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File indexing completed on 2025-01-18 09:57:03 

0001 // This file is part of Eigen, a lightweight C++ template library
0002 // for linear algebra.
0003 //
0004 // Copyright (C) 2009 Mark Borgerding mark a borgerding net
0005 //
0006 // This Source Code Form is subject to the terms of the Mozilla
0007 // Public License v. 2.0. If a copy of the MPL was not distributed
0008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
0009 
0010 namespace Eigen { 
0011 
0012 namespace internal {
0013 
0014   // This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft
0015   // Copyright 2003-2009 Mark Borgerding
0016 
0017 template <typename _Scalar>
0018 struct kiss_cpx_fft
0019 {
0020   typedef _Scalar Scalar;
0021   typedef std::complex<Scalar> Complex;
0022   std::vector<Complex> m_twiddles;
0023   std::vector<int> m_stageRadix;
0024   std::vector<int> m_stageRemainder;
0025   std::vector<Complex> m_scratchBuf;
0026   bool m_inverse;
0027 
0028   inline void make_twiddles(int nfft, bool inverse)
0029   {
0030     using numext::sin;
0031     using numext::cos;
0032     m_inverse = inverse;
0033     m_twiddles.resize(nfft);
0034     double phinc =  0.25 * double(EIGEN_PI) / nfft;
0035     Scalar flip = inverse ? Scalar(1) : Scalar(-1);
0036     m_twiddles[0] = Complex(Scalar(1), Scalar(0));
0037     if ((nfft&1)==0)
0038       m_twiddles[nfft/2] = Complex(Scalar(-1), Scalar(0));
0039     int i=1;
0040     for (;i*8<nfft;++i)
0041     {
0042       Scalar c = Scalar(cos(i*8*phinc));
0043       Scalar s = Scalar(sin(i*8*phinc));
0044       m_twiddles[i] = Complex(c, s*flip);
0045       m_twiddles[nfft-i] = Complex(c, -s*flip);
0046     }
0047     for (;i*4<nfft;++i)
0048     {
0049       Scalar c = Scalar(cos((2*nfft-8*i)*phinc));
0050       Scalar s = Scalar(sin((2*nfft-8*i)*phinc));
0051       m_twiddles[i] = Complex(s, c*flip);
0052       m_twiddles[nfft-i] = Complex(s, -c*flip);
0053     }
0054     for (;i*8<3*nfft;++i)
0055     {
0056       Scalar c = Scalar(cos((8*i-2*nfft)*phinc));
0057       Scalar s = Scalar(sin((8*i-2*nfft)*phinc));
0058       m_twiddles[i] = Complex(-s, c*flip);
0059       m_twiddles[nfft-i] = Complex(-s, -c*flip);
0060     }
0061     for (;i*2<nfft;++i)
0062     {
0063       Scalar c = Scalar(cos((4*nfft-8*i)*phinc));
0064       Scalar s = Scalar(sin((4*nfft-8*i)*phinc));
0065       m_twiddles[i] = Complex(-c, s*flip);
0066       m_twiddles[nfft-i] = Complex(-c, -s*flip);
0067     }
0068   }
0069 
0070   void factorize(int nfft)
0071   {
0072     //start factoring out 4's, then 2's, then 3,5,7,9,...
0073     int n= nfft;
0074     int p=4;
0075     do {
0076       while (n % p) {
0077         switch (p) {
0078           case 4: p = 2; break;
0079           case 2: p = 3; break;
0080           default: p += 2; break;
0081         }
0082         if (p*p>n)
0083           p=n;// impossible to have a factor > sqrt(n)
0084       }
0085       n /= p;
0086       m_stageRadix.push_back(p);
0087       m_stageRemainder.push_back(n);
0088       if ( p > 5 )
0089         m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic
0090     }while(n>1);
0091   }
0092 
0093   template <typename _Src>
0094     inline
0095     void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride)
0096     {
0097       int p = m_stageRadix[stage];
0098       int m = m_stageRemainder[stage];
0099       Complex * Fout_beg = xout;
0100       Complex * Fout_end = xout + p*m;
0101 
0102       if (m>1) {
0103         do{
0104           // recursive call:
0105           // DFT of size m*p performed by doing
0106           // p instances of smaller DFTs of size m, 
0107           // each one takes a decimated version of the input
0108           work(stage+1, xout , xin, fstride*p,in_stride);
0109           xin += fstride*in_stride;
0110         }while( (xout += m) != Fout_end );
0111       }else{
0112         do{
0113           *xout = *xin;
0114           xin += fstride*in_stride;
0115         }while(++xout != Fout_end );
0116       }
0117       xout=Fout_beg;
0118 
0119       // recombine the p smaller DFTs 
0120       switch (p) {
0121         case 2: bfly2(xout,fstride,m); break;
0122         case 3: bfly3(xout,fstride,m); break;
0123         case 4: bfly4(xout,fstride,m); break;
0124         case 5: bfly5(xout,fstride,m); break;
0125         default: bfly_generic(xout,fstride,m,p); break;
0126       }
0127     }
0128 
0129   inline
0130     void bfly2( Complex * Fout, const size_t fstride, int m)
0131     {
0132       for (int k=0;k<m;++k) {
0133         Complex t = Fout[m+k] * m_twiddles[k*fstride];
0134         Fout[m+k] = Fout[k] - t;
0135         Fout[k] += t;
0136       }
0137     }
0138 
0139   inline
0140     void bfly4( Complex * Fout, const size_t fstride, const size_t m)
0141     {
0142       Complex scratch[6];
0143       int negative_if_inverse = m_inverse * -2 +1;
0144       for (size_t k=0;k<m;++k) {
0145         scratch[0] = Fout[k+m] * m_twiddles[k*fstride];
0146         scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];
0147         scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];
0148         scratch[5] = Fout[k] - scratch[1];
0149 
0150         Fout[k] += scratch[1];
0151         scratch[3] = scratch[0] + scratch[2];
0152         scratch[4] = scratch[0] - scratch[2];
0153         scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
0154 
0155         Fout[k+2*m]  = Fout[k] - scratch[3];
0156         Fout[k] += scratch[3];
0157         Fout[k+m] = scratch[5] + scratch[4];
0158         Fout[k+3*m] = scratch[5] - scratch[4];
0159       }
0160     }
0161 
0162   inline
0163     void bfly3( Complex * Fout, const size_t fstride, const size_t m)
0164     {
0165       size_t k=m;
0166       const size_t m2 = 2*m;
0167       Complex *tw1,*tw2;
0168       Complex scratch[5];
0169       Complex epi3;
0170       epi3 = m_twiddles[fstride*m];
0171 
0172       tw1=tw2=&m_twiddles[0];
0173 
0174       do{
0175         scratch[1]=Fout[m] * *tw1;
0176         scratch[2]=Fout[m2] * *tw2;
0177 
0178         scratch[3]=scratch[1]+scratch[2];
0179         scratch[0]=scratch[1]-scratch[2];
0180         tw1 += fstride;
0181         tw2 += fstride*2;
0182         Fout[m] = Complex( Fout->real() - Scalar(.5)*scratch[3].real() , Fout->imag() - Scalar(.5)*scratch[3].imag() );
0183         scratch[0] *= epi3.imag();
0184         *Fout += scratch[3];
0185         Fout[m2] = Complex(  Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
0186         Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );
0187         ++Fout;
0188       }while(--k);
0189     }
0190 
0191   inline
0192     void bfly5( Complex * Fout, const size_t fstride, const size_t m)
0193     {
0194       Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
0195       size_t u;
0196       Complex scratch[13];
0197       Complex * twiddles = &m_twiddles[0];
0198       Complex *tw;
0199       Complex ya,yb;
0200       ya = twiddles[fstride*m];
0201       yb = twiddles[fstride*2*m];
0202 
0203       Fout0=Fout;
0204       Fout1=Fout0+m;
0205       Fout2=Fout0+2*m;
0206       Fout3=Fout0+3*m;
0207       Fout4=Fout0+4*m;
0208 
0209       tw=twiddles;
0210       for ( u=0; u<m; ++u ) {
0211         scratch[0] = *Fout0;
0212 
0213         scratch[1]  = *Fout1 * tw[u*fstride];
0214         scratch[2]  = *Fout2 * tw[2*u*fstride];
0215         scratch[3]  = *Fout3 * tw[3*u*fstride];
0216         scratch[4]  = *Fout4 * tw[4*u*fstride];
0217 
0218         scratch[7] = scratch[1] + scratch[4];
0219         scratch[10] = scratch[1] - scratch[4];
0220         scratch[8] = scratch[2] + scratch[3];
0221         scratch[9] = scratch[2] - scratch[3];
0222 
0223         *Fout0 +=  scratch[7];
0224         *Fout0 +=  scratch[8];
0225 
0226         scratch[5] = scratch[0] + Complex(
0227             (scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),
0228             (scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())
0229             );
0230 
0231         scratch[6] = Complex(
0232             (scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),
0233             -(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())
0234             );
0235 
0236         *Fout1 = scratch[5] - scratch[6];
0237         *Fout4 = scratch[5] + scratch[6];
0238 
0239         scratch[11] = scratch[0] +
0240           Complex(
0241               (scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),
0242               (scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())
0243               );
0244 
0245         scratch[12] = Complex(
0246             -(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
0247             (scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
0248             );
0249 
0250         *Fout2=scratch[11]+scratch[12];
0251         *Fout3=scratch[11]-scratch[12];
0252 
0253         ++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
0254       }
0255     }
0256 
0257   /* perform the butterfly for one stage of a mixed radix FFT */
0258   inline
0259     void bfly_generic(
0260         Complex * Fout,
0261         const size_t fstride,
0262         int m,
0263         int p
0264         )
0265     {
0266       int u,k,q1,q;
0267       Complex * twiddles = &m_twiddles[0];
0268       Complex t;
0269       int Norig = static_cast<int>(m_twiddles.size());
0270       Complex * scratchbuf = &m_scratchBuf[0];
0271 
0272       for ( u=0; u<m; ++u ) {
0273         k=u;
0274         for ( q1=0 ; q1<p ; ++q1 ) {
0275           scratchbuf[q1] = Fout[ k  ];
0276           k += m;
0277         }
0278 
0279         k=u;
0280         for ( q1=0 ; q1<p ; ++q1 ) {
0281           int twidx=0;
0282           Fout[ k ] = scratchbuf[0];
0283           for (q=1;q<p;++q ) {
0284             twidx += static_cast<int>(fstride) * k;
0285             if (twidx>=Norig) twidx-=Norig;
0286             t=scratchbuf[q] * twiddles[twidx];
0287             Fout[ k ] += t;
0288           }
0289           k += m;
0290         }
0291       }
0292     }
0293 };
0294 
0295 template <typename _Scalar>
0296 struct kissfft_impl
0297 {
0298   typedef _Scalar Scalar;
0299   typedef std::complex<Scalar> Complex;
0300 
0301   void clear() 
0302   {
0303     m_plans.clear();
0304     m_realTwiddles.clear();
0305   }
0306 
0307   inline
0308     void fwd( Complex * dst,const Complex *src,int nfft)
0309     {
0310       get_plan(nfft,false).work(0, dst, src, 1,1);
0311     }
0312 
0313   inline
0314     void fwd2( Complex * dst,const Complex *src,int n0,int n1)
0315     {
0316         EIGEN_UNUSED_VARIABLE(dst);
0317         EIGEN_UNUSED_VARIABLE(src);
0318         EIGEN_UNUSED_VARIABLE(n0);
0319         EIGEN_UNUSED_VARIABLE(n1);
0320     }
0321 
0322   inline
0323     void inv2( Complex * dst,const Complex *src,int n0,int n1)
0324     {
0325         EIGEN_UNUSED_VARIABLE(dst);
0326         EIGEN_UNUSED_VARIABLE(src);
0327         EIGEN_UNUSED_VARIABLE(n0);
0328         EIGEN_UNUSED_VARIABLE(n1);
0329     }
0330 
0331   // real-to-complex forward FFT
0332   // perform two FFTs of src even and src odd
0333   // then twiddle to recombine them into the half-spectrum format
0334   // then fill in the conjugate symmetric half
0335   inline
0336     void fwd( Complex * dst,const Scalar * src,int nfft) 
0337     {
0338       if ( nfft&3  ) {
0339         // use generic mode for odd
0340         m_tmpBuf1.resize(nfft);
0341         get_plan(nfft,false).work(0, &m_tmpBuf1[0], src, 1,1);
0342         std::copy(m_tmpBuf1.begin(),m_tmpBuf1.begin()+(nfft>>1)+1,dst );
0343       }else{
0344         int ncfft = nfft>>1;
0345         int ncfft2 = nfft>>2;
0346         Complex * rtw = real_twiddles(ncfft2);
0347 
0348         // use optimized mode for even real
0349         fwd( dst, reinterpret_cast<const Complex*> (src), ncfft);
0350         Complex dc(dst[0].real() +  dst[0].imag());
0351         Complex nyquist(dst[0].real() -  dst[0].imag());
0352         int k;
0353         for ( k=1;k <= ncfft2 ; ++k ) {
0354           Complex fpk = dst[k];
0355           Complex fpnk = conj(dst[ncfft-k]);
0356           Complex f1k = fpk + fpnk;
0357           Complex f2k = fpk - fpnk;
0358           Complex tw= f2k * rtw[k-1];
0359           dst[k] =  (f1k + tw) * Scalar(.5);
0360           dst[ncfft-k] =  conj(f1k -tw)*Scalar(.5);
0361         }
0362         dst[0] = dc;
0363         dst[ncfft] = nyquist;
0364       }
0365     }
0366 
0367   // inverse complex-to-complex
0368   inline
0369     void inv(Complex * dst,const Complex  *src,int nfft)
0370     {
0371       get_plan(nfft,true).work(0, dst, src, 1,1);
0372     }
0373 
0374   // half-complex to scalar
0375   inline
0376     void inv( Scalar * dst,const Complex * src,int nfft) 
0377     {
0378       if (nfft&3) {
0379         m_tmpBuf1.resize(nfft);
0380         m_tmpBuf2.resize(nfft);
0381         std::copy(src,src+(nfft>>1)+1,m_tmpBuf1.begin() );
0382         for (int k=1;k<(nfft>>1)+1;++k)
0383           m_tmpBuf1[nfft-k] = conj(m_tmpBuf1[k]);
0384         inv(&m_tmpBuf2[0],&m_tmpBuf1[0],nfft);
0385         for (int k=0;k<nfft;++k)
0386           dst[k] = m_tmpBuf2[k].real();
0387       }else{
0388         // optimized version for multiple of 4
0389         int ncfft = nfft>>1;
0390         int ncfft2 = nfft>>2;
0391         Complex * rtw = real_twiddles(ncfft2);
0392         m_tmpBuf1.resize(ncfft);
0393         m_tmpBuf1[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() );
0394         for (int k = 1; k <= ncfft / 2; ++k) {
0395           Complex fk = src[k];
0396           Complex fnkc = conj(src[ncfft-k]);
0397           Complex fek = fk + fnkc;
0398           Complex tmp = fk - fnkc;
0399           Complex fok = tmp * conj(rtw[k-1]);
0400           m_tmpBuf1[k] = fek + fok;
0401           m_tmpBuf1[ncfft-k] = conj(fek - fok);
0402         }
0403         get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf1[0], 1,1);
0404       }
0405     }
0406 
0407   protected:
0408   typedef kiss_cpx_fft<Scalar> PlanData;
0409   typedef std::map<int,PlanData> PlanMap;
0410 
0411   PlanMap m_plans;
0412   std::map<int, std::vector<Complex> > m_realTwiddles;
0413   std::vector<Complex> m_tmpBuf1;
0414   std::vector<Complex> m_tmpBuf2;
0415 
0416   inline
0417     int PlanKey(int nfft, bool isinverse) const { return (nfft<<1) | int(isinverse); }
0418 
0419   inline
0420     PlanData & get_plan(int nfft, bool inverse)
0421     {
0422       // TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles
0423       PlanData & pd = m_plans[ PlanKey(nfft,inverse) ];
0424       if ( pd.m_twiddles.size() == 0 ) {
0425         pd.make_twiddles(nfft,inverse);
0426         pd.factorize(nfft);
0427       }
0428       return pd;
0429     }
0430 
0431   inline
0432     Complex * real_twiddles(int ncfft2)
0433     {
0434       using std::acos;
0435       std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
0436       if ( (int)twidref.size() != ncfft2 ) {
0437         twidref.resize(ncfft2);
0438         int ncfft= ncfft2<<1;
0439         Scalar pi =  acos( Scalar(-1) );
0440         for (int k=1;k<=ncfft2;++k) 
0441           twidref[k-1] = exp( Complex(0,-pi * (Scalar(k) / ncfft + Scalar(.5)) ) );
0442       }
0443       return &twidref[0];
0444     }
0445 };
0446 
0447 } // end namespace internal
0448 
0449 } // end namespace Eigen
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