git.sesse.net Git - kdenlive/blob - src/kiss_fft/kissfft.hh

   1 #ifndef KISSFFT_CLASS_HH
   2 #include <complex>
   3 #include <vector>
   4
   5 namespace kissfft_utils {
   6
   7 template <typename T_scalar>
   8 struct traits
   9 {
  10     typedef T_scalar scalar_type;
  11     typedef std::complex<scalar_type> cpx_type;
  12     void fill_twiddles( std::complex<T_scalar> * dst ,int nfft,bool inverse)
  13     {
  14         T_scalar phinc =  (inverse?2:-2)* acos( (T_scalar) -1)  / nfft;
  15         for (int i=0;i<nfft;++i)
  16             dst[i] = exp( std::complex<T_scalar>(0,i*phinc) );
  17     }
  18
  19     void prepare(
  20             std::vector< std::complex<T_scalar> > & dst,
  21             int nfft,bool inverse,
  22             std::vector<int> & stageRadix,
  23             std::vector<int> & stageRemainder )
  24     {
  25         _twiddles.resize(nfft);
  26         fill_twiddles( &_twiddles[0],nfft,inverse);
  27         dst = _twiddles;
  28
  29         //factorize
  30         //start factoring out 4's, then 2's, then 3,5,7,9,...
  31         int n= nfft;
  32         int p=4;
  33         do {
  34             while (n % p) {
  35                 switch (p) {
  36                     case 4: p = 2; break;
  37                     case 2: p = 3; break;
  38                     default: p += 2; break;
  39                 }
  40                 if (p*p>n)
  41                     p=n;// no more factors
  42             }
  43             n /= p;
  44             stageRadix.push_back(p);
  45             stageRemainder.push_back(n);
  46         }while(n>1);
  47     }
  48     std::vector<cpx_type> _twiddles;
  49
  50
  51     const cpx_type twiddle(int i) { return _twiddles[i]; }
  52 };
  53
  54 }
  55
  56 template <typename T_Scalar,
  57          typename T_traits=kissfft_utils::traits<T_Scalar>
  58          >
  59 class kissfft
  60 {
  61     public:
  62         typedef T_traits traits_type;
  63         typedef typename traits_type::scalar_type scalar_type;
  64         typedef typename traits_type::cpx_type cpx_type;
  65
  66         kissfft(int nfft,bool inverse,const traits_type & traits=traits_type() )
  67             :_nfft(nfft),_inverse(inverse),_traits(traits)
  68         {
  69             _traits.prepare(_twiddles, _nfft,_inverse ,_stageRadix, _stageRemainder);
  70         }
  71
  72         void transform(const cpx_type * src , cpx_type * dst)
  73         {
  74             kf_work(0, dst, src, 1,1);
  75         }
  76
  77     private:
  78         void kf_work( int stage,cpx_type * Fout, const cpx_type * f, size_t fstride,size_t in_stride)
  79         {
  80             int p = _stageRadix[stage];
  81             int m = _stageRemainder[stage];
  82             cpx_type * Fout_beg = Fout;
  83             cpx_type * Fout_end = Fout + p*m;
  84
  85             if (m==1) {
  86                 do{
  87                     *Fout = *f;
  88                     f += fstride*in_stride;
  89                 }while(++Fout != Fout_end );
  90             }else{
  91                 do{
  92                     // recursive call:
  93                     // DFT of size m*p performed by doing
  94                     // p instances of smaller DFTs of size m,
  95                     // each one takes a decimated version of the input
  96                     kf_work(stage+1, Fout , f, fstride*p,in_stride);
  97                     f += fstride*in_stride;
  98                 }while( (Fout += m) != Fout_end );
  99             }
 100
 101             Fout=Fout_beg;
 102
 103             // recombine the p smaller DFTs
 104             switch (p) {
 105                 case 2: kf_bfly2(Fout,fstride,m); break;
 106                 case 3: kf_bfly3(Fout,fstride,m); break;
 107                 case 4: kf_bfly4(Fout,fstride,m); break;
 108                 case 5: kf_bfly5(Fout,fstride,m); break;
 109                 default: kf_bfly_generic(Fout,fstride,m,p); break;
 110             }
 111         }
 112
 113         // these were #define macros in the original kiss_fft
 114         void C_ADD( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a+b;}
 115         void C_MUL( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a*b;}
 116         void C_SUB( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a-b;}
 117         void C_ADDTO( cpx_type & c,const cpx_type & a) { c+=a;}
 118         void C_FIXDIV( cpx_type & ,int ) {} // NO-OP for float types
 119         scalar_type S_MUL( const scalar_type & a,const scalar_type & b) { return a*b;}
 120         scalar_type HALF_OF( const scalar_type & a) { return a*.5;}
 121         void C_MULBYSCALAR(cpx_type & c,const scalar_type & a) {c*=a;}
 122
 123         void kf_bfly2( cpx_type * Fout, const size_t fstride, int m)
 124         {
 125             for (int k=0;k<m;++k) {
 126                 cpx_type t = Fout[m+k] * _traits.twiddle(k*fstride);
 127                 Fout[m+k] = Fout[k] - t;
 128                 Fout[k] += t;
 129             }
 130         }
 131
 132         void kf_bfly4( cpx_type * Fout, const size_t fstride, const size_t m)
 133         {
 134             cpx_type scratch[7];
 135             int negative_if_inverse = _inverse * -2 +1;
 136             for (size_t k=0;k<m;++k) {
 137                 scratch[0] = Fout[k+m] * _traits.twiddle(k*fstride);
 138                 scratch[1] = Fout[k+2*m] * _traits.twiddle(k*fstride*2);
 139                 scratch[2] = Fout[k+3*m] * _traits.twiddle(k*fstride*3);
 140                 scratch[5] = Fout[k] - scratch[1];
 141
 142                 Fout[k] += scratch[1];
 143                 scratch[3] = scratch[0] + scratch[2];
 144                 scratch[4] = scratch[0] - scratch[2];
 145                 scratch[4] = cpx_type( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
 146
 147                 Fout[k+2*m]  = Fout[k] - scratch[3];
 148                 Fout[k] += scratch[3];
 149                 Fout[k+m] = scratch[5] + scratch[4];
 150                 Fout[k+3*m] = scratch[5] - scratch[4];
 151             }
 152         }
 153
 154         void kf_bfly3( cpx_type * Fout, const size_t fstride, const size_t m)
 155         {
 156             size_t k=m;
 157             const size_t m2 = 2*m;
 158             cpx_type *tw1,*tw2;
 159             cpx_type scratch[5];
 160             cpx_type epi3;
 161             epi3 = _twiddles[fstride*m];
 162
 163             tw1=tw2=&_twiddles[0];
 164
 165             do{
 166                 C_FIXDIV(*Fout,3); C_FIXDIV(Fout[m],3); C_FIXDIV(Fout[m2],3);
 167
 168                 C_MUL(scratch[1],Fout[m] , *tw1);
 169                 C_MUL(scratch[2],Fout[m2] , *tw2);
 170
 171                 C_ADD(scratch[3],scratch[1],scratch[2]);
 172                 C_SUB(scratch[0],scratch[1],scratch[2]);
 173                 tw1 += fstride;
 174                 tw2 += fstride*2;
 175
 176                 Fout[m] = cpx_type( Fout->real() - HALF_OF(scratch[3].real() ) , Fout->imag() - HALF_OF(scratch[3].imag() ) );
 177
 178                 C_MULBYSCALAR( scratch[0] , epi3.imag() );
 179
 180                 C_ADDTO(*Fout,scratch[3]);
 181
 182                 Fout[m2] = cpx_type(  Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
 183
 184                 C_ADDTO( Fout[m] , cpx_type( -scratch[0].imag(),scratch[0].real() ) );
 185                 ++Fout;
 186             }while(--k);
 187         }
 188
 189         void kf_bfly5( cpx_type * Fout, const size_t fstride, const size_t m)
 190         {
 191             cpx_type *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
 192             size_t u;
 193             cpx_type scratch[13];
 194             cpx_type * twiddles = &_twiddles[0];
 195             cpx_type *tw;
 196             cpx_type ya,yb;
 197             ya = twiddles[fstride*m];
 198             yb = twiddles[fstride*2*m];
 199
 200             Fout0=Fout;
 201             Fout1=Fout0+m;
 202             Fout2=Fout0+2*m;
 203             Fout3=Fout0+3*m;
 204             Fout4=Fout0+4*m;
 205
 206             tw=twiddles;
 207             for ( u=0; u<m; ++u ) {
 208                 C_FIXDIV( *Fout0,5); C_FIXDIV( *Fout1,5); C_FIXDIV( *Fout2,5); C_FIXDIV( *Fout3,5); C_FIXDIV( *Fout4,5);
 209                 scratch[0] = *Fout0;
 210
 211                 C_MUL(scratch[1] ,*Fout1, tw[u*fstride]);
 212                 C_MUL(scratch[2] ,*Fout2, tw[2*u*fstride]);
 213                 C_MUL(scratch[3] ,*Fout3, tw[3*u*fstride]);
 214                 C_MUL(scratch[4] ,*Fout4, tw[4*u*fstride]);
 215
 216                 C_ADD( scratch[7],scratch[1],scratch[4]);
 217                 C_SUB( scratch[10],scratch[1],scratch[4]);
 218                 C_ADD( scratch[8],scratch[2],scratch[3]);
 219                 C_SUB( scratch[9],scratch[2],scratch[3]);
 220
 221                 C_ADDTO( *Fout0, scratch[7]);
 222                 C_ADDTO( *Fout0, scratch[8]);
 223
 224                 scratch[5] = scratch[0] + cpx_type(
 225                         S_MUL(scratch[7].real(),ya.real() ) + S_MUL(scratch[8].real() ,yb.real() ),
 226                         S_MUL(scratch[7].imag(),ya.real()) + S_MUL(scratch[8].imag(),yb.real())
 227                         );
 228
 229                 scratch[6] =  cpx_type(
 230                         S_MUL(scratch[10].imag(),ya.imag()) + S_MUL(scratch[9].imag(),yb.imag()),
 231                         -S_MUL(scratch[10].real(),ya.imag()) - S_MUL(scratch[9].real(),yb.imag())
 232                         );
 233
 234                 C_SUB(*Fout1,scratch[5],scratch[6]);
 235                 C_ADD(*Fout4,scratch[5],scratch[6]);
 236
 237                 scratch[11] = scratch[0] +
 238                     cpx_type(
 239                             S_MUL(scratch[7].real(),yb.real()) + S_MUL(scratch[8].real(),ya.real()),
 240                             S_MUL(scratch[7].imag(),yb.real()) + S_MUL(scratch[8].imag(),ya.real())
 241                             );
 242
 243                 scratch[12] = cpx_type(
 244                         -S_MUL(scratch[10].imag(),yb.imag()) + S_MUL(scratch[9].imag(),ya.imag()),
 245                         S_MUL(scratch[10].real(),yb.imag()) - S_MUL(scratch[9].real(),ya.imag())
 246                         );
 247
 248                 C_ADD(*Fout2,scratch[11],scratch[12]);
 249                 C_SUB(*Fout3,scratch[11],scratch[12]);
 250
 251                 ++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
 252             }
 253         }
 254
 255         /* perform the butterfly for one stage of a mixed radix FFT */
 256         void kf_bfly_generic(
 257                 cpx_type * Fout,
 258                 const size_t fstride,
 259                 int m,
 260                 int p
 261                 )
 262         {
 263             int u,k,q1,q;
 264             cpx_type * twiddles = &_twiddles[0];
 265             cpx_type t;
 266             int Norig = _nfft;
 267             cpx_type scratchbuf[p];
 268
 269             for ( u=0; u<m; ++u ) {
 270                 k=u;
 271                 for ( q1=0 ; q1<p ; ++q1 ) {
 272                     scratchbuf[q1] = Fout[ k  ];
 273                     C_FIXDIV(scratchbuf[q1],p);
 274                     k += m;
 275                 }
 276
 277                 k=u;
 278                 for ( q1=0 ; q1<p ; ++q1 ) {
 279                     int twidx=0;
 280                     Fout[ k ] = scratchbuf[0];
 281                     for (q=1;q<p;++q ) {
 282                         twidx += fstride * k;
 283                         if (twidx>=Norig) twidx-=Norig;
 284                         C_MUL(t,scratchbuf[q] , twiddles[twidx] );
 285                         C_ADDTO( Fout[ k ] ,t);
 286                     }
 287                     k += m;
 288                 }
 289             }
 290         }
 291
 292         int _nfft;
 293         bool _inverse;
 294         std::vector<cpx_type> _twiddles;
 295         std::vector<int> _stageRadix;
 296         std::vector<int> _stageRemainder;
 297         traits_type _traits;
 298 };
 299 #endif