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various comment changes
This commit is contained in:
Mark Borgerding
parent
09b4733255
commit
f13e000b45
@ -1,5 +1,5 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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// for linear algebra.
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//
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// Copyright (C) 2009 Mark Borgerding mark a borgerding net
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//
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@ -29,14 +29,14 @@
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#include "src/FFT/ei_kissfft_impl.h"
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#define DEFAULT_FFT_IMPL ei_kissfft_impl
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// FFTW: faster, GPL-not LGPL, bigger code size
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// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size
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#ifdef FFTW_PATIENT // definition of FFTW_PATIENT indicates the caller has included fftw3.h, we can use FFTW routines
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// TODO
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// #include "src/FFT/ei_fftw_impl.h"
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// #define DEFAULT_FFT_IMPL ei_fftw_impl
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#endif
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// intel Math Kernel Library: fastest, commerical
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// intel Math Kernel Library: fastest, commerical -- incompatible with Eigen in GPL form
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#ifdef _MKL_DFTI_H_ // mkl_dfti.h has been included, we can use MKL FFT routines
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// TODO
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// #include "src/FFT/ei_imkl_impl.h"
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@ -1,5 +1,5 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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// for linear algebra.
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//
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// Copyright (C) 2009 Mark Borgerding mark a borgerding net
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//
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@ -28,252 +28,255 @@
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namespace Eigen {
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// This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft
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// Copyright 2003-2009 Mark Borgerding
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template <typename _Scalar>
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struct ei_kiss_cpx_fft
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{
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typedef _Scalar Scalar;
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typedef std::complex<Scalar> Complex;
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std::vector<Complex> m_twiddles;
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std::vector<int> m_stageRadix;
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std::vector<int> m_stageRemainder;
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bool m_inverse;
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void make_twiddles(int nfft,bool inverse)
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struct ei_kiss_cpx_fft
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{
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m_inverse = inverse;
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m_twiddles.resize(nfft);
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Scalar phinc = (inverse?2:-2)* acos( (Scalar) -1) / nfft;
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for (int i=0;i<nfft;++i)
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m_twiddles[i] = exp( Complex(0,i*phinc) );
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}
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typedef _Scalar Scalar;
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typedef std::complex<Scalar> Complex;
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std::vector<Complex> m_twiddles;
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std::vector<int> m_stageRadix;
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std::vector<int> m_stageRemainder;
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bool m_inverse;
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void conjugate()
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{
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m_inverse = !m_inverse;
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for ( size_t i=0;i<m_twiddles.size() ;++i)
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m_twiddles[i] = conj( m_twiddles[i] );
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}
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void make_twiddles(int nfft,bool inverse)
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{
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m_inverse = inverse;
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m_twiddles.resize(nfft);
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Scalar phinc = (inverse?2:-2)* acos( (Scalar) -1) / nfft;
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for (int i=0;i<nfft;++i)
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m_twiddles[i] = exp( Complex(0,i*phinc) );
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}
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void factorize(int nfft)
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{
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//start factoring out 4's, then 2's, then 3,5,7,9,...
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int n= nfft;
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int p=4;
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do {
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while (n % p) {
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switch (p) {
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case 4: p = 2; break;
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case 2: p = 3; break;
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default: p += 2; break;
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void conjugate()
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{
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m_inverse = !m_inverse;
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for ( size_t i=0;i<m_twiddles.size() ;++i)
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m_twiddles[i] = conj( m_twiddles[i] );
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}
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void factorize(int nfft)
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{
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//start factoring out 4's, then 2's, then 3,5,7,9,...
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int n= nfft;
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int p=4;
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do {
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while (n % p) {
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switch (p) {
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case 4: p = 2; break;
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case 2: p = 3; break;
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default: p += 2; break;
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}
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if (p*p>n)
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p=n;// impossible to have a factor > sqrt(n)
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}
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n /= p;
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m_stageRadix.push_back(p);
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m_stageRemainder.push_back(n);
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}while(n>1);
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}
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template <typename _Src>
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void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride)
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{
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int p = m_stageRadix[stage];
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int m = m_stageRemainder[stage];
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Complex * Fout_beg = xout;
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Complex * Fout_end = xout + p*m;
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if (m>1) {
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do{
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// recursive call:
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// DFT of size m*p performed by doing
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// p instances of smaller DFTs of size m,
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// each one takes a decimated version of the input
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work(stage+1, xout , xin, fstride*p,in_stride);
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xin += fstride*in_stride;
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}while( (xout += m) != Fout_end );
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}else{
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do{
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*xout = *xin;
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xin += fstride*in_stride;
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}while(++xout != Fout_end );
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}
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xout=Fout_beg;
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// recombine the p smaller DFTs
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switch (p) {
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case 2: bfly2(xout,fstride,m); break;
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case 3: bfly3(xout,fstride,m); break;
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case 4: bfly4(xout,fstride,m); break;
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case 5: bfly5(xout,fstride,m); break;
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default: bfly_generic(xout,fstride,m,p); break;
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}
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if (p*p>n)
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p=n;// impossible to have a factor > sqrt(n)
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}
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n /= p;
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m_stageRadix.push_back(p);
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m_stageRemainder.push_back(n);
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}while(n>1);
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}
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template <typename _Src>
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void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride)
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{
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int p = m_stageRadix[stage];
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int m = m_stageRemainder[stage];
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Complex * Fout_beg = xout;
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Complex * Fout_end = xout + p*m;
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void bfly2( Complex * Fout, const size_t fstride, int m)
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{
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for (int k=0;k<m;++k) {
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Complex t = Fout[m+k] * m_twiddles[k*fstride];
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Fout[m+k] = Fout[k] - t;
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Fout[k] += t;
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}
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}
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void bfly4( Complex * Fout, const size_t fstride, const size_t m)
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{
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Complex scratch[6];
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int negative_if_inverse = m_inverse * -2 +1;
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for (size_t k=0;k<m;++k) {
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scratch[0] = Fout[k+m] * m_twiddles[k*fstride];
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scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];
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scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];
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scratch[5] = Fout[k] - scratch[1];
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Fout[k] += scratch[1];
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scratch[3] = scratch[0] + scratch[2];
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scratch[4] = scratch[0] - scratch[2];
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scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
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Fout[k+2*m] = Fout[k] - scratch[3];
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Fout[k] += scratch[3];
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Fout[k+m] = scratch[5] + scratch[4];
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Fout[k+3*m] = scratch[5] - scratch[4];
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}
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}
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void bfly3( Complex * Fout, const size_t fstride, const size_t m)
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{
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size_t k=m;
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const size_t m2 = 2*m;
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Complex *tw1,*tw2;
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Complex scratch[5];
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Complex epi3;
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epi3 = m_twiddles[fstride*m];
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tw1=tw2=&m_twiddles[0];
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if (m>1) {
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do{
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// recursive call:
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// DFT of size m*p performed by doing
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// p instances of smaller DFTs of size m,
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// each one takes a decimated version of the input
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work(stage+1, xout , xin, fstride*p,in_stride);
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xin += fstride*in_stride;
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}while( (xout += m) != Fout_end );
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}else{
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do{
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*xout = *xin;
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xin += fstride*in_stride;
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}while(++xout != Fout_end );
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scratch[1]=Fout[m] * *tw1;
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scratch[2]=Fout[m2] * *tw2;
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scratch[3]=scratch[1]+scratch[2];
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scratch[0]=scratch[1]-scratch[2];
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tw1 += fstride;
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tw2 += fstride*2;
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Fout[m] = Complex( Fout->real() - .5*scratch[3].real() , Fout->imag() - .5*scratch[3].imag() );
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scratch[0] *= epi3.imag();
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*Fout += scratch[3];
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Fout[m2] = Complex( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
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Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );
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++Fout;
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}while(--k);
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}
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xout=Fout_beg;
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// recombine the p smaller DFTs
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switch (p) {
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case 2: bfly2(xout,fstride,m); break;
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case 3: bfly3(xout,fstride,m); break;
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case 4: bfly4(xout,fstride,m); break;
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case 5: bfly5(xout,fstride,m); break;
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default: bfly_generic(xout,fstride,m,p); break;
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}
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}
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void bfly5( Complex * Fout, const size_t fstride, const size_t m)
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{
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Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
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size_t u;
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Complex scratch[13];
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Complex * twiddles = &m_twiddles[0];
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Complex *tw;
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Complex ya,yb;
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ya = twiddles[fstride*m];
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yb = twiddles[fstride*2*m];
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void bfly2( Complex * Fout, const size_t fstride, int m)
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{
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for (int k=0;k<m;++k) {
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Complex t = Fout[m+k] * m_twiddles[k*fstride];
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Fout[m+k] = Fout[k] - t;
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Fout[k] += t;
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}
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}
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Fout0=Fout;
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Fout1=Fout0+m;
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Fout2=Fout0+2*m;
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Fout3=Fout0+3*m;
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Fout4=Fout0+4*m;
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void bfly4( Complex * Fout, const size_t fstride, const size_t m)
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{
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Complex scratch[6];
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int negative_if_inverse = m_inverse * -2 +1;
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for (size_t k=0;k<m;++k) {
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scratch[0] = Fout[k+m] * m_twiddles[k*fstride];
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scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];
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scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];
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scratch[5] = Fout[k] - scratch[1];
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tw=twiddles;
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for ( u=0; u<m; ++u ) {
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scratch[0] = *Fout0;
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Fout[k] += scratch[1];
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scratch[3] = scratch[0] + scratch[2];
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scratch[4] = scratch[0] - scratch[2];
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scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
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scratch[1] = *Fout1 * tw[u*fstride];
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scratch[2] = *Fout2 * tw[2*u*fstride];
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scratch[3] = *Fout3 * tw[3*u*fstride];
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scratch[4] = *Fout4 * tw[4*u*fstride];
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Fout[k+2*m] = Fout[k] - scratch[3];
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Fout[k] += scratch[3];
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Fout[k+m] = scratch[5] + scratch[4];
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Fout[k+3*m] = scratch[5] - scratch[4];
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}
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}
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scratch[7] = scratch[1] + scratch[4];
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scratch[10] = scratch[1] - scratch[4];
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scratch[8] = scratch[2] + scratch[3];
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scratch[9] = scratch[2] - scratch[3];
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void bfly3( Complex * Fout, const size_t fstride, const size_t m)
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{
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size_t k=m;
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const size_t m2 = 2*m;
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Complex *tw1,*tw2;
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Complex scratch[5];
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Complex epi3;
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epi3 = m_twiddles[fstride*m];
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*Fout0 += scratch[7];
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*Fout0 += scratch[8];
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tw1=tw2=&m_twiddles[0];
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do{
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scratch[1]=Fout[m] * *tw1;
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scratch[2]=Fout[m2] * *tw2;
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scratch[3]=scratch[1]+scratch[2];
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scratch[0]=scratch[1]-scratch[2];
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tw1 += fstride;
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tw2 += fstride*2;
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Fout[m] = Complex( Fout->real() - .5*scratch[3].real() , Fout->imag() - .5*scratch[3].imag() );
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scratch[0] *= epi3.imag();
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*Fout += scratch[3];
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Fout[m2] = Complex( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
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Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );
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++Fout;
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}while(--k);
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}
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void bfly5( Complex * Fout, const size_t fstride, const size_t m)
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{
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Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
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size_t u;
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Complex scratch[13];
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Complex * twiddles = &m_twiddles[0];
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Complex *tw;
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Complex ya,yb;
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ya = twiddles[fstride*m];
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yb = twiddles[fstride*2*m];
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Fout0=Fout;
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Fout1=Fout0+m;
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Fout2=Fout0+2*m;
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Fout3=Fout0+3*m;
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Fout4=Fout0+4*m;
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tw=twiddles;
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for ( u=0; u<m; ++u ) {
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scratch[0] = *Fout0;
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scratch[1] = *Fout1 * tw[u*fstride];
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scratch[2] = *Fout2 * tw[2*u*fstride];
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scratch[3] = *Fout3 * tw[3*u*fstride];
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scratch[4] = *Fout4 * tw[4*u*fstride];
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scratch[7] = scratch[1] + scratch[4];
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scratch[10] = scratch[1] - scratch[4];
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scratch[8] = scratch[2] + scratch[3];
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scratch[9] = scratch[2] - scratch[3];
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*Fout0 += scratch[7];
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*Fout0 += scratch[8];
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scratch[5] = scratch[0] + Complex(
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(scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),
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(scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())
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);
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scratch[6] = Complex(
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(scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),
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-(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())
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);
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*Fout1 = scratch[5] - scratch[6];
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*Fout4 = scratch[5] + scratch[6];
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scratch[11] = scratch[0] +
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Complex(
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(scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),
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(scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())
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scratch[5] = scratch[0] + Complex(
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(scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),
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(scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())
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);
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scratch[12] = Complex(
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-(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
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(scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
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);
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scratch[6] = Complex(
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(scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),
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-(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())
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);
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*Fout2=scratch[11]+scratch[12];
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*Fout3=scratch[11]-scratch[12];
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*Fout1 = scratch[5] - scratch[6];
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*Fout4 = scratch[5] + scratch[6];
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++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
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}
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}
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scratch[11] = scratch[0] +
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Complex(
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(scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),
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(scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())
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);
|
||||
|
||||
/* 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_twiddles.size();
|
||||
Complex * scratchbuf = (Complex*)alloca(p*sizeof(Complex) );
|
||||
scratch[12] = Complex(
|
||||
-(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
|
||||
(scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
|
||||
);
|
||||
|
||||
for ( u=0; u<m; ++u ) {
|
||||
k=u;
|
||||
for ( q1=0 ; q1<p ; ++q1 ) {
|
||||
scratchbuf[q1] = Fout[ k ];
|
||||
k += m;
|
||||
*Fout2=scratch[11]+scratch[12];
|
||||
*Fout3=scratch[11]-scratch[12];
|
||||
|
||||
++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
|
||||
}
|
||||
}
|
||||
|
||||
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;
|
||||
/* 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_twiddles.size();
|
||||
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;
|
||||
}
|
||||
k += m;
|
||||
}
|
||||
}
|
||||
}
|
||||
};
|
||||
};
|
||||
|
||||
template <typename _Scalar>
|
||||
struct ei_kissfft_impl
|
||||
{
|
||||
struct ei_kissfft_impl
|
||||
{
|
||||
typedef _Scalar Scalar;
|
||||
typedef std::complex<Scalar> Complex;
|
||||
|
||||
@ -284,10 +287,10 @@ namespace Eigen {
|
||||
}
|
||||
|
||||
template <typename _Src>
|
||||
void fwd( Complex * dst,const _Src *src,int nfft)
|
||||
{
|
||||
get_plan(nfft,false).work(0, dst, src, 1,1);
|
||||
}
|
||||
void fwd( Complex * dst,const _Src *src,int nfft)
|
||||
{
|
||||
get_plan(nfft,false).work(0, dst, src, 1,1);
|
||||
}
|
||||
|
||||
// real-to-complex forward FFT
|
||||
// perform two FFTs of src even and src odd
|
||||
@ -363,11 +366,10 @@ namespace Eigen {
|
||||
}
|
||||
}
|
||||
|
||||
private:
|
||||
|
||||
private:
|
||||
typedef ei_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_scratchBuf;
|
||||
@ -376,25 +378,7 @@ namespace Eigen {
|
||||
|
||||
PlanData & get_plan(int nfft,bool inverse)
|
||||
{
|
||||
/* TODO: figure out why this does not work (g++ 4.3.2)
|
||||
* for some reason this does not work
|
||||
*
|
||||
PlanMap::iterator it;
|
||||
it = m_plans.find( PlanKey(nfft,inverse) );
|
||||
if (it == m_plans.end() ) {
|
||||
// create new entry
|
||||
it = m_plans.insert( make_pair( PlanKey(nfft,inverse) , PlanData() ) );
|
||||
MapIt it2 = m_plans.find( PlanKey(nfft,!inverse) );
|
||||
if (it2 != m_plans.end() ) {
|
||||
it->second = it2.second;
|
||||
it->second.conjugate();
|
||||
}else{
|
||||
it->second.make_twiddles(nfft,inverse);
|
||||
it->second.factorize(nfft);
|
||||
}
|
||||
}
|
||||
return it->second;
|
||||
*/
|
||||
// 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);
|
||||
@ -421,5 +405,5 @@ namespace Eigen {
|
||||
for (int k=0;k<n;++k)
|
||||
dst[k] *= s;
|
||||
}
|
||||
};
|
||||
};
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user