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// KISS FFT 1.3.0
//
// Copyright (c) 2003-2010 Mark Borgerding
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice, this
// list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// * Neither the author nor the names of any contributors may be used to endorse
// or promote products derived from this software without specific prior
// written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
#ifndef KISSFFT_CLASS_HH
#include <complex>
#include <vector>
namespace kissfft_utils {
template <typename T_scalar>
struct traits
{
typedef T_scalar scalar_type;
typedef std::complex<scalar_type> cpx_type;
void fill_twiddles( std::complex<T_scalar> * dst ,int nfft,bool inverse)
{
T_scalar phinc = (inverse?2:-2)* acos( (T_scalar) -1) / nfft;
for (int i=0;i<nfft;++i)
dst[i] = exp( std::complex<T_scalar>(0,i*phinc) );
}
void prepare(
std::vector< std::complex<T_scalar> > & dst,
int nfft,bool inverse,
std::vector<int> & stageRadix,
std::vector<int> & stageRemainder )
{
_twiddles.resize(nfft);
fill_twiddles( &_twiddles[0],nfft,inverse);
dst = _twiddles;
//factorize
//start factoring out 4's, then 2's, then 3,5,7,9,...
int n= nfft;
int p=4;
do {
while (n % p) {
switch (p) {
case 4: p = 2; break;
case 2: p = 3; break;
default: p += 2; break;
}
if (p*p>n)
p=n;// no more factors
}
n /= p;
stageRadix.push_back(p);
stageRemainder.push_back(n);
}while(n>1);
}
std::vector<cpx_type> _twiddles;
const cpx_type twiddle(int i) { return _twiddles[i]; }
};
}
template <typename T_Scalar,
typename T_traits=kissfft_utils::traits<T_Scalar>
>
class kissfft
{
public:
typedef T_traits traits_type;
typedef typename traits_type::scalar_type scalar_type;
typedef typename traits_type::cpx_type cpx_type;
kissfft(int nfft,bool inverse,const traits_type & traits=traits_type() )
:_nfft(nfft),_inverse(inverse),_traits(traits)
{
_traits.prepare(_twiddles, _nfft,_inverse ,_stageRadix, _stageRemainder);
}
void transform(const cpx_type * src , cpx_type * dst)
{
kf_work(0, dst, src, 1,1);
}
private:
void kf_work( int stage,cpx_type * Fout, const cpx_type * f, size_t fstride,size_t in_stride)
{
int p = _stageRadix[stage];
int m = _stageRemainder[stage];
cpx_type * Fout_beg = Fout;
cpx_type * Fout_end = Fout + p*m;
if (m==1) {
do{
*Fout = *f;
f += fstride*in_stride;
}while(++Fout != Fout_end );
}else{
do{
// recursive call:
// DFT of size m*p performed by doing
// p instances of smaller DFTs of size m,
// each one takes a decimated version of the input
kf_work(stage+1, Fout , f, fstride*p,in_stride);
f += fstride*in_stride;
}while( (Fout += m) != Fout_end );
}
Fout=Fout_beg;
// recombine the p smaller DFTs
switch (p) {
case 2: kf_bfly2(Fout,fstride,m); break;
case 3: kf_bfly3(Fout,fstride,m); break;
case 4: kf_bfly4(Fout,fstride,m); break;
case 5: kf_bfly5(Fout,fstride,m); break;
default: kf_bfly_generic(Fout,fstride,m,p); break;
}
}
// these were #define macros in the original kiss_fft
void C_ADD( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a+b;}
void C_MUL( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a*b;}
void C_SUB( cpx_type & c,const cpx_type & a,const cpx_type & b) { c=a-b;}
void C_ADDTO( cpx_type & c,const cpx_type & a) { c+=a;}
void C_FIXDIV( cpx_type & ,int ) {} // NO-OP for float types
scalar_type S_MUL( const scalar_type & a,const scalar_type & b) { return a*b;}
scalar_type HALF_OF( const scalar_type & a) { return a*.5;}
void C_MULBYSCALAR(cpx_type & c,const scalar_type & a) {c*=a;}
void kf_bfly2( cpx_type * Fout, const size_t fstride, int m)
{
for (int k=0;k<m;++k) {
cpx_type t = Fout[m+k] * _traits.twiddle(k*fstride);
Fout[m+k] = Fout[k] - t;
Fout[k] += t;
}
}
void kf_bfly4( cpx_type * Fout, const size_t fstride, const size_t m)
{
cpx_type scratch[7];
int negative_if_inverse = _inverse * -2 +1;
for (size_t k=0;k<m;++k) {
scratch[0] = Fout[k+m] * _traits.twiddle(k*fstride);
scratch[1] = Fout[k+2*m] * _traits.twiddle(k*fstride*2);
scratch[2] = Fout[k+3*m] * _traits.twiddle(k*fstride*3);
scratch[5] = Fout[k] - scratch[1];
Fout[k] += scratch[1];
scratch[3] = scratch[0] + scratch[2];
scratch[4] = scratch[0] - scratch[2];
scratch[4] = cpx_type( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
Fout[k+2*m] = Fout[k] - scratch[3];
Fout[k] += scratch[3];
Fout[k+m] = scratch[5] + scratch[4];
Fout[k+3*m] = scratch[5] - scratch[4];
}
}
void kf_bfly3( cpx_type * Fout, const size_t fstride, const size_t m)
{
size_t k=m;
const size_t m2 = 2*m;
cpx_type *tw1,*tw2;
cpx_type scratch[5];
cpx_type epi3;
epi3 = _twiddles[fstride*m];
tw1=tw2=&_twiddles[0];
do{
C_FIXDIV(*Fout,3); C_FIXDIV(Fout[m],3); C_FIXDIV(Fout[m2],3);
C_MUL(scratch[1],Fout[m] , *tw1);
C_MUL(scratch[2],Fout[m2] , *tw2);
C_ADD(scratch[3],scratch[1],scratch[2]);
C_SUB(scratch[0],scratch[1],scratch[2]);
tw1 += fstride;
tw2 += fstride*2;
Fout[m] = cpx_type( Fout->real() - HALF_OF(scratch[3].real() ) , Fout->imag() - HALF_OF(scratch[3].imag() ) );
C_MULBYSCALAR( scratch[0] , epi3.imag() );
C_ADDTO(*Fout,scratch[3]);
Fout[m2] = cpx_type( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
C_ADDTO( Fout[m] , cpx_type( -scratch[0].imag(),scratch[0].real() ) );
++Fout;
}while(--k);
}
void kf_bfly5( cpx_type * Fout, const size_t fstride, const size_t m)
{
cpx_type *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
size_t u;
cpx_type scratch[13];
cpx_type * twiddles = &_twiddles[0];
cpx_type *tw;
cpx_type 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 ) {
C_FIXDIV( *Fout0,5); C_FIXDIV( *Fout1,5); C_FIXDIV( *Fout2,5); C_FIXDIV( *Fout3,5); C_FIXDIV( *Fout4,5);
scratch[0] = *Fout0;
C_MUL(scratch[1] ,*Fout1, tw[u*fstride]);
C_MUL(scratch[2] ,*Fout2, tw[2*u*fstride]);
C_MUL(scratch[3] ,*Fout3, tw[3*u*fstride]);
C_MUL(scratch[4] ,*Fout4, tw[4*u*fstride]);
C_ADD( scratch[7],scratch[1],scratch[4]);
C_SUB( scratch[10],scratch[1],scratch[4]);
C_ADD( scratch[8],scratch[2],scratch[3]);
C_SUB( scratch[9],scratch[2],scratch[3]);
C_ADDTO( *Fout0, scratch[7]);
C_ADDTO( *Fout0, scratch[8]);
scratch[5] = scratch[0] + cpx_type(
S_MUL(scratch[7].real(),ya.real() ) + S_MUL(scratch[8].real() ,yb.real() ),
S_MUL(scratch[7].imag(),ya.real()) + S_MUL(scratch[8].imag(),yb.real())
);
scratch[6] = cpx_type(
S_MUL(scratch[10].imag(),ya.imag()) + S_MUL(scratch[9].imag(),yb.imag()),
-S_MUL(scratch[10].real(),ya.imag()) - S_MUL(scratch[9].real(),yb.imag())
);
C_SUB(*Fout1,scratch[5],scratch[6]);
C_ADD(*Fout4,scratch[5],scratch[6]);
scratch[11] = scratch[0] +
cpx_type(
S_MUL(scratch[7].real(),yb.real()) + S_MUL(scratch[8].real(),ya.real()),
S_MUL(scratch[7].imag(),yb.real()) + S_MUL(scratch[8].imag(),ya.real())
);
scratch[12] = cpx_type(
-S_MUL(scratch[10].imag(),yb.imag()) + S_MUL(scratch[9].imag(),ya.imag()),
S_MUL(scratch[10].real(),yb.imag()) - S_MUL(scratch[9].real(),ya.imag())
);
C_ADD(*Fout2,scratch[11],scratch[12]);
C_SUB(*Fout3,scratch[11],scratch[12]);
++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
}
}
/* perform the butterfly for one stage of a mixed radix FFT */
void kf_bfly_generic(
cpx_type * Fout,
const size_t fstride,
int m,
int p
)
{
int u,k,q1,q;
cpx_type * twiddles = &_twiddles[0];
cpx_type t;
int Norig = _nfft;
std::vector<cpx_type> scratchbuf(p);
for ( u=0; u<m; ++u ) {
k=u;
for ( q1=0 ; q1<p ; ++q1 ) {
scratchbuf[q1] = Fout[ k ];
C_FIXDIV(scratchbuf[q1],p);
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;
C_MUL(t,scratchbuf[q] , twiddles[twidx] );
C_ADDTO( Fout[ k ] ,t);
}
k += m;
}
}
}
int _nfft;
bool _inverse;
std::vector<cpx_type> _twiddles;
std::vector<int> _stageRadix;
std::vector<int> _stageRemainder;
traits_type _traits;
};
#endif
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