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fftpf.h
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fftpf.h
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#ifndef FFTPF_H
#define FFTPF_H
#include "splab_vector.h"
#define PRIMEFACTOR 37
#define PRIMEFACTORHALF (PRIMEFACTOR+1)/2
#define PRIMECOUNT 20
namespace splab
{
template<class Type>
class FFTPF
{
public:
FFTPF();
~FFTPF();
void fft( const Vector<Type> &xn, Vector< complex<Type> > &Xk );
void ifft( const Vector< complex<Type> > &Xk, Vector<Type> &xn );
void fft( const Vector< complex<Type> > &xn,
Vector< complex<Type> > &Xk );
void ifft( const Vector< complex<Type> > &Xk,
Vector< complex<Type> > &xn );
private:
bool bAlloc;
int mNOldSize, mNFactor, nNewFactorSize, nHalfFactorSize,
groupOffset, dataOffset, blockOffset, adr, groupNo,
dataNo, blockNo, twNo;
int mSofarRadix[PRIMECOUNT], mActualRadix[PRIMECOUNT],
mRemainRadix[PRIMECOUNT];
Type tPI, t2PI, tIRT2, tIRT3, omega, twRe, twIim;
Type *pftwRe, *pftgRe, *pfzRe, *pfvRe, *pfwRe, *pftwIm, *pftgIm,
*pfzIm, *pfvIm, *pfwIm;
Type twiddleRe[PRIMEFACTOR], trigRe[PRIMEFACTOR], zRe[PRIMEFACTOR],
twiddleIm[PRIMEFACTOR], trigIm[PRIMEFACTOR], zIm[PRIMEFACTOR],
vRe[PRIMEFACTORHALF], wRe[PRIMEFACTORHALF],
vIm[PRIMEFACTORHALF], wIm[PRIMEFACTORHALF];
Type c3_1,
c5_1, c5_2, c5_3, c5_4, c5_5,
c7_1, c7_2, c7_3, c7_4, c7_5, c7_6,
c9_2, c9_3, c9_4, c9_5, c9_6, c9_7, c9_8, c9_9,
c11_1, c11_2, c11_3, c11_4, c11_5, c11_6, c11_7, c11_8,
c11_9, c11_10, c13_1, c13_2, c13_3, c13_4, c13_5, c13_6,
c13_7, c13_8, c13_9, c13_10, c13_11, c13_12, c16_2, c16_3,
c16_4, c16_5;
Type ttmp,
t1_re, t1_im, t2_re, t2_im, t3_re, t3_im, t4_re, t4_im,
t5_re, t5_im, t6_re, t6_im, t7_re, t7_im, t8_re, t8_im,
t9_re, t9_im, t10_re, t10_im, t11_re, t11_im, t12_re, t12_im,
t13_re, t13_im, t14_re, t14_im, t15_re, t15_im, t16_re, t16_im,
t17_re, t17_im, t18_re, t18_im, t19_re, t19_im, t20_re, t20_im,
t21_re, t21_im, t22_re, t22_im,
m1_re, m1_im, m2_re, m2_im, m3_re, m3_im, m4_re, m4_im,
m5_re, m5_im, m6_re, m6_im, m7_re, m7_im, m8_re, m8_im,
m9_re, m9_im, m10_re, m10_im, m11_re, m11_im, m12_re, m12_im;
void releaseMem();
void allocateMem();
void factorize( int n, int &nFact, int *fact);
void primeSetup( int nPoints );
void permute( const Vector<Type> &xn, Vector< complex<Type> > &yn );
void permute( const Vector< complex<Type> > &xn, Vector< complex<Type> > &yn,
bool bTrans=true );
void initTrig( int radix );
void radix2( Type *aRe, Type *aIm );
void radix3( Type *aRe, Type *aIm );
void radix4( Type *aRe, Type *aIm );
void radix5( Type *aRe, Type *aIm );
void radix7( Type *aRe, Type *aIm );
void radix8( Type *aRe, Type *aIm );
void radix9( Type *aRe, Type *aIm );
void radix10( Type *aRe, Type *aIm );
void radix11( Type *aRe, Type *aIm );
void radix13( Type *aRe, Type *aIm );
void radix16( Type *aRe, Type *aIm );
void radixOther( int radix );
void twiddleFFT( int sofarRadix, int radix, int remainRadix,
Vector< complex<Type> > &yn );
};
// class FFTPF
template<class Type>
FFTPF<Type>::FFTPF()
{
bAlloc = false;
mNOldSize = nNewFactorSize = nHalfFactorSize = 0;
pftwRe = twiddleRe;
pftwIm = twiddleIm;
pftgRe = trigRe;
pftgIm = trigIm;
pfzRe = zRe;
pfzIm = zIm;
pfvRe = vRe;
pfvIm = vIm;
pfwRe = wRe;
pfwIm = wIm;
tIRT2 = Type(sqrt(2.0)/2);
tIRT3 = Type(sqrt(3.0)/2);
tPI = Type(4*atan(1.0));
t2PI = 2*tPI;
Type tphi = t2PI/5;
c3_1 = -1.5;
c5_1 = Type((cos(tphi)-cos(2*tphi))/2);
c5_2 = Type(sin(tphi));
c5_3 = Type(sin(2*tphi));
c5_4 = Type((c5_3+c5_2));
c5_3 = c5_2-c5_3;
c5_5 = 1.25;
tphi = t2PI/7;
c7_1 = Type(cos(tphi));
c7_2 = Type(cos(2*tphi));
c7_3 = Type(cos(3*tphi));
c7_4 = Type(sin(tphi));
c7_5 = Type(sin(2*tphi));
c7_6 = Type(sin(3*tphi));
tphi = t2PI/9;
c9_4 = Type(cos(tphi));
c9_8 = Type(sin(8*tphi));
c9_3 = Type(cos(2*tphi));
c9_7 = Type(sin(2*tphi));
c9_5 = Type(cos(3*tphi));
c9_2 = Type(cos(4*tphi));
c9_6 = Type(sin(5*tphi));
tphi = t2PI/11;
c11_1 = Type(cos(tphi));
c11_2 = Type(cos(2*tphi));
c11_3 = Type(cos(3*tphi));
c11_4 = Type(cos(4*tphi));
c11_5 = Type(cos(5*tphi));
c11_6 = Type(sin(tphi));
c11_7 = Type(sin(2*tphi));
c11_8 = Type(sin(3*tphi));
c11_9 = Type(sin(4*tphi));
c11_10 = Type(sin(5*tphi));
tphi = t2PI/13;
c13_1 = Type(cos(tphi));
c13_2 = Type(cos(2*tphi));
c13_3 = Type(cos(3*tphi));
c13_4 = Type(cos(4*tphi));
c13_5 = Type(cos(5*tphi));
c13_6 = Type(cos(6*tphi));
c13_7 = Type(sin(tphi));
c13_8 = Type(sin(2*tphi));
c13_9 = Type(sin(3*tphi));
c13_10 = Type(sin(4*tphi));
c13_11 = Type(sin(5*tphi));
c13_12 = Type(sin(6*tphi));
tphi = t2PI/16;
c16_2 = Type(sin(tphi));
c16_5 = Type(cos(tphi));
c16_3 = c16_2+c16_5;
c16_4 = c16_5-c16_2;
}
template<class Type>
FFTPF<Type>::~FFTPF()
{
releaseMem();
}
template<class Type>
void FFTPF<Type>::releaseMem()
{
if ( !bAlloc)
return;
if ( NULL != pftwRe )
delete []pftwRe;
if ( NULL != pftwIm )
delete []pftwIm;
if ( NULL != pftgRe )
delete []pftgRe;
if ( NULL != pftgIm )
delete []pftgIm;
if ( NULL != pfzRe )
delete []pfzRe;
if ( NULL != pfzIm )
delete []pfzIm;
if ( NULL != pfvRe )
delete []pfvRe;
if ( NULL != pfvIm )
delete []pfvIm;
if ( NULL != pfwRe )
delete []pfwRe;
if ( NULL != pfwIm )
delete []pfwIm;
bAlloc = false;
nNewFactorSize = nHalfFactorSize = 0;
}
/**
* allocate memory
*/
template<class Type>
inline void FFTPF<Type>::allocateMem()
{
pftwRe = new Type[nNewFactorSize];
pftwIm = new Type[nNewFactorSize];
pftgRe = new Type[nNewFactorSize];
pftgIm = new Type[nNewFactorSize];
pfzRe = new Type[nNewFactorSize];
pfzIm = new Type[nNewFactorSize];
pfvRe = new Type[nHalfFactorSize];
pfvIm = new Type[nHalfFactorSize];
pfwRe = new Type[nHalfFactorSize];
pfwIm = new Type[nHalfFactorSize];
bAlloc = true;
}
/**
* factoring the transformation length.
*/
template<class Type>
void FFTPF<Type>::factorize( int n, int &nFact, int *fact )
{
int i, j=0, k,
nRadix = 11, radices[12],
factors[PRIMECOUNT];
radices[1] = 2; radices[2] = 3; radices[3] = 4; radices[4] = 5;
radices[5] = 7; radices[6] = 8; radices[7] = 9; radices[8] = 10;
radices[9] = 11; radices[10] = 13; radices[11] = 16;
if( 1 == n )
{
j = 1;
factors[1] = 1;
}
i = nRadix;
while( (n>1) && (i>0) )
{
if( (n%radices[i]) != 0 )
--i;
else
{
n = n/radices[i];
j++;
factors[j] = radices[i];
}
}
if( 2 == factors[j] )
{
i = j-1;
while( (i>0) && (factors[i]!=8) )
i--;
if( i > 0 )
{
factors[j] = 4;
factors[i] = 4;
}
}
if( n > 1 )
{
for( k=2; k<sqrt(1.0*n)+1; ++k )
while( 0 == (n%k) )
{
n = n/k;
j++;
factors[j] = k;
}
if( n > 1 )
{
j++;
factors[j] = n;
}
}
for( i=1; i<=j; ++i )
fact[i] = factors[j-i+1];
nFact = j;
}
/**
* After N is factored the parameters that control the stages are generated.
* For each stage we have:
* mSofarRadix : the product of the radices so far.
* mActualRadix : the radix handled in this stage.
* mRemainRadix : the product of the remaining radices.
*/
template<class Type>
void FFTPF<Type>::primeSetup( int nPoints )
{
factorize( nPoints, mNFactor, mActualRadix );
if( mActualRadix[1] > PRIMEFACTOR )
{
bool bdone = true;
if( bAlloc )
{
if( mActualRadix[1] <= nNewFactorSize )
bdone=false;
else
{
releaseMem();
bdone=true;
}
}
if( bdone )
{
nNewFactorSize = mActualRadix[1];
nHalfFactorSize = (nNewFactorSize+1)/2;
allocateMem();
}
}
mSofarRadix[1] = 1;
mRemainRadix[0] = nPoints;
mRemainRadix[1] = nPoints/mActualRadix[1];
for( int i=2; i<=mNFactor; ++i )
{
mSofarRadix[i] = mSofarRadix[i-1] * mActualRadix[i-1];
mRemainRadix[i] = mRemainRadix[i-1] / mActualRadix[i];
}
mNOldSize = nPoints;
}
/**
* The sequence "yn" is the permuted input sequence "xn" so that the
* following transformations can be performed in-place,and the final
* result is the normal order.
*/
template<class Type>
void FFTPF<Type>::permute( const Vector<Type> &xn,
Vector< complex<Type> > &yn )
{
int i, j, k=0, nPoint = xn.size(),
count[PRIMECOUNT];
for( i=1; i<=mNFactor; ++i )
count[i] = 0;
for( i=0; i<=nPoint-2; ++i )
{
yn[i] = xn[k];
j = 1;
k += mRemainRadix[j];
count[1] = count[1]+1;
while( count[j] >= mActualRadix[j] )
{
count[j] = 0;
k = k - mRemainRadix[j-1] + mRemainRadix[j+1];
j++;
count[j] = count[j] + 1;
}
}
yn[nPoint-1] = xn[nPoint-1];
}
template<class Type>
void FFTPF<Type>::permute( const Vector< complex<Type> > &xn,
Vector< complex<Type> > &yn,
bool bTrans )
{
int i, j, k=0, nPoint = xn.size(),
count[PRIMECOUNT];
for( i=1; i<=mNFactor; ++i )
count[i] = 0;
for( i=0; i<=nPoint-2; ++i )
{
yn[i] = xn[k];
j = 1;
k += mRemainRadix[j];
count[1] = count[1]+1;
while( count[j] >= mActualRadix[j] )
{
count[j] = 0;
k = k - mRemainRadix[j-1] + mRemainRadix[j+1];
j++;
count[j] = count[j] + 1;
}
}
yn[nPoint-1] = xn[nPoint-1];
if( !bTrans )
for( i=0; i< nPoint; ++i )
yn[i] = conj(yn[i]);
}
/**
* initialise sine/cosine table.
*/
template<class Type>
inline void FFTPF<Type>::initTrig( int radix )
{
Type w, xre, xim;
w = 2*tPI/radix;
pftgRe[0] = 1;
pftgIm[0] = 0;
xre = Type(cos(w));
xim = -Type(sin(w));
pftgRe[1] = xre;
pftgIm[1] = xim;
for( int i=2; i<radix; ++i )
{
pftgRe[i] = xre*pftgRe[i-1] - xim*pftgIm[i-1];
pftgIm[i] = xim*pftgRe[i-1] + xre*pftgIm[i-1];
}
}
/**
* length 2 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix2( Type *aRe, Type *aIm )
{
t1_re = aRe[0];
aRe[0] = t1_re+aRe[1];
aRe[1] = t1_re-aRe[1];
t1_im = aIm[0];
aIm[0] = t1_im+aIm[1];
aIm[1] = t1_im-aIm[1];
}
/**
* length 3 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix3( Type *aRe, Type *aIm )
{
t1_re = aRe[1]+aRe[2];
t2_re = (aRe[2]-aRe[1])*tIRT3;
aRe[0] = aRe[0]+t1_re;
t1_re = aRe[0]+t1_re*c3_1;
t1_im = aIm[1]+aIm[2];
t2_im = (aIm[2]-aIm[1])*tIRT3;
aIm[0] = aIm[0]+t1_im;
t1_im = aIm[0]+t1_im*c3_1;
aRe[1] = t1_re-t2_im;
aRe[2] = t1_re+t2_im;
aIm[1] = t1_im+t2_re;
aIm[2] = t1_im-t2_re;
}
/**
* length 4 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix4( Type *aRe, Type *aIm )
{
t1_re = aRe[0]+aRe[2];
m2_re = aRe[0]-aRe[2];
t2_re = aRe[1]+aRe[3];
aRe[0] = t1_re+t2_re;
aRe[2] = t1_re-t2_re;
t1_re = aIm[0]+aIm[2];
m2_im = aIm[0]-aIm[2];
t2_re = aIm[1]+aIm[3];
aIm[0] = t1_re+t2_re;
aIm[2] = t1_re-t2_re;
t1_re = aRe[1]-aRe[3];
t2_re = aIm[1]-aIm[3];
aRe[1] = m2_re+t2_re;
aRe[3] = m2_re-t2_re;
aIm[1] = m2_im-t1_re;
aIm[3] = m2_im+t1_re;
}
/**
* length 5 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix5( Type *aRe, Type *aIm )
{
t1_re = aRe[1]+aRe[4];
t2_re = aRe[2]-aRe[3];
t3_re = aRe[1]-aRe[4];
t4_re = aRe[2]+aRe[3];
t5_re = (t1_re-t4_re)*c5_1;
t1_re = t1_re+t4_re;
aRe[0] = aRe[0]+t1_re;
t1_re = aRe[0]-t1_re*c5_5;
t4_re = t1_re-t5_re;
t1_re = t1_re+t5_re;
t5_re = (t3_re+t2_re)*c5_2;
t3_re = t5_re-t3_re*c5_4;
t2_re = t5_re-t2_re*c5_3;
t1_im = aIm[1]+aIm[4];
t2_im = aIm[2]-aIm[3];
t3_im = aIm[1]-aIm[4];
t4_im = aIm[2]+aIm[3];
t5_re = (t1_im-t4_im)*c5_1; t1_im = t1_im+t4_im;
aIm[0] = aIm[0]+t1_im;
t1_im = aIm[0]-t1_im*c5_5;
t4_im = t1_im-t5_re;
t1_im = t1_im+t5_re;
t5_re = (t3_im+t2_im)*c5_2;
t3_im = t5_re-t3_im*c5_4;
t2_im = t5_re-t2_im*c5_3;
aRe[1] = t1_re+t2_im;
aIm[1] = t1_im-t2_re;
aRe[2] = t4_re-t3_im;
aIm[2] = t4_im+t3_re;
aRe[3] = t4_re+t3_im;
aIm[3] = t4_im-t3_re;
aRe[4] = t1_re-t2_im;
aIm[4] = t1_im+t2_re;
}
/**
* length 7 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix7( Type *aRe, Type *aIm )
{
t1_re = aRe[1]+aRe[6];
t1_im = aIm[1]+aIm[6];
t2_re = aRe[2]+aRe[5];
t2_im = aIm[2]+aIm[5];
t3_re = aRe[3]+aRe[4];
t3_im = aIm[3]+aIm[4];
t4_re = aRe[6]-aRe[1];
t4_im = aIm[6]-aIm[1];
t5_re = aRe[5]-aRe[2];
t5_im = aIm[5]-aIm[2];
t6_re = aRe[4]-aRe[3];
t6_im = aIm[4]-aIm[3];
t7_re = aRe[0]-Type(0.5*t3_re);
t7_im = aIm[0]-Type(0.5*t3_im);
t8_re = t1_re-t3_re;
t8_im = t1_im-t3_im;
t9_re = t2_re-t3_re;
t9_im = t2_im-t3_im;
m1_re = t7_re+c7_1*t8_re+c7_2*t9_re;
m1_im = t7_im+c7_1*t8_im+c7_2*t9_im;
m2_re = t7_re+c7_2*t8_re+c7_3*t9_re;
m2_im = t7_im+c7_2*t8_im+c7_3*t9_im;
m3_re = t7_re+c7_3*t8_re+c7_1*t9_re;
m3_im = t7_im+c7_3*t8_im+c7_1*t9_im;
m4_re = c7_6*t4_re-c7_4*t5_re+c7_5*t6_re;
m4_im = c7_6*t4_im-c7_4*t5_im+c7_5*t6_im;
m5_re = c7_5*t4_re-c7_6*t5_re-c7_4*t6_re;
m5_im = c7_5*t4_im-c7_6*t5_im-c7_4*t6_im;
m6_re = c7_4*t4_re+c7_5*t5_re+c7_6*t6_re;
m6_im = c7_4*t4_im+c7_5*t5_im+c7_6*t6_im;
aRe[0] = aRe[0]+t1_re+t2_re+t3_re;
aIm[0] = aIm[0]+t1_im+t2_im+t3_im;
aRe[1] = m1_re-m6_im;
aIm[1] = m1_im+m6_re;
aRe[2] = m2_re-m5_im;
aIm[2] = m2_im+m5_re;
aRe[3] = m3_re-m4_im;
aIm[3] = m3_im+m4_re;
aRe[4] = m3_re+m4_im;
aIm[4] = m3_im-m4_re;
aRe[5] = m2_re+m5_im;
aIm[5] = m2_im-m5_re;
aRe[6] = m1_re+m6_im;
aIm[6] = m1_im-m6_re;
}
/**
* length 8 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix8( Type *aRe, Type *aIm )
{
t1_re = aRe[0]+aRe[4];
t2_re = aRe[0]-aRe[4];
t3_re = aRe[1]-aRe[7];
t4_re = aRe[1]+aRe[7];
t7_re = aRe[2]+aRe[6];
t6_re = aRe[2]-aRe[6];
t5_re = aRe[3]+aRe[5];
t8_re = aRe[3]-aRe[5];
m2_re = t1_re+t7_re;
m2_im = t1_re-t7_re;
m1_re = t4_re+t5_re;
t4_re = (t4_re-t5_re)*tIRT2;
aRe[0] = m2_re+m1_re;
aRe[4] = m2_re-m1_re;
m2_re = t2_re+t4_re;
m1_re = t2_re-t4_re;
t1_im = t3_re-t8_re;
t3_re = (t3_re+t8_re)*tIRT2;
t2_im = t3_re+t6_re;
t4_im = t3_re-t6_re;
t1_re = aIm[0]+aIm[4];
t2_re = aIm[0]-aIm[4];
t3_re = aIm[1]-aIm[7];
t4_re = aIm[1]+aIm[7];
t5_re = aIm[3]+aIm[5];
t6_re = aIm[2]-aIm[6];
t7_re = aIm[2]+aIm[6];
t8_re = aIm[3]-aIm[5];
m1_im = t1_re+t7_re;
t1_re = t1_re-t7_re;
t7_re = t4_re+t5_re;
t4_re = (t4_re-t5_re)*tIRT2;
aIm[0] = m1_im+t7_re;
aIm[4] = m1_im-t7_re;
t7_re = t2_re+t4_re;
t2_re = t2_re-t4_re;
t4_re = t3_re-t8_re;
t3_re = (t3_re+t8_re)*tIRT2;
t5_re = t3_re+t6_re;
t3_re = t3_re-t6_re;
aRe[1] = m2_re+t5_re;
aIm[1] = t7_re-t2_im;
aRe[2] = m2_im+t4_re;
aIm[2] = t1_re-t1_im;
aRe[3] = m1_re+t3_re;
aIm[3] = t2_re-t4_im;
aRe[5] = m1_re-t3_re;
aIm[5] = t2_re+t4_im;
aRe[6] = m2_im-t4_re;
aIm[6] = t1_re+t1_im;
aRe[7] = m2_re-t5_re;
aIm[7] = t7_re+t2_im;
}
/**
* length 9 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix9( Type *aRe, Type *aIm )
{
t1_re = aRe[1]+aRe[8];
t2_re = aRe[1]-aRe[8];
t3_re = aRe[2]+aRe[7];
t4_re = aRe[2]-aRe[7];
t5_re = aRe[3]+aRe[6];
ttmp = aRe[0]+t5_re;
t7_re = aRe[4]+aRe[5];
t8_re = aRe[4]-aRe[5];
t8_im = (aRe[6]-aRe[3])*tIRT3;
t7_im = aRe[0]+t5_re*c9_5;
t5_re = t1_re+t3_re+t7_re;
aRe[0] = ttmp+t5_re;
t5_im = ttmp+t5_re*c9_5;
t3_im = (t7_re-t3_re)*c9_2;
t7_re = (t7_re-t1_re)*c9_3;
t3_re = (t1_re-t3_re)*c9_4;
t1_im = t7_im+t3_im+t3_re;
t3_im = t7_im-t3_im-t7_re;
t7_im = t7_im+t7_re-t3_re;
t6_im = (t4_re-t2_re-t8_re)*tIRT3;
t4_im = (t4_re+t8_re)*c9_6;
t8_re = (t8_re-t2_re)*c9_7;
t2_re = (t2_re+t4_re)*c9_8;
t2_im = t8_im+t4_im+t2_re;
t4_im = t8_im-t4_im-t8_re;
t8_im = t8_im+t8_re-t2_re;
t1_re = aIm[1]+aIm[8];
t2_re = aIm[1]-aIm[8];
t3_re = aIm[2]+aIm[7];
t4_re = aIm[2]-aIm[7];
t5_re = aIm[3]+aIm[6];
t6_re = (aIm[6]-aIm[3])*tIRT3;
t7_re = aIm[4]+aIm[5];
t8_re = aIm[4]-aIm[5];
ttmp = aIm[0]+t5_re;
t9_im = aIm[0]+t5_re*c9_5;
t5_re = t1_re+t3_re+t7_re;
aIm[0] = ttmp+t5_re;
t5_re = ttmp+t5_re*c9_5;
ttmp = (t7_re-t3_re)*c9_2;
t7_re = (t7_re-t1_re)*c9_3;
t3_re = (t1_re-t3_re)*c9_4;
t1_re = t9_im+ttmp+t3_re;
ttmp = t9_im-ttmp-t7_re;
t7_re = t9_im+t7_re-t3_re;
t9_re = (t4_re-t2_re-t8_re)*tIRT3;
t3_re = (t4_re+t8_re)*c9_6;
t8_re = (t8_re-t2_re)*c9_7;
t4_re = (t2_re+t4_re)*c9_8;
t2_re = t6_re+t3_re+t4_re;
t3_re = t6_re-t8_re-t3_re;
t8_re = t6_re+t8_re-t4_re;
aRe[1] = t1_im-t2_re;
aIm[1] = t1_re+t2_im;
aRe[2] = t3_im+t3_re;
aIm[2] = ttmp-t4_im;
aRe[3] = t5_im-t9_re;
aIm[3] = t5_re+t6_im;
aRe[4] = t7_im-t8_re;
aIm[4] = t7_re+t8_im;
aRe[5] = t7_im+t8_re;
aIm[5] = t7_re-t8_im;
aRe[6] = t5_im+t9_re;
aIm[6] = t5_re-t6_im;
aRe[7] = t3_im-t3_re;
aIm[7] = ttmp+t4_im;
aRe[8] = t1_im+t2_re;
aIm[8] = t1_re-t2_im;
}
/**
* length 10 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix10( Type *aRe, Type *aIm )
{
t1_re = aRe[2]+aRe[8];
t2_re = aRe[4]-aRe[6];
t3_re = aRe[2]-aRe[8];
t4_re = aRe[4]+aRe[6];
t5_re = (t1_re-t4_re)*c5_1;
t1_re = t1_re+t4_re;
m9_re = aRe[0]+t1_re;
t1_re = m9_re-t1_re*c5_5;
t4_re = t1_re-t5_re;
t1_re = t1_re+t5_re;
t5_re = (t3_re+t2_re)*c5_2;
t3_re = t5_re-t3_re*c5_4;
t2_re = t5_re-t2_re*c5_3;
t1_im = aIm[2]+aIm[8];
t2_im = aIm[4]-aIm[6];
t3_im = aIm[2]-aIm[8];
t4_im = aIm[4]+aIm[6];
t5_re = (t1_im-t4_im)*c5_1;
t1_im = t1_im+t4_im;
m9_im = aIm[0]+t1_im;
t1_im = m9_im-t1_im*c5_5;
t4_im = t1_im-t5_re;
t1_im = t1_im+t5_re;
t5_re = (t3_im+t2_im)*c5_2;
t3_im = t5_re-t3_im*c5_4;
t2_im = t5_re-t2_im*c5_3;
m1_re = t1_re+t2_im;
m1_im = t1_im-t2_re;
m2_re = t4_re-t3_im;
m2_im = t4_im+t3_re;
m3_re = t4_re+t3_im;
m3_im = t4_im-t3_re;
m4_re = t1_re-t2_im;
m4_im = t1_im+t2_re;
t1_re = aRe[7]+aRe[3];
t2_re = aRe[9]-aRe[1];
t3_re = aRe[7]-aRe[3];
t4_re = aRe[9]+aRe[1];
t5_re = (t1_re-t4_re)*c5_1;
t1_re = t1_re+t4_re;
t9_re = aRe[5]+t1_re;
t1_re = t9_re-t1_re*c5_5;
t4_re = t1_re-t5_re;
t1_re = t1_re+t5_re;
t5_re = (t3_re+t2_re)*c5_2;
t3_re = t5_re-t3_re*c5_4;
t2_re = t5_re-t2_re*c5_3;
t1_im = aIm[7]+aIm[3];
t2_im = aIm[9]-aIm[1];
t3_im = aIm[7]-aIm[3];
t4_im = aIm[9]+aIm[1];
t5_re = (t1_im-t4_im)*c5_1;
t1_im = t1_im+t4_im;
t9_im = aIm[5]+t1_im;
t1_im = t9_im-t1_im*c5_5;
t4_im = t1_im-t5_re;
t1_im = t1_im+t5_re;
t5_re = (t3_im+t2_im)*c5_2;
t3_im = t5_re-t3_im*c5_4;
t2_im = t5_re-t2_im*c5_3;
m5_re = t1_re+t2_im;
m5_im = t1_im-t2_re;
m6_re = t4_re-t3_im;
m6_im = t4_im+t3_re;
m7_re = t4_re+t3_im;
m7_im = t4_im-t3_re;
m8_re = t1_re-t2_im;
m8_im = t1_im+t2_re;
aRe[0] = m9_re+t9_re;
aIm[0] = m9_im+t9_im;
aRe[1] = m1_re-m5_re;
aIm[1] = m1_im-m5_im;
aRe[2] = m2_re+m6_re;
aIm[2] = m2_im+m6_im;
aRe[3] = m3_re-m7_re;
aIm[3] = m3_im-m7_im;
aRe[4] = m4_re+m8_re;
aIm[4] = m4_im+m8_im;
aRe[5] = m9_re-t9_re;
aIm[5] = m9_im-t9_im;
aRe[6] = m1_re+m5_re;
aIm[6] = m1_im+m5_im;
aRe[7] = m2_re-m6_re;
aIm[7] = m2_im-m6_im;
aRe[8] = m3_re+m7_re;
aIm[8] = m3_im+m7_im;
aRe[9] = m4_re-m8_re;
aIm[9] = m4_im-m8_im;
}
/**
* length 11 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix11( Type *aRe, Type *aIm )
{
t1_re = aRe[1]+aRe[10];
t1_im = aIm[1]+aIm[10];
t2_re = aRe[2]+aRe[9];
t2_im = aIm[2]+aIm[9];
t3_re = aRe[3]+aRe[8];
t3_im = aIm[3]+aIm[8];
t4_re = aRe[4]+aRe[7];
t4_im = aIm[4]+aIm[7];
t5_re = aRe[5]+aRe[6];
t5_im = aIm[5]+aIm[6];
t6_re = aRe[10]-aRe[1];
t6_im = aIm[10]-aIm[1];
t7_re = aRe[9]-aRe[2];
t7_im = aIm[9]-aIm[2];
t8_re = aRe[8]-aRe[3];
t8_im = aIm[8]-aIm[3];
t9_re = aRe[7]-aRe[4];
t9_im = aIm[7]-aIm[4];
t10_re = aRe[6]-aRe[5];
t10_im = aIm[6]-aIm[5];
t11_re = aRe[0]-Type(0.5*t5_re);
t11_im = aIm[0]-Type(0.5*t5_im);
t12_re = t1_re-t5_re;
t12_im = t1_im-t5_im;
t13_re = t2_re-t5_re;
t13_im = t2_im-t5_im;
t14_re = t3_re-t5_re;
t14_im = t3_im-t5_im;
t15_re = t4_re-t5_re;
t15_im = t4_im-t5_im;
m1_re = t11_re+c11_1*t12_re+c11_2*t13_re+c11_3*t14_re+c11_4*t15_re;
m1_im = t11_im+c11_1*t12_im+c11_2*t13_im+c11_3*t14_im+c11_4*t15_im;
m2_re = t11_re+c11_2*t12_re+c11_4*t13_re+c11_5*t14_re+c11_3*t15_re;
m2_im = t11_im+c11_2*t12_im+c11_4*t13_im+c11_5*t14_im+c11_3*t15_im;
m3_re = t11_re+c11_3*t12_re+c11_5*t13_re+c11_2*t14_re+c11_1*t15_re;
m3_im = t11_im+c11_3*t12_im+c11_5*t13_im+c11_2*t14_im+c11_1*t15_im;
m4_re = t11_re+c11_4*t12_re+c11_3*t13_re+c11_1*t14_re+c11_5*t15_re;
m4_im = t11_im+c11_4*t12_im+c11_3*t13_im+c11_1*t14_im+c11_5*t15_im;
m5_re = t11_re+c11_5*t12_re+c11_1*t13_re+c11_4*t14_re+c11_2*t15_re;
m5_im = t11_im+c11_5*t12_im+c11_1*t13_im+c11_4*t14_im+c11_2*t15_im;
m6_re = c11_10*t6_re-c11_6*t7_re+c11_9*t8_re-c11_7*t9_re+c11_8*t10_re;
m6_im = c11_10*t6_im-c11_6*t7_im+c11_9*t8_im-c11_7*t9_im+c11_8*t10_im;
m7_re = c11_9*t6_re-c11_8*t7_re+c11_6*t8_re+c11_10*t9_re-c11_7*t10_re;
m7_im = c11_9*t6_im-c11_8*t7_im+c11_6*t8_im+c11_10*t9_im-c11_7*t10_im;
m8_re = c11_8*t6_re-c11_10*t7_re-c11_7*t8_re+c11_6*t9_re+c11_9*t10_re;
m8_im = c11_8*t6_im-c11_10*t7_im-c11_7*t8_im+c11_6*t9_im+c11_9*t10_im;
m9_re = c11_7*t6_re+c11_9*t7_re-c11_10*t8_re-c11_8*t9_re-c11_6*t10_re;
m9_im = c11_7*t6_im+c11_9*t7_im-c11_10*t8_im-c11_8*t9_im-c11_6*t10_im;
m10_re = c11_6*t6_re+c11_7*t7_re+c11_8*t8_re+c11_9*t9_re+c11_10*t10_re;
m10_im = c11_6*t6_im+c11_7*t7_im+c11_8*t8_im+c11_9*t9_im+c11_10*t10_im;
aRe[0] = aRe[0]+t1_re+t2_re+t3_re+t4_re+t5_re;
aIm[0] = aIm[0]+t1_im+t2_im+t3_im+t4_im+t5_im;
aRe[1] = m1_re-m10_im;
aIm[1] = m1_im+m10_re;
aRe[2] = m2_re-m9_im;
aIm[2] = m2_im+m9_re;
aRe[3] = m3_re-m8_im;
aIm[3] = m3_im+m8_re;
aRe[4] = m4_re-m7_im;
aIm[4] = m4_im+m7_re;
aRe[5] = m5_re-m6_im;
aIm[5] = m5_im+m6_re;
aRe[6] = m5_re+m6_im;
aIm[6] = m5_im-m6_re;
aRe[7] = m4_re+m7_im;
aIm[7] = m4_im-m7_re;
aRe[8] = m3_re+m8_im;
aIm[8] = m3_im-m8_re;
aRe[9] = m2_re+m9_im;
aIm[9] = m2_im-m9_re;
aRe[10] = m1_re+m10_im;
aIm[10] = m1_im-m10_re;
}
/**
* length 13 DFT
*/
template<class Type>
inline void FFTPF<Type>::radix13( Type *aRe, Type *aIm )
{
t1_re = aRe[1]+aRe[12];
t1_im = aIm[1]+aIm[12];
t2_re = aRe[2]+aRe[11];
t2_im = aIm[2]+aIm[11];
t3_re = aRe[3]+aRe[10];
t3_im = aIm[3]+aIm[10];
t4_re = aRe[4]+aRe[9];
t4_im = aIm[4]+aIm[9];
t5_re = aRe[5]+aRe[8];
t5_im = aIm[5]+aIm[8];
t6_re = aRe[6]+aRe[7];
t6_im = aIm[6]+aIm[7];
t7_re = aRe[12]-aRe[1];
t7_im = aIm[12]-aIm[1];
t8_re = aRe[11]-aRe[2];
t8_im = aIm[11]-aIm[2];
t9_re = aRe[10]-aRe[3];
t9_im = aIm[10]-aIm[3];
t10_re = aRe[9]-aRe[4];
t10_im = aIm[9]-aIm[4];
t11_re = aRe[8]-aRe[5];
t11_im = aIm[8]-aIm[5];
t12_re = aRe[7]-aRe[6];
t12_im = aIm[7]-aIm[6];
t13_re = aRe[0]-Type(0.5*t6_re);
t13_im = aIm[0]-Type(0.5*t6_im);
t14_re = t1_re-t6_re;
t14_im = t1_im-t6_im;
t15_re = t2_re-t6_re;
t15_im = t2_im-t6_im;
t16_re = t3_re-t6_re;
t16_im = t3_im-t6_im;
t17_re = t4_re-t6_re;
t17_im = t4_im-t6_im;
t18_re = t5_re-t6_re;
t18_im = t5_im-t6_im;
m1_re = t13_re + c13_1*t14_re + c13_2*t15_re + c13_3*t16_re +
c13_4*t17_re + c13_5*t18_re;
m1_im = t13_im + c13_1*t14_im + c13_2*t15_im + c13_3*t16_im +
c13_4*t17_im + c13_5*t18_im;
m2_re = t13_re + c13_2*t14_re + c13_4*t15_re + c13_6*t16_re +
c13_5*t17_re + c13_3*t18_re;
m2_im = t13_im + c13_2*t14_im + c13_4*t15_im + c13_6*t16_im +
c13_5*t17_im + c13_3*t18_im;
m3_re = t13_re + c13_3*t14_re + c13_6*t15_re + c13_4*t16_re +
c13_1*t17_re + c13_2*t18_re;
m3_im = t13_im + c13_3*t14_im + c13_6*t15_im + c13_4*t16_im +
c13_1*t17_im + c13_2*t18_im;
m4_re = t13_re + c13_4*t14_re + c13_5*t15_re + c13_1*t16_re +
c13_3*t17_re + c13_6*t18_re;
m4_im = t13_im + c13_4*t14_im + c13_5*t15_im + c13_1*t16_im +
c13_3*t17_im + c13_6*t18_im;
m5_re = t13_re + c13_5*t14_re + c13_3*t15_re + c13_2*t16_re +
c13_6*t17_re + c13_1*t18_re;
m5_im = t13_im + c13_5*t14_im + c13_3*t15_im + c13_2*t16_im +