| // This file is part of Eigen, a lightweight C++ template library | |
| // for linear algebra. | |
| // | |
| // Copyright (C) 2009 Mark Borgerding mark a borgerding net | |
| // | |
| // This Source Code Form is subject to the terms of the Mozilla | |
| // Public License v. 2.0. If a copy of the MPL was not distributed | |
| // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. | |
| namespace Eigen { | |
| namespace internal { | |
| // This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft | |
| // Copyright 2003-2009 Mark Borgerding | |
| template <typename _Scalar> | |
| struct kiss_cpx_fft | |
| { | |
| typedef _Scalar Scalar; | |
| typedef std::complex<Scalar> Complex; | |
| std::vector<Complex> m_twiddles; | |
| std::vector<int> m_stageRadix; | |
| std::vector<int> m_stageRemainder; | |
| std::vector<Complex> m_scratchBuf; | |
| bool m_inverse; | |
| inline | |
| void make_twiddles(int nfft,bool inverse) | |
| { | |
| using std::acos; | |
| 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) ); | |
| } | |
| void factorize(int nfft) | |
| { | |
| //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;// impossible to have a factor > sqrt(n) | |
| } | |
| n /= p; | |
| m_stageRadix.push_back(p); | |
| m_stageRemainder.push_back(n); | |
| if ( p > 5 ) | |
| m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic | |
| }while(n>1); | |
| } | |
| template <typename _Src> | |
| inline | |
| 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; | |
| } | |
| } | |
| inline | |
| 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; | |
| } | |
| } | |
| inline | |
| 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]; | |
| } | |
| } | |
| inline | |
| 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() - Scalar(.5)*scratch[3].real() , Fout->imag() - Scalar(.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); | |
| } | |
| inline | |
| 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 */ | |
| inline | |
| 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 = static_cast<int>(m_twiddles.size()); | |
| Complex * scratchbuf = &m_scratchBuf[0]; | |
| 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 += static_cast<int>(fstride) * k; | |
| if (twidx>=Norig) twidx-=Norig; | |
| t=scratchbuf[q] * twiddles[twidx]; | |
| Fout[ k ] += t; | |
| } | |
| k += m; | |
| } | |
| } | |
| } | |
| }; | |
| template <typename _Scalar> | |
| struct kissfft_impl | |
| { | |
| typedef _Scalar Scalar; | |
| typedef std::complex<Scalar> Complex; | |
| void clear() | |
| { | |
| m_plans.clear(); | |
| m_realTwiddles.clear(); | |
| } | |
| inline | |
| void fwd( Complex * dst,const Complex *src,int nfft) | |
| { | |
| get_plan(nfft,false).work(0, dst, src, 1,1); | |
| } | |
| inline | |
| void fwd2( Complex * dst,const Complex *src,int n0,int n1) | |
| { | |
| EIGEN_UNUSED_VARIABLE(dst); | |
| EIGEN_UNUSED_VARIABLE(src); | |
| EIGEN_UNUSED_VARIABLE(n0); | |
| EIGEN_UNUSED_VARIABLE(n1); | |
| } | |
| inline | |
| void inv2( Complex * dst,const Complex *src,int n0,int n1) | |
| { | |
| EIGEN_UNUSED_VARIABLE(dst); | |
| EIGEN_UNUSED_VARIABLE(src); | |
| EIGEN_UNUSED_VARIABLE(n0); | |
| EIGEN_UNUSED_VARIABLE(n1); | |
| } | |
| // real-to-complex forward FFT | |
| // perform two FFTs of src even and src odd | |
| // then twiddle to recombine them into the half-spectrum format | |
| // then fill in the conjugate symmetric half | |
| inline | |
| void fwd( Complex * dst,const Scalar * src,int nfft) | |
| { | |
| if ( nfft&3 ) { | |
| // use generic mode for odd | |
| m_tmpBuf1.resize(nfft); | |
| get_plan(nfft,false).work(0, &m_tmpBuf1[0], src, 1,1); | |
| std::copy(m_tmpBuf1.begin(),m_tmpBuf1.begin()+(nfft>>1)+1,dst ); | |
| }else{ | |
| int ncfft = nfft>>1; | |
| int ncfft2 = nfft>>2; | |
| Complex * rtw = real_twiddles(ncfft2); | |
| // use optimized mode for even real | |
| fwd( dst, reinterpret_cast<const Complex*> (src), ncfft); | |
| Complex dc(dst[0].real() + dst[0].imag()); | |
| Complex nyquist(dst[0].real() - dst[0].imag()); | |
| int k; | |
| for ( k=1;k <= ncfft2 ; ++k ) { | |
| Complex fpk = dst[k]; | |
| Complex fpnk = conj(dst[ncfft-k]); | |
| Complex f1k = fpk + fpnk; | |
| Complex f2k = fpk - fpnk; | |
| Complex tw= f2k * rtw[k-1]; | |
| dst[k] = (f1k + tw) * Scalar(.5); | |
| dst[ncfft-k] = conj(f1k -tw)*Scalar(.5); | |
| } | |
| dst[0] = dc; | |
| dst[ncfft] = nyquist; | |
| } | |
| } | |
| // inverse complex-to-complex | |
| inline | |
| void inv(Complex * dst,const Complex *src,int nfft) | |
| { | |
| get_plan(nfft,true).work(0, dst, src, 1,1); | |
| } | |
| // half-complex to scalar | |
| inline | |
| void inv( Scalar * dst,const Complex * src,int nfft) | |
| { | |
| if (nfft&3) { | |
| m_tmpBuf1.resize(nfft); | |
| m_tmpBuf2.resize(nfft); | |
| std::copy(src,src+(nfft>>1)+1,m_tmpBuf1.begin() ); | |
| for (int k=1;k<(nfft>>1)+1;++k) | |
| m_tmpBuf1[nfft-k] = conj(m_tmpBuf1[k]); | |
| inv(&m_tmpBuf2[0],&m_tmpBuf1[0],nfft); | |
| for (int k=0;k<nfft;++k) | |
| dst[k] = m_tmpBuf2[k].real(); | |
| }else{ | |
| // optimized version for multiple of 4 | |
| int ncfft = nfft>>1; | |
| int ncfft2 = nfft>>2; | |
| Complex * rtw = real_twiddles(ncfft2); | |
| m_tmpBuf1.resize(ncfft); | |
| m_tmpBuf1[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() ); | |
| for (int k = 1; k <= ncfft / 2; ++k) { | |
| Complex fk = src[k]; | |
| Complex fnkc = conj(src[ncfft-k]); | |
| Complex fek = fk + fnkc; | |
| Complex tmp = fk - fnkc; | |
| Complex fok = tmp * conj(rtw[k-1]); | |
| m_tmpBuf1[k] = fek + fok; | |
| m_tmpBuf1[ncfft-k] = conj(fek - fok); | |
| } | |
| get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf1[0], 1,1); | |
| } | |
| } | |
| protected: | |
| typedef kiss_cpx_fft<Scalar> PlanData; | |
| typedef std::map<int,PlanData> PlanMap; | |
| PlanMap m_plans; | |
| std::map<int, std::vector<Complex> > m_realTwiddles; | |
| std::vector<Complex> m_tmpBuf1; | |
| std::vector<Complex> m_tmpBuf2; | |
| inline | |
| int PlanKey(int nfft, bool isinverse) const { return (nfft<<1) | int(isinverse); } | |
| inline | |
| PlanData & get_plan(int nfft, bool inverse) | |
| { | |
| // TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles | |
| PlanData & pd = m_plans[ PlanKey(nfft,inverse) ]; | |
| if ( pd.m_twiddles.size() == 0 ) { | |
| pd.make_twiddles(nfft,inverse); | |
| pd.factorize(nfft); | |
| } | |
| return pd; | |
| } | |
| inline | |
| Complex * real_twiddles(int ncfft2) | |
| { | |
| using std::acos; | |
| std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there | |
| if ( (int)twidref.size() != ncfft2 ) { | |
| twidref.resize(ncfft2); | |
| int ncfft= ncfft2<<1; | |
| Scalar pi = acos( Scalar(-1) ); | |
| for (int k=1;k<=ncfft2;++k) | |
| twidref[k-1] = exp( Complex(0,-pi * (Scalar(k) / ncfft + Scalar(.5)) ) ); | |
| } | |
| return &twidref[0]; | |
| } | |
| }; | |
| } // end namespace internal | |
| } // end namespace Eigen | |
| /* vim: set filetype=cpp et sw=2 ts=2 ai: */ |