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audacity/lib-src/libnyquist/nyquist/ffts/src/fftlib.c
Leland Lucius 9fb0ce5b82 Update Nyquist to v3.09.
2015-04-07 22:10:17 -05:00

3177 lines
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/*******************************************************************
lower level fft stuff including routines called in fftext.c and fft2d.c
*******************************************************************/
/* inline declarations modified by RBD for C99 compiler */
#include "fftlib.h"
#include <math.h>
#define MCACHE (11-(sizeof(float)/8)) // fft's with M bigger than this bust primary cache
#ifdef WIN32
#define inline __inline
#endif
// some math constants to 40 decimal places
#define MYPI 3.141592653589793238462643383279502884197 // pi
#define MYROOT2 1.414213562373095048801688724209698078569 // sqrt(2)
#define MYCOSPID8 0.9238795325112867561281831893967882868224 // cos(pi/8)
#define MYSINPID8 0.3826834323650897717284599840303988667613 // sin(pi/8)
/*************************************************
routines to initialize tables used by fft routines
**************************************************/
void fftCosInit(long M, float *Utbl){
/* Compute Utbl, the cosine table for ffts */
/* of size (pow(2,M)/4 +1) */
/* INPUTS */
/* M = log2 of fft size */
/* OUTPUTS */
/* *Utbl = cosine table */
unsigned long fftN = POW2(M);
unsigned long i1;
Utbl[0] = 1.0;
for (i1 = 1; i1 < fftN/4; i1++)
Utbl[i1] = cos( (2.0 * MYPI * i1) / fftN );
Utbl[fftN/4] = 0.0;
}
void fftBRInit(long M, short *BRLow){
/* 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 */
long Mroot_1 = M / 2 - 1;
long Nroot_1 = POW2(Mroot_1);
long i1;
long bitsum;
long bitmask;
long 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
*************************************************/
//inline void bitrevR2(float *ioptr, long M, short *BRLow);
static inline void bitrevR2(float *ioptr, long M, short *BRLow){
/*** bit reverse and first radix 2 stage of forward or inverse fft ***/
float f0r;
float f0i;
float f1r;
float f1i;
float f2r;
float f2i;
float f3r;
float f3i;
float f4r;
float f4i;
float f5r;
float f5i;
float f6r;
float f6i;
float f7r;
float f7i;
float t0r;
float t0i;
float t1r;
float t1i;
float *p0r;
float *p1r;
float *IOP;
float *iolimit;
long Colstart;
long iCol;
unsigned long posA;
unsigned long posAi;
unsigned long posB;
unsigned long posBi;
const unsigned long Nrems2 = POW2((M+3)/2);
const unsigned long Nroot_1_ColInc = POW2(M)-Nrems2;
const unsigned long Nroot_1 = POW2(M/2-1)-1;
const unsigned long 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 + BRLow[Colstart]*4;
IOP = ioptr + (Colstart << ColstartShift);
p1r = IOP + BRLow[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 + BRLow[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;
};
};
}
//inline void fft2pt(float *ioptr);
static inline void fft2pt(float *ioptr){
/*** RADIX 2 fft ***/
float f0r, f0i, f1r, f1i;
float 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;
}
//inline void fft4pt(float *ioptr);
static inline void fft4pt(float *ioptr){
/*** RADIX 4 fft ***/
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float 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;
}
//inline void fft8pt(float *ioptr);
static inline void fft8pt(float *ioptr){
/*** RADIX 8 fft ***/
float w0r = 1.0/MYROOT2; /* cos(pi/4) */
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
float t0r, t0i, t1r, t1i;
const float 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;
}
//inline void bfR2(float *ioptr, long M, long NDiffU);
static inline void bfR2(float *ioptr, long M, long NDiffU){
/*** 2nd radix 2 stage ***/
unsigned long pos;
unsigned long posi;
unsigned long pinc;
unsigned long pnext;
unsigned long NSameU;
unsigned long SameUCnt;
float *pstrt;
float *p0r, *p1r, *p2r, *p3r;
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
const float Two = 2.0;
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;
}
}
//inline void bfR4(float *ioptr, long M, long NDiffU);
static inline void bfR4(float *ioptr, long M, long NDiffU){
/*** 1 radix 4 stage ***/
unsigned long pos;
unsigned long posi;
unsigned long pinc;
unsigned long pnext;
unsigned long pnexti;
unsigned long NSameU;
unsigned long SameUCnt;
float *pstrt;
float *p0r, *p1r, *p2r, *p3r;
float w1r = 1.0/MYROOT2; /* cos(pi/4) */
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
float t1r, t1i;
const float 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;
}
// inline void bfstages(float *ioptr, long M, float *Utbl, long Ustride, long NDiffU, long StageCnt);
static inline void bfstages(float *ioptr, long M, float *Utbl, long Ustride, long NDiffU, long StageCnt){
/*** RADIX 8 Stages ***/
unsigned long pos;
unsigned long posi;
unsigned long pinc;
unsigned long pnext;
unsigned long NSameU;
unsigned long Uinc;
unsigned long Uinc2;
unsigned long Uinc4;
unsigned long DiffUCnt;
unsigned long SameUCnt;
unsigned long U2toU3;
float *pstrt;
float *p0r, *p1r, *p2r, *p3r;
float *u0r, *u0i, *u1r, *u1i, *u2r, *u2i;
float w0r, w0i, w1r, w1i, w2r, w2i, w3r, w3i;
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
float t0r, t0i, t1r, t1i;
const float 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 = NSameU * Ustride;
Uinc2 = Uinc * 2;
Uinc4 = Uinc * 4;
U2toU3 = (POW2(M) / 8)*Ustride;
for (; StageCnt > 0 ; StageCnt--){
u0r = &Utbl[0];
u0i = &Utbl[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 (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 (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;
}
}
void fftrecurs(float *ioptr, long M, float *Utbl, long Ustride, long NDiffU, long StageCnt);
void fftrecurs(float *ioptr, long M, float *Utbl, long Ustride, long NDiffU, long StageCnt){
/* recursive bfstages calls to maximize on chip cache efficiency */
long i1;
if (M <= 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 */
}
}
void ffts1(float *ioptr, long M, long Rows, float *Utbl, short *BRLow){
/* 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) */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* *Utbl = cosine table */
/* *BRLow = bit reversed counter table */
/* OUTPUTS */
/* *ioptr = output data array */
long StageCnt;
long NDiffU;
switch (M){
case 0:
break;
case 1:
for (;Rows>0;Rows--){
fft2pt(ioptr); /* a 2 pt fft */
ioptr += 2*POW2(M);
}
break;
case 2:
for (;Rows>0;Rows--){
fft4pt(ioptr); /* a 4 pt fft */
ioptr += 2*POW2(M);
}
break;
case 3:
for (;Rows>0;Rows--){
fft8pt(ioptr); /* an 8 pt fft */
ioptr += 2*POW2(M);
}
break;
default:
for (;Rows>0;Rows--){
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 <= MCACHE)
bfstages(ioptr, M, Utbl, 1, NDiffU, StageCnt); /* RADIX 8 Stages */
else{
fftrecurs(ioptr, M, Utbl, 1, NDiffU, StageCnt); /* RADIX 8 Stages */
}
ioptr += 2*POW2(M);
}
}
}
/************************************************
parts of iffts1
*************************************************/
// inline void scbitrevR2(float *ioptr, long M, short *BRLow, float scale);
static inline void scbitrevR2(float *ioptr, long M, short *BRLow, float scale){
/*** scaled bit reverse and first radix 2 stage forward or inverse fft ***/
float f0r;
float f0i;
float f1r;
float f1i;
float f2r;
float f2i;
float f3r;
float f3i;
float f4r;
float f4i;
float f5r;
float f5i;
float f6r;
float f6i;
float f7r;
float f7i;
float t0r;
float t0i;
float t1r;
float t1i;
float *p0r;
float *p1r;
float *IOP;
float *iolimit;
long Colstart;
long iCol;
unsigned long posA;
unsigned long posAi;
unsigned long posB;
unsigned long posBi;
const unsigned long Nrems2 = POW2((M+3)/2);
const unsigned long Nroot_1_ColInc = POW2(M)-Nrems2;
const unsigned long Nroot_1 = POW2(M/2-1)-1;
const unsigned long 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 + BRLow[Colstart]*4;
IOP = ioptr + (Colstart << ColstartShift);
p1r = IOP + BRLow[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 + BRLow[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;
};
};
}
//inline void ifft2pt(float *ioptr, float scale);
static inline void ifft2pt(float *ioptr, float scale){
/*** RADIX 2 ifft ***/
float f0r, f0i, f1r, f1i;
float 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;
}
// inline void ifft4pt(float *ioptr, float scale);
static inline void ifft4pt(float *ioptr, float scale){
/*** RADIX 4 ifft ***/
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float 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;
}
//inline void ifft8pt(float *ioptr, float scale);
static inline void ifft8pt(float *ioptr, float scale){
/*** RADIX 8 ifft ***/
float w0r = 1.0/MYROOT2; /* cos(pi/4) */
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
float t0r, t0i, t1r, t1i;
const float 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;
}
//inline void ibfR2(float *ioptr, long M, long NDiffU);
static inline void ibfR2(float *ioptr, long M, long NDiffU){
/*** 2nd radix 2 stage ***/
unsigned long pos;
unsigned long posi;
unsigned long pinc;
unsigned long pnext;
unsigned long NSameU;
unsigned long SameUCnt;
float *pstrt;
float *p0r, *p1r, *p2r, *p3r;
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
const float Two = 2.0;
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;
}
}
//inline void ibfR4(float *ioptr, long M, long NDiffU);
static inline void ibfR4(float *ioptr, long M, long NDiffU){
/*** 1 radix 4 stage ***/
unsigned long pos;
unsigned long posi;
unsigned long pinc;
unsigned long pnext;
unsigned long pnexti;
unsigned long NSameU;
unsigned long SameUCnt;
float *pstrt;
float *p0r, *p1r, *p2r, *p3r;
float w1r = 1.0/MYROOT2; /* cos(pi/4) */
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
float t1r, t1i;
const float 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;
}
//inline void ibfstages(float *ioptr, long M, float *Utbl, long Ustride, long NDiffU, long StageCnt);
static inline void ibfstages(float *ioptr, long M, float *Utbl, long Ustride, long NDiffU, long StageCnt){
/*** RADIX 8 Stages ***/
unsigned long pos;
unsigned long posi;
unsigned long pinc;
unsigned long pnext;
unsigned long NSameU;
unsigned long Uinc;
unsigned long Uinc2;
unsigned long Uinc4;
unsigned long DiffUCnt;
unsigned long SameUCnt;
unsigned long U2toU3;
float *pstrt;
float *p0r, *p1r, *p2r, *p3r;
float *u0r, *u0i, *u1r, *u1i, *u2r, *u2i;
float w0r, w0i, w1r, w1i, w2r, w2i, w3r, w3i;
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
float t0r, t0i, t1r, t1i;
const float 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 = NSameU * Ustride;
Uinc2 = Uinc * 2;
Uinc4 = Uinc * 4;
U2toU3 = (POW2(M) / 8)*Ustride;
for (; StageCnt > 0 ; StageCnt--){
u0r = &Utbl[0];
u0i = &Utbl[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 (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 (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;
}
}
void ifftrecurs(float *ioptr, long M, float *Utbl, long Ustride, long NDiffU, long StageCnt);
void ifftrecurs(float *ioptr, long M, float *Utbl, long Ustride, long NDiffU, long StageCnt){
/* recursive bfstages calls to maximize on chip cache efficiency */
long i1;
if (M <= 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 */
}
}
void iffts1(float *ioptr, long M, long Rows, float *Utbl, short *BRLow){
/* Compute in-place inverse complex fft on the rows of the input array */
/* INPUTS */
/* *ioptr = input data array */
/* M = log2 of fft size */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* *Utbl = cosine table */
/* *BRLow = bit reversed counter table */
/* OUTPUTS */
/* *ioptr = output data array */
long StageCnt;
long NDiffU;
const float scale = 1.0/POW2(M);
switch (M){
case 0:
break;
case 1:
for (;Rows>0;Rows--){
ifft2pt(ioptr, scale); /* a 2 pt fft */
ioptr += 2*POW2(M);
}
break;
case 2:
for (;Rows>0;Rows--){
ifft4pt(ioptr, scale); /* a 4 pt fft */
ioptr += 2*POW2(M);
}
break;
case 3:
for (;Rows>0;Rows--){
ifft8pt(ioptr, scale); /* an 8 pt fft */
ioptr += 2*POW2(M);
}
break;
default:
for (;Rows>0;Rows--){
scbitrevR2(ioptr, M, BRLow, scale); /* 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 ){
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 <= MCACHE)
ibfstages(ioptr, M, Utbl, 1, NDiffU, StageCnt); /* RADIX 8 Stages */
else{
ifftrecurs(ioptr, M, Utbl, 1, NDiffU, StageCnt); /* RADIX 8 Stages */
}
ioptr += 2*POW2(M);
}
}
}
/************************************************
parts of rffts1
*************************************************/
//inline void rfft1pt(float *ioptr);
static inline void rfft1pt(float *ioptr){
/*** RADIX 2 rfft ***/
float f0r, f0i;
float 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;
}
//inline void rfft2pt(float *ioptr);
static inline void rfft2pt(float *ioptr){
/*** RADIX 4 rfft ***/
float f0r, f0i, f1r, f1i;
float 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;
}
//inline void rfft4pt(float *ioptr);
static inline void rfft4pt(float *ioptr){
/*** RADIX 8 rfft ***/
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float t0r, t0i, t1r, t1i;
float w0r = 1.0/MYROOT2; /* cos(pi/4) */
const float Two = 2.0;
const float 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;
}
//inline void rfft8pt(float *ioptr);
static inline void rfft8pt(float *ioptr){
/*** RADIX 16 rfft ***/
float w0r = 1.0/MYROOT2; /* cos(pi/4) */
float w1r = MYCOSPID8; /* cos(pi/8) */
float w1i = MYSINPID8; /* sin(pi/8) */
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
float t0r, t0i, t1r, t1i;
const float Two = 2.0;
const float 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;
}
//inline void frstage(float *ioptr, long M, float *Utbl);
static inline void frstage(float *ioptr, long M, float *Utbl){
/* Finish RFFT */
unsigned long pos;
unsigned long posi;
unsigned long diffUcnt;
float *p0r, *p1r;
float *u0r, *u0i;
float w0r, w0i;
float f0r, f0i, f1r, f1i, f4r, f4i, f5r, f5i;
float t0r, t0i, t1r, t1i;
const float Two = 2.0;
pos = POW2(M-1);
posi = pos + 1;
p0r = ioptr;
p1r = ioptr + pos/2;
u0r = Utbl + 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 = Utbl + 1;
u0i = Utbl + (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;
};
}
void rffts1(float *ioptr, long M, long Rows, float *Utbl, short *BRLow){
/* 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 */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* *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]). */
float scale;
long StageCnt;
long NDiffU;
M=M-1;
switch (M){
case -1:
break;
case 0:
for (;Rows>0;Rows--){
rfft1pt(ioptr); /* a 2 pt fft */
ioptr += 2*POW2(M);
}
case 1:
for (;Rows>0;Rows--){
rfft2pt(ioptr); /* a 4 pt fft */
ioptr += 2*POW2(M);
}
break;
case 2:
for (;Rows>0;Rows--){
rfft4pt(ioptr); /* an 8 pt fft */
ioptr += 2*POW2(M);
}
break;
case 3:
for (;Rows>0;Rows--){
rfft8pt(ioptr); /* a 16 pt fft */
ioptr += 2*POW2(M);
}
break;
default:
scale = 0.5;
for (;Rows>0;Rows--){
scbitrevR2(ioptr, M, BRLow, scale); /* 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 <= MCACHE){
bfstages(ioptr, M, Utbl, 2, NDiffU, StageCnt); /* RADIX 8 Stages */
frstage(ioptr, M+1, Utbl);
}
else{
fftrecurs(ioptr, M, Utbl, 2, NDiffU, StageCnt); /* RADIX 8 Stages */
frstage(ioptr, M+1, Utbl);
}
ioptr += 2*POW2(M);
}
}
}
/************************************************
parts of riffts1
*************************************************/
//inline void rifft1pt(float *ioptr, float scale);
static inline void rifft1pt(float *ioptr, float scale){
/*** RADIX 2 rifft ***/
float f0r, f0i;
float 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;
}
//inline void rifft2pt(float *ioptr, float scale);
static inline void rifft2pt(float *ioptr, float scale){
/*** RADIX 4 rifft ***/
float f0r, f0i, f1r, f1i;
float t0r, t0i;
const float Two = 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;
}
//inline void rifft4pt(float *ioptr, float scale);
static inline void rifft4pt(float *ioptr, float scale){
/*** RADIX 8 rifft ***/
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float t0r, t0i, t1r, t1i;
float w0r = 1.0/MYROOT2; /* cos(pi/4) */
const float Two = 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;
}
//inline void rifft8pt(float *ioptr, float scale);
static inline void rifft8pt(float *ioptr, float scale){
/*** RADIX 16 rifft ***/
float w0r = 1.0/MYROOT2; /* cos(pi/4) */
float w1r = MYCOSPID8; /* cos(pi/8) */
float w1i = MYSINPID8; /* sin(pi/8) */
float f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
float f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
float t0r, t0i, t1r, t1i;
const float Two = 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;
}
//inline void ifrstage(float *ioptr, long M, float *Utbl);
static inline void ifrstage(float *ioptr, long M, float *Utbl){
/* Start RIFFT */
unsigned long pos;
unsigned long posi;
unsigned long diffUcnt;
float *p0r, *p1r;
float *u0r, *u0i;
float w0r, w0i;
float f0r, f0i, f1r, f1i, f4r, f4i, f5r, f5i;
float t0r, t0i, t1r, t1i;
const float Two = 2.0;
pos = POW2(M-1);
posi = pos + 1;
p0r = ioptr;
p1r = ioptr + pos/2;
u0r = Utbl + 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 = Utbl + 1;
u0i = Utbl + (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;
};
}
void riffts1(float *ioptr, long M, long Rows, float *Utbl, short *BRLow){
/* 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]). */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* *Utbl = cosine table */
/* *BRLow = bit reversed counter table */
/* OUTPUTS */
/* *ioptr = real output data array */
float scale;
long StageCnt;
long NDiffU;
scale = 1.0/POW2(M);
M=M-1;
switch (M){
case -1:
break;
case 0:
for (;Rows>0;Rows--){
rifft1pt(ioptr, scale); /* a 2 pt fft */
ioptr += 2*POW2(M);
}
case 1:
for (;Rows>0;Rows--){
rifft2pt(ioptr, scale); /* a 4 pt fft */
ioptr += 2*POW2(M);
}
break;
case 2:
for (;Rows>0;Rows--){
rifft4pt(ioptr, scale); /* an 8 pt fft */
ioptr += 2*POW2(M);
}
break;
case 3:
for (;Rows>0;Rows--){
rifft8pt(ioptr, scale); /* a 16 pt fft */
ioptr += 2*POW2(M);
}
break;
default:
for (;Rows>0;Rows--){
ifrstage(ioptr, M+1, Utbl);
scbitrevR2(ioptr, M, BRLow, scale); /* 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 ){
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 <= MCACHE){
ibfstages(ioptr, M, Utbl, 2, NDiffU, StageCnt); /* RADIX 8 Stages */
}
else{
ifftrecurs(ioptr, M, Utbl, 2, NDiffU, StageCnt); /* RADIX 8 Stages */
}
ioptr += 2*POW2(M);
}
}
}
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