#ifndef KISSFFT_CLASS_HH
#define KISSFFT_CLASS_HH
#include <complex>
#include <vector>

namespace kissfft_utils {

template <typename T_scalar>
struct traits
{
    typedef T_scalar scalar_type;
    typedef std::complex<scalar_type> cpx_type;
    static void fill_twiddles( cpx_type * dst,
                        std::size_t nfft,
                        bool inverse )
    {
        const T_scalar phinc =  (inverse?2:-2)* acos( (T_scalar) -1)  / nfft;
        for (std::size_t i=0;i<nfft;++i)
            dst[i] = std::exp( cpx_type(0,i*phinc) );
    }

    static void prepare(
            std::vector< cpx_type > & _twiddles,
            std::size_t nfft,
            bool inverse,
            std::vector<std::size_t> & stageRadix,
            std::vector<std::size_t> & stageRemainder )
    {
        _twiddles.resize(nfft);
        fill_twiddles( &_twiddles[0],nfft,inverse);

        //factorize
        //start factoring out 4's, then 2's, then 3,5,7,9,...
        std::size_t n= nfft;
        std::size_t p=4;
        do {
            while (n % p) {
                switch (p) {
                    case 4: p = 2; break;
                    case 2: p = 3; break;
                    default: p += 2; break;
                }
                if (p*p>n)
                    p = n;// no more factors
            }
            n /= p;
            stageRadix.push_back(p);
            stageRemainder.push_back(n);
        }while(n>1);
    }
};

}

template <typename T_Scalar,
         typename T_traits=kissfft_utils::traits<T_Scalar> 
         >
class kissfft
{
    public:
        typedef T_traits traits_type;
        typedef typename traits_type::scalar_type scalar_type;
        typedef typename traits_type::cpx_type cpx_type;

        kissfft( std::size_t nfft,
                 bool inverse )
            :_nfft(nfft)
            ,_inverse(inverse)
        {
            T_traits::prepare(_twiddles, _nfft,_inverse ,_stageRadix, _stageRemainder);
        }

        void transform( const cpx_type * src,
                        cpx_type * dst ) const
        {
            kf_work(0, dst, src, 1,1);
        }

    private:
        void kf_work( std::size_t stage,
                      cpx_type * Fout,
                      const cpx_type * f,
                      std::size_t fstride,
                      std::size_t in_stride) const
        {
            const std::size_t p = _stageRadix[stage];
            const std::size_t m = _stageRemainder[stage];
            cpx_type * const Fout_beg = Fout;
            cpx_type * const Fout_end = Fout + p*m;

            if (m==1) {
                do{
                    *Fout = *f;
                    f += fstride*in_stride;
                }while(++Fout != Fout_end );
            }else{
                do{
                    // recursive call:
                    // DFT of size m*p performed by doing
                    // p instances of smaller DFTs of size m, 
                    // each one takes a decimated version of the input
                    kf_work(stage+1, Fout , f, fstride*p,in_stride);
                    f += fstride*in_stride;
                }while( (Fout += m) != Fout_end );
            }

            Fout=Fout_beg;

            // recombine the p smaller DFTs 
            switch (p) {
                case 2: kf_bfly2(Fout,fstride,m); break;
                case 3: kf_bfly3(Fout,fstride,m); break;
                case 4: kf_bfly4(Fout,fstride,m); break;
                case 5: kf_bfly5(Fout,fstride,m); break;
                default: kf_bfly_generic(Fout,fstride,m,p); break;
            }
        }

        void kf_bfly2( cpx_type * Fout, const size_t fstride, std::size_t m) const
        {
            for (std::size_t k=0;k<m;++k) {
                const cpx_type t = Fout[m+k] * _twiddles[k*fstride];
                Fout[m+k] = Fout[k] - t;
                Fout[k] += t;
            }
        }

        void kf_bfly4( cpx_type * Fout, const std::size_t fstride, const std::size_t m) const
        {
            cpx_type scratch[7];
            const scalar_type negative_if_inverse = _inverse ? -1 : +1;
            for (std::size_t k=0;k<m;++k) {
                scratch[0] = Fout[k+  m] * _twiddles[k*fstride  ];
                scratch[1] = Fout[k+2*m] * _twiddles[k*fstride*2];
                scratch[2] = Fout[k+3*m] * _twiddles[k*fstride*3];
                scratch[5] = Fout[k] - scratch[1];

                Fout[k] += scratch[1];
                scratch[3] = scratch[0] + scratch[2];
                scratch[4] = scratch[0] - scratch[2];
                scratch[4] = cpx_type( scratch[4].imag()*negative_if_inverse ,
                                      -scratch[4].real()*negative_if_inverse );

                Fout[k+2*m]  = Fout[k] - scratch[3];
                Fout[k    ]+= scratch[3];
                Fout[k+  m] = scratch[5] + scratch[4];
                Fout[k+3*m] = scratch[5] - scratch[4];
            }
        }

        void kf_bfly3( cpx_type * Fout, const std::size_t fstride, const std::size_t m) const
        {
            std::size_t k=m;
            const std::size_t m2 = 2*m;
            const cpx_type *tw1,*tw2;
            cpx_type scratch[5];
            const cpx_type epi3 = _twiddles[fstride*m];

            tw1=tw2=&_twiddles[0];

            do{
                scratch[1] = Fout[m]  * *tw1;
                scratch[2] = Fout[m2] * *tw2;

                scratch[3] = scratch[1] + scratch[2];
                scratch[0] = scratch[1] - scratch[2];
                tw1 += fstride;
                tw2 += fstride*2;

                Fout[m] = Fout[0] - scratch[3]*scalar_type(0.5);
                scratch[0] *= epi3.imag();

                Fout[0] += scratch[3];

                Fout[m2] = cpx_type(  Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );

                Fout[m] += cpx_type( -scratch[0].imag(),scratch[0].real() );
                ++Fout;
            }while(--k);
        }

        void kf_bfly5( cpx_type * Fout, const std::size_t fstride, const std::size_t m) const
        {
            cpx_type *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
            cpx_type scratch[13];
            const cpx_type ya = _twiddles[fstride*m];
            const cpx_type yb = _twiddles[fstride*2*m];

            Fout0=Fout;
            Fout1=Fout0+m;
            Fout2=Fout0+2*m;
            Fout3=Fout0+3*m;
            Fout4=Fout0+4*m;

            for ( std::size_t u=0; u<m; ++u ) {
                scratch[0] = *Fout0;

                scratch[1] = *Fout1 * _twiddles[  u*fstride];
                scratch[2] = *Fout2 * _twiddles[2*u*fstride];
                scratch[3] = *Fout3 * _twiddles[3*u*fstride];
                scratch[4] = *Fout4 * _twiddles[4*u*fstride];

                scratch[7] = scratch[1] + scratch[4];
                scratch[10]= scratch[1] - scratch[4];
                scratch[8] = scratch[2] + scratch[3];
                scratch[9] = scratch[2] - scratch[3];

                *Fout0 += scratch[7];
                *Fout0 += scratch[8];

                scratch[5] = scratch[0] + cpx_type(
                        scratch[7].real()*ya.real() + scratch[8].real()*yb.real(),
                        scratch[7].imag()*ya.real() + scratch[8].imag()*yb.real()
                        );

                scratch[6] =  cpx_type( 
                         scratch[10].imag()*ya.imag() + scratch[9].imag()*yb.imag(),
                        -scratch[10].real()*ya.imag() - scratch[9].real()*yb.imag()
                        );

                *Fout1 = scratch[5] - scratch[6];
                *Fout4 = scratch[5] + scratch[6];

                scratch[11] = scratch[0] + 
                    cpx_type(
                            scratch[7].real()*yb.real() + scratch[8].real()*ya.real(),
                            scratch[7].imag()*yb.real() + scratch[8].imag()*ya.real()
                            );

                scratch[12] = cpx_type(
                        -scratch[10].imag()*yb.imag() + scratch[9].imag()*ya.imag(),
                         scratch[10].real()*yb.imag() - scratch[9].real()*ya.imag()
                        );

                *Fout2 = scratch[11] + scratch[12];
                *Fout3 = scratch[11] - scratch[12];

                ++Fout0;
                ++Fout1;
                ++Fout2;
                ++Fout3;
                ++Fout4;
            }
        }

        /* perform the butterfly for one stage of a mixed radix FFT */
        void kf_bfly_generic(
                cpx_type * Fout,
                const size_t fstride,
                std::size_t m,
                std::size_t p
                ) const
        {
            const cpx_type * twiddles = &_twiddles[0];
            cpx_type scratchbuf[p];

            for ( std::size_t u=0; u<m; ++u ) {
                std::size_t k = u;
                for ( std::size_t q1=0 ; q1<p ; ++q1 ) {
                    scratchbuf[q1] = Fout[ k  ];
                    k += m;
                }

                k=u;
                for ( std::size_t q1=0 ; q1<p ; ++q1 ) {
                    std::size_t twidx=0;
                    Fout[ k ] = scratchbuf[0];
                    for ( std::size_t q=1;q<p;++q ) {
                        twidx += fstride * k;
                        if (twidx>=_nfft)
                          twidx-=_nfft;
                        Fout[ k ] += scratchbuf[q] * twiddles[twidx];
                    }
                    k += m;
                }
            }
        }

        std::size_t _nfft;
        bool _inverse;
        std::vector<cpx_type> _twiddles;
        std::vector<std::size_t> _stageRadix;
        std::vector<std::size_t> _stageRemainder;
};
#endif