fft.cpp

using cd = complex<double>;
const double PI = acos(-1);

void fft(vector<cd>& a, bool invert) {
  int n = a.size();

  for (int i = 1, j = 0; i < n; i++) {
    int bit = n >> 1;
    for (; j & bit; bit >>= 1) j ^= bit;
    j ^= bit;

    if (i < j) swap(a[i], a[j]);
  }

  for (int len = 2; len <= n; len <<= 1) {
    double ang = 2 * PI / len * (invert ? -1 : 1);
    cd wlen(cos(ang), sin(ang));
    for (int i = 0; i < n; i += len) {
      cd w(1);
      for (int j = 0; j < len / 2; j++) {
        cd u = a[i + j], v = a[i + j + len / 2] * w;
        a[i + j] = u + v;
        a[i + j + len / 2] = u - v;
        w *= wlen;
      }
    }
  }

  if (invert) {
    for (cd& x : a) x /= n;
  }
}

void fft_2d(vector<vector<cd>>& V, bool invert) {
  for (int i = 0; i < V.size(); i++) fft(V[i], invert);
  for (int i = 0; i < V.front().size(); i++) {
    vector<cd> col(V.size());
    for (int k = 0; k < V.size(); k++) col[k] = V[k][i];
    fft(col, invert);
    for (int k = 0; k < V.size(); k++) V[k][i] = col[k];
  }
}