summaryrefslogtreecommitdiffstats
path: root/src/EigenUnsupported/src/FFT/ei_kissfft_impl.h
diff options
context:
space:
mode:
Diffstat (limited to 'src/EigenUnsupported/src/FFT/ei_kissfft_impl.h')
-rw-r--r--src/EigenUnsupported/src/FFT/ei_kissfft_impl.h449
1 files changed, 449 insertions, 0 deletions
diff --git a/src/EigenUnsupported/src/FFT/ei_kissfft_impl.h b/src/EigenUnsupported/src/FFT/ei_kissfft_impl.h
new file mode 100644
index 0000000..430953a
--- /dev/null
+++ b/src/EigenUnsupported/src/FFT/ei_kissfft_impl.h
@@ -0,0 +1,449 @@
+// 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 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
generated by cgit v1.2.1 (git 2.18.0) at 2025-04-05 06:47:40 +0200