mirror of
https://gitlab.com/libeigen/eigen.git
synced 2025-04-23 10:09:36 +08:00
added real-optimized inverse FFT (NFFT must be multiple of 4)
This commit is contained in:
Mark Borgerding
parent
03ed6f9bfb
commit
09b4733255
@ -53,7 +53,7 @@ template <> string nameof<long double>() {return "long double";}
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using namespace Eigen;
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template <typename T>
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void bench(int nfft)
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void bench(int nfft,bool fwd)
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{
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typedef typename NumTraits<T>::Real Scalar;
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typedef typename std::complex<Scalar> Complex;
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@ -69,7 +69,10 @@ void bench(int nfft)
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for (int k=0;k<8;++k) {
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timer.start();
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for(int i = 0; i < nits; i++)
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fft.fwd( outbuf , inbuf);
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if (fwd)
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fft.fwd( outbuf , inbuf);
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else
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fft.inv(inbuf,outbuf);
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timer.stop();
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}
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@ -82,16 +85,27 @@ void bench(int nfft)
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mflops /= 2;
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}
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if (fwd)
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cout << " fwd";
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else
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cout << " inv";
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cout << " NFFT=" << nfft << " " << (double(1e-6*nfft*nits)/timer.value()) << " MS/s " << mflops << "MFLOPS\n";
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}
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int main(int argc,char ** argv)
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{
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bench<complex<float> >(NFFT);
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bench<float>(NFFT);
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bench<complex<double> >(NFFT);
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bench<double>(NFFT);
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bench<complex<long double> >(NFFT);
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bench<long double>(NFFT);
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bench<complex<float> >(NFFT,true);
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bench<complex<float> >(NFFT,false);
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bench<float>(NFFT,true);
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bench<float>(NFFT,false);
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bench<complex<double> >(NFFT,true);
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bench<complex<double> >(NFFT,false);
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bench<double>(NFFT,true);
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bench<double>(NFFT,false);
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bench<complex<long double> >(NFFT,true);
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bench<complex<long double> >(NFFT,false);
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bench<long double>(NFFT,true);
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bench<long double>(NFFT,false);
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return 0;
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}
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@ -28,390 +28,398 @@
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namespace Eigen {
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template <typename _Scalar>
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struct ei_kiss_cpx_fft
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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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{
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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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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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ei_kiss_cpx_fft() { }
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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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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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}
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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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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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);
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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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*Fout2=scratch[11]+scratch[12];
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*Fout3=scratch[11]-scratch[12];
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++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
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}
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}
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/* perform the butterfly for one stage of a mixed radix FFT */
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void bfly_generic(
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Complex * Fout,
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const size_t fstride,
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int m,
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int p
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)
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{
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int u,k,q1,q;
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Complex * twiddles = &m_twiddles[0];
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Complex t;
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int Norig = m_twiddles.size();
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Complex * scratchbuf = (Complex*)alloca(p*sizeof(Complex) );
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for ( u=0; u<m; ++u ) {
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k=u;
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for ( q1=0 ; q1<p ; ++q1 ) {
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scratchbuf[q1] = Fout[ k ];
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k += m;
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}
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void invert()
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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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k=u;
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for ( q1=0 ; q1<p ; ++q1 ) {
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int twidx=0;
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Fout[ k ] = scratchbuf[0];
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for (q=1;q<p;++q ) {
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twidx += fstride * k;
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if (twidx>=Norig) twidx-=Norig;
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t=scratchbuf[q] * twiddles[twidx];
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Fout[ k ] += t;
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}
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k += m;
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}
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void factorize(int nfft)
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{
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if (m_stageRadix.size()==0 || m_stageRadix[0] * m_stageRemainder[0] != nfft)
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{
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m_stageRadix.resize(0);
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m_stageRemainder.resize(0);
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//factorize
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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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}
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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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}
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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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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];
|
||||
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);
|
||||
}
|
||||
|
||||
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 */
|
||||
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;
|
||||
}
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
template <typename _Scalar>
|
||||
struct ei_kissfft_impl
|
||||
{
|
||||
typedef _Scalar Scalar;
|
||||
typedef std::complex<Scalar> Complex;
|
||||
ei_kissfft_impl() {}
|
||||
typedef _Scalar Scalar;
|
||||
typedef std::complex<Scalar> Complex;
|
||||
|
||||
void clear()
|
||||
{
|
||||
void clear()
|
||||
{
|
||||
m_plans.clear();
|
||||
m_realTwiddles.clear();
|
||||
}
|
||||
}
|
||||
|
||||
template <typename _Src>
|
||||
void fwd( Complex * dst,const _Src *src,int nfft)
|
||||
{
|
||||
template <typename _Src>
|
||||
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
|
||||
// then twiddle to recombine them into the half-spectrum format
|
||||
// then fill in the conjugate symmetric half
|
||||
void fwd( Complex * dst,const Scalar * src,int nfft)
|
||||
{
|
||||
// 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
|
||||
void fwd( Complex * dst,const Scalar * src,int nfft)
|
||||
{
|
||||
if ( nfft&3 ) {
|
||||
// use generic mode for odd
|
||||
get_plan(nfft,false).work(0, dst, src, 1,1);
|
||||
// use generic mode for odd
|
||||
get_plan(nfft,false).work(0, dst, src, 1,1);
|
||||
}else{
|
||||
int ncfft = nfft>>1;
|
||||
int ncfft2 = nfft>>2;
|
||||
Complex * rtw = real_twiddles(ncfft2);
|
||||
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];
|
||||
// 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[k] = (f1k + tw) * Scalar(.5);
|
||||
dst[ncfft-k] = conj(f1k -tw)*Scalar(.5);
|
||||
}
|
||||
|
||||
// place conjugate-symmetric half at the end for completeness
|
||||
// TODO: make this configurable ( opt-out )
|
||||
for ( k=1;k < ncfft ; ++k )
|
||||
dst[nfft-k] = conj(dst[k]);
|
||||
|
||||
dst[0] = dc;
|
||||
dst[ncfft] = nyquist;
|
||||
// place conjugate-symmetric half at the end for completeness
|
||||
// TODO: make this configurable ( opt-out )
|
||||
for ( k=1;k < ncfft ; ++k )
|
||||
dst[nfft-k] = conj(dst[k]);
|
||||
dst[0] = dc;
|
||||
dst[ncfft] = nyquist;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// half-complex to scalar
|
||||
void inv( Scalar * dst,const Complex * src,int nfft)
|
||||
{
|
||||
// TODO add optimized version for even numbers
|
||||
std::vector<Complex> tmp(nfft);
|
||||
inv(&tmp[0],src,nfft);
|
||||
for (int k=0;k<nfft;++k)
|
||||
dst[k] = tmp[k].real();
|
||||
}
|
||||
|
||||
void inv(Complex * dst,const Complex *src,int nfft)
|
||||
{
|
||||
// inverse complex-to-complex
|
||||
void inv(Complex * dst,const Complex *src,int nfft)
|
||||
{
|
||||
get_plan(nfft,true).work(0, dst, src, 1,1);
|
||||
scale(dst, nfft, Scalar(1)/nfft );
|
||||
}
|
||||
}
|
||||
|
||||
private:
|
||||
// half-complex to scalar
|
||||
void inv( Scalar * dst,const Complex * src,int nfft)
|
||||
{
|
||||
if (nfft&3) {
|
||||
m_scratchBuf.resize(nfft);
|
||||
inv(&m_scratchBuf[0],src,nfft);
|
||||
for (int k=0;k<nfft;++k)
|
||||
dst[k] = m_scratchBuf[k].real();
|
||||
}else{
|
||||
// optimized version for multiple of 4
|
||||
int ncfft = nfft>>1;
|
||||
int ncfft2 = nfft>>2;
|
||||
Complex * rtw = real_twiddles(ncfft2);
|
||||
m_scratchBuf.resize(ncfft);
|
||||
m_scratchBuf[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_scratchBuf[k] = fek + fok;
|
||||
m_scratchBuf[ncfft-k] = conj(fek - fok);
|
||||
}
|
||||
scale(&m_scratchBuf[0], ncfft, Scalar(1)/nfft );
|
||||
get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_scratchBuf[0], 1,1);
|
||||
}
|
||||
}
|
||||
|
||||
typedef ei_kiss_cpx_fft<Scalar> PlanData;
|
||||
private:
|
||||
|
||||
typedef std::map<int,PlanData> PlanMap;
|
||||
PlanMap m_plans;
|
||||
std::map<int, std::vector<Complex> > m_realTwiddles;
|
||||
typedef ei_kiss_cpx_fft<Scalar> PlanData;
|
||||
|
||||
int PlanKey(int nfft,bool isinverse) const { return (nfft<<1) | isinverse; }
|
||||
typedef std::map<int,PlanData> PlanMap;
|
||||
PlanMap m_plans;
|
||||
std::map<int, std::vector<Complex> > m_realTwiddles;
|
||||
std::vector<Complex> m_scratchBuf;
|
||||
|
||||
PlanData & get_plan(int nfft,bool inverse)
|
||||
{
|
||||
/*
|
||||
int PlanKey(int nfft,bool isinverse) const { return (nfft<<1) | isinverse; }
|
||||
|
||||
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
|
||||
*
|
||||
typedef typename std::map<int,PlanData>::iterator MapIt;
|
||||
MapIt 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.invert();
|
||||
}else{
|
||||
it->second.make_twiddles(nfft,inverse);
|
||||
it->second.factorize(nfft);
|
||||
}
|
||||
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;
|
||||
*/
|
||||
PlanData & pd = m_plans[ PlanKey(nfft,inverse) ];
|
||||
if ( pd.m_twiddles.size() == 0 ) {
|
||||
pd.make_twiddles(nfft,inverse);
|
||||
pd.factorize(nfft);
|
||||
pd.make_twiddles(nfft,inverse);
|
||||
pd.factorize(nfft);
|
||||
}
|
||||
return pd;
|
||||
}
|
||||
}
|
||||
|
||||
Complex * real_twiddles(int ncfft2)
|
||||
{
|
||||
Complex * real_twiddles(int ncfft2)
|
||||
{
|
||||
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 * ((double) (k) / ncfft + .5) ) );
|
||||
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 * ((double) (k) / ncfft + .5) ) );
|
||||
}
|
||||
return &twidref[0];
|
||||
}
|
||||
}
|
||||
|
||||
void scale(Complex *dst,int n,Scalar s)
|
||||
{
|
||||
void scale(Complex *dst,int n,Scalar s)
|
||||
{
|
||||
for (int k=0;k<n;++k)
|
||||
dst[k] *= s;
|
||||
}
|
||||
dst[k] *= s;
|
||||
}
|
||||
};
|
||||
}
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user