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sdrangel/sdrbase/dsp/gfft.h

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//==============================================================================
// g_fft.h:
//
// FFT library
// Copyright (C) 2013
// Dave Freese, W1HKJ
//
// based on public domain code by John Green <green_jt@vsdec.npt.nuwc.navy.mil>
// original version is available at
// http://hyperarchive.lcs.mit.edu/
// /HyperArchive/Archive/dev/src/ffts-for-risc-2-c.hqx
//
// ported to C++ for fldigi by Dave Freese, W1HKJ
//
// This file is part of fldigi.
//
// Fldigi is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// Fldigi is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with fldigi. If not, see <http://www.gnu.org/licenses/>.
//==============================================================================
#ifndef CGREEN_FFT_H
#define CGREEN_FFT_H
#include <complex>
template <typename FFT_TYPE>
class g_fft {
#define FFT_RECIPLN2 1.442695040888963407359924681001892137426 // 1.0/log(2)
// some useful conversions between a number and its power of 2
#define LOG2(a) (FFT_RECIPLN2*log(a)) // floating point logarithm base 2
#define POW2(m) ((unsigned int) 1 << (m)) // integer power of 2 for m<32
// fft's with M bigger than this bust primary cache
#define MCACHE (11 - (sizeof(FFT_TYPE) / 8))
// some math constants to 40 decimal places
#define FFT_PI 3.141592653589793238462643383279502884197 // pi
#define FFT_ROOT2 1.414213562373095048801688724209698078569 // sqrt(2)
#define FFT_COSPID8 0.9238795325112867561281831893967882868224 // cos(pi/8)
#define FFT_SINPID8 0.3826834323650897717284599840303988667613 // sin(pi/8)
private:
int FFT_size;
int FFT_N;
FFT_TYPE *FFT_table_1[32];
short int *FFT_table_2[32];
FFT_TYPE *Utbl;
short *BRLow;
void fftInit();
int ConvertFFTSize(int);
// base fft methods
void riffts1(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, short *BRLow);
void ifrstage(FFT_TYPE *ioptr, int M, FFT_TYPE *inUtbl);
void rifft8pt(FFT_TYPE *ioptr, FFT_TYPE scale);
void rifft4pt(FFT_TYPE *ioptr, FFT_TYPE scale);
void rifft2pt(FFT_TYPE *ioptr, FFT_TYPE scale);
void rifft1pt(FFT_TYPE *ioptr, FFT_TYPE scale);
void rffts1(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, short *BRLow);
void frstage(FFT_TYPE *ioptr, int M, FFT_TYPE *inUtbl);
void rfft8pt(FFT_TYPE *ioptr);
void rfft4pt(FFT_TYPE *ioptr);
void rfft2pt(FFT_TYPE *ioptr);
void rfft1pt(FFT_TYPE *ioptr);
void iffts1(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, short *BRLow);
void ifftrecurs(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, int Ustride,
int NDiffU, int StageCnt);
void ibfstages(FFT_TYPE *ioptr, int M, FFT_TYPE *inUtbl, int Ustride,
int NDiffU, int StageCnt);
void ibfR4(FFT_TYPE *ioptr, int M, int NDiffU);
void ibfR2(FFT_TYPE *ioptr, int M, int NDiffU);
void ifft8pt(FFT_TYPE *ioptr, FFT_TYPE scale);
void ifft4pt(FFT_TYPE *ioptr, FFT_TYPE scale);
void ifft2pt(FFT_TYPE *ioptr, FFT_TYPE scale);
void scbitrevR2(FFT_TYPE *ioptr, int M, short *inBRLow, FFT_TYPE scale);
void ffts1(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, short *BRLow);
void fftrecurs(FFT_TYPE *ioptr, int M,
FFT_TYPE *Utbl, int Ustride, int NDiffU,
int StageCnt);
void bfstages(FFT_TYPE *ioptr, int M,
FFT_TYPE *inUtbl, int Ustride,
int NDiffU, int StageCnt);
void bfR4(FFT_TYPE *ioptr, int M, int NDiffU);
void bfR2(FFT_TYPE *ioptr, int M, int NDiffU);
void fft8pt(FFT_TYPE *ioptr);
void fft4pt(FFT_TYPE *ioptr);
void fft2pt(FFT_TYPE *ioptr);
void bitrevR2(FFT_TYPE *ioptr, int M, short *inBRLow);
void fftBRInit(int M, short *BRLow);
void fftCosInit(int M, FFT_TYPE *Utbl);
public:
g_fft (int M = 8192)
{
if (M < 16) M = 16;
if (M > 268435456) M = 268435456;
FFT_size = M;
fftInit();
}
~g_fft()
{
for (int i = 0; i < 32; i++)
{
if (FFT_table_1[i] != 0) delete [] FFT_table_1[i];
if (FFT_table_2[i] != 0) delete [] FFT_table_2[i];
}
}
void ComplexFFT(std::complex<FFT_TYPE> *buf);
void InverseComplexFFT(std::complex<FFT_TYPE> *buf);
void RealFFT(std::complex<FFT_TYPE> *buf);
void InverseRealFFT(std::complex<FFT_TYPE> *buf);
FFT_TYPE GetInverseComplexFFTScale();
FFT_TYPE GetInverseRealFFTScale();
};
//------------------------------------------------------------------------------
// Compute Utbl, the cosine table for ffts
// of size (pow(2,M)/4 +1)
// INPUTS
// M = log2 of fft size
// OUTPUTS
// *Utbl = cosine table
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::fftCosInit(int M, FFT_TYPE *Utbl)
{
unsigned int fftN = POW2(M);
unsigned int i1;
Utbl[0] = FFT_TYPE(1.0);
for (i1 = 1; i1 < fftN/4; i1++)
Utbl[i1] = (FFT_TYPE)cos((2.0 * FFT_PI * (float)i1) / (float)fftN);
Utbl[fftN/4] = FFT_TYPE(0.0);
}
//------------------------------------------------------------------------------
// Compute BRLow, the bit reversed table for ffts
// of size pow(2,M/2 -1)
// INPUTS
// M = log2 of fft size
// OUTPUTS
// *BRLow = bit reversed counter table
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::fftBRInit(int M, short *BRLow)
{
int Mroot_1 = M / 2 - 1;
int Nroot_1 = POW2(Mroot_1);
int i1;
int bitsum;
int bitmask;
int bit;
for (i1 = 0; i1 < Nroot_1; i1++) {
bitsum = 0;
bitmask = 1;
for (bit = 1; bit <= Mroot_1; bitmask <<= 1, bit++)
if (i1 & bitmask)
bitsum = bitsum + (Nroot_1 >> bit);
BRLow[i1] = bitsum;
}
}
//------------------------------------------------------------------------------
// parts of ffts1
// bit reverse and first radix 2 stage of forward or inverse fft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::bitrevR2(FFT_TYPE *ioptr, int M, short *inBRLow)
{
FFT_TYPE f0r;
FFT_TYPE f0i;
FFT_TYPE f1r;
FFT_TYPE f1i;
FFT_TYPE f2r;
FFT_TYPE f2i;
FFT_TYPE f3r;
FFT_TYPE f3i;
FFT_TYPE f4r;
FFT_TYPE f4i;
FFT_TYPE f5r;
FFT_TYPE f5i;
FFT_TYPE f6r;
FFT_TYPE f6i;
FFT_TYPE f7r;
FFT_TYPE f7i;
FFT_TYPE t0r;
FFT_TYPE t0i;
FFT_TYPE t1r;
FFT_TYPE t1i;
FFT_TYPE *p0r;
FFT_TYPE *p1r;
FFT_TYPE *IOP;
FFT_TYPE *iolimit;
int Colstart;
int iCol;
unsigned int posA;
unsigned int posAi;
unsigned int posB;
unsigned int posBi;
const unsigned int Nrems2 = POW2((M + 3) / 2);
const unsigned int Nroot_1_ColInc = POW2(M) - Nrems2;
const unsigned int Nroot_1 = POW2(M / 2 - 1) - 1;
const unsigned int ColstartShift = (M + 1) / 2 + 1;
posA = POW2(M); // 1/2 of POW2(M) complex
posAi = posA + 1;
posB = posA + 2;
posBi = posB + 1;
iolimit = ioptr + Nrems2;
for (; ioptr < iolimit; ioptr += POW2(M / 2 + 1)) {
for (Colstart = Nroot_1; Colstart >= 0; Colstart--) {
iCol = Nroot_1;
p0r = ioptr + Nroot_1_ColInc + inBRLow[Colstart] * 4;
IOP = ioptr + (Colstart << ColstartShift);
p1r = IOP + inBRLow[iCol] * 4;
f0r = *(p0r);
f0i = *(p0r + 1);
f1r = *(p0r + posA);
f1i = *(p0r + posAi);
for (; iCol > Colstart;) {
f2r = *(p0r + 2);
f2i = *(p0r + (2 + 1));
f3r = *(p0r + posB);
f3i = *(p0r + posBi);
f4r = *(p1r);
f4i = *(p1r + 1);
f5r = *(p1r + posA);
f5i = *(p1r + posAi);
f6r = *(p1r + 2);
f6i = *(p1r + (2 + 1));
f7r = *(p1r + posB);
f7i = *(p1r + posBi);
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r + f3r;
t1i = f2i + f3i;
f3r = f2r - f3r;
f3i = f2i - f3i;
f0r = f4r + f5r;
f0i = f4i + f5i;
f5r = f4r - f5r;
f5i = f4i - f5i;
f2r = f6r + f7r;
f2i = f6i + f7i;
f7r = f6r - f7r;
f7i = f6i - f7i;
*(p1r) = t0r;
*(p1r + 1) = t0i;
*(p1r + 2) = f1r;
*(p1r + (2 + 1)) = f1i;
*(p1r + posA) = t1r;
*(p1r + posAi) = t1i;
*(p1r + posB) = f3r;
*(p1r + posBi) = f3i;
*(p0r) = f0r;
*(p0r + 1) = f0i;
*(p0r + 2) = f5r;
*(p0r + (2 + 1)) = f5i;
*(p0r + posA) = f2r;
*(p0r + posAi) = f2i;
*(p0r + posB) = f7r;
*(p0r + posBi) = f7i;
p0r -= Nrems2;
f0r = *(p0r);
f0i = *(p0r + 1);
f1r = *(p0r + posA);
f1i = *(p0r + posAi);
iCol -= 1;
p1r = IOP + inBRLow[iCol] * 4;
}
f2r = *(p0r + 2);
f2i = *(p0r + (2 + 1));
f3r = *(p0r + posB);
f3i = *(p0r + posBi);
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r + f3r;
t1i = f2i + f3i;
f3r = f2r - f3r;
f3i = f2i - f3i;
*(p0r) = t0r;
*(p0r + 1) = t0i;
*(p0r + 2) = f1r;
*(p0r + (2 + 1)) = f1i;
*(p0r + posA) = t1r;
*(p0r + posAi) = t1i;
*(p0r + posB) = f3r;
*(p0r + posBi) = f3i;
}
}
}
//------------------------------------------------------------------------------
// RADIX 2 fft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::fft2pt(FFT_TYPE *ioptr)
{
FFT_TYPE f0r, f0i, f1r, f1i;
FFT_TYPE t0r, t0i;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
f1r = ioptr[2];
f1i = ioptr[3];
// Butterflys
// f0 - - - t0
// f1 - 1 - f1
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
// store result
ioptr[0] = t0r;
ioptr[1] = t0i;
ioptr[2] = f1r;
ioptr[3] = f1i;
}
//------------------------------------------------------------------------------
// RADIX 4 fft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::fft4pt(FFT_TYPE *ioptr)
{
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE t0r, t0i, t1r, t1i;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
f1r = ioptr[4];
f1i = ioptr[5];
f2r = ioptr[2];
f2i = ioptr[3];
f3r = ioptr[6];
f3i = ioptr[7];
// Butterflys
// f0 - - t0 - - f0
// f1 - 1 - f1 - - f1
// f2 - - f2 - 1 - f2
// f3 - 1 - t1 - -i - f3
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r - f3r;
t1i = f2i - f3i;
f2r = f2r + f3r;
f2i = f2i + f3i;
f0r = t0r + f2r;
f0i = t0i + f2i;
f2r = t0r - f2r;
f2i = t0i - f2i;
f3r = f1r - t1i;
f3i = f1i + t1r;
f1r = f1r + t1i;
f1i = f1i - t1r;
// store result
ioptr[0] = f0r;
ioptr[1] = f0i;
ioptr[2] = f1r;
ioptr[3] = f1i;
ioptr[4] = f2r;
ioptr[5] = f2i;
ioptr[6] = f3r;
ioptr[7] = f3i;
}
//------------------------------------------------------------------------------
// RADIX 8 fft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::fft8pt(FFT_TYPE *ioptr)
{
FFT_TYPE w0r = 1.0 / FFT_ROOT2; // cos(pi/4)
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
FFT_TYPE t0r, t0i, t1r, t1i;
const FFT_TYPE Two = 2.0;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
f1r = ioptr[8];
f1i = ioptr[9];
f2r = ioptr[4];
f2i = ioptr[5];
f3r = ioptr[12];
f3i = ioptr[13];
f4r = ioptr[2];
f4i = ioptr[3];
f5r = ioptr[10];
f5i = ioptr[11];
f6r = ioptr[6];
f6i = ioptr[7];
f7r = ioptr[14];
f7i = ioptr[15];
// Butterflys
// f0 - - t0 - - f0 - - f0
// f1 - 1 - f1 - - f1 - - f1
// f2 - - f2 - 1 - f2 - - f2
// f3 - 1 - t1 - -i - f3 - - f3
// f4 - - t0 - - f4 - 1 - t0
// f5 - 1 - f5 - - f5 - w3 - f4
// f6 - - f6 - 1 - f6 - -i - t1
// f7 - 1 - t1 - -i - f7 - iw3- f6
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r - f3r;
t1i = f2i - f3i;
f2r = f2r + f3r;
f2i = f2i + f3i;
f0r = t0r + f2r;
f0i = t0i + f2i;
f2r = t0r - f2r;
f2i = t0i - f2i;
f3r = f1r - t1i;
f3i = f1i + t1r;
f1r = f1r + t1i;
f1i = f1i - t1r;
t0r = f4r + f5r;
t0i = f4i + f5i;
f5r = f4r - f5r;
f5i = f4i - f5i;
t1r = f6r - f7r;
t1i = f6i - f7i;
f6r = f6r + f7r;
f6i = f6i + f7i;
f4r = t0r + f6r;
f4i = t0i + f6i;
f6r = t0r - f6r;
f6i = t0i - f6i;
f7r = f5r - t1i;
f7i = f5i + t1r;
f5r = f5r + t1i;
f5i = f5i - t1r;
t0r = f0r - f4r;
t0i = f0i - f4i;
f0r = f0r + f4r;
f0i = f0i + f4i;
t1r = f2r - f6i;
t1i = f2i + f6r;
f2r = f2r + f6i;
f2i = f2i - f6r;
f4r = f1r - f5r * w0r - f5i * w0r;
f4i = f1i + f5r * w0r - f5i * w0r;
f1r = f1r * Two - f4r;
f1i = f1i * Two - f4i;
f6r = f3r + f7r * w0r - f7i * w0r;
f6i = f3i + f7r * w0r + f7i * w0r;
f3r = f3r * Two - f6r;
f3i = f3i * Two - f6i;
// store result
ioptr[0] = f0r;
ioptr[1] = f0i;
ioptr[2] = f1r;
ioptr[3] = f1i;
ioptr[4] = f2r;
ioptr[5] = f2i;
ioptr[6] = f3r;
ioptr[7] = f3i;
ioptr[8] = t0r;
ioptr[9] = t0i;
ioptr[10] = f4r;
ioptr[11] = f4i;
ioptr[12] = t1r;
ioptr[13] = t1i;
ioptr[14] = f6r;
ioptr[15] = f6i;
}
//------------------------------------------------------------------------------
// 2nd radix 2 stage
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::bfR2(FFT_TYPE *ioptr, int M, int NDiffU)
{
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int NSameU;
unsigned int SameUCnt;
FFT_TYPE *pstrt;
FFT_TYPE *p0r, *p1r, *p2r, *p3r;
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
pinc = NDiffU * 2; // 2 floats per complex
pnext = pinc * 4;
pos = 2;
posi = pos + 1;
NSameU = POW2(M) / 4 / NDiffU; // 4 Us at a time
pstrt = ioptr;
p0r = pstrt;
p1r = pstrt + pinc;
p2r = p1r + pinc;
p3r = p2r + pinc;
// Butterflys
// f0 - - f4
// f1 - 1 - f5
// f2 - - f6
// f3 - 1 - f7
// Butterflys
// f0 - - f4
// f1 - 1 - f5
// f2 - - f6
// f3 - 1 - f7
for (SameUCnt = NSameU; SameUCnt > 0; SameUCnt--) {
f0r = *p0r;
f1r = *p1r;
f0i = *(p0r + 1);
f1i = *(p1r + 1);
f2r = *p2r;
f3r = *p3r;
f2i = *(p2r + 1);
f3i = *(p3r + 1);
f4r = f0r + f1r;
f4i = f0i + f1i;
f5r = f0r - f1r;
f5i = f0i - f1i;
f6r = f2r + f3r;
f6i = f2i + f3i;
f7r = f2r - f3r;
f7i = f2i - f3i;
*p0r = f4r;
*(p0r + 1) = f4i;
*p1r = f5r;
*(p1r + 1) = f5i;
*p2r = f6r;
*(p2r + 1) = f6i;
*p3r = f7r;
*(p3r + 1) = f7i;
f0r = *(p0r + pos);
f1i = *(p1r + posi);
f0i = *(p0r + posi);
f1r = *(p1r + pos);
f2r = *(p2r + pos);
f3i = *(p3r + posi);
f2i = *(p2r + posi);
f3r = *(p3r + pos);
f4r = f0r + f1i;
f4i = f0i - f1r;
f5r = f0r - f1i;
f5i = f0i + f1r;
f6r = f2r + f3i;
f6i = f2i - f3r;
f7r = f2r - f3i;
f7i = f2i + f3r;
*(p0r + pos) = f4r;
*(p0r + posi) = f4i;
*(p1r + pos) = f5r;
*(p1r + posi) = f5i;
*(p2r + pos) = f6r;
*(p2r + posi) = f6i;
*(p3r + pos) = f7r;
*(p3r + posi) = f7i;
p0r += pnext;
p1r += pnext;
p2r += pnext;
p3r += pnext;
}
}
//------------------------------------------------------------------------------
// 1 radix 4 stage
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::bfR4(FFT_TYPE *ioptr, int M, int NDiffU)
{
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int pnexti;
unsigned int NSameU;
unsigned int SameUCnt;
FFT_TYPE *pstrt;
FFT_TYPE *p0r, *p1r, *p2r, *p3r;
FFT_TYPE w1r = 1.0 / FFT_ROOT2; // cos(pi/4)
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
FFT_TYPE t1r, t1i;
const FFT_TYPE Two = 2.0;
pinc = NDiffU * 2; // 2 floats per complex
pnext = pinc * 4;
pnexti = pnext + 1;
pos = 2;
posi = pos + 1;
NSameU = POW2(M) / 4 / NDiffU; // 4 pts per butterfly
pstrt = ioptr;
p0r = pstrt;
p1r = pstrt + pinc;
p2r = p1r + pinc;
p3r = p2r + pinc;
// Butterflys
// f0 - - f0 - - f4
// f1 - 1 - f5 - - f5
// f2 - - f6 - 1 - f6
// f3 - 1 - f3 - -i - f7
// Butterflys
// f0 - - f4 - - f4
// f1 - -i - t1 - - f5
// f2 - - f2 - w1 - f6
// f3 - -i - f7 - iw1- f7
f0r = *p0r;
f1r = *p1r;
f2r = *p2r;
f3r = *p3r;
f0i = *(p0r + 1);
f1i = *(p1r + 1);
f2i = *(p2r + 1);
f3i = *(p3r + 1);
f5r = f0r - f1r;
f5i = f0i - f1i;
f0r = f0r + f1r;
f0i = f0i + f1i;
f6r = f2r + f3r;
f6i = f2i + f3i;
f3r = f2r - f3r;
f3i = f2i - f3i;
for (SameUCnt = NSameU - 1; SameUCnt > 0; SameUCnt--) {
f7r = f5r - f3i;
f7i = f5i + f3r;
f5r = f5r + f3i;
f5i = f5i - f3r;
f4r = f0r + f6r;
f4i = f0i + f6i;
f6r = f0r - f6r;
f6i = f0i - f6i;
f2r = *(p2r + pos);
f2i = *(p2r + posi);
f1r = *(p1r + pos);
f1i = *(p1r + posi);
f3i = *(p3r + posi);
f0r = *(p0r + pos);
f3r = *(p3r + pos);
f0i = *(p0r + posi);
*p3r = f7r;
*p0r = f4r;
*(p3r + 1) = f7i;
*(p0r + 1) = f4i;
*p1r = f5r;
*p2r = f6r;
*(p1r + 1) = f5i;
*(p2r + 1) = f6i;
f7r = f2r - f3i;
f7i = f2i + f3r;
f2r = f2r + f3i;
f2i = f2i - f3r;
f4r = f0r + f1i;
f4i = f0i - f1r;
t1r = f0r - f1i;
t1i = f0i + f1r;
f5r = t1r - f7r * w1r + f7i * w1r;
f5i = t1i - f7r * w1r - f7i * w1r;
f7r = t1r * Two - f5r;
f7i = t1i * Two - f5i;
f6r = f4r - f2r * w1r - f2i * w1r;
f6i = f4i + f2r * w1r - f2i * w1r;
f4r = f4r * Two - f6r;
f4i = f4i * Two - f6i;
f3r = *(p3r + pnext);
f0r = *(p0r + pnext);
f3i = *(p3r + pnexti);
f0i = *(p0r + pnexti);
f2r = *(p2r + pnext);
f2i = *(p2r + pnexti);
f1r = *(p1r + pnext);
f1i = *(p1r + pnexti);
*(p2r + pos) = f6r;
*(p1r + pos) = f5r;
*(p2r + posi) = f6i;
*(p1r + posi) = f5i;
*(p3r + pos) = f7r;
*(p0r + pos) = f4r;
*(p3r + posi) = f7i;
*(p0r + posi) = f4i;
f6r = f2r + f3r;
f6i = f2i + f3i;
f3r = f2r - f3r;
f3i = f2i - f3i;
f5r = f0r - f1r;
f5i = f0i - f1i;
f0r = f0r + f1r;
f0i = f0i + f1i;
p3r += pnext;
p0r += pnext;
p1r += pnext;
p2r += pnext;
}
f7r = f5r - f3i;
f7i = f5i + f3r;
f5r = f5r + f3i;
f5i = f5i - f3r;
f4r = f0r + f6r;
f4i = f0i + f6i;
f6r = f0r - f6r;
f6i = f0i - f6i;
f2r = *(p2r + pos);
f2i = *(p2r + posi);
f1r = *(p1r + pos);
f1i = *(p1r + posi);
f3i = *(p3r + posi);
f0r = *(p0r + pos);
f3r = *(p3r + pos);
f0i = *(p0r + posi);
*p3r = f7r;
*p0r = f4r;
*(p3r + 1) = f7i;
*(p0r + 1) = f4i;
*p1r = f5r;
*p2r = f6r;
*(p1r + 1) = f5i;
*(p2r + 1) = f6i;
f7r = f2r - f3i;
f7i = f2i + f3r;
f2r = f2r + f3i;
f2i = f2i - f3r;
f4r = f0r + f1i;
f4i = f0i - f1r;
t1r = f0r - f1i;
t1i = f0i + f1r;
f5r = t1r - f7r * w1r + f7i * w1r;
f5i = t1i - f7r * w1r - f7i * w1r;
f7r = t1r * Two - f5r;
f7i = t1i * Two - f5i;
f6r = f4r - f2r * w1r - f2i * w1r;
f6i = f4i + f2r * w1r - f2i * w1r;
f4r = f4r * Two - f6r;
f4i = f4i * Two - f6i;
*(p2r + pos) = f6r;
*(p1r + pos) = f5r;
*(p2r + posi) = f6i;
*(p1r + posi) = f5i;
*(p3r + pos) = f7r;
*(p0r + pos) = f4r;
*(p3r + posi) = f7i;
*(p0r + posi) = f4i;
}
//------------------------------------------------------------------------------
// RADIX 8 Stages
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::bfstages(FFT_TYPE *ioptr, int M, FFT_TYPE *inUtbl, int Ustride,
int NDiffU, int StageCnt)
{
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int NSameU;
int Uinc;
int Uinc2;
int Uinc4;
unsigned int DiffUCnt;
unsigned int SameUCnt;
unsigned int U2toU3;
FFT_TYPE *pstrt;
FFT_TYPE *p0r, *p1r, *p2r, *p3r;
FFT_TYPE *u0r, *u0i, *u1r, *u1i, *u2r, *u2i;
FFT_TYPE w0r, w0i, w1r, w1i, w2r, w2i, w3r, w3i;
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
FFT_TYPE t0r, t0i, t1r, t1i;
const FFT_TYPE Two = FFT_TYPE(2.0);
pinc = NDiffU * 2; // 2 floats per complex
pnext = pinc * 8;
pos = pinc * 4;
posi = pos + 1;
NSameU = POW2(M) / 8 / NDiffU; // 8 pts per butterfly
Uinc = (int) NSameU * Ustride;
Uinc2 = Uinc * 2;
Uinc4 = Uinc * 4;
U2toU3 = (POW2(M) / 8) * Ustride;
for (; StageCnt > 0; StageCnt--) {
u0r = &inUtbl[0];
u0i = &inUtbl[POW2(M - 2) * Ustride];
u1r = u0r;
u1i = u0i;
u2r = u0r;
u2i = u0i;
w0r = *u0r;
w0i = *u0i;
w1r = *u1r;
w1i = *u1i;
w2r = *u2r;
w2i = *u2i;
w3r = *(u2r + U2toU3);
w3i = *(u2i - U2toU3);
pstrt = ioptr;
p0r = pstrt;
p1r = pstrt + pinc;
p2r = p1r + pinc;
p3r = p2r + pinc;
// Butterflys
// f0 - - t0 - - f0 - - f0
// f1 - w0- f1 - - f1 - - f1
// f2 - - f2 - w1- f2 - - f4
// f3 - w0- t1 - iw1- f3 - - f5
//
// f4 - - t0 - - f4 - w2- t0
// f5 - w0- f5 - - f5 - w3- t1
// f6 - - f6 - w1- f6 - iw2- f6
// f7 - w0- t1 - iw1- f7 - iw3- f7
for (DiffUCnt = NDiffU; DiffUCnt > 0; DiffUCnt--) {
f0r = *p0r;
f0i = *(p0r + 1);
f1r = *p1r;
f1i = *(p1r + 1);
for (SameUCnt = NSameU - 1; SameUCnt > 0; SameUCnt--) {
f2r = *p2r;
f2i = *(p2r + 1);
f3r = *p3r;
f3i = *(p3r + 1);
t0r = f0r + f1r * w0r + f1i * w0i;
t0i = f0i - f1r * w0i + f1i * w0r;
f1r = f0r * Two - t0r;
f1i = f0i * Two - t0i;
f4r = *(p0r + pos);
f4i = *(p0r + posi);
f5r = *(p1r + pos);
f5i = *(p1r + posi);
f6r = *(p2r + pos);
f6i = *(p2r + posi);
f7r = *(p3r + pos);
f7i = *(p3r + posi);
t1r = f2r - f3r * w0r - f3i * w0i;
t1i = f2i + f3r * w0i - f3i * w0r;
f2r = f2r * Two - t1r;
f2i = f2i * Two - t1i;
f0r = t0r + f2r * w1r + f2i * w1i;
f0i = t0i - f2r * w1i + f2i * w1r;
f2r = t0r * Two - f0r;
f2i = t0i * Two - f0i;
f3r = f1r + t1r * w1i - t1i * w1r;
f3i = f1i + t1r * w1r + t1i * w1i;
f1r = f1r * Two - f3r;
f1i = f1i * Two - f3i;
t0r = f4r + f5r * w0r + f5i * w0i;
t0i = f4i - f5r * w0i + f5i * w0r;
f5r = f4r * Two - t0r;
f5i = f4i * Two - t0i;
t1r = f6r - f7r * w0r - f7i * w0i;
t1i = f6i + f7r * w0i - f7i * w0r;
f6r = f6r * Two - t1r;
f6i = f6i * Two - t1i;
f4r = t0r + f6r * w1r + f6i * w1i;
f4i = t0i - f6r * w1i + f6i * w1r;
f6r = t0r * Two - f4r;
f6i = t0i * Two - f4i;
f7r = f5r + t1r * w1i - t1i * w1r;
f7i = f5i + t1r * w1r + t1i * w1i;
f5r = f5r * Two - f7r;
f5i = f5i * Two - f7i;
t0r = f0r - f4r * w2r - f4i * w2i;
t0i = f0i + f4r * w2i - f4i * w2r;
f0r = f0r * Two - t0r;
f0i = f0i * Two - t0i;
t1r = f1r - f5r * w3r - f5i * w3i;
t1i = f1i + f5r * w3i - f5i * w3r;
f1r = f1r * Two - t1r;
f1i = f1i * Two - t1i;
*(p0r + pos) = t0r;
*(p1r + pos) = t1r;
*(p0r + posi) = t0i;
*(p1r + posi) = t1i;
*p0r = f0r;
*p1r = f1r;
*(p0r + 1) = f0i;
*(p1r + 1) = f1i;
p0r += pnext;
f0r = *p0r;
f0i = *(p0r + 1);
p1r += pnext;
f1r = *p1r;
f1i = *(p1r + 1);
f4r = f2r - f6r * w2i + f6i * w2r;
f4i = f2i - f6r * w2r - f6i * w2i;
f6r = f2r * Two - f4r;
f6i = f2i * Two - f4i;
f5r = f3r - f7r * w3i + f7i * w3r;
f5i = f3i - f7r * w3r - f7i * w3i;
f7r = f3r * Two - f5r;
f7i = f3i * Two - f5i;
*p2r = f4r;
*p3r = f5r;
*(p2r + 1) = f4i;
*(p3r + 1) = f5i;
*(p2r + pos) = f6r;
*(p3r + pos) = f7r;
*(p2r + posi) = f6i;
*(p3r + posi) = f7i;
p2r += pnext;
p3r += pnext;
}
f2r = *p2r;
f2i = *(p2r + 1);
f3r = *p3r;
f3i = *(p3r + 1);
t0r = f0r + f1r * w0r + f1i * w0i;
t0i = f0i - f1r * w0i + f1i * w0r;
f1r = f0r * Two - t0r;
f1i = f0i * Two - t0i;
f4r = *(p0r + pos);
f4i = *(p0r + posi);
f5r = *(p1r + pos);
f5i = *(p1r + posi);
f6r = *(p2r + pos);
f6i = *(p2r + posi);
f7r = *(p3r + pos);
f7i = *(p3r + posi);
t1r = f2r - f3r * w0r - f3i * w0i;
t1i = f2i + f3r * w0i - f3i * w0r;
f2r = f2r * Two - t1r;
f2i = f2i * Two - t1i;
f0r = t0r + f2r * w1r + f2i * w1i;
f0i = t0i - f2r * w1i + f2i * w1r;
f2r = t0r * Two - f0r;
f2i = t0i * Two - f0i;
f3r = f1r + t1r * w1i - t1i * w1r;
f3i = f1i + t1r * w1r + t1i * w1i;
f1r = f1r * Two - f3r;
f1i = f1i * Two - f3i;
if ((int) DiffUCnt == NDiffU / 2)
Uinc4 = -Uinc4;
u0r += Uinc4;
u0i -= Uinc4;
u1r += Uinc2;
u1i -= Uinc2;
u2r += Uinc;
u2i -= Uinc;
pstrt += 2;
t0r = f4r + f5r * w0r + f5i * w0i;
t0i = f4i - f5r * w0i + f5i * w0r;
f5r = f4r * Two - t0r;
f5i = f4i * Two - t0i;
t1r = f6r - f7r * w0r - f7i * w0i;
t1i = f6i + f7r * w0i - f7i * w0r;
f6r = f6r * Two - t1r;
f6i = f6i * Two - t1i;
f4r = t0r + f6r * w1r + f6i * w1i;
f4i = t0i - f6r * w1i + f6i * w1r;
f6r = t0r * Two - f4r;
f6i = t0i * Two - f4i;
f7r = f5r + t1r * w1i - t1i * w1r;
f7i = f5i + t1r * w1r + t1i * w1i;
f5r = f5r * Two - f7r;
f5i = f5i * Two - f7i;
w0r = *u0r;
w0i = *u0i;
w1r = *u1r;
w1i = *u1i;
if ((int) DiffUCnt <= NDiffU / 2)
w0r = -w0r;
t0r = f0r - f4r * w2r - f4i * w2i;
t0i = f0i + f4r * w2i - f4i * w2r;
f0r = f0r * Two - t0r;
f0i = f0i * Two - t0i;
f4r = f2r - f6r * w2i + f6i * w2r;
f4i = f2i - f6r * w2r - f6i * w2i;
f6r = f2r * Two - f4r;
f6i = f2i * Two - f4i;
*(p0r + pos) = t0r;
*p2r = f4r;
*(p0r + posi) = t0i;
*(p2r + 1) = f4i;
w2r = *u2r;
w2i = *u2i;
*p0r = f0r;
*(p2r + pos) = f6r;
*(p0r + 1) = f0i;
*(p2r + posi) = f6i;
p0r = pstrt;
p2r = pstrt + pinc + pinc;
t1r = f1r - f5r * w3r - f5i * w3i;
t1i = f1i + f5r * w3i - f5i * w3r;
f1r = f1r * Two - t1r;
f1i = f1i * Two - t1i;
f5r = f3r - f7r * w3i + f7i * w3r;
f5i = f3i - f7r * w3r - f7i * w3i;
f7r = f3r * Two - f5r;
f7i = f3i * Two - f5i;
*(p1r + pos) = t1r;
*p3r = f5r;
*(p1r + posi) = t1i;
*(p3r + 1) = f5i;
w3r = *(u2r + U2toU3);
w3i = *(u2i - U2toU3);
*p1r = f1r;
*(p3r + pos) = f7r;
*(p1r + 1) = f1i;
*(p3r + posi) = f7i;
p1r = pstrt + pinc;
p3r = p2r + pinc;
}
NSameU /= 8;
Uinc /= 8;
Uinc2 /= 8;
Uinc4 = Uinc * 4;
NDiffU *= 8;
pinc *= 8;
pnext *= 8;
pos *= 8;
posi = pos + 1;
}
}
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::fftrecurs(FFT_TYPE *ioptr, int M,
FFT_TYPE *Utbl, int Ustride, int NDiffU,
int StageCnt)
{
// recursive bfstages calls to maximize on chip cache efficiency
int i1;
if (M <= (int) MCACHE) // fits on chip ?
bfstages(ioptr, M, Utbl, Ustride, NDiffU, StageCnt); // RADIX 8 Stages
else {
for (i1 = 0; i1 < 8; i1++) {
fftrecurs(&ioptr[i1 * POW2(M - 3) * 2], M - 3, Utbl, 8 * Ustride,
NDiffU, StageCnt - 1); // RADIX 8 Stages
}
bfstages(ioptr, M, Utbl, Ustride, POW2(M - 3), 1); // RADIX 8 Stage
}
}
//------------------------------------------------------------------------------
// Compute in-place complex fft on the rows of the input array
// INPUTS
// *ioptr = input data array
// M = log2 of fft size (ex M=10 for 1024 point fft)
// *Utbl = cosine table
// *BRLow = bit reversed counter table
// OUTPUTS
// *ioptr = output data array
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ffts1(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, short *BRLow)
{
int StageCnt;
int NDiffU;
switch (M) {
case 0:
break;
case 1:
fft2pt(ioptr); // a 2 pt fft
break;
case 2:
fft4pt(ioptr); // a 4 pt fft
break;
case 3:
fft8pt(ioptr); // an 8 pt fft
break;
default:
bitrevR2(ioptr, M, BRLow); // bit reverse and first radix 2 stage
StageCnt = (M - 1) / 3; // number of radix 8 stages
NDiffU = 2; // one radix 2 stage already complete
if ((M - 1 - (StageCnt * 3)) == 1) {
bfR2(ioptr, M, NDiffU); // 1 radix 2 stage
NDiffU *= 2;
}
if ((M - 1 - (StageCnt * 3)) == 2) {
bfR4(ioptr, M, NDiffU); // 1 radix 4 stage
NDiffU *= 4;
}
if (M <= (int) MCACHE)
bfstages(ioptr, M, Utbl, 1, NDiffU, StageCnt); // RADIX 8 Stages
else
fftrecurs(ioptr, M, Utbl, 1, NDiffU, StageCnt); // RADIX 8 Stages
}
}
//------------------------------------------------------------------------------
// parts of iffts1
// scaled bit reverse and first radix 2 stage forward or inverse fft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::scbitrevR2(FFT_TYPE *ioptr, int M, short *inBRLow, FFT_TYPE scale)
{
FFT_TYPE f0r;
FFT_TYPE f0i;
FFT_TYPE f1r;
FFT_TYPE f1i;
FFT_TYPE f2r;
FFT_TYPE f2i;
FFT_TYPE f3r;
FFT_TYPE f3i;
FFT_TYPE f4r;
FFT_TYPE f4i;
FFT_TYPE f5r;
FFT_TYPE f5i;
FFT_TYPE f6r;
FFT_TYPE f6i;
FFT_TYPE f7r;
FFT_TYPE f7i;
FFT_TYPE t0r;
FFT_TYPE t0i;
FFT_TYPE t1r;
FFT_TYPE t1i;
FFT_TYPE *p0r;
FFT_TYPE *p1r;
FFT_TYPE *IOP;
FFT_TYPE *iolimit;
int Colstart;
int iCol;
unsigned int posA;
unsigned int posAi;
unsigned int posB;
unsigned int posBi;
const unsigned int Nrems2 = POW2((M + 3) / 2);
const unsigned int Nroot_1_ColInc = POW2(M) - Nrems2;
const unsigned int Nroot_1 = POW2(M / 2 - 1) - 1;
const unsigned int ColstartShift = (M + 1) / 2 + 1;
posA = POW2(M); // 1/2 of POW2(M) complexes
posAi = posA + 1;
posB = posA + 2;
posBi = posB + 1;
iolimit = ioptr + Nrems2;
for (; ioptr < iolimit; ioptr += POW2(M / 2 + 1)) {
for (Colstart = Nroot_1; Colstart >= 0; Colstart--) {
iCol = Nroot_1;
p0r = ioptr + Nroot_1_ColInc + inBRLow[Colstart] * 4;
IOP = ioptr + (Colstart << ColstartShift);
p1r = IOP + inBRLow[iCol] * 4;
f0r = *(p0r);
f0i = *(p0r + 1);
f1r = *(p0r + posA);
f1i = *(p0r + posAi);
for (; iCol > Colstart;) {
f2r = *(p0r + 2);
f2i = *(p0r + (2 + 1));
f3r = *(p0r + posB);
f3i = *(p0r + posBi);
f4r = *(p1r);
f4i = *(p1r + 1);
f5r = *(p1r + posA);
f5i = *(p1r + posAi);
f6r = *(p1r + 2);
f6i = *(p1r + (2 + 1));
f7r = *(p1r + posB);
f7i = *(p1r + posBi);
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r + f3r;
t1i = f2i + f3i;
f3r = f2r - f3r;
f3i = f2i - f3i;
f0r = f4r + f5r;
f0i = f4i + f5i;
f5r = f4r - f5r;
f5i = f4i - f5i;
f2r = f6r + f7r;
f2i = f6i + f7i;
f7r = f6r - f7r;
f7i = f6i - f7i;
*(p1r) = scale * t0r;
*(p1r + 1) = scale * t0i;
*(p1r + 2) = scale * f1r;
*(p1r + (2 + 1)) = scale * f1i;
*(p1r + posA) = scale * t1r;
*(p1r + posAi) = scale * t1i;
*(p1r + posB) = scale * f3r;
*(p1r + posBi) = scale * f3i;
*(p0r) = scale * f0r;
*(p0r + 1) = scale * f0i;
*(p0r + 2) = scale * f5r;
*(p0r + (2 + 1)) = scale * f5i;
*(p0r + posA) = scale * f2r;
*(p0r + posAi) = scale * f2i;
*(p0r + posB) = scale * f7r;
*(p0r + posBi) = scale * f7i;
p0r -= Nrems2;
f0r = *(p0r);
f0i = *(p0r + 1);
f1r = *(p0r + posA);
f1i = *(p0r + posAi);
iCol -= 1;
p1r = IOP + inBRLow[iCol] * 4;
}
f2r = *(p0r + 2);
f2i = *(p0r + (2 + 1));
f3r = *(p0r + posB);
f3i = *(p0r + posBi);
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r + f3r;
t1i = f2i + f3i;
f3r = f2r - f3r;
f3i = f2i - f3i;
*(p0r) = scale * t0r;
*(p0r + 1) = scale * t0i;
*(p0r + 2) = scale * f1r;
*(p0r + (2 + 1)) = scale * f1i;
*(p0r + posA) = scale * t1r;
*(p0r + posAi) = scale * t1i;
*(p0r + posB) = scale * f3r;
*(p0r + posBi) = scale * f3i;
}
}
}
//------------------------------------------------------------------------------
// RADIX 2 ifft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ifft2pt(FFT_TYPE *ioptr, FFT_TYPE scale)
{
FFT_TYPE f0r, f0i, f1r, f1i;
FFT_TYPE t0r, t0i;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
f1r = ioptr[2];
f1i = ioptr[3];
// Butterflys
// f0 - - t0
// f1 - 1 - f1
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
// store result
ioptr[0] = scale * t0r;
ioptr[1] = scale * t0i;
ioptr[2] = scale * f1r;
ioptr[3] = scale * f1i;
}
//------------------------------------------------------------------------------
// RADIX 4 ifft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ifft4pt(FFT_TYPE *ioptr, FFT_TYPE scale)
{
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE t0r, t0i, t1r, t1i;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
f1r = ioptr[4];
f1i = ioptr[5];
f2r = ioptr[2];
f2i = ioptr[3];
f3r = ioptr[6];
f3i = ioptr[7];
// Butterflys
// f0 - - t0 - - f0
// f1 - 1 - f1 - - f1
// f2 - - f2 - 1 - f2
// f3 - 1 - t1 - i - f3
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r - f3r;
t1i = f2i - f3i;
f2r = f2r + f3r;
f2i = f2i + f3i;
f0r = t0r + f2r;
f0i = t0i + f2i;
f2r = t0r - f2r;
f2i = t0i - f2i;
f3r = f1r + t1i;
f3i = f1i - t1r;
f1r = f1r - t1i;
f1i = f1i + t1r;
// store result
ioptr[0] = scale * f0r;
ioptr[1] = scale * f0i;
ioptr[2] = scale * f1r;
ioptr[3] = scale * f1i;
ioptr[4] = scale * f2r;
ioptr[5] = scale * f2i;
ioptr[6] = scale * f3r;
ioptr[7] = scale * f3i;
}
//------------------------------------------------------------------------------
// RADIX 8 ifft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ifft8pt(FFT_TYPE *ioptr, FFT_TYPE scale)
{
FFT_TYPE w0r = 1.0 / FFT_ROOT2; // cos(pi/4)
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
FFT_TYPE t0r, t0i, t1r, t1i;
const FFT_TYPE Two = 2.0;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
f1r = ioptr[8];
f1i = ioptr[9];
f2r = ioptr[4];
f2i = ioptr[5];
f3r = ioptr[12];
f3i = ioptr[13];
f4r = ioptr[2];
f4i = ioptr[3];
f5r = ioptr[10];
f5i = ioptr[11];
f6r = ioptr[6];
f6i = ioptr[7];
f7r = ioptr[14];
f7i = ioptr[15];
// Butterflys
// f0 - - t0 - - f0 - - f0
// f1 - 1 - f1 - - f1 - - f1
// f2 - - f2 - 1 - f2 - - f2
// f3 - 1 - t1 - i - f3 - - f3
// f4 - - t0 - - f4 - 1 - t0
// f5 - 1 - f5 - - f5 - w3 - f4
// f6 - - f6 - 1 - f6 - i - t1
// f7 - 1 - t1 - i - f7 - iw3- f6
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r - f3r;
t1i = f2i - f3i;
f2r = f2r + f3r;
f2i = f2i + f3i;
f0r = t0r + f2r;
f0i = t0i + f2i;
f2r = t0r - f2r;
f2i = t0i - f2i;
f3r = f1r + t1i;
f3i = f1i - t1r;
f1r = f1r - t1i;
f1i = f1i + t1r;
t0r = f4r + f5r;
t0i = f4i + f5i;
f5r = f4r - f5r;
f5i = f4i - f5i;
t1r = f6r - f7r;
t1i = f6i - f7i;
f6r = f6r + f7r;
f6i = f6i + f7i;
f4r = t0r + f6r;
f4i = t0i + f6i;
f6r = t0r - f6r;
f6i = t0i - f6i;
f7r = f5r + t1i;
f7i = f5i - t1r;
f5r = f5r - t1i;
f5i = f5i + t1r;
t0r = f0r - f4r;
t0i = f0i - f4i;
f0r = f0r + f4r;
f0i = f0i + f4i;
t1r = f2r + f6i;
t1i = f2i - f6r;
f2r = f2r - f6i;
f2i = f2i + f6r;
f4r = f1r - f5r * w0r + f5i * w0r;
f4i = f1i - f5r * w0r - f5i * w0r;
f1r = f1r * Two - f4r;
f1i = f1i * Two - f4i;
f6r = f3r + f7r * w0r + f7i * w0r;
f6i = f3i - f7r * w0r + f7i * w0r;
f3r = f3r * Two - f6r;
f3i = f3i * Two - f6i;
// store result
ioptr[0] = scale * f0r;
ioptr[1] = scale * f0i;
ioptr[2] = scale * f1r;
ioptr[3] = scale * f1i;
ioptr[4] = scale * f2r;
ioptr[5] = scale * f2i;
ioptr[6] = scale * f3r;
ioptr[7] = scale * f3i;
ioptr[8] = scale * t0r;
ioptr[9] = scale * t0i;
ioptr[10] = scale * f4r;
ioptr[11] = scale * f4i;
ioptr[12] = scale * t1r;
ioptr[13] = scale * t1i;
ioptr[14] = scale * f6r;
ioptr[15] = scale * f6i;
}
//------------------------------------------------------------------------------
// 2nd radix 2 stage
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ibfR2(FFT_TYPE *ioptr, int M, int NDiffU)
{
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int NSameU;
unsigned int SameUCnt;
FFT_TYPE *pstrt;
FFT_TYPE *p0r, *p1r, *p2r, *p3r;
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
pinc = NDiffU * 2; // 2 floats per complex
pnext = pinc * 4;
pos = 2;
posi = pos + 1;
NSameU = POW2(M) / 4 / NDiffU; // 4 Us at a time
pstrt = ioptr;
p0r = pstrt;
p1r = pstrt + pinc;
p2r = p1r + pinc;
p3r = p2r + pinc;
// Butterflys
// f0 - - f4
// f1 - 1 - f5
// f2 - - f6
// f3 - 1 - f7
// Butterflys
// f0 - - f4
// f1 - 1 - f5
// f2 - - f6
// f3 - 1 - f7
for (SameUCnt = NSameU; SameUCnt > 0; SameUCnt--) {
f0r = *p0r;
f1r = *p1r;
f0i = *(p0r + 1);
f1i = *(p1r + 1);
f2r = *p2r;
f3r = *p3r;
f2i = *(p2r + 1);
f3i = *(p3r + 1);
f4r = f0r + f1r;
f4i = f0i + f1i;
f5r = f0r - f1r;
f5i = f0i - f1i;
f6r = f2r + f3r;
f6i = f2i + f3i;
f7r = f2r - f3r;
f7i = f2i - f3i;
*p0r = f4r;
*(p0r + 1) = f4i;
*p1r = f5r;
*(p1r + 1) = f5i;
*p2r = f6r;
*(p2r + 1) = f6i;
*p3r = f7r;
*(p3r + 1) = f7i;
f0r = *(p0r + pos);
f1i = *(p1r + posi);
f0i = *(p0r + posi);
f1r = *(p1r + pos);
f2r = *(p2r + pos);
f3i = *(p3r + posi);
f2i = *(p2r + posi);
f3r = *(p3r + pos);
f4r = f0r - f1i;
f4i = f0i + f1r;
f5r = f0r + f1i;
f5i = f0i - f1r;
f6r = f2r - f3i;
f6i = f2i + f3r;
f7r = f2r + f3i;
f7i = f2i - f3r;
*(p0r + pos) = f4r;
*(p0r + posi) = f4i;
*(p1r + pos) = f5r;
*(p1r + posi) = f5i;
*(p2r + pos) = f6r;
*(p2r + posi) = f6i;
*(p3r + pos) = f7r;
*(p3r + posi) = f7i;
p0r += pnext;
p1r += pnext;
p2r += pnext;
p3r += pnext;
}
}
//------------------------------------------------------------------------------
// 1 radix 4 stage
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ibfR4(FFT_TYPE *ioptr, int M, int NDiffU)
{
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int pnexti;
unsigned int NSameU;
unsigned int SameUCnt;
FFT_TYPE *pstrt;
FFT_TYPE *p0r, *p1r, *p2r, *p3r;
FFT_TYPE w1r = 1.0 / FFT_ROOT2; // cos(pi/4)
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
FFT_TYPE t1r, t1i;
const FFT_TYPE Two = 2.0;
pinc = NDiffU * 2; // 2 floats per complex
pnext = pinc * 4;
pnexti = pnext + 1;
pos = 2;
posi = pos + 1;
NSameU = POW2(M) / 4 / NDiffU; // 4 pts per butterfly
pstrt = ioptr;
p0r = pstrt;
p1r = pstrt + pinc;
p2r = p1r + pinc;
p3r = p2r + pinc;
// Butterflys
// f0 - - f0 - - f4
// f1 - 1 - f5 - - f5
// f2 - - f6 - 1 - f6
// f3 - 1 - f3 - -i - f7
// Butterflys
// f0 - - f4 - - f4
// f1 - -i - t1 - - f5
// f2 - - f2 - w1 - f6
// f3 - -i - f7 - iw1- f7
f0r = *p0r;
f1r = *p1r;
f2r = *p2r;
f3r = *p3r;
f0i = *(p0r + 1);
f1i = *(p1r + 1);
f2i = *(p2r + 1);
f3i = *(p3r + 1);
f5r = f0r - f1r;
f5i = f0i - f1i;
f0r = f0r + f1r;
f0i = f0i + f1i;
f6r = f2r + f3r;
f6i = f2i + f3i;
f3r = f2r - f3r;
f3i = f2i - f3i;
for (SameUCnt = NSameU - 1; SameUCnt > 0; SameUCnt--) {
f7r = f5r + f3i;
f7i = f5i - f3r;
f5r = f5r - f3i;
f5i = f5i + f3r;
f4r = f0r + f6r;
f4i = f0i + f6i;
f6r = f0r - f6r;
f6i = f0i - f6i;
f2r = *(p2r + pos);
f2i = *(p2r + posi);
f1r = *(p1r + pos);
f1i = *(p1r + posi);
f3i = *(p3r + posi);
f0r = *(p0r + pos);
f3r = *(p3r + pos);
f0i = *(p0r + posi);
*p3r = f7r;
*p0r = f4r;
*(p3r + 1) = f7i;
*(p0r + 1) = f4i;
*p1r = f5r;
*p2r = f6r;
*(p1r + 1) = f5i;
*(p2r + 1) = f6i;
f7r = f2r + f3i;
f7i = f2i - f3r;
f2r = f2r - f3i;
f2i = f2i + f3r;
f4r = f0r - f1i;
f4i = f0i + f1r;
t1r = f0r + f1i;
t1i = f0i - f1r;
f5r = t1r - f7r * w1r - f7i * w1r;
f5i = t1i + f7r * w1r - f7i * w1r;
f7r = t1r * Two - f5r;
f7i = t1i * Two - f5i;
f6r = f4r - f2r * w1r + f2i * w1r;
f6i = f4i - f2r * w1r - f2i * w1r;
f4r = f4r * Two - f6r;
f4i = f4i * Two - f6i;
f3r = *(p3r + pnext);
f0r = *(p0r + pnext);
f3i = *(p3r + pnexti);
f0i = *(p0r + pnexti);
f2r = *(p2r + pnext);
f2i = *(p2r + pnexti);
f1r = *(p1r + pnext);
f1i = *(p1r + pnexti);
*(p2r + pos) = f6r;
*(p1r + pos) = f5r;
*(p2r + posi) = f6i;
*(p1r + posi) = f5i;
*(p3r + pos) = f7r;
*(p0r + pos) = f4r;
*(p3r + posi) = f7i;
*(p0r + posi) = f4i;
f6r = f2r + f3r;
f6i = f2i + f3i;
f3r = f2r - f3r;
f3i = f2i - f3i;
f5r = f0r - f1r;
f5i = f0i - f1i;
f0r = f0r + f1r;
f0i = f0i + f1i;
p3r += pnext;
p0r += pnext;
p1r += pnext;
p2r += pnext;
}
f7r = f5r + f3i;
f7i = f5i - f3r;
f5r = f5r - f3i;
f5i = f5i + f3r;
f4r = f0r + f6r;
f4i = f0i + f6i;
f6r = f0r - f6r;
f6i = f0i - f6i;
f2r = *(p2r + pos);
f2i = *(p2r + posi);
f1r = *(p1r + pos);
f1i = *(p1r + posi);
f3i = *(p3r + posi);
f0r = *(p0r + pos);
f3r = *(p3r + pos);
f0i = *(p0r + posi);
*p3r = f7r;
*p0r = f4r;
*(p3r + 1) = f7i;
*(p0r + 1) = f4i;
*p1r = f5r;
*p2r = f6r;
*(p1r + 1) = f5i;
*(p2r + 1) = f6i;
f7r = f2r + f3i;
f7i = f2i - f3r;
f2r = f2r - f3i;
f2i = f2i + f3r;
f4r = f0r - f1i;
f4i = f0i + f1r;
t1r = f0r + f1i;
t1i = f0i - f1r;
f5r = t1r - f7r * w1r - f7i * w1r;
f5i = t1i + f7r * w1r - f7i * w1r;
f7r = t1r * Two - f5r;
f7i = t1i * Two - f5i;
f6r = f4r - f2r * w1r + f2i * w1r;
f6i = f4i - f2r * w1r - f2i * w1r;
f4r = f4r * Two - f6r;
f4i = f4i * Two - f6i;
*(p2r + pos) = f6r;
*(p1r + pos) = f5r;
*(p2r + posi) = f6i;
*(p1r + posi) = f5i;
*(p3r + pos) = f7r;
*(p0r + pos) = f4r;
*(p3r + posi) = f7i;
*(p0r + posi) = f4i;
}
//------------------------------------------------------------------------------
// RADIX 8 Stages
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ibfstages(FFT_TYPE *ioptr, int M, FFT_TYPE *inUtbl, int Ustride,
int NDiffU, int StageCnt)
{
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int NSameU;
int Uinc;
int Uinc2;
int Uinc4;
unsigned int DiffUCnt;
unsigned int SameUCnt;
unsigned int U2toU3;
FFT_TYPE *pstrt;
FFT_TYPE *p0r, *p1r, *p2r, *p3r;
FFT_TYPE *u0r, *u0i, *u1r, *u1i, *u2r, *u2i;
FFT_TYPE w0r, w0i, w1r, w1i, w2r, w2i, w3r, w3i;
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
FFT_TYPE t0r, t0i, t1r, t1i;
const FFT_TYPE Two = 2.0;
pinc = NDiffU * 2; // 2 floats per complex
pnext = pinc * 8;
pos = pinc * 4;
posi = pos + 1;
NSameU = POW2(M) / 8 / NDiffU; // 8 pts per butterfly
Uinc = (int) NSameU * Ustride;
Uinc2 = Uinc * 2;
Uinc4 = Uinc * 4;
U2toU3 = (POW2(M) / 8) * Ustride;
for (; StageCnt > 0; StageCnt--) {
u0r = &inUtbl[0];
u0i = &inUtbl[POW2(M - 2) * Ustride];
u1r = u0r;
u1i = u0i;
u2r = u0r;
u2i = u0i;
w0r = *u0r;
w0i = *u0i;
w1r = *u1r;
w1i = *u1i;
w2r = *u2r;
w2i = *u2i;
w3r = *(u2r + U2toU3);
w3i = *(u2i - U2toU3);
pstrt = ioptr;
p0r = pstrt;
p1r = pstrt + pinc;
p2r = p1r + pinc;
p3r = p2r + pinc;
// Butterflys
// f0 - - t0 - - f0 - - f0
// f1 - w0- f1 - - f1 - - f1
// f2 - - f2 - w1- f2 - - f4
// f3 - w0- t1 - iw1- f3 - - f5
// f4 - - t0 - - f4 - w2- t0
// f5 - w0- f5 - - f5 - w3- t1
// f6 - - f6 - w1- f6 - iw2- f6
// f7 - w0- t1 - iw1- f7 - iw3- f7
for (DiffUCnt = NDiffU; DiffUCnt > 0; DiffUCnt--) {
f0r = *p0r;
f0i = *(p0r + 1);
f1r = *p1r;
f1i = *(p1r + 1);
for (SameUCnt = NSameU - 1; SameUCnt > 0; SameUCnt--) {
f2r = *p2r;
f2i = *(p2r + 1);
f3r = *p3r;
f3i = *(p3r + 1);
t0r = f0r + f1r * w0r - f1i * w0i;
t0i = f0i + f1r * w0i + f1i * w0r;
f1r = f0r * Two - t0r;
f1i = f0i * Two - t0i;
f4r = *(p0r + pos);
f4i = *(p0r + posi);
f5r = *(p1r + pos);
f5i = *(p1r + posi);
f6r = *(p2r + pos);
f6i = *(p2r + posi);
f7r = *(p3r + pos);
f7i = *(p3r + posi);
t1r = f2r - f3r * w0r + f3i * w0i;
t1i = f2i - f3r * w0i - f3i * w0r;
f2r = f2r * Two - t1r;
f2i = f2i * Two - t1i;
f0r = t0r + f2r * w1r - f2i * w1i;
f0i = t0i + f2r * w1i + f2i * w1r;
f2r = t0r * Two - f0r;
f2i = t0i * Two - f0i;
f3r = f1r + t1r * w1i + t1i * w1r;
f3i = f1i - t1r * w1r + t1i * w1i;
f1r = f1r * Two - f3r;
f1i = f1i * Two - f3i;
t0r = f4r + f5r * w0r - f5i * w0i;
t0i = f4i + f5r * w0i + f5i * w0r;
f5r = f4r * Two - t0r;
f5i = f4i * Two - t0i;
t1r = f6r - f7r * w0r + f7i * w0i;
t1i = f6i - f7r * w0i - f7i * w0r;
f6r = f6r * Two - t1r;
f6i = f6i * Two - t1i;
f4r = t0r + f6r * w1r - f6i * w1i;
f4i = t0i + f6r * w1i + f6i * w1r;
f6r = t0r * Two - f4r;
f6i = t0i * Two - f4i;
f7r = f5r + t1r * w1i + t1i * w1r;
f7i = f5i - t1r * w1r + t1i * w1i;
f5r = f5r * Two - f7r;
f5i = f5i * Two - f7i;
t0r = f0r - f4r * w2r + f4i * w2i;
t0i = f0i - f4r * w2i - f4i * w2r;
f0r = f0r * Two - t0r;
f0i = f0i * Two - t0i;
t1r = f1r - f5r * w3r + f5i * w3i;
t1i = f1i - f5r * w3i - f5i * w3r;
f1r = f1r * Two - t1r;
f1i = f1i * Two - t1i;
*(p0r + pos) = t0r;
*(p0r + posi) = t0i;
*p0r = f0r;
*(p0r + 1) = f0i;
p0r += pnext;
f0r = *p0r;
f0i = *(p0r + 1);
*(p1r + pos) = t1r;
*(p1r + posi) = t1i;
*p1r = f1r;
*(p1r + 1) = f1i;
p1r += pnext;
f1r = *p1r;
f1i = *(p1r + 1);
f4r = f2r - f6r * w2i - f6i * w2r;
f4i = f2i + f6r * w2r - f6i * w2i;
f6r = f2r * Two - f4r;
f6i = f2i * Two - f4i;
f5r = f3r - f7r * w3i - f7i * w3r;
f5i = f3i + f7r * w3r - f7i * w3i;
f7r = f3r * Two - f5r;
f7i = f3i * Two - f5i;
*p2r = f4r;
*(p2r + 1) = f4i;
*(p2r + pos) = f6r;
*(p2r + posi) = f6i;
p2r += pnext;
*p3r = f5r;
*(p3r + 1) = f5i;
*(p3r + pos) = f7r;
*(p3r + posi) = f7i;
p3r += pnext;
}
f2r = *p2r;
f2i = *(p2r + 1);
f3r = *p3r;
f3i = *(p3r + 1);
t0r = f0r + f1r * w0r - f1i * w0i;
t0i = f0i + f1r * w0i + f1i * w0r;
f1r = f0r * Two - t0r;
f1i = f0i * Two - t0i;
f4r = *(p0r + pos);
f4i = *(p0r + posi);
f5r = *(p1r + pos);
f5i = *(p1r + posi);
f6r = *(p2r + pos);
f6i = *(p2r + posi);
f7r = *(p3r + pos);
f7i = *(p3r + posi);
t1r = f2r - f3r * w0r + f3i * w0i;
t1i = f2i - f3r * w0i - f3i * w0r;
f2r = f2r * Two - t1r;
f2i = f2i * Two - t1i;
f0r = t0r + f2r * w1r - f2i * w1i;
f0i = t0i + f2r * w1i + f2i * w1r;
f2r = t0r * Two - f0r;
f2i = t0i * Two - f0i;
f3r = f1r + t1r * w1i + t1i * w1r;
f3i = f1i - t1r * w1r + t1i * w1i;
f1r = f1r * Two - f3r;
f1i = f1i * Two - f3i;
if ((int) DiffUCnt == NDiffU / 2)
Uinc4 = -Uinc4;
u0r += Uinc4;
u0i -= Uinc4;
u1r += Uinc2;
u1i -= Uinc2;
u2r += Uinc;
u2i -= Uinc;
pstrt += 2;
t0r = f4r + f5r * w0r - f5i * w0i;
t0i = f4i + f5r * w0i + f5i * w0r;
f5r = f4r * Two - t0r;
f5i = f4i * Two - t0i;
t1r = f6r - f7r * w0r + f7i * w0i;
t1i = f6i - f7r * w0i - f7i * w0r;
f6r = f6r * Two - t1r;
f6i = f6i * Two - t1i;
f4r = t0r + f6r * w1r - f6i * w1i;
f4i = t0i + f6r * w1i + f6i * w1r;
f6r = t0r * Two - f4r;
f6i = t0i * Two - f4i;
f7r = f5r + t1r * w1i + t1i * w1r;
f7i = f5i - t1r * w1r + t1i * w1i;
f5r = f5r * Two - f7r;
f5i = f5i * Two - f7i;
w0r = *u0r;
w0i = *u0i;
w1r = *u1r;
w1i = *u1i;
if ((int) DiffUCnt <= NDiffU / 2)
w0r = -w0r;
t0r = f0r - f4r * w2r + f4i * w2i;
t0i = f0i - f4r * w2i - f4i * w2r;
f0r = f0r * Two - t0r;
f0i = f0i * Two - t0i;
f4r = f2r - f6r * w2i - f6i * w2r;
f4i = f2i + f6r * w2r - f6i * w2i;
f6r = f2r * Two - f4r;
f6i = f2i * Two - f4i;
*(p0r + pos) = t0r;
*p2r = f4r;
*(p0r + posi) = t0i;
*(p2r + 1) = f4i;
w2r = *u2r;
w2i = *u2i;
*p0r = f0r;
*(p2r + pos) = f6r;
*(p0r + 1) = f0i;
*(p2r + posi) = f6i;
p0r = pstrt;
p2r = pstrt + pinc + pinc;
t1r = f1r - f5r * w3r + f5i * w3i;
t1i = f1i - f5r * w3i - f5i * w3r;
f1r = f1r * Two - t1r;
f1i = f1i * Two - t1i;
f5r = f3r - f7r * w3i - f7i * w3r;
f5i = f3i + f7r * w3r - f7i * w3i;
f7r = f3r * Two - f5r;
f7i = f3i * Two - f5i;
*(p1r + pos) = t1r;
*p3r = f5r;
*(p1r + posi) = t1i;
*(p3r + 1) = f5i;
w3r = *(u2r + U2toU3);
w3i = *(u2i - U2toU3);
*p1r = f1r;
*(p3r + pos) = f7r;
*(p1r + 1) = f1i;
*(p3r + posi) = f7i;
p1r = pstrt + pinc;
p3r = p2r + pinc;
}
NSameU /= 8;
Uinc /= 8;
Uinc2 /= 8;
Uinc4 = Uinc * 4;
NDiffU *= 8;
pinc *= 8;
pnext *= 8;
pos *= 8;
posi = pos + 1;
}
}
//------------------------------------------------------------------------------
// recursive bfstages calls to maximize on chip cache efficiency
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ifftrecurs(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, int Ustride,
int NDiffU, int StageCnt)
{
int i1;
if (M <= (int) MCACHE)
ibfstages(ioptr, M, Utbl, Ustride, NDiffU, StageCnt); // RADIX 8 Stages
else {
for (i1 = 0; i1 < 8; i1++) {
ifftrecurs(&ioptr[i1 * POW2(M - 3) * 2], M - 3, Utbl, 8 * Ustride,
NDiffU, StageCnt - 1); // RADIX 8 Stages
}
ibfstages(ioptr, M, Utbl, Ustride, POW2(M - 3), 1); // RADIX 8 Stage
}
}
//------------------------------------------------------------------------------
// Compute in-place inverse complex fft on the rows of the input array
// INPUTS
// *ioptr = input data array
// M = log2 of fft size
// *Utbl = cosine table
// *BRLow = bit reversed counter table
// OUTPUTS
// *ioptr = output data array
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::iffts1(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, short *BRLow)
{
int StageCnt;
int NDiffU;
const FFT_TYPE scale = 1.0 / POW2(M);
switch (M) {
case 0:
break;
case 1:
ifft2pt(ioptr, scale); // a 2 pt fft
break;
case 2:
ifft4pt(ioptr, scale); // a 4 pt fft
break;
case 3:
ifft8pt(ioptr, scale); // an 8 pt fft
break;
default:
// bit reverse and first radix 2 stage
scbitrevR2(ioptr, M, BRLow, scale);
StageCnt = (M - 1) / 3; // number of radix 8 stages
NDiffU = 2; // one radix 2 stage already complete
if ((M - 1 - (StageCnt * 3)) == 1) {
ibfR2(ioptr, M, NDiffU); // 1 radix 2 stage
NDiffU *= 2;
}
if ((M - 1 - (StageCnt * 3)) == 2) {
ibfR4(ioptr, M, NDiffU); // 1 radix 4 stage
NDiffU *= 4;
}
if (M <= (int) MCACHE)
ibfstages(ioptr, M, Utbl, 1, NDiffU, StageCnt); // RADIX 8 Stages
else
ifftrecurs(ioptr, M, Utbl, 1, NDiffU, StageCnt); // RADIX 8 Stages
}
}
//------------------------------------------------------------------------------
// parts of rffts1
// RADIX 2 rfft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::rfft1pt(FFT_TYPE *ioptr)
{
FFT_TYPE f0r, f0i;
FFT_TYPE t0r, t0i;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
// finish rfft
t0r = f0r + f0i;
t0i = f0r - f0i;
// store result
ioptr[0] = t0r;
ioptr[1] = t0i;
}
//------------------------------------------------------------------------------
// RADIX 4 rfft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::rfft2pt(FFT_TYPE *ioptr)
{
FFT_TYPE f0r, f0i, f1r, f1i;
FFT_TYPE t0r, t0i;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
f1r = ioptr[2];
f1i = ioptr[3];
// Butterflys
// f0 - - t0
// f1 - 1 - f1
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f1i - f0i;
// finish rfft
f0r = t0r + t0i;
f0i = t0r - t0i;
// store result
ioptr[0] = f0r;
ioptr[1] = f0i;
ioptr[2] = f1r;
ioptr[3] = f1i;
}
//------------------------------------------------------------------------------
// RADIX 8 rfft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::rfft4pt(FFT_TYPE *ioptr)
{
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE t0r, t0i, t1r, t1i;
FFT_TYPE w0r = 1.0 / FFT_ROOT2; // cos(pi/4)
const FFT_TYPE Two = 2.0;
const FFT_TYPE scale = 0.5;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
f1r = ioptr[4];
f1i = ioptr[5];
f2r = ioptr[2];
f2i = ioptr[3];
f3r = ioptr[6];
f3i = ioptr[7];
// Butterflys
// f0 - - t0 - - f0
// f1 - 1 - f1 - - f1
// f2 - - f2 - 1 - f2
// f3 - 1 - t1 - -i - f3
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r - f3r;
t1i = f2i - f3i;
f2r = f2r + f3r;
f2i = f2i + f3i;
f0r = t0r + f2r;
f0i = t0i + f2i;
f2r = t0r - f2r;
f2i = f2i - t0i; // neg for rfft
f3r = f1r - t1i;
f3i = f1i + t1r;
f1r = f1r + t1i;
f1i = f1i - t1r;
// finish rfft
t0r = f0r + f0i; // compute Re(x[0])
t0i = f0r - f0i; // compute Re(x[N/2])
t1r = f1r + f3r;
t1i = f1i - f3i;
f0r = f1i + f3i;
f0i = f3r - f1r;
f1r = t1r + w0r * f0r + w0r * f0i;
f1i = t1i - w0r * f0r + w0r * f0i;
f3r = Two * t1r - f1r;
f3i = f1i - Two * t1i;
// store result
ioptr[4] = f2r;
ioptr[5] = f2i;
ioptr[0] = t0r;
ioptr[1] = t0i;
ioptr[2] = scale * f1r;
ioptr[3] = scale * f1i;
ioptr[6] = scale * f3r;
ioptr[7] = scale * f3i;
}
//------------------------------------------------------------------------------
// RADIX 16 rfft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::rfft8pt(FFT_TYPE *ioptr)
{
FFT_TYPE w0r = 1.0 / FFT_ROOT2; // cos(pi/4)
FFT_TYPE w1r = FFT_COSPID8; // cos(pi/8)
FFT_TYPE w1i = FFT_SINPID8; // sin(pi/8)
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
FFT_TYPE t0r, t0i, t1r, t1i;
const FFT_TYPE Two = 2.0;
const FFT_TYPE scale = 0.5;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
f1r = ioptr[8];
f1i = ioptr[9];
f2r = ioptr[4];
f2i = ioptr[5];
f3r = ioptr[12];
f3i = ioptr[13];
f4r = ioptr[2];
f4i = ioptr[3];
f5r = ioptr[10];
f5i = ioptr[11];
f6r = ioptr[6];
f6i = ioptr[7];
f7r = ioptr[14];
f7i = ioptr[15];
// Butterflys
// f0 - - t0 - - f0 - - f0
// f1 - 1 - f1 - - f1 - - f1
// f2 - - f2 - 1 - f2 - - f2
// f3 - 1 - t1 - -i - f3 - - f3
// f4 - - t0 - - f4 - 1 - t0
// f5 - 1 - f5 - - f5 - w3 - f4
// f6 - - f6 - 1 - f6 - -i - t1
// f7 - 1 - t1 - -i - f7 - iw3- f6
t0r = f0r + f1r;
t0i = f0i + f1i;
f1r = f0r - f1r;
f1i = f0i - f1i;
t1r = f2r - f3r;
t1i = f2i - f3i;
f2r = f2r + f3r;
f2i = f2i + f3i;
f0r = t0r + f2r;
f0i = t0i + f2i;
f2r = t0r - f2r;
f2i = t0i - f2i;
f3r = f1r - t1i;
f3i = f1i + t1r;
f1r = f1r + t1i;
f1i = f1i - t1r;
t0r = f4r + f5r;
t0i = f4i + f5i;
f5r = f4r - f5r;
f5i = f4i - f5i;
t1r = f6r - f7r;
t1i = f6i - f7i;
f6r = f6r + f7r;
f6i = f6i + f7i;
f4r = t0r + f6r;
f4i = t0i + f6i;
f6r = t0r - f6r;
f6i = t0i - f6i;
f7r = f5r - t1i;
f7i = f5i + t1r;
f5r = f5r + t1i;
f5i = f5i - t1r;
t0r = f0r - f4r;
t0i = f4i - f0i; // neg for rfft
f0r = f0r + f4r;
f0i = f0i + f4i;
t1r = f2r - f6i;
t1i = f2i + f6r;
f2r = f2r + f6i;
f2i = f2i - f6r;
f4r = f1r - f5r * w0r - f5i * w0r;
f4i = f1i + f5r * w0r - f5i * w0r;
f1r = f1r * Two - f4r;
f1i = f1i * Two - f4i;
f6r = f3r + f7r * w0r - f7i * w0r;
f6i = f3i + f7r * w0r + f7i * w0r;
f3r = f3r * Two - f6r;
f3i = f3i * Two - f6i;
// finish rfft
f5r = f0r + f0i; // compute Re(x[0])
f5i = f0r - f0i; // compute Re(x[N/2])
f0r = f2r + t1r;
f0i = f2i - t1i;
f7r = f2i + t1i;
f7i = t1r - f2r;
f2r = f0r + w0r * f7r + w0r * f7i;
f2i = f0i - w0r * f7r + w0r * f7i;
t1r = Two * f0r - f2r;
t1i = f2i - Two * f0i;
f0r = f1r + f6r;
f0i = f1i - f6i;
f7r = f1i + f6i;
f7i = f6r - f1r;
f1r = f0r + w1r * f7r + w1i * f7i;
f1i = f0i - w1i * f7r + w1r * f7i;
f6r = Two * f0r - f1r;
f6i = f1i - Two * f0i;
f0r = f3r + f4r;
f0i = f3i - f4i;
f7r = f3i + f4i;
f7i = f4r - f3r;
f3r = f0r + w1i * f7r + w1r * f7i;
f3i = f0i - w1r * f7r + w1i * f7i;
f4r = Two * f0r - f3r;
f4i = f3i - Two * f0i;
// store result
ioptr[8] = t0r;
ioptr[9] = t0i;
ioptr[0] = f5r;
ioptr[1] = f5i;
ioptr[4] = scale * f2r;
ioptr[5] = scale * f2i;
ioptr[12] = scale * t1r;
ioptr[13] = scale * t1i;
ioptr[2] = scale * f1r;
ioptr[3] = scale * f1i;
ioptr[6] = scale * f3r;
ioptr[7] = scale * f3i;
ioptr[10] = scale * f4r;
ioptr[11] = scale * f4i;
ioptr[14] = scale * f6r;
ioptr[15] = scale * f6i;
}
//------------------------------------------------------------------------------
// Finish RFFT
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::frstage(FFT_TYPE *ioptr, int M, FFT_TYPE *inUtbl)
{
unsigned int pos;
unsigned int posi;
unsigned int diffUcnt;
FFT_TYPE *p0r, *p1r;
FFT_TYPE *u0r, *u0i;
FFT_TYPE w0r, w0i;
FFT_TYPE f0r, f0i, f1r, f1i, f4r, f4i, f5r, f5i;
FFT_TYPE t0r, t0i, t1r, t1i;
const FFT_TYPE Two = 2.0;
pos = POW2(M - 1);
posi = pos + 1;
p0r = ioptr;
p1r = ioptr + pos / 2;
u0r = inUtbl + POW2(M - 3);
w0r = *u0r, f0r = *(p0r);
f0i = *(p0r + 1);
f4r = *(p0r + pos);
f4i = *(p0r + posi);
f1r = *(p1r);
f1i = *(p1r + 1);
f5r = *(p1r + pos);
f5i = *(p1r + posi);
t0r = Two * f0r + Two * f0i; // compute Re(x[0])
t0i = Two * f0r - Two * f0i; // compute Re(x[N/2])
t1r = f4r + f4r;
t1i = -f4i - f4i;
f0r = f1r + f5r;
f0i = f1i - f5i;
f4r = f1i + f5i;
f4i = f5r - f1r;
f1r = f0r + w0r * f4r + w0r * f4i;
f1i = f0i - w0r * f4r + w0r * f4i;
f5r = Two * f0r - f1r;
f5i = f1i - Two * f0i;
*(p0r) = t0r;
*(p0r + 1) = t0i;
*(p0r + pos) = t1r;
*(p0r + posi) = t1i;
*(p1r) = f1r;
*(p1r + 1) = f1i;
*(p1r + pos) = f5r;
*(p1r + posi) = f5i;
u0r = inUtbl + 1;
u0i = inUtbl + (POW2(M - 2) - 1);
w0r = *u0r, w0i = *u0i;
p0r = (ioptr + 2);
p1r = (ioptr + (POW2(M - 2) - 1) * 2);
// Butterflys
// f0 - t0 - - f0
// f5 - t1 - w0 - f5
// f1 - t0 - - f1
// f4 - t1 -iw0 - f4
for (diffUcnt = POW2(M - 3) - 1; diffUcnt > 0; diffUcnt--) {
f0r = *(p0r);
f0i = *(p0r + 1);
f5r = *(p1r + pos);
f5i = *(p1r + posi);
f1r = *(p1r);
f1i = *(p1r + 1);
f4r = *(p0r + pos);
f4i = *(p0r + posi);
t0r = f0r + f5r;
t0i = f0i - f5i;
t1r = f0i + f5i;
t1i = f5r - f0r;
f0r = t0r + w0r * t1r + w0i * t1i;
f0i = t0i - w0i * t1r + w0r * t1i;
f5r = Two * t0r - f0r;
f5i = f0i - Two * t0i;
t0r = f1r + f4r;
t0i = f1i - f4i;
t1r = f1i + f4i;
t1i = f4r - f1r;
f1r = t0r + w0i * t1r + w0r * t1i;
f1i = t0i - w0r * t1r + w0i * t1i;
f4r = Two * t0r - f1r;
f4i = f1i - Two * t0i;
*(p0r) = f0r;
*(p0r + 1) = f0i;
*(p1r + pos) = f5r;
*(p1r + posi) = f5i;
w0r = *++u0r;
w0i = *--u0i;
*(p1r) = f1r;
*(p1r + 1) = f1i;
*(p0r + pos) = f4r;
*(p0r + posi) = f4i;
p0r += 2;
p1r -= 2;
}
}
//------------------------------------------------------------------------------
// Compute in-place real fft on the rows of the input array
// The result is the complex spectra of the positive frequencies
// except the location for the first complex number contains the real
// values for DC and Nyquest
// INPUTS
// *ioptr = real input data array
// M = log2 of fft size
// *Utbl = cosine table
// *BRLow = bit reversed counter table
// OUTPUTS
// *ioptr = output data array in the following order
// Re(x[0]), Re(x[N/2]), Re(x[1]), Im(x[1]), Re(x[2]), Im(x[2]),
// ... Re(x[N/2-1]), Im(x[N/2-1]).
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::rffts1(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, short *BRLow)
{
FFT_TYPE scale;
int StageCnt;
int NDiffU;
M = M - 1;
switch (M) {
case -1:
break;
case 0:
rfft1pt(ioptr); // a 2 pt fft
break;
case 1:
rfft2pt(ioptr); // a 4 pt fft
break;
case 2:
rfft4pt(ioptr); // an 8 pt fft
break;
case 3:
rfft8pt(ioptr); // a 16 pt fft
break;
default:
scale = 0.5;
// bit reverse and first radix 2 stage
scbitrevR2(ioptr, M, BRLow, scale);
StageCnt = (M - 1) / 3; // number of radix 8 stages
NDiffU = 2; // one radix 2 stage already complete
if ((M - 1 - (StageCnt * 3)) == 1) {
bfR2(ioptr, M, NDiffU); // 1 radix 2 stage
NDiffU *= 2;
}
if ((M - 1 - (StageCnt * 3)) == 2) {
bfR4(ioptr, M, NDiffU); // 1 radix 4 stage
NDiffU *= 4;
}
if (M <= (int) MCACHE)
bfstages(ioptr, M, Utbl, 2, NDiffU, StageCnt); // RADIX 8 Stages
else
fftrecurs(ioptr, M, Utbl, 2, NDiffU, StageCnt); // RADIX 8 Stages
frstage(ioptr, M + 1, Utbl);
}
}
//------------------------------------------------------------------------------
// parts of riffts1
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
// RADIX 2 rifft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::rifft1pt(FFT_TYPE *ioptr, FFT_TYPE scale)
{
FFT_TYPE f0r, f0i;
FFT_TYPE t0r, t0i;
// bit reversed load
f0r = ioptr[0];
f0i = ioptr[1];
// finish rfft
t0r = f0r + f0i;
t0i = f0r - f0i;
// store result
ioptr[0] = scale * t0r;
ioptr[1] = scale * t0i;
}
//------------------------------------------------------------------------------
// RADIX 4 rifft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::rifft2pt(FFT_TYPE *ioptr, FFT_TYPE scale)
{
FFT_TYPE f0r, f0i, f1r, f1i;
FFT_TYPE t0r, t0i;
const FFT_TYPE Two = FFT_TYPE(2.0);
// bit reversed load
t0r = ioptr[0];
t0i = ioptr[1];
f1r = Two * ioptr[2];
f1i = Two * ioptr[3];
// start rifft
f0r = t0r + t0i;
f0i = t0r - t0i;
// Butterflys
// f0 - - t0
// f1 - 1 - f1
t0r = f0r + f1r;
t0i = f0i - f1i;
f1r = f0r - f1r;
f1i = f0i + f1i;
// store result
ioptr[0] = scale * t0r;
ioptr[1] = scale * t0i;
ioptr[2] = scale * f1r;
ioptr[3] = scale * f1i;
}
//------------------------------------------------------------------------------
// RADIX 8 rifft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::rifft4pt(FFT_TYPE *ioptr, FFT_TYPE scale)
{
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE t0r, t0i, t1r, t1i;
FFT_TYPE w0r = 1.0 / FFT_ROOT2; // cos(pi/4)
const FFT_TYPE Two = FFT_TYPE(2.0);
// bit reversed load
t0r = ioptr[0];
t0i = ioptr[1];
f2r = ioptr[2];
f2i = ioptr[3];
f1r = Two * ioptr[4];
f1i = Two * ioptr[5];
f3r = ioptr[6];
f3i = ioptr[7];
// start rfft
f0r = t0r + t0i; // compute Re(x[0])
f0i = t0r - t0i; // compute Re(x[N/2])
t1r = f2r + f3r;
t1i = f2i - f3i;
t0r = f2r - f3r;
t0i = f2i + f3i;
f2r = t1r - w0r * t0r - w0r * t0i;
f2i = t1i + w0r * t0r - w0r * t0i;
f3r = Two * t1r - f2r;
f3i = f2i - Two * t1i;
// Butterflys
// f0 - - t0 - - f0
// f1 - 1 - f1 - - f1
// f2 - - f2 - 1 - f2
// f3 - 1 - t1 - i - f3
t0r = f0r + f1r;
t0i = f0i - f1i;
f1r = f0r - f1r;
f1i = f0i + f1i;
t1r = f2r - f3r;
t1i = f2i - f3i;
f2r = f2r + f3r;
f2i = f2i + f3i;
f0r = t0r + f2r;
f0i = t0i + f2i;
f2r = t0r - f2r;
f2i = t0i - f2i;
f3r = f1r + t1i;
f3i = f1i - t1r;
f1r = f1r - t1i;
f1i = f1i + t1r;
// store result
ioptr[0] = scale * f0r;
ioptr[1] = scale * f0i;
ioptr[2] = scale * f1r;
ioptr[3] = scale * f1i;
ioptr[4] = scale * f2r;
ioptr[5] = scale * f2i;
ioptr[6] = scale * f3r;
ioptr[7] = scale * f3i;
}
//------------------------------------------------------------------------------
// RADIX 16 rifft
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::rifft8pt(FFT_TYPE *ioptr, FFT_TYPE scale)
{
FFT_TYPE w0r = (FFT_TYPE) (1.0 / FFT_ROOT2); // cos(pi/4)
FFT_TYPE w1r = FFT_COSPID8; // cos(pi/8)
FFT_TYPE w1i = FFT_SINPID8; // sin(pi/8)
FFT_TYPE f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
FFT_TYPE f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
FFT_TYPE t0r, t0i, t1r, t1i;
const FFT_TYPE Two = FFT_TYPE(2.0);
// bit reversed load
t0r = ioptr[0];
t0i = ioptr[1];
f4r = ioptr[2];
f4i = ioptr[3];
f2r = ioptr[4];
f2i = ioptr[5];
f6r = ioptr[6];
f6i = ioptr[7];
f1r = Two * ioptr[8];
f1i = Two * ioptr[9];
f5r = ioptr[10];
f5i = ioptr[11];
f3r = ioptr[12];
f3i = ioptr[13];
f7r = ioptr[14];
f7i = ioptr[15];
// start rfft
f0r = t0r + t0i; // compute Re(x[0])
f0i = t0r - t0i; // compute Re(x[N/2])
t0r = f2r + f3r;
t0i = f2i - f3i;
t1r = f2r - f3r;
t1i = f2i + f3i;
f2r = t0r - w0r * t1r - w0r * t1i;
f2i = t0i + w0r * t1r - w0r * t1i;
f3r = Two * t0r - f2r;
f3i = f2i - Two * t0i;
t0r = f4r + f7r;
t0i = f4i - f7i;
t1r = f4r - f7r;
t1i = f4i + f7i;
f4r = t0r - w1i * t1r - w1r * t1i;
f4i = t0i + w1r * t1r - w1i * t1i;
f7r = Two * t0r - f4r;
f7i = f4i - Two * t0i;
t0r = f6r + f5r;
t0i = f6i - f5i;
t1r = f6r - f5r;
t1i = f6i + f5i;
f6r = t0r - w1r * t1r - w1i * t1i;
f6i = t0i + w1i * t1r - w1r * t1i;
f5r = Two * t0r - f6r;
f5i = f6i - Two * t0i;
// Butterflys
// f0 - - t0 - - f0 - - f0
// f1* - 1 - f1 - - f1 - - f1
// f2 - - f2 - 1 - f2 - - f2
// f3 - 1 - t1 - i - f3 - - f3
// f4 - - t0 - - f4 - 1 - t0
// f5 - 1 - f5 - - f5 - w3 - f4
// f6 - - f6 - 1 - f6 - i - t1
// f7 - 1 - t1 - i - f7 - iw3- f6
t0r = f0r + f1r;
t0i = f0i - f1i;
f1r = f0r - f1r;
f1i = f0i + f1i;
t1r = f2r - f3r;
t1i = f2i - f3i;
f2r = f2r + f3r;
f2i = f2i + f3i;
f0r = t0r + f2r;
f0i = t0i + f2i;
f2r = t0r - f2r;
f2i = t0i - f2i;
f3r = f1r + t1i;
f3i = f1i - t1r;
f1r = f1r - t1i;
f1i = f1i + t1r;
t0r = f4r + f5r;
t0i = f4i + f5i;
f5r = f4r - f5r;
f5i = f4i - f5i;
t1r = f6r - f7r;
t1i = f6i - f7i;
f6r = f6r + f7r;
f6i = f6i + f7i;
f4r = t0r + f6r;
f4i = t0i + f6i;
f6r = t0r - f6r;
f6i = t0i - f6i;
f7r = f5r + t1i;
f7i = f5i - t1r;
f5r = f5r - t1i;
f5i = f5i + t1r;
t0r = f0r - f4r;
t0i = f0i - f4i;
f0r = f0r + f4r;
f0i = f0i + f4i;
t1r = f2r + f6i;
t1i = f2i - f6r;
f2r = f2r - f6i;
f2i = f2i + f6r;
f4r = f1r - f5r * w0r + f5i * w0r;
f4i = f1i - f5r * w0r - f5i * w0r;
f1r = f1r * Two - f4r;
f1i = f1i * Two - f4i;
f6r = f3r + f7r * w0r + f7i * w0r;
f6i = f3i - f7r * w0r + f7i * w0r;
f3r = f3r * Two - f6r;
f3i = f3i * Two - f6i;
// store result
ioptr[0] = scale * f0r;
ioptr[1] = scale * f0i;
ioptr[2] = scale * f1r;
ioptr[3] = scale * f1i;
ioptr[4] = scale * f2r;
ioptr[5] = scale * f2i;
ioptr[6] = scale * f3r;
ioptr[7] = scale * f3i;
ioptr[8] = scale * t0r;
ioptr[9] = scale * t0i;
ioptr[10] = scale * f4r;
ioptr[11] = scale * f4i;
ioptr[12] = scale * t1r;
ioptr[13] = scale * t1i;
ioptr[14] = scale * f6r;
ioptr[15] = scale * f6i;
}
//------------------------------------------------------------------------------
// Start RIFFT
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ifrstage(FFT_TYPE *ioptr, int M, FFT_TYPE *inUtbl)
{
unsigned int pos;
unsigned int posi;
unsigned int diffUcnt;
FFT_TYPE *p0r, *p1r;
FFT_TYPE *u0r, *u0i;
FFT_TYPE w0r, w0i;
FFT_TYPE f0r, f0i, f1r, f1i, f4r, f4i, f5r, f5i;
FFT_TYPE t0r, t0i, t1r, t1i;
const FFT_TYPE Two = FFT_TYPE(2.0);
pos = POW2(M - 1);
posi = pos + 1;
p0r = ioptr;
p1r = ioptr + pos / 2;
u0r = inUtbl + POW2(M - 3);
w0r = *u0r, f0r = *(p0r);
f0i = *(p0r + 1);
f4r = *(p0r + pos);
f4i = *(p0r + posi);
f1r = *(p1r);
f1i = *(p1r + 1);
f5r = *(p1r + pos);
f5i = *(p1r + posi);
t0r = f0r + f0i;
t0i = f0r - f0i;
t1r = f4r + f4r;
t1i = -f4i - f4i;
f0r = f1r + f5r;
f0i = f1i - f5i;
f4r = f1r - f5r;
f4i = f1i + f5i;
f1r = f0r - w0r * f4r - w0r * f4i;
f1i = f0i + w0r * f4r - w0r * f4i;
f5r = Two * f0r - f1r;
f5i = f1i - Two * f0i;
*(p0r) = t0r;
*(p0r + 1) = t0i;
*(p0r + pos) = t1r;
*(p0r + posi) = t1i;
*(p1r) = f1r;
*(p1r + 1) = f1i;
*(p1r + pos) = f5r;
*(p1r + posi) = f5i;
u0r = inUtbl + 1;
u0i = inUtbl + (POW2(M - 2) - 1);
w0r = *u0r, w0i = *u0i;
p0r = (ioptr + 2);
p1r = (ioptr + (POW2(M - 2) - 1) * 2);
// Butterflys
// f0 - t0 - f0
// f1 - t1 -w0- f1
// f2 - t0 - f2
// f3 - t1 -iw0- f3
for (diffUcnt = POW2(M - 3) - 1; diffUcnt > 0; diffUcnt--) {
f0r = *(p0r);
f0i = *(p0r + 1);
f5r = *(p1r + pos);
f5i = *(p1r + posi);
f1r = *(p1r);
f1i = *(p1r + 1);
f4r = *(p0r + pos);
f4i = *(p0r + posi);
t0r = f0r + f5r;
t0i = f0i - f5i;
t1r = f0r - f5r;
t1i = f0i + f5i;
f0r = t0r - w0i * t1r - w0r * t1i;
f0i = t0i + w0r * t1r - w0i * t1i;
f5r = Two * t0r - f0r;
f5i = f0i - Two * t0i;
t0r = f1r + f4r;
t0i = f1i - f4i;
t1r = f1r - f4r;
t1i = f1i + f4i;
f1r = t0r - w0r * t1r - w0i * t1i;
f1i = t0i + w0i * t1r - w0r * t1i;
f4r = Two * t0r - f1r;
f4i = f1i - Two * t0i;
*(p0r) = f0r;
*(p0r + 1) = f0i;
*(p1r + pos) = f5r;
*(p1r + posi) = f5i;
w0r = *++u0r;
w0i = *--u0i;
*(p1r) = f1r;
*(p1r + 1) = f1i;
*(p0r + pos) = f4r;
*(p0r + posi) = f4i;
p0r += 2;
p1r -= 2;
}
}
//------------------------------------------------------------------------------
// Compute in-place real ifft on the rows of the input array
// data order as from rffts1
// INPUTS
// *ioptr = input data array in the following order
// M = log2 of fft size
// Re(x[0]), Re(x[N/2]), Re(x[1]), Im(x[1]),
// Re(x[2]), Im(x[2]), ... Re(x[N/2-1]), Im(x[N/2-1]).
// *Utbl = cosine table
// *BRLow = bit reversed counter table
// OUTPUTS
// *ioptr = real output data array
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::riffts1(FFT_TYPE *ioptr, int M, FFT_TYPE *Utbl, short *BRLow)
{
FFT_TYPE scale;
int StageCnt;
int NDiffU;
scale = (FFT_TYPE)(1.0 / (float)((int)POW2(M)));
M = M - 1;
switch (M) {
case -1:
break;
case 0:
rifft1pt(ioptr, scale); // a 2 pt fft
break;
case 1:
rifft2pt(ioptr, scale); // a 4 pt fft
break;
case 2:
rifft4pt(ioptr, scale); // an 8 pt fft
break;
case 3:
rifft8pt(ioptr, scale); // a 16 pt fft
break;
default:
ifrstage(ioptr, M + 1, Utbl);
// bit reverse and first radix 2 stage
scbitrevR2(ioptr, M, BRLow, scale);
StageCnt = (M - 1) / 3; // number of radix 8 stages
NDiffU = 2; // one radix 2 stage already complete
if ((M - 1 - (StageCnt * 3)) == 1) {
ibfR2(ioptr, M, NDiffU); // 1 radix 2 stage
NDiffU *= 2;
}
if ((M - 1 - (StageCnt * 3)) == 2) {
ibfR4(ioptr, M, NDiffU); // 1 radix 4 stage
NDiffU *= 4;
}
if (M <= (int) MCACHE)
ibfstages(ioptr, M, Utbl, 2, NDiffU, StageCnt); // RADIX 8 Stages
else
ifftrecurs(ioptr, M, Utbl, 2, NDiffU, StageCnt); // RADIX 8 Stages
}
}
//==============================================================================
// End of original C functions
//
// Wrapper methods for simple class access
//==============================================================================
//------------------------------------------------------------------------------
// malloc and init cosine and bit reversed tables for a given size
// fft, ifft, rfft, rifft
// INPUTS
// M = log2 of fft size (ex M=10 for 1024 point fft)
// OUTPUTS
// private cosine and bit reversed tables
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::fftInit()
{
for (int i = 0; i < 32; i++)
{
FFT_table_1[i] = (FFT_TYPE*)0;
FFT_table_2[i] = (short int*)0;
}
FFT_N = ConvertFFTSize(FFT_size);
// create and initialize cos table
FFT_table_1[FFT_N] = new FFT_TYPE[(POW2(FFT_N) / 4 + 1)];
fftCosInit(FFT_N, FFT_table_1[FFT_N]);
// create and initialize bit reverse tables
FFT_table_2[FFT_N/2] = new short[POW2(FFT_N/2 - 1)];
fftBRInit(FFT_N, FFT_table_2[FFT_N/2]);
if ((FFT_N % 2) == 0) { // FFT_N/2 = (FFT_N-1)/2 if FFT_N is odd. Prevents memory leak
FFT_table_2[(FFT_N - 1) / 2] = new short[POW2((FFT_N - 1) / 2 - 1)];
}
fftBRInit(FFT_N - 1, FFT_table_2[(FFT_N - 1) / 2]);
Utbl = ((FFT_TYPE**) FFT_table_1)[FFT_N];
BRLow = ((short**) FFT_table_2)[FFT_N / 2];
}
//------------------------------------------------------------------------------
// convert from N to LOG2(N)
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
int g_fft<FFT_TYPE>::ConvertFFTSize(int N)
{
if (N <= 0) N = -N;
switch (N) {
case 0x00000001: return 0; // 1
case 0x00000002: return 1; // 2
case 0x00000004: return 2; // 4
case 0x00000008: return 3; // 8
case 0x00000010: return 4; // 16
case 0x00000020: return 5; // 32
case 0x00000040: return 6; // 64
case 0x00000080: return 7; // 128
case 0x00000100: return 8; // 256
case 0x00000200: return 9; // 512
case 0x00000400: return 10; // 1024
case 0x00000800: return 11; // 2048
case 0x00001000: return 12; // 4096
case 0x00002000: return 13; // 8192
case 0x00004000: return 14; // 16384
case 0x00008000: return 15; // 32768
case 0x00010000: return 16; // 65536
case 0x00020000: return 17; // 131072
case 0x00040000: return 18; // 262144
case 0x00080000: return 19; // 525288
case 0x00100000: return 20; // 1048576
case 0x00200000: return 21; // 2097152
case 0x00400000: return 22; // 4194304
case 0x00800000: return 23; // 8388608
case 0x01000000: return 24; // 16777216
case 0x02000000: return 25; // 33554432
case 0x04000000: return 26; // 67108864
case 0x08000000: return 27; // 134217728
case 0x10000000: return 28; // 268435456
}
return 0;
}
//------------------------------------------------------------------------------
// Compute in-place complex FFT
// FFTsize: FFT length in samples
// buf: array of FFTsize*2 FFT_TYPE values,
// in interleaved real/imaginary format
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::ComplexFFT(std::complex<FFT_TYPE> *buf)
{
void *ptr = buf;
FFT_TYPE *nbuf = static_cast<FFT_TYPE *>(ptr);
ffts1(nbuf, FFT_N, Utbl, BRLow);
}
//------------------------------------------------------------------------------
// Compute in-place inverse complex FFT
// FFTsize: FFT length in samples
// buf: array of FFTsize*2 FFT_TYPE values,
// in interleaved real/imaginary format
// Output should be scaled by the return value of
// GetInverseComplexFFTScale(fft_struct, FFTsize).
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::InverseComplexFFT(std::complex<FFT_TYPE> *buf)
{
void *ptr = buf;
FFT_TYPE *nbuf = static_cast<FFT_TYPE *>(ptr);
iffts1(nbuf, FFT_N, Utbl, BRLow);
}
//------------------------------------------------------------------------------
// Compute in-place real FFT
// FFTsize: FFT length in samples
// buf: array of FFTsize FFT_TYPE values; output is in interleaved
// real/imaginary format, except for buf[1] which is the real
// part for the Nyquist frequency
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::RealFFT(std::complex<FFT_TYPE> *buf)
{
void *ptr = buf;
FFT_TYPE *nbuf = static_cast<FFT_TYPE *>(ptr);
rffts1(nbuf, FFT_N, Utbl, BRLow);
}
//------------------------------------------------------------------------------
// Compute in-place inverse real FFT
// FFTsize: FFT length in samples
// buf: array of FFTsize FFT_TYPE values; input is expected to be in
// interleaved real/imaginary format, except for buf[1] which
// is the real part for the Nyquist frequency
// Output should be scaled by the return value of
// GetInverseRealFFTScale(fft_struct, FFTsize).
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
void g_fft<FFT_TYPE>::InverseRealFFT(std::complex<FFT_TYPE> *buf)
{
void *ptr = buf;
FFT_TYPE *nbuf = static_cast<FFT_TYPE *>(ptr);
riffts1(nbuf, FFT_N, Utbl, BRLow);
}
//------------------------------------------------------------------------------
// Returns the amplitude scale that should be applied to the result of
// an inverse complex FFT with a length of 'FFTsize' samples.
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
FFT_TYPE g_fft<FFT_TYPE>::GetInverseComplexFFTScale()
{
return FFT_TYPE(1.0);
}
//------------------------------------------------------------------------------
// Returns the amplitude scale that should be applied to the result of
// an inverse real FFT with a length of 'FFTsize' samples.
//------------------------------------------------------------------------------
template <typename FFT_TYPE>
FFT_TYPE g_fft<FFT_TYPE>::GetInverseRealFFTScale()
{
return FFT_TYPE(1.0);
}
#endif
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