mirror of
https://github.com/mborgerding/kissfft.git
synced 2025-05-27 21:20:27 -04:00
b10fb43644
All uses of these function were replaced by their implementation (which is mostly easier to read than the functions themselves).
286 lines
9.5 KiB
C++
286 lines
9.5 KiB
C++
#ifndef KISSFFT_CLASS_HH
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#define KISSFFT_CLASS_HH
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#include <complex>
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#include <vector>
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namespace kissfft_utils {
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template <typename T_scalar>
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struct traits
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{
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typedef T_scalar scalar_type;
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typedef std::complex<scalar_type> cpx_type;
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static void fill_twiddles( cpx_type * dst,
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std::size_t nfft,
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bool inverse )
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{
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const T_scalar phinc = (inverse?2:-2)* acos( (T_scalar) -1) / nfft;
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for (std::size_t i=0;i<nfft;++i)
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dst[i] = std::exp( cpx_type(0,i*phinc) );
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}
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static void prepare(
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std::vector< cpx_type > & _twiddles,
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std::size_t nfft,
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bool inverse,
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std::vector<std::size_t> & stageRadix,
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std::vector<std::size_t> & stageRemainder )
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{
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_twiddles.resize(nfft);
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fill_twiddles( &_twiddles[0],nfft,inverse);
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//factorize
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//start factoring out 4's, then 2's, then 3,5,7,9,...
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std::size_t n= nfft;
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std::size_t p=4;
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do {
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while (n % p) {
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switch (p) {
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case 4: p = 2; break;
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case 2: p = 3; break;
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default: p += 2; break;
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}
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if (p*p>n)
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p = n;// no more factors
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}
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n /= p;
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stageRadix.push_back(p);
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stageRemainder.push_back(n);
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}while(n>1);
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}
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};
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}
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template <typename T_Scalar,
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typename T_traits=kissfft_utils::traits<T_Scalar>
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>
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class kissfft
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{
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public:
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typedef T_traits traits_type;
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typedef typename traits_type::scalar_type scalar_type;
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typedef typename traits_type::cpx_type cpx_type;
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kissfft( std::size_t nfft,
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bool inverse )
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:_nfft(nfft)
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,_inverse(inverse)
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{
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T_traits::prepare(_twiddles, _nfft,_inverse ,_stageRadix, _stageRemainder);
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}
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void transform( const cpx_type * src,
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cpx_type * dst ) const
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{
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kf_work(0, dst, src, 1,1);
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}
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private:
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void kf_work( std::size_t stage,
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cpx_type * Fout,
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const cpx_type * f,
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std::size_t fstride,
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std::size_t in_stride) const
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{
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const std::size_t p = _stageRadix[stage];
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const std::size_t m = _stageRemainder[stage];
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cpx_type * const Fout_beg = Fout;
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cpx_type * const Fout_end = Fout + p*m;
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if (m==1) {
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do{
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*Fout = *f;
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f += fstride*in_stride;
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}while(++Fout != Fout_end );
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}else{
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do{
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// recursive call:
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// DFT of size m*p performed by doing
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// p instances of smaller DFTs of size m,
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// each one takes a decimated version of the input
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kf_work(stage+1, Fout , f, fstride*p,in_stride);
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f += fstride*in_stride;
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}while( (Fout += m) != Fout_end );
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}
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Fout=Fout_beg;
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// recombine the p smaller DFTs
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switch (p) {
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case 2: kf_bfly2(Fout,fstride,m); break;
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case 3: kf_bfly3(Fout,fstride,m); break;
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case 4: kf_bfly4(Fout,fstride,m); break;
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case 5: kf_bfly5(Fout,fstride,m); break;
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default: kf_bfly_generic(Fout,fstride,m,p); break;
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}
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}
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void kf_bfly2( cpx_type * Fout, const size_t fstride, std::size_t m) const
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{
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for (std::size_t k=0;k<m;++k) {
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const cpx_type t = Fout[m+k] * _twiddles[k*fstride];
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Fout[m+k] = Fout[k] - t;
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Fout[k] += t;
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}
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}
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void kf_bfly4( cpx_type * Fout, const std::size_t fstride, const std::size_t m) const
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{
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cpx_type scratch[7];
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const scalar_type negative_if_inverse = _inverse ? -1 : +1;
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for (std::size_t k=0;k<m;++k) {
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scratch[0] = Fout[k+ m] * _twiddles[k*fstride ];
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scratch[1] = Fout[k+2*m] * _twiddles[k*fstride*2];
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scratch[2] = Fout[k+3*m] * _twiddles[k*fstride*3];
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scratch[5] = Fout[k] - scratch[1];
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Fout[k] += scratch[1];
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scratch[3] = scratch[0] + scratch[2];
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scratch[4] = scratch[0] - scratch[2];
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scratch[4] = cpx_type( scratch[4].imag()*negative_if_inverse ,
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-scratch[4].real()*negative_if_inverse );
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Fout[k+2*m] = Fout[k] - scratch[3];
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Fout[k ]+= scratch[3];
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Fout[k+ m] = scratch[5] + scratch[4];
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Fout[k+3*m] = scratch[5] - scratch[4];
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}
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}
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void kf_bfly3( cpx_type * Fout, const std::size_t fstride, const std::size_t m) const
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{
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std::size_t k=m;
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const std::size_t m2 = 2*m;
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const cpx_type *tw1,*tw2;
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cpx_type scratch[5];
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const cpx_type epi3 = _twiddles[fstride*m];
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tw1=tw2=&_twiddles[0];
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do{
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scratch[1] = Fout[m] * *tw1;
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scratch[2] = Fout[m2] * *tw2;
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scratch[3] = scratch[1] + scratch[2];
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scratch[0] = scratch[1] - scratch[2];
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tw1 += fstride;
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tw2 += fstride*2;
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Fout[m] = Fout[0] - scratch[3]*scalar_type(0.5);
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scratch[0] *= epi3.imag();
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Fout[0] += scratch[3];
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Fout[m2] = cpx_type( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
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Fout[m] += cpx_type( -scratch[0].imag(),scratch[0].real() );
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++Fout;
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}while(--k);
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}
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void kf_bfly5( cpx_type * Fout, const std::size_t fstride, const std::size_t m) const
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{
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cpx_type *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
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cpx_type scratch[13];
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const cpx_type ya = _twiddles[fstride*m];
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const cpx_type yb = _twiddles[fstride*2*m];
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Fout0=Fout;
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Fout1=Fout0+m;
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Fout2=Fout0+2*m;
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Fout3=Fout0+3*m;
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Fout4=Fout0+4*m;
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for ( std::size_t u=0; u<m; ++u ) {
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scratch[0] = *Fout0;
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scratch[1] = *Fout1 * _twiddles[ u*fstride];
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scratch[2] = *Fout2 * _twiddles[2*u*fstride];
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scratch[3] = *Fout3 * _twiddles[3*u*fstride];
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scratch[4] = *Fout4 * _twiddles[4*u*fstride];
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scratch[7] = scratch[1] + scratch[4];
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scratch[10]= scratch[1] - scratch[4];
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scratch[8] = scratch[2] + scratch[3];
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scratch[9] = scratch[2] - scratch[3];
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*Fout0 += scratch[7];
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*Fout0 += scratch[8];
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scratch[5] = scratch[0] + cpx_type(
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scratch[7].real()*ya.real() + scratch[8].real()*yb.real(),
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scratch[7].imag()*ya.real() + scratch[8].imag()*yb.real()
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);
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scratch[6] = cpx_type(
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scratch[10].imag()*ya.imag() + scratch[9].imag()*yb.imag(),
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-scratch[10].real()*ya.imag() - scratch[9].real()*yb.imag()
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);
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*Fout1 = scratch[5] - scratch[6];
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*Fout4 = scratch[5] + scratch[6];
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scratch[11] = scratch[0] +
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cpx_type(
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scratch[7].real()*yb.real() + scratch[8].real()*ya.real(),
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scratch[7].imag()*yb.real() + scratch[8].imag()*ya.real()
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);
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scratch[12] = cpx_type(
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-scratch[10].imag()*yb.imag() + scratch[9].imag()*ya.imag(),
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scratch[10].real()*yb.imag() - scratch[9].real()*ya.imag()
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);
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*Fout2 = scratch[11] + scratch[12];
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*Fout3 = scratch[11] - scratch[12];
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++Fout0;
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++Fout1;
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++Fout2;
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++Fout3;
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++Fout4;
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}
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}
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/* perform the butterfly for one stage of a mixed radix FFT */
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void kf_bfly_generic(
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cpx_type * Fout,
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const size_t fstride,
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std::size_t m,
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std::size_t p
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) const
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{
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const cpx_type * twiddles = &_twiddles[0];
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cpx_type scratchbuf[p];
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for ( std::size_t u=0; u<m; ++u ) {
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std::size_t k = u;
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for ( std::size_t q1=0 ; q1<p ; ++q1 ) {
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scratchbuf[q1] = Fout[ k ];
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k += m;
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}
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k=u;
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for ( std::size_t q1=0 ; q1<p ; ++q1 ) {
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std::size_t twidx=0;
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Fout[ k ] = scratchbuf[0];
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for ( std::size_t q=1;q<p;++q ) {
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twidx += fstride * k;
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if (twidx>=_nfft)
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twidx-=_nfft;
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Fout[ k ] += scratchbuf[q] * twiddles[twidx];
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}
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k += m;
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}
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}
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}
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std::size_t _nfft;
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bool _inverse;
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std::vector<cpx_type> _twiddles;
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std::vector<std::size_t> _stageRadix;
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std::vector<std::size_t> _stageRemainder;
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};
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#endif
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