| // 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/. |
| |
| #include "./InternalHeaderCheck.h" |
| |
| 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 numext::sin; |
| using numext::cos; |
| m_inverse = inverse; |
| m_twiddles.resize(nfft); |
| double phinc = 0.25 * double(EIGEN_PI) / nfft; |
| Scalar flip = inverse ? Scalar(1) : Scalar(-1); |
| m_twiddles[0] = Complex(Scalar(1), Scalar(0)); |
| if ((nfft&1)==0) |
| m_twiddles[nfft/2] = Complex(Scalar(-1), Scalar(0)); |
| int i=1; |
| for (;i*8<nfft;++i) |
| { |
| Scalar c = Scalar(cos(i*8*phinc)); |
| Scalar s = Scalar(sin(i*8*phinc)); |
| m_twiddles[i] = Complex(c, s*flip); |
| m_twiddles[nfft-i] = Complex(c, -s*flip); |
| } |
| for (;i*4<nfft;++i) |
| { |
| Scalar c = Scalar(cos((2*nfft-8*i)*phinc)); |
| Scalar s = Scalar(sin((2*nfft-8*i)*phinc)); |
| m_twiddles[i] = Complex(s, c*flip); |
| m_twiddles[nfft-i] = Complex(s, -c*flip); |
| } |
| for (;i*8<3*nfft;++i) |
| { |
| Scalar c = Scalar(cos((8*i-2*nfft)*phinc)); |
| Scalar s = Scalar(sin((8*i-2*nfft)*phinc)); |
| m_twiddles[i] = Complex(-s, c*flip); |
| m_twiddles[nfft-i] = Complex(-s, -c*flip); |
| } |
| for (;i*2<nfft;++i) |
| { |
| Scalar c = Scalar(cos((4*nfft-8*i)*phinc)); |
| Scalar s = Scalar(sin((4*nfft-8*i)*phinc)); |
| m_twiddles[i] = Complex(-c, s*flip); |
| m_twiddles[nfft-i] = Complex(-c, -s*flip); |
| } |
| } |
| |
| 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 |
