301 lines
10 KiB
C++
301 lines
10 KiB
C++
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#ifndef KISSFFT_CLASS_HH
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#define KISSFFT_CLASS_HH
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#include <complex>
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#include <vector>
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namespace kissfft_utils {
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template <typename T_scalar>
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struct traits
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{
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typedef T_scalar scalar_type;
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typedef std::complex<scalar_type> cpx_type;
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void fill_twiddles( std::complex<T_scalar> * dst ,int nfft,bool inverse)
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{
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T_scalar phinc = (inverse?2:-2)* acos( (T_scalar) -1) / nfft;
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for (int i=0;i<nfft;++i)
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dst[i] = exp( std::complex<T_scalar>(0,i*phinc) );
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}
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void prepare(
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std::vector< std::complex<T_scalar> > & dst,
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int nfft,bool inverse,
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std::vector<int> & stageRadix,
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std::vector<int> & stageRemainder )
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{
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_twiddles.resize(nfft);
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fill_twiddles( &_twiddles[0],nfft,inverse);
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dst = _twiddles;
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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;// no more factors
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}
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n /= p;
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stageRadix.push_back(p);
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stageRemainder.push_back(n);
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}while(n>1);
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}
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std::vector<cpx_type> _twiddles;
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const cpx_type twiddle(int i) { return _twiddles[i]; }
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};
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}
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template <typename T_Scalar,
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typename T_traits=kissfft_utils::traits<T_Scalar>
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>
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class kissfft
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{
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public:
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typedef T_traits traits_type;
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typedef typename traits_type::scalar_type scalar_type;
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typedef typename traits_type::cpx_type cpx_type;
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kissfft(int nfft,bool inverse,const traits_type & traits=traits_type() )
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:_nfft(nfft),_inverse(inverse),_traits(traits)
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{
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_traits.prepare(_twiddles, _nfft,_inverse ,_stageRadix, _stageRemainder);
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}
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void transform(const cpx_type * src , cpx_type * dst)
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{
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kf_work(0, dst, src, 1,1);
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}
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private:
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void kf_work( int stage,cpx_type * Fout, const cpx_type * f, size_t fstride,size_t in_stride)
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{
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int p = _stageRadix[stage];
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int m = _stageRemainder[stage];
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cpx_type * Fout_beg = Fout;
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cpx_type * Fout_end = Fout + p*m;
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if (m==1) {
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do{
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*Fout = *f;
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f += fstride*in_stride;
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}while(++Fout != Fout_end );
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}else{
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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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kf_work(stage+1, Fout , f, fstride*p,in_stride);
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f += fstride*in_stride;
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}while( (Fout += m) != Fout_end );
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}
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Fout=Fout_beg;
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// recombine the p smaller DFTs
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switch (p) {
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case 2: kf_bfly2(Fout,fstride,m); break;
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case 3: kf_bfly3(Fout,fstride,m); break;
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case 4: kf_bfly4(Fout,fstride,m); break;
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case 5: kf_bfly5(Fout,fstride,m); break;
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default: kf_bfly_generic(Fout,fstride,m,p); break;
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}
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}
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// these were #define macros in the original kiss_fft
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void C_ADD( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a+b;}
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void C_MUL( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a*b;}
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void C_SUB( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a-b;}
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void C_ADDTO( cpx_type & c,const cpx_type & a) { c+=a;}
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void C_FIXDIV( cpx_type & ,int ) {} // NO-OP for float types
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scalar_type S_MUL( const scalar_type & a,const scalar_type & b) { return a*b;}
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scalar_type HALF_OF( const scalar_type & a) { return a*.5;}
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void C_MULBYSCALAR(cpx_type & c,const scalar_type & a) {c*=a;}
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void kf_bfly2( cpx_type * 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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cpx_type t = Fout[m+k] * _traits.twiddle(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 kf_bfly4( cpx_type * Fout, const size_t fstride, const size_t m)
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{
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cpx_type scratch[7];
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int negative_if_inverse = _inverse * -2 +1;
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for (size_t k=0;k<m;++k) {
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scratch[0] = Fout[k+m] * _traits.twiddle(k*fstride);
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scratch[1] = Fout[k+2*m] * _traits.twiddle(k*fstride*2);
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scratch[2] = Fout[k+3*m] * _traits.twiddle(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] = cpx_type( 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 kf_bfly3( cpx_type * 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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cpx_type *tw1,*tw2;
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cpx_type scratch[5];
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cpx_type epi3;
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epi3 = _twiddles[fstride*m];
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tw1=tw2=&_twiddles[0];
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do{
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C_FIXDIV(*Fout,3); C_FIXDIV(Fout[m],3); C_FIXDIV(Fout[m2],3);
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C_MUL(scratch[1],Fout[m] , *tw1);
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C_MUL(scratch[2],Fout[m2] , *tw2);
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C_ADD(scratch[3],scratch[1],scratch[2]);
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C_SUB(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] = cpx_type( Fout->real() - HALF_OF(scratch[3].real() ) , Fout->imag() - HALF_OF(scratch[3].imag() ) );
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C_MULBYSCALAR( scratch[0] , epi3.imag() );
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C_ADDTO(*Fout,scratch[3]);
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Fout[m2] = cpx_type( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
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C_ADDTO( Fout[m] , cpx_type( -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 kf_bfly5( cpx_type * Fout, const size_t fstride, const size_t m)
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{
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cpx_type *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
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size_t u;
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cpx_type scratch[13];
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cpx_type * twiddles = &_twiddles[0];
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cpx_type *tw;
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cpx_type 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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C_FIXDIV( *Fout0,5); C_FIXDIV( *Fout1,5); C_FIXDIV( *Fout2,5); C_FIXDIV( *Fout3,5); C_FIXDIV( *Fout4,5);
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scratch[0] = *Fout0;
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C_MUL(scratch[1] ,*Fout1, tw[u*fstride]);
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C_MUL(scratch[2] ,*Fout2, tw[2*u*fstride]);
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C_MUL(scratch[3] ,*Fout3, tw[3*u*fstride]);
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C_MUL(scratch[4] ,*Fout4, tw[4*u*fstride]);
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C_ADD( scratch[7],scratch[1],scratch[4]);
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C_SUB( scratch[10],scratch[1],scratch[4]);
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C_ADD( scratch[8],scratch[2],scratch[3]);
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C_SUB( scratch[9],scratch[2],scratch[3]);
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C_ADDTO( *Fout0, scratch[7]);
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C_ADDTO( *Fout0, scratch[8]);
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scratch[5] = scratch[0] + cpx_type(
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S_MUL(scratch[7].real(),ya.real() ) + S_MUL(scratch[8].real() ,yb.real() ),
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S_MUL(scratch[7].imag(),ya.real()) + S_MUL(scratch[8].imag(),yb.real())
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);
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scratch[6] = cpx_type(
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S_MUL(scratch[10].imag(),ya.imag()) + S_MUL(scratch[9].imag(),yb.imag()),
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-S_MUL(scratch[10].real(),ya.imag()) - S_MUL(scratch[9].real(),yb.imag())
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);
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C_SUB(*Fout1,scratch[5],scratch[6]);
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C_ADD(*Fout4,scratch[5],scratch[6]);
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scratch[11] = scratch[0] +
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cpx_type(
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S_MUL(scratch[7].real(),yb.real()) + S_MUL(scratch[8].real(),ya.real()),
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S_MUL(scratch[7].imag(),yb.real()) + S_MUL(scratch[8].imag(),ya.real())
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);
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scratch[12] = cpx_type(
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-S_MUL(scratch[10].imag(),yb.imag()) + S_MUL(scratch[9].imag(),ya.imag()),
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S_MUL(scratch[10].real(),yb.imag()) - S_MUL(scratch[9].real(),ya.imag())
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);
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C_ADD(*Fout2,scratch[11],scratch[12]);
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C_SUB(*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 kf_bfly_generic(
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cpx_type * 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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cpx_type * twiddles = &_twiddles[0];
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cpx_type t;
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int Norig = _nfft;
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cpx_type scratchbuf[p];
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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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C_FIXDIV(scratchbuf[q1],p);
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k += m;
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}
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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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C_MUL(t,scratchbuf[q] , twiddles[twidx] );
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C_ADDTO( Fout[ k ] ,t);
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}
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k += m;
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}
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}
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}
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int _nfft;
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bool _inverse;
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std::vector<cpx_type> _twiddles;
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std::vector<int> _stageRadix;
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std::vector<int> _stageRemainder;
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traits_type _traits;
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};
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#endif
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