Chris@184: #ifndef KISSFFT_CLASS_HH
Chris@184: #define KISSFFT_CLASS_HH
Chris@184: #include <complex>
Chris@184: #include <vector>
Chris@184: 
Chris@184: namespace kissfft_utils {
Chris@184: 
Chris@184: template <typename T_scalar>
Chris@184: struct traits
Chris@184: {
Chris@184:     typedef T_scalar scalar_type;
Chris@184:     typedef std::complex<scalar_type> cpx_type;
Chris@184:     void fill_twiddles( std::complex<T_scalar> * dst ,int nfft,bool inverse)
Chris@184:     {
Chris@184:         T_scalar phinc =  (inverse?2:-2)* acos( (T_scalar) -1)  / nfft;
Chris@184:         for (int i=0;i<nfft;++i)
Chris@184:             dst[i] = exp( std::complex<T_scalar>(0,i*phinc) );
Chris@184:     }
Chris@184: 
Chris@184:     void prepare(
Chris@184:             std::vector< std::complex<T_scalar> > & dst,
Chris@184:             int nfft,bool inverse, 
Chris@184:             std::vector<int> & stageRadix, 
Chris@184:             std::vector<int> & stageRemainder )
Chris@184:     {
Chris@184:         _twiddles.resize(nfft);
Chris@184:         fill_twiddles( &_twiddles[0],nfft,inverse);
Chris@184:         dst = _twiddles;
Chris@184: 
Chris@184:         //factorize
Chris@184:         //start factoring out 4's, then 2's, then 3,5,7,9,...
Chris@184:         int n= nfft;
Chris@184:         int p=4;
Chris@184:         do {
Chris@184:             while (n % p) {
Chris@184:                 switch (p) {
Chris@184:                     case 4: p = 2; break;
Chris@184:                     case 2: p = 3; break;
Chris@184:                     default: p += 2; break;
Chris@184:                 }
Chris@184:                 if (p*p>n)
Chris@184:                     p=n;// no more factors
Chris@184:             }
Chris@184:             n /= p;
Chris@184:             stageRadix.push_back(p);
Chris@184:             stageRemainder.push_back(n);
Chris@184:         }while(n>1);
Chris@184:     }
Chris@184:     std::vector<cpx_type> _twiddles;
Chris@184: 
Chris@184: 
Chris@184:     const cpx_type twiddle(int i) { return _twiddles[i]; }
Chris@184: };
Chris@184: 
Chris@184: }
Chris@184: 
Chris@184: template <typename T_Scalar,
Chris@184:          typename T_traits=kissfft_utils::traits<T_Scalar> 
Chris@184:          >
Chris@184: class kissfft
Chris@184: {
Chris@184:     public:
Chris@184:         typedef T_traits traits_type;
Chris@184:         typedef typename traits_type::scalar_type scalar_type;
Chris@184:         typedef typename traits_type::cpx_type cpx_type;
Chris@184: 
Chris@184:         kissfft(int nfft,bool inverse,const traits_type & traits=traits_type() ) 
Chris@184:             :_nfft(nfft),_inverse(inverse),_traits(traits)
Chris@184:         {
Chris@184:             _traits.prepare(_twiddles, _nfft,_inverse ,_stageRadix, _stageRemainder);
Chris@184:         }
Chris@184: 
Chris@184:         void transform(const cpx_type * src , cpx_type * dst)
Chris@184:         {
Chris@184:             kf_work(0, dst, src, 1,1);
Chris@184:         }
Chris@184: 
Chris@184:     private:
Chris@184:         void kf_work( int stage,cpx_type * Fout, const cpx_type * f, size_t fstride,size_t in_stride)
Chris@184:         {
Chris@184:             int p = _stageRadix[stage];
Chris@184:             int m = _stageRemainder[stage];
Chris@184:             cpx_type * Fout_beg = Fout;
Chris@184:             cpx_type * Fout_end = Fout + p*m;
Chris@184: 
Chris@184:             if (m==1) {
Chris@184:                 do{
Chris@184:                     *Fout = *f;
Chris@184:                     f += fstride*in_stride;
Chris@184:                 }while(++Fout != Fout_end );
Chris@184:             }else{
Chris@184:                 do{
Chris@184:                     // recursive call:
Chris@184:                     // DFT of size m*p performed by doing
Chris@184:                     // p instances of smaller DFTs of size m, 
Chris@184:                     // each one takes a decimated version of the input
Chris@184:                     kf_work(stage+1, Fout , f, fstride*p,in_stride);
Chris@184:                     f += fstride*in_stride;
Chris@184:                 }while( (Fout += m) != Fout_end );
Chris@184:             }
Chris@184: 
Chris@184:             Fout=Fout_beg;
Chris@184: 
Chris@184:             // recombine the p smaller DFTs 
Chris@184:             switch (p) {
Chris@184:                 case 2: kf_bfly2(Fout,fstride,m); break;
Chris@184:                 case 3: kf_bfly3(Fout,fstride,m); break;
Chris@184:                 case 4: kf_bfly4(Fout,fstride,m); break;
Chris@184:                 case 5: kf_bfly5(Fout,fstride,m); break;
Chris@184:                 default: kf_bfly_generic(Fout,fstride,m,p); break;
Chris@184:             }
Chris@184:         }
Chris@184: 
Chris@184:         // these were #define macros in the original kiss_fft
Chris@184:         void C_ADD( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a+b;}
Chris@184:         void C_MUL( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a*b;}
Chris@184:         void C_SUB( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a-b;}
Chris@184:         void C_ADDTO( cpx_type & c,const cpx_type & a) { c+=a;}
Chris@184:         void C_FIXDIV( cpx_type & ,int ) {} // NO-OP for float types
Chris@184:         scalar_type S_MUL( const scalar_type & a,const scalar_type & b) { return a*b;}
Chris@184:         scalar_type HALF_OF( const scalar_type & a) { return a*.5;}
Chris@184:         void C_MULBYSCALAR(cpx_type & c,const scalar_type & a) {c*=a;}
Chris@184: 
Chris@184:         void kf_bfly2( cpx_type * Fout, const size_t fstride, int m)
Chris@184:         {
Chris@184:             for (int k=0;k<m;++k) {
Chris@184:                 cpx_type t = Fout[m+k] * _traits.twiddle(k*fstride);
Chris@184:                 Fout[m+k] = Fout[k] - t;
Chris@184:                 Fout[k] += t;
Chris@184:             }
Chris@184:         }
Chris@184: 
Chris@184:         void kf_bfly4( cpx_type * Fout, const size_t fstride, const size_t m)
Chris@184:         {
Chris@184:             cpx_type scratch[7];
Chris@184:             int negative_if_inverse = _inverse * -2 +1;
Chris@184:             for (size_t k=0;k<m;++k) {
Chris@184:                 scratch[0] = Fout[k+m] * _traits.twiddle(k*fstride);
Chris@184:                 scratch[1] = Fout[k+2*m] * _traits.twiddle(k*fstride*2);
Chris@184:                 scratch[2] = Fout[k+3*m] * _traits.twiddle(k*fstride*3);
Chris@184:                 scratch[5] = Fout[k] - scratch[1];
Chris@184: 
Chris@184:                 Fout[k] += scratch[1];
Chris@184:                 scratch[3] = scratch[0] + scratch[2];
Chris@184:                 scratch[4] = scratch[0] - scratch[2];
Chris@184:                 scratch[4] = cpx_type( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
Chris@184: 
Chris@184:                 Fout[k+2*m]  = Fout[k] - scratch[3];
Chris@184:                 Fout[k] += scratch[3];
Chris@184:                 Fout[k+m] = scratch[5] + scratch[4];
Chris@184:                 Fout[k+3*m] = scratch[5] - scratch[4];
Chris@184:             }
Chris@184:         }
Chris@184: 
Chris@184:         void kf_bfly3( cpx_type * Fout, const size_t fstride, const size_t m)
Chris@184:         {
Chris@184:             size_t k=m;
Chris@184:             const size_t m2 = 2*m;
Chris@184:             cpx_type *tw1,*tw2;
Chris@184:             cpx_type scratch[5];
Chris@184:             cpx_type epi3;
Chris@184:             epi3 = _twiddles[fstride*m];
Chris@184: 
Chris@184:             tw1=tw2=&_twiddles[0];
Chris@184: 
Chris@184:             do{
Chris@184:                 C_FIXDIV(*Fout,3); C_FIXDIV(Fout[m],3); C_FIXDIV(Fout[m2],3);
Chris@184: 
Chris@184:                 C_MUL(scratch[1],Fout[m] , *tw1);
Chris@184:                 C_MUL(scratch[2],Fout[m2] , *tw2);
Chris@184: 
Chris@184:                 C_ADD(scratch[3],scratch[1],scratch[2]);
Chris@184:                 C_SUB(scratch[0],scratch[1],scratch[2]);
Chris@184:                 tw1 += fstride;
Chris@184:                 tw2 += fstride*2;
Chris@184: 
Chris@184:                 Fout[m] = cpx_type( Fout->real() - HALF_OF(scratch[3].real() ) , Fout->imag() - HALF_OF(scratch[3].imag() ) );
Chris@184: 
Chris@184:                 C_MULBYSCALAR( scratch[0] , epi3.imag() );
Chris@184: 
Chris@184:                 C_ADDTO(*Fout,scratch[3]);
Chris@184: 
Chris@184:                 Fout[m2] = cpx_type(  Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
Chris@184: 
Chris@184:                 C_ADDTO( Fout[m] , cpx_type( -scratch[0].imag(),scratch[0].real() ) );
Chris@184:                 ++Fout;
Chris@184:             }while(--k);
Chris@184:         }
Chris@184: 
Chris@184:         void kf_bfly5( cpx_type * Fout, const size_t fstride, const size_t m)
Chris@184:         {
Chris@184:             cpx_type *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
Chris@184:             size_t u;
Chris@184:             cpx_type scratch[13];
Chris@184:             cpx_type * twiddles = &_twiddles[0];
Chris@184:             cpx_type *tw;
Chris@184:             cpx_type ya,yb;
Chris@184:             ya = twiddles[fstride*m];
Chris@184:             yb = twiddles[fstride*2*m];
Chris@184: 
Chris@184:             Fout0=Fout;
Chris@184:             Fout1=Fout0+m;
Chris@184:             Fout2=Fout0+2*m;
Chris@184:             Fout3=Fout0+3*m;
Chris@184:             Fout4=Fout0+4*m;
Chris@184: 
Chris@184:             tw=twiddles;
Chris@184:             for ( u=0; u<m; ++u ) {
Chris@184:                 C_FIXDIV( *Fout0,5); C_FIXDIV( *Fout1,5); C_FIXDIV( *Fout2,5); C_FIXDIV( *Fout3,5); C_FIXDIV( *Fout4,5);
Chris@184:                 scratch[0] = *Fout0;
Chris@184: 
Chris@184:                 C_MUL(scratch[1] ,*Fout1, tw[u*fstride]);
Chris@184:                 C_MUL(scratch[2] ,*Fout2, tw[2*u*fstride]);
Chris@184:                 C_MUL(scratch[3] ,*Fout3, tw[3*u*fstride]);
Chris@184:                 C_MUL(scratch[4] ,*Fout4, tw[4*u*fstride]);
Chris@184: 
Chris@184:                 C_ADD( scratch[7],scratch[1],scratch[4]);
Chris@184:                 C_SUB( scratch[10],scratch[1],scratch[4]);
Chris@184:                 C_ADD( scratch[8],scratch[2],scratch[3]);
Chris@184:                 C_SUB( scratch[9],scratch[2],scratch[3]);
Chris@184: 
Chris@184:                 C_ADDTO( *Fout0, scratch[7]);
Chris@184:                 C_ADDTO( *Fout0, scratch[8]);
Chris@184: 
Chris@184:                 scratch[5] = scratch[0] + cpx_type(
Chris@184:                         S_MUL(scratch[7].real(),ya.real() ) + S_MUL(scratch[8].real() ,yb.real() ),
Chris@184:                         S_MUL(scratch[7].imag(),ya.real()) + S_MUL(scratch[8].imag(),yb.real())
Chris@184:                         );
Chris@184: 
Chris@184:                 scratch[6] =  cpx_type( 
Chris@184:                         S_MUL(scratch[10].imag(),ya.imag()) + S_MUL(scratch[9].imag(),yb.imag()),
Chris@184:                         -S_MUL(scratch[10].real(),ya.imag()) - S_MUL(scratch[9].real(),yb.imag()) 
Chris@184:                         );
Chris@184: 
Chris@184:                 C_SUB(*Fout1,scratch[5],scratch[6]);
Chris@184:                 C_ADD(*Fout4,scratch[5],scratch[6]);
Chris@184: 
Chris@184:                 scratch[11] = scratch[0] + 
Chris@184:                     cpx_type(
Chris@184:                             S_MUL(scratch[7].real(),yb.real()) + S_MUL(scratch[8].real(),ya.real()),
Chris@184:                             S_MUL(scratch[7].imag(),yb.real()) + S_MUL(scratch[8].imag(),ya.real())
Chris@184:                             );
Chris@184: 
Chris@184:                 scratch[12] = cpx_type(
Chris@184:                         -S_MUL(scratch[10].imag(),yb.imag()) + S_MUL(scratch[9].imag(),ya.imag()),
Chris@184:                         S_MUL(scratch[10].real(),yb.imag()) - S_MUL(scratch[9].real(),ya.imag())
Chris@184:                         );
Chris@184: 
Chris@184:                 C_ADD(*Fout2,scratch[11],scratch[12]);
Chris@184:                 C_SUB(*Fout3,scratch[11],scratch[12]);
Chris@184: 
Chris@184:                 ++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
Chris@184:             }
Chris@184:         }
Chris@184: 
Chris@184:         /* perform the butterfly for one stage of a mixed radix FFT */
Chris@184:         void kf_bfly_generic(
Chris@184:                 cpx_type * Fout,
Chris@184:                 const size_t fstride,
Chris@184:                 int m,
Chris@184:                 int p
Chris@184:                 )
Chris@184:         {
Chris@184:             int u,k,q1,q;
Chris@184:             cpx_type * twiddles = &_twiddles[0];
Chris@184:             cpx_type t;
Chris@184:             int Norig = _nfft;
Chris@184:             cpx_type scratchbuf[p];
Chris@184: 
Chris@184:             for ( u=0; u<m; ++u ) {
Chris@184:                 k=u;
Chris@184:                 for ( q1=0 ; q1<p ; ++q1 ) {
Chris@184:                     scratchbuf[q1] = Fout[ k  ];
Chris@184:                     C_FIXDIV(scratchbuf[q1],p);
Chris@184:                     k += m;
Chris@184:                 }
Chris@184: 
Chris@184:                 k=u;
Chris@184:                 for ( q1=0 ; q1<p ; ++q1 ) {
Chris@184:                     int twidx=0;
Chris@184:                     Fout[ k ] = scratchbuf[0];
Chris@184:                     for (q=1;q<p;++q ) {
Chris@184:                         twidx += fstride * k;
Chris@184:                         if (twidx>=Norig) twidx-=Norig;
Chris@184:                         C_MUL(t,scratchbuf[q] , twiddles[twidx] );
Chris@184:                         C_ADDTO( Fout[ k ] ,t);
Chris@184:                     }
Chris@184:                     k += m;
Chris@184:                 }
Chris@184:             }
Chris@184:         }
Chris@184: 
Chris@184:         int _nfft;
Chris@184:         bool _inverse;
Chris@184:         std::vector<cpx_type> _twiddles;
Chris@184:         std::vector<int> _stageRadix;
Chris@184:         std::vector<int> _stageRemainder;
Chris@184:         traits_type _traits;
Chris@184: };
Chris@184: #endif