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

const double PI = 3.141592653589793238460;

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

// Cooley–Tukey FFT (in-place, divide-and-conquer)
// Higher memory requirements and redundancy although more intuitive
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;
    }
}

// Cooley-Tukey FFT (in-place, breadth-first, decimation-in-frequency)
// Better optimized but less intuitive
// !!! Warning : in some cases this code make result different from not optimased version above (need to fix bug)
// The bug is now fixed @2017/05/30
void fft(CArray &x)
{
	// DFT
	unsigned int N = x.size(), k = N, n;
	double thetaT = 3.14159265358979323846264338328L / N;
	Complex phiT = Complex(cos(thetaT), -sin(thetaT)), T;
	while (k > 1)
	{
		n = k;
		k >>= 1;
		phiT = phiT * phiT;
		T = 1.0L;
		for (unsigned int l = 0; l < k; l++)
		{
			for (unsigned int a = l; a < N; a += n)
			{
				unsigned int b = a + k;
				Complex t = x[a] - x[b];
				x[a] += x[b];
				x[b] = t * T;
			}
			T *= phiT;
		}
	}
	// Decimate
	unsigned int m = (unsigned int)log2(N);
	for (unsigned int a = 0; a < N; a++)
	{
		unsigned int b = a;
		// Reverse bits
		b = (((b & 0xaaaaaaaa) >> 1) | ((b & 0x55555555) << 1));
		b = (((b & 0xcccccccc) >> 2) | ((b & 0x33333333) << 2));
		b = (((b & 0xf0f0f0f0) >> 4) | ((b & 0x0f0f0f0f) << 4));
		b = (((b & 0xff00ff00) >> 8) | ((b & 0x00ff00ff) << 8));
		b = ((b >> 16) | (b << 16)) >> (32 - m);
		if (b > a)
		{
			Complex t = x[a];
			x[a] = x[b];
			x[b] = t;
		}
	}
	//// Normalize (This section make it not working correctly)
	//Complex f = 1.0 / sqrt(N);
	//for (unsigned int i = 0; i < N; i++)
	//	x[i] *= f;
}

// inverse fft (in-place)
void ifft(CArray& x)
{
    // conjugate the complex numbers
    x = x.apply(std::conj);

    // forward fft
    fft( x );

    // conjugate the complex numbers again
    x = x.apply(std::conj);

    // scale the numbers
    x /= x.size();
}

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;
    }

    // inverse fft
    ifft(data);

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