comparison ext/kissfft/kissfft.hh @ 184:76ec2365b250

Bring in kissfft into this repo (formerly a subrepo, but the remote is not responding)

+#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