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ei_kissfft_impl.h
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2009 Mark Borgerding mark a borgerding net
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10namespace Eigen {
11
12namespace internal {
13
14 // This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft
15 // Copyright 2003-2009 Mark Borgerding
16
17template <typename _Scalar>
18struct kiss_cpx_fft
19{
20 typedef _Scalar Scalar;
21 typedef std::complex<Scalar> Complex;
22 std::vector<Complex> m_twiddles;
23 std::vector<int> m_stageRadix;
24 std::vector<int> m_stageRemainder;
25 std::vector<Complex> m_scratchBuf;
26 bool m_inverse;
27
28 inline void make_twiddles(int nfft, bool inverse)
29 {
30 using numext::sin;
31 using numext::cos;
32 m_inverse = inverse;
33 m_twiddles.resize(nfft);
34 double phinc = 0.25 * double(EIGEN_PI) / nfft;
35 Scalar flip = inverse ? Scalar(1) : Scalar(-1);
36 m_twiddles[0] = Complex(Scalar(1), Scalar(0));
37 if ((nfft&1)==0)
38 m_twiddles[nfft/2] = Complex(Scalar(-1), Scalar(0));
39 int i=1;
40 for (;i*8<nfft;++i)
41 {
42 Scalar c = Scalar(cos(i*8*phinc));
43 Scalar s = Scalar(sin(i*8*phinc));
44 m_twiddles[i] = Complex(c, s*flip);
45 m_twiddles[nfft-i] = Complex(c, -s*flip);
46 }
47 for (;i*4<nfft;++i)
48 {
49 Scalar c = Scalar(cos((2*nfft-8*i)*phinc));
50 Scalar s = Scalar(sin((2*nfft-8*i)*phinc));
51 m_twiddles[i] = Complex(s, c*flip);
52 m_twiddles[nfft-i] = Complex(s, -c*flip);
53 }
54 for (;i*8<3*nfft;++i)
55 {
56 Scalar c = Scalar(cos((8*i-2*nfft)*phinc));
57 Scalar s = Scalar(sin((8*i-2*nfft)*phinc));
58 m_twiddles[i] = Complex(-s, c*flip);
59 m_twiddles[nfft-i] = Complex(-s, -c*flip);
60 }
61 for (;i*2<nfft;++i)
62 {
63 Scalar c = Scalar(cos((4*nfft-8*i)*phinc));
64 Scalar s = Scalar(sin((4*nfft-8*i)*phinc));
65 m_twiddles[i] = Complex(-c, s*flip);
66 m_twiddles[nfft-i] = Complex(-c, -s*flip);
67 }
68 }
69
70 void factorize(int nfft)
71 {
72 //start factoring out 4's, then 2's, then 3,5,7,9,...
73 int n= nfft;
74 int p=4;
75 do {
76 while (n % p) {
77 switch (p) {
78 case 4: p = 2; break;
79 case 2: p = 3; break;
80 default: p += 2; break;
81 }
82 if (p*p>n)
83 p=n;// impossible to have a factor > sqrt(n)
84 }
85 n /= p;
86 m_stageRadix.push_back(p);
87 m_stageRemainder.push_back(n);
88 if ( p > 5 )
89 m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic
90 }while(n>1);
91 }
92
93 template <typename _Src>
94 inline
95 void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride)
96 {
97 int p = m_stageRadix[stage];
98 int m = m_stageRemainder[stage];
99 Complex * Fout_beg = xout;
100 Complex * Fout_end = xout + p*m;
101
102 if (m>1) {
103 do{
104 // recursive call:
105 // DFT of size m*p performed by doing
106 // p instances of smaller DFTs of size m,
107 // each one takes a decimated version of the input
108 work(stage+1, xout , xin, fstride*p,in_stride);
109 xin += fstride*in_stride;
110 }while( (xout += m) != Fout_end );
111 }else{
112 do{
113 *xout = *xin;
114 xin += fstride*in_stride;
115 }while(++xout != Fout_end );
116 }
117 xout=Fout_beg;
118
119 // recombine the p smaller DFTs
120 switch (p) {
121 case 2: bfly2(xout,fstride,m); break;
122 case 3: bfly3(xout,fstride,m); break;
123 case 4: bfly4(xout,fstride,m); break;
124 case 5: bfly5(xout,fstride,m); break;
125 default: bfly_generic(xout,fstride,m,p); break;
126 }
127 }
128
129 inline
130 void bfly2( Complex * Fout, const size_t fstride, int m)
131 {
132 for (int k=0;k<m;++k) {
133 Complex t = Fout[m+k] * m_twiddles[k*fstride];
134 Fout[m+k] = Fout[k] - t;
135 Fout[k] += t;
136 }
137 }
138
139 inline
140 void bfly4( Complex * Fout, const size_t fstride, const size_t m)
141 {
142 Complex scratch[6];
143 int negative_if_inverse = m_inverse * -2 +1;
144 for (size_t k=0;k<m;++k) {
145 scratch[0] = Fout[k+m] * m_twiddles[k*fstride];
146 scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];
147 scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];
148 scratch[5] = Fout[k] - scratch[1];
149
150 Fout[k] += scratch[1];
151 scratch[3] = scratch[0] + scratch[2];
152 scratch[4] = scratch[0] - scratch[2];
153 scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
154
155 Fout[k+2*m] = Fout[k] - scratch[3];
156 Fout[k] += scratch[3];
157 Fout[k+m] = scratch[5] + scratch[4];
158 Fout[k+3*m] = scratch[5] - scratch[4];
159 }
160 }
161
162 inline
163 void bfly3( Complex * Fout, const size_t fstride, const size_t m)
164 {
165 size_t k=m;
166 const size_t m2 = 2*m;
167 Complex *tw1,*tw2;
168 Complex scratch[5];
169 Complex epi3;
170 epi3 = m_twiddles[fstride*m];
171
172 tw1=tw2=&m_twiddles[0];
173
174 do{
175 scratch[1]=Fout[m] * *tw1;
176 scratch[2]=Fout[m2] * *tw2;
177
178 scratch[3]=scratch[1]+scratch[2];
179 scratch[0]=scratch[1]-scratch[2];
180 tw1 += fstride;
181 tw2 += fstride*2;
182 Fout[m] = Complex( Fout->real() - Scalar(.5)*scratch[3].real() , Fout->imag() - Scalar(.5)*scratch[3].imag() );
183 scratch[0] *= epi3.imag();
184 *Fout += scratch[3];
185 Fout[m2] = Complex( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
186 Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );
187 ++Fout;
188 }while(--k);
189 }
190
191 inline
192 void bfly5( Complex * Fout, const size_t fstride, const size_t m)
193 {
194 Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
195 size_t u;
196 Complex scratch[13];
197 Complex * twiddles = &m_twiddles[0];
198 Complex *tw;
199 Complex ya,yb;
200 ya = twiddles[fstride*m];
201 yb = twiddles[fstride*2*m];
202
203 Fout0=Fout;
204 Fout1=Fout0+m;
205 Fout2=Fout0+2*m;
206 Fout3=Fout0+3*m;
207 Fout4=Fout0+4*m;
208
209 tw=twiddles;
210 for ( u=0; u<m; ++u ) {
211 scratch[0] = *Fout0;
212
213 scratch[1] = *Fout1 * tw[u*fstride];
214 scratch[2] = *Fout2 * tw[2*u*fstride];
215 scratch[3] = *Fout3 * tw[3*u*fstride];
216 scratch[4] = *Fout4 * tw[4*u*fstride];
217
218 scratch[7] = scratch[1] + scratch[4];
219 scratch[10] = scratch[1] - scratch[4];
220 scratch[8] = scratch[2] + scratch[3];
221 scratch[9] = scratch[2] - scratch[3];
222
223 *Fout0 += scratch[7];
224 *Fout0 += scratch[8];
225
226 scratch[5] = scratch[0] + Complex(
227 (scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),
228 (scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())
229 );
230
231 scratch[6] = Complex(
232 (scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),
233 -(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())
234 );
235
236 *Fout1 = scratch[5] - scratch[6];
237 *Fout4 = scratch[5] + scratch[6];
238
239 scratch[11] = scratch[0] +
240 Complex(
241 (scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),
242 (scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())
243 );
244
245 scratch[12] = Complex(
246 -(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
247 (scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
248 );
249
250 *Fout2=scratch[11]+scratch[12];
251 *Fout3=scratch[11]-scratch[12];
252
253 ++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
254 }
255 }
256
257 /* perform the butterfly for one stage of a mixed radix FFT */
258 inline
259 void bfly_generic(
260 Complex * Fout,
261 const size_t fstride,
262 int m,
263 int p
264 )
265 {
266 int u,k,q1,q;
267 Complex * twiddles = &m_twiddles[0];
268 Complex t;
269 int Norig = static_cast<int>(m_twiddles.size());
270 Complex * scratchbuf = &m_scratchBuf[0];
271
272 for ( u=0; u<m; ++u ) {
273 k=u;
274 for ( q1=0 ; q1<p ; ++q1 ) {
275 scratchbuf[q1] = Fout[ k ];
276 k += m;
277 }
278
279 k=u;
280 for ( q1=0 ; q1<p ; ++q1 ) {
281 int twidx=0;
282 Fout[ k ] = scratchbuf[0];
283 for (q=1;q<p;++q ) {
284 twidx += static_cast<int>(fstride) * k;
285 if (twidx>=Norig) twidx-=Norig;
286 t=scratchbuf[q] * twiddles[twidx];
287 Fout[ k ] += t;
288 }
289 k += m;
290 }
291 }
292 }
293};
294
295template <typename _Scalar>
296struct kissfft_impl
297{
298 typedef _Scalar Scalar;
299 typedef std::complex<Scalar> Complex;
300
301 void clear()
302 {
303 m_plans.clear();
304 m_realTwiddles.clear();
305 }
306
307 inline
308 void fwd( Complex * dst,const Complex *src,int nfft)
309 {
310 get_plan(nfft,false).work(0, dst, src, 1,1);
311 }
312
313 inline
314 void fwd2( Complex * dst,const Complex *src,int n0,int n1)
315 {
316 EIGEN_UNUSED_VARIABLE(dst);
317 EIGEN_UNUSED_VARIABLE(src);
318 EIGEN_UNUSED_VARIABLE(n0);
319 EIGEN_UNUSED_VARIABLE(n1);
320 }
321
322 inline
323 void inv2( Complex * dst,const Complex *src,int n0,int n1)
324 {
325 EIGEN_UNUSED_VARIABLE(dst);
326 EIGEN_UNUSED_VARIABLE(src);
327 EIGEN_UNUSED_VARIABLE(n0);
328 EIGEN_UNUSED_VARIABLE(n1);
329 }
330
331 // real-to-complex forward FFT
332 // perform two FFTs of src even and src odd
333 // then twiddle to recombine them into the half-spectrum format
334 // then fill in the conjugate symmetric half
335 inline
336 void fwd( Complex * dst,const Scalar * src,int nfft)
337 {
338 if ( nfft&3 ) {
339 // use generic mode for odd
340 m_tmpBuf1.resize(nfft);
341 get_plan(nfft,false).work(0, &m_tmpBuf1[0], src, 1,1);
342 std::copy(m_tmpBuf1.begin(),m_tmpBuf1.begin()+(nfft>>1)+1,dst );
343 }else{
344 int ncfft = nfft>>1;
345 int ncfft2 = nfft>>2;
346 Complex * rtw = real_twiddles(ncfft2);
347
348 // use optimized mode for even real
349 fwd( dst, reinterpret_cast<const Complex*> (src), ncfft);
350 Complex dc(dst[0].real() + dst[0].imag());
351 Complex nyquist(dst[0].real() - dst[0].imag());
352 int k;
353 for ( k=1;k <= ncfft2 ; ++k ) {
354 Complex fpk = dst[k];
355 Complex fpnk = conj(dst[ncfft-k]);
356 Complex f1k = fpk + fpnk;
357 Complex f2k = fpk - fpnk;
358 Complex tw= f2k * rtw[k-1];
359 dst[k] = (f1k + tw) * Scalar(.5);
360 dst[ncfft-k] = conj(f1k -tw)*Scalar(.5);
361 }
362 dst[0] = dc;
363 dst[ncfft] = nyquist;
364 }
365 }
366
367 // inverse complex-to-complex
368 inline
369 void inv(Complex * dst,const Complex *src,int nfft)
370 {
371 get_plan(nfft,true).work(0, dst, src, 1,1);
372 }
373
374 // half-complex to scalar
375 inline
376 void inv( Scalar * dst,const Complex * src,int nfft)
377 {
378 if (nfft&3) {
379 m_tmpBuf1.resize(nfft);
380 m_tmpBuf2.resize(nfft);
381 std::copy(src,src+(nfft>>1)+1,m_tmpBuf1.begin() );
382 for (int k=1;k<(nfft>>1)+1;++k)
383 m_tmpBuf1[nfft-k] = conj(m_tmpBuf1[k]);
384 inv(&m_tmpBuf2[0],&m_tmpBuf1[0],nfft);
385 for (int k=0;k<nfft;++k)
386 dst[k] = m_tmpBuf2[k].real();
387 }else{
388 // optimized version for multiple of 4
389 int ncfft = nfft>>1;
390 int ncfft2 = nfft>>2;
391 Complex * rtw = real_twiddles(ncfft2);
392 m_tmpBuf1.resize(ncfft);
393 m_tmpBuf1[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() );
394 for (int k = 1; k <= ncfft / 2; ++k) {
395 Complex fk = src[k];
396 Complex fnkc = conj(src[ncfft-k]);
397 Complex fek = fk + fnkc;
398 Complex tmp = fk - fnkc;
399 Complex fok = tmp * conj(rtw[k-1]);
400 m_tmpBuf1[k] = fek + fok;
401 m_tmpBuf1[ncfft-k] = conj(fek - fok);
402 }
403 get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf1[0], 1,1);
404 }
405 }
406
407 protected:
408 typedef kiss_cpx_fft<Scalar> PlanData;
409 typedef std::map<int,PlanData> PlanMap;
410
411 PlanMap m_plans;
412 std::map<int, std::vector<Complex> > m_realTwiddles;
413 std::vector<Complex> m_tmpBuf1;
414 std::vector<Complex> m_tmpBuf2;
415
416 inline
417 int PlanKey(int nfft, bool isinverse) const { return (nfft<<1) | int(isinverse); }
418
419 inline
420 PlanData & get_plan(int nfft, bool inverse)
421 {
422 // TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles
423 PlanData & pd = m_plans[ PlanKey(nfft,inverse) ];
424 if ( pd.m_twiddles.size() == 0 ) {
425 pd.make_twiddles(nfft,inverse);
426 pd.factorize(nfft);
427 }
428 return pd;
429 }
430
431 inline
432 Complex * real_twiddles(int ncfft2)
433 {
434 using std::acos;
435 std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
436 if ( (int)twidref.size() != ncfft2 ) {
437 twidref.resize(ncfft2);
438 int ncfft= ncfft2<<1;
439 Scalar pi = acos( Scalar(-1) );
440 for (int k=1;k<=ncfft2;++k)
441 twidref[k-1] = exp( Complex(0,-pi * (Scalar(k) / ncfft + Scalar(.5)) ) );
442 }
443 return &twidref[0];
444 }
445};
446
447} // end namespace internal
448
449} // end namespace Eigen
Namespace containing all symbols from the Eigen library.
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cos_op< typename Derived::Scalar >, const Derived > cos(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_real_op< typename Derived::Scalar >, const Derived > real(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_inverse_op< typename Derived::Scalar >, const Derived > inverse(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_exp_op< typename Derived::Scalar >, const Derived > exp(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_conjugate_op< typename Derived::Scalar >, const Derived > conj(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_imag_op< typename Derived::Scalar >, const Derived > imag(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sin_op< typename Derived::Scalar >, const Derived > sin(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_acos_op< typename Derived::Scalar >, const Derived > acos(const Eigen::ArrayBase< Derived > &x)