| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. Eigen itself is part of the KDE project. |
| // |
| // Copyright (C) 2009 Mark Borgerding mark a borgerding net |
| // |
| // Eigen is free software; you can redistribute it and/or |
| // modify it under the terms of the GNU Lesser General Public |
| // License as published by the Free Software Foundation; either |
| // version 3 of the License, or (at your option) any later version. |
| // |
| // Alternatively, you can redistribute it and/or |
| // modify it under the terms of the GNU General Public License as |
| // published by the Free Software Foundation; either version 2 of |
| // the License, or (at your option) any later version. |
| // |
| // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY |
| // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
| // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the |
| // GNU General Public License for more details. |
| // |
| // You should have received a copy of the GNU Lesser General Public |
| // License and a copy of the GNU General Public License along with |
| // Eigen. If not, see <http://www.gnu.org/licenses/>. |
| |
| #include <complex> |
| #include <vector> |
| |
| namespace Eigen { |
| |
| template <typename _Scalar> |
| struct simple_fft_traits |
| { |
| typedef _Scalar Scalar; |
| typedef std::complex<Scalar> Complex; |
| simple_fft_traits() : m_nfft(0) {} |
| |
| template <typename _Src> |
| void fwd( Complex * dst,const _Src *src,int nfft) |
| { |
| prepare(nfft,false); |
| work(0, dst, src, 1,1); |
| scale(dst); |
| } |
| |
| void fwd( Complex * dst,const Scalar * src,int nfft) |
| { |
| if ( nfft&1 ) { |
| // use generic mode for odd |
| prepare(nfft,false); |
| work(0, dst, src, 1,1); |
| scale(dst); |
| }else{ |
| int ncfft = nfft>>1; |
| // use optimized mode for even real |
| prepare(nfft,false); |
| work(0,dst, reinterpret_cast<const Complex*> (src),2,1); |
| Complex dc = dst[0].real() + dst[0].imag(); |
| Complex nyquist = dst[0].real() - dst[0].imag(); |
| |
| int k; |
| for ( k=1;k <= ncfft/2 ; ++k ) { |
| /** |
| fpk = st->tmpbuf[k]; |
| fpnk.r = st->tmpbuf[ncfft-k].r; |
| fpnk.i = - st->tmpbuf[ncfft-k].i; |
| |
| C_ADD( f1k, fpk , fpnk ); |
| C_SUB( f2k, fpk , fpnk ); |
| C_MUL( tw , f2k , st->super_twiddles[k-1]); |
| |
| freqdata[k].r = HALF_OF(f1k.r + tw.r); |
| freqdata[k].i = HALF_OF(f1k.i + tw.i); |
| freqdata[ncfft-k].r = HALF_OF(f1k.r - tw.r); |
| freqdata[ncfft-k].i = HALF_OF(tw.i - f1k.i); |
| */ |
| Complex fpk = dst[k]; |
| Complex fpnk = conj(dst[ncfft-k]); |
| |
| Complex f1k = fpk + fpnk; |
| Complex f2k = fpnk - fpk; |
| //Complex tw = f2k * exp( Complex(0,-3.14159265358979323846264338327 * ((double)k / ncfft + 1) ) ); // TODO repalce this with index into twiddles |
| Complex tw = f2k * m_twiddles[2*k];; |
| |
| dst[k] = (f1k + tw) * Scalar(.5); |
| dst[ncfft-k] = conj(f1k -tw)*Scalar(.5); |
| } |
| // place conjugate-symmetric half at the end for completeness |
| // TODO: make this configurable ( opt-out ) |
| for ( k=1;k < ncfft ; ++k ) |
| dst[nfft-k] = conj(dst[k]); |
| |
| dst[0] = dc; |
| dst[ncfft] = nyquist; |
| } |
| } |
| |
| void inv(Complex * dst,const Complex *src,int nfft) |
| { |
| prepare(nfft,true); |
| work(0, dst, src, 1,1); |
| scale(dst); |
| } |
| |
| void prepare(int nfft,bool inverse) |
| { |
| if (m_nfft == nfft) { |
| // reuse the twiddles, conjugate if necessary |
| if (inverse != m_inverse) |
| for (int i=0;i<nfft;++i) |
| m_twiddles[i] = conj( m_twiddles[i] ); |
| m_inverse = inverse; |
| return; |
| } |
| m_nfft = nfft; |
| m_inverse = inverse; |
| m_twiddles.resize(nfft); |
| Scalar phinc = (inverse?2:-2)* acos( (Scalar) -1) / nfft; |
| for (int i=0;i<nfft;++i) |
| m_twiddles[i] = exp( Complex(0,i*phinc) ); |
| |
| m_stageRadix.resize(0); |
| m_stageRemainder.resize(0); |
| //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; |
| m_stageRadix.push_back(p); |
| m_stageRemainder.push_back(n); |
| }while(n>1); |
| } |
| |
| void scale(Complex *dst) |
| { |
| if (m_inverse) { |
| Scalar s = 1./m_nfft; |
| for (int k=0;k<m_nfft;++k) |
| dst[k] *= s; |
| } |
| } |
| |
| private: |
| |
| template <typename _Src> |
| void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride) |
| { |
| int p = m_stageRadix[stage]; |
| int m = m_stageRemainder[stage]; |
| Complex * Fout_beg = xout; |
| Complex * Fout_end = xout + p*m; |
| |
| if (m>1) { |
| 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 |
| work(stage+1, xout , xin, fstride*p,in_stride); |
| xin += fstride*in_stride; |
| }while( (xout += m) != Fout_end ); |
| }else{ |
| do{ |
| *xout = *xin; |
| xin += fstride*in_stride; |
| }while(++xout != Fout_end ); |
| } |
| xout=Fout_beg; |
| |
| // recombine the p smaller DFTs |
| switch (p) { |
| case 2: bfly2(xout,fstride,m); break; |
| case 3: bfly3(xout,fstride,m); break; |
| case 4: bfly4(xout,fstride,m); break; |
| case 5: bfly5(xout,fstride,m); break; |
| default: bfly_generic(xout,fstride,m,p); break; |
| } |
| } |
| |
| void bfly2( Complex * Fout, const size_t fstride, int m) |
| { |
| for (int k=0;k<m;++k) { |
| Complex t = Fout[m+k] * m_twiddles[k*fstride]; |
| Fout[m+k] = Fout[k] - t; |
| Fout[k] += t; |
| } |
| } |
| |
| void bfly4( Complex * Fout, const size_t fstride, const size_t m) |
| { |
| Complex scratch[6]; |
| int negative_if_inverse = m_inverse * -2 +1; |
| for (size_t k=0;k<m;++k) { |
| scratch[0] = Fout[k+m] * m_twiddles[k*fstride]; |
| scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2]; |
| scratch[2] = Fout[k+3*m] * 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] = Complex( 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 bfly3( Complex * Fout, const size_t fstride, const size_t m) |
| { |
| size_t k=m; |
| const size_t m2 = 2*m; |
| Complex *tw1,*tw2; |
| Complex scratch[5]; |
| Complex epi3; |
| epi3 = m_twiddles[fstride*m]; |
| |
| tw1=tw2=&m_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] = Complex( Fout->real() - .5*scratch[3].real() , Fout->imag() - .5*scratch[3].imag() ); |
| scratch[0] *= epi3.imag(); |
| *Fout += scratch[3]; |
| Fout[m2] = Complex( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() ); |
| Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() ); |
| ++Fout; |
| }while(--k); |
| } |
| |
| void bfly5( Complex * Fout, const size_t fstride, const size_t m) |
| { |
| Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4; |
| size_t u; |
| Complex scratch[13]; |
| Complex * twiddles = &m_twiddles[0]; |
| Complex *tw; |
| Complex 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 ) { |
| scratch[0] = *Fout0; |
| |
| scratch[1] = *Fout1 * tw[u*fstride]; |
| scratch[2] = *Fout2 * tw[2*u*fstride]; |
| scratch[3] = *Fout3 * tw[3*u*fstride]; |
| scratch[4] = *Fout4 * tw[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] + Complex( |
| (scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ), |
| (scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real()) |
| ); |
| |
| scratch[6] = Complex( |
| (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] + |
| Complex( |
| (scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()), |
| (scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real()) |
| ); |
| |
| scratch[12] = Complex( |
| -(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 bfly_generic( |
| Complex * Fout, |
| const size_t fstride, |
| int m, |
| int p |
| ) |
| { |
| int u,k,q1,q; |
| Complex * twiddles = &m_twiddles[0]; |
| Complex t; |
| int Norig = m_nfft; |
| Complex * scratchbuf = (Complex*)alloca(p*sizeof(Complex) ); |
| |
| for ( u=0; u<m; ++u ) { |
| k=u; |
| for ( q1=0 ; q1<p ; ++q1 ) { |
| scratchbuf[q1] = Fout[ k ]; |
| 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; |
| t=scratchbuf[q] * twiddles[twidx]; |
| Fout[ k ] += t; |
| } |
| k += m; |
| } |
| } |
| } |
| |
| int m_nfft; |
| bool m_inverse; |
| std::vector<Complex> m_twiddles; |
| std::vector<int> m_stageRadix; |
| std::vector<int> m_stageRemainder; |
| }; |
| } |
