(size_t n, float* a, float* w);
void cftbsub(size_t n, float* a, float* w);
void cft1st(size_t n, float* a, float* w);
void cftmdl(size_t n, size_t l, float* a, float* w);
void rftfsub(size_t n, float* a, size_t nc, float* c);
void rftbsub(size_t n, float* a, size_t nc, float* c);

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

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

  ip[0] = nw;
  ip[1] = 1;
  if (nw > 2) {
    nwh = nw >> 1;
    delta = atanf(1.0f) / nwh;
    w[0] = 1;
    w[1] = 0;
    w[nwh] = (float)cos(delta * nwh);
    w[nwh + 1] = w[nwh];
    if (nwh > 2) {
      for (j = 2; j < nwh; j += 2) {
        x = (float)cos(delta * j);
        y = (float)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(size_t nc, size_t* ip, float* c) {
  size_t j, nch;
  float delta;

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

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

void bitrv2(size_t n, size_t* ip, float* a) {
  size_t j, j1, k, k1, l, m, m2;
  float 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(size_t n, float* a, float* w) {
  size_t j, j1, j2, j3, l;
  float 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(size_t n, float* a, float* w) {
  size_t j, j1, j2, j3, l;
  float 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(size_t n, float* a, float* w) {
  size_t j, k1, k2;
  float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
  float 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(size_t n, size_t l, float* a, float* w) {
  size_t j, j1, j2, j3, k, k1, k2, m, m2;
  float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
  float 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(size_t n, float* a, size_t nc, float* c) {
  size_t j, k, kk, ks, m;
  float 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 = 0.5f - 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(size_t n, float* a, size_t nc, float* c) {
  size_t j, k, kk, ks, m;
  float 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 = 0.5f - 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];
}

}  // namespace

void WebRtc_rdft(size_t n, int isgn, float* a, size_t* ip, float* w) {
  size_t nw, nc;
  float xi;

  nw = ip[0];
  if (n > (nw << 2)) {
    nw = n >> 2;
    makewt(nw, ip, w);
  }
  nc = ip[1];
  if (n > (nc << 2)) {
    nc = n >> 2;
    makect(nc, ip, w + nw);
  }
  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);
    }
    xi = a[0] - a[1];
    a[0] += a[1];
    a[1] = xi;
  } else {
    a[1] = 0.5f * (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);
    }
  }
}

}  // namespace webrtc