kissfft.hh

#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;
    void fill_twiddles( std::complex<T_scalar> * dst ,int nfft,bool inverse)
    {
        T_scalar phinc =  (inverse?2:-2)* acos( (T_scalar) -1)  / nfft;
        for (int i=0;i<nfft;++i)
            dst[i] = exp( std::complex<T_scalar>(0,i*phinc) );
    }

    void prepare(
            std::vector< std::complex<T_scalar> > & dst,
            int nfft,bool inverse, 
            std::vector<int> & stageRadix, 
            std::vector<int> & stageRemainder )
    {
        _twiddles.resize(nfft);
        fill_twiddles( &_twiddles[0],nfft,inverse);
        dst = _twiddles;

        //factorize
        //start factoring out 4's, then 2's, then 3,5,7,9,...
        int n= nfft;
        int 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);
    }
    std::vector<cpx_type> _twiddles;


    const cpx_type twiddle(int i) { return _twiddles[i]; }
};

}

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(int nfft,bool inverse,const traits_type & traits=traits_type() ) 
            :_nfft(nfft),_inverse(inverse),_traits(traits)
        {
            _traits.prepare(_twiddles, _nfft,_inverse ,_stageRadix, _stageRemainder);
        }

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

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

        // these were #define macros in the original kiss_fft
        void C_ADD( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a+b;}
        void C_MUL( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a*b;}
        void C_SUB( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a-b;}
        void C_ADDTO( cpx_type & c,const cpx_type & a) { c+=a;}
        void C_FIXDIV( cpx_type & ,int ) {} // NO-OP for float types
        scalar_type S_MUL( const scalar_type & a,const scalar_type & b) { return a*b;}
        scalar_type HALF_OF( const scalar_type & a) { return a*.5;}
        void C_MULBYSCALAR(cpx_type & c,const scalar_type & a) {c*=a;}

        void kf_bfly2( cpx_type * Fout, const size_t fstride, int m)
        {
            for (int k=0;k<m;++k) {
                cpx_type t = Fout[m+k] * _traits.twiddle(k*fstride);
                Fout[m+k] = Fout[k] - t;
                Fout[k] += t;
            }
        }

        void kf_bfly4( cpx_type * Fout, const size_t fstride, const size_t m)
        {
            cpx_type scratch[7];
            int negative_if_inverse = _inverse * -2 +1;
            for (size_t k=0;k<m;++k) {
                scratch[0] = Fout[k+m] * _traits.twiddle(k*fstride);
                scratch[1] = Fout[k+2*m] * _traits.twiddle(k*fstride*2);
                scratch[2] = Fout[k+3*m] * _traits.twiddle(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 size_t fstride, const size_t m)
        {
            size_t k=m;
            const size_t m2 = 2*m;
            cpx_type *tw1,*tw2;
            cpx_type scratch[5];
            cpx_type epi3;
            epi3 = _twiddles[fstride*m];

            tw1=tw2=&_twiddles[0];

            do{
                C_FIXDIV(*Fout,3); C_FIXDIV(Fout[m],3); C_FIXDIV(Fout[m2],3);

                C_MUL(scratch[1],Fout[m] , *tw1);
                C_MUL(scratch[2],Fout[m2] , *tw2);

                C_ADD(scratch[3],scratch[1],scratch[2]);
                C_SUB(scratch[0],scratch[1],scratch[2]);
                tw1 += fstride;
                tw2 += fstride*2;

                Fout[m] = cpx_type( Fout->real() - HALF_OF(scratch[3].real() ) , Fout->imag() - HALF_OF(scratch[3].imag() ) );

                C_MULBYSCALAR( scratch[0] , epi3.imag() );

                C_ADDTO(*Fout,scratch[3]);

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

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

        void kf_bfly5( cpx_type * Fout, const size_t fstride, const size_t m)
        {
            cpx_type *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
            size_t u;
            cpx_type scratch[13];
            cpx_type * twiddles = &_twiddles[0];
            cpx_type *tw;
            cpx_type ya,yb;
            ya = twiddles[fstride*m];
            yb = twiddles[fstride*2*m];

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

            tw=twiddles;
            for ( u=0; u<m; ++u ) {
                C_FIXDIV( *Fout0,5); C_FIXDIV( *Fout1,5); C_FIXDIV( *Fout2,5); C_FIXDIV( *Fout3,5); C_FIXDIV( *Fout4,5);
                scratch[0] = *Fout0;

                C_MUL(scratch[1] ,*Fout1, tw[u*fstride]);
                C_MUL(scratch[2] ,*Fout2, tw[2*u*fstride]);
                C_MUL(scratch[3] ,*Fout3, tw[3*u*fstride]);
                C_MUL(scratch[4] ,*Fout4, tw[4*u*fstride]);

                C_ADD( scratch[7],scratch[1],scratch[4]);
                C_SUB( scratch[10],scratch[1],scratch[4]);
                C_ADD( scratch[8],scratch[2],scratch[3]);
                C_SUB( scratch[9],scratch[2],scratch[3]);

                C_ADDTO( *Fout0, scratch[7]);
                C_ADDTO( *Fout0, scratch[8]);

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

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

                C_SUB(*Fout1,scratch[5],scratch[6]);
                C_ADD(*Fout4,scratch[5],scratch[6]);

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

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

                C_ADD(*Fout2,scratch[11],scratch[12]);
                C_SUB(*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,
                int m,
                int p
                )
        {
            int u,k,q1,q;
            cpx_type * twiddles = &_twiddles[0];
            cpx_type t;
            int Norig = _nfft;
            cpx_type scratchbuf[p];

            for ( u=0; u<m; ++u ) {
                k=u;
                for ( q1=0 ; q1<p ; ++q1 ) {
                    scratchbuf[q1] = Fout[ k  ];
                    C_FIXDIV(scratchbuf[q1],p);
                    k += m;
                }

                k=u;
                for ( q1=0 ; q1<p ; ++q1 ) {
                    int twidx=0;
                    Fout[ k ] = scratchbuf[0];
                    for (q=1;q<p;++q ) {
                        twidx += fstride * k;
                        if (twidx>=Norig) twidx-=Norig;
                        C_MUL(t,scratchbuf[q] , twiddles[twidx] );
                        C_ADDTO( Fout[ k ] ,t);
                    }
                    k += m;
                }
            }
        }

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