#include <complex>
#include <iostream>
#include <valarray>

const double PI = 3.141592653589793238460;

typedef std::complex<double> Complex;
typedef std::valarray<Complex> CArray;


void fft(CArray& x)
{
    const size_t N = x.size();
    if (N <= 1) return;

    // divide
    CArray even = x[std::slice(0, N / 2, 2)];
    CArray  odd = x[std::slice(1, N / 2, 2)];

    // conquer
    fft(even);
    fft(odd);

    // combine
    for (size_t k = 0; k < N / 2; ++k)
    {
        Complex t = std::polar(1.0, -2 * PI * k / N) * odd[k];
        x[k] = even[k] + t;
        x[k + N / 2] = even[k] - t;
    }
}
int main()
{
    const Complex test[] = { 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0 };
    CArray data(test, 8);

    // forward fft
    fft(data);

    std::cout << "fft" << std::endl;
    for (int i = 0; i < 8; ++i)
    {
        std::cout << data[i] << std::endl;
    }

    return 0;
}