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fftlib.c
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fftlib.c
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/* FFT library */
/* Library of in-place fast fourier transforms */
/* Forward and inverse complex transforms */
/* and real forward transform */
/* Optimized for RISC processors with many registers */
/* Version 1.1 John Green NUWC New London CT January 96 */
/* Version 1.1 renamed as fftlib from fftbig */
/* Version 1.1 removed (float *)((char *) ptr) optimization */
/* Version 1.0 John Green NUWC New London CT December 95 */
/* (John Green) green_jt@vsdec.nl.nuwc.navy.mil */
/* green_jt@vsdec.nl.nuwc.navy.mil */
#include <math.h>
#include "fftlib.h"
#define MAXMROOT 9 /* 2^(MAXMROOT-1) = # of elements in BRcnt */
/* Bit reversed counter */
static const unsigned char BRcnt[256] = {
0, 128, 64, 192, 32, 160, 96, 224, 16, 144, 80, 208,
48, 176, 112, 240, 8, 136, 72, 200, 40, 168, 104, 232,
24, 152, 88, 216, 56, 184, 120, 248, 4, 132, 68, 196,
36, 164, 100, 228, 20, 148, 84, 212, 52, 180, 116, 244,
12, 140, 76, 204, 44, 172, 108, 236, 28, 156, 92, 220,
60, 188, 124, 252, 2, 130, 66, 194, 34, 162, 98, 226,
18, 146, 82, 210, 50, 178, 114, 242, 10, 138, 74, 202,
42, 170, 106, 234, 26, 154, 90, 218, 58, 186, 122, 250,
6, 134, 70, 198, 38, 166, 102, 230, 22, 150, 86, 214,
54, 182, 118, 246, 14, 142, 78, 206, 46, 174, 110, 238,
30, 158, 94, 222, 62, 190, 126, 254, 1, 129, 65, 193,
33, 161, 97, 225, 17, 145, 81, 209, 49, 177, 113, 241,
9, 137, 73, 201, 41, 169, 105, 233, 25, 153, 89, 217,
57, 185, 121, 249, 5, 133, 69, 197, 37, 165, 101, 229,
21, 149, 85, 213, 53, 181, 117, 245, 13, 141, 77, 205,
45, 173, 109, 237, 29, 157, 93, 221, 61, 189, 125, 253,
3, 131, 67, 195, 35, 163, 99, 227, 19, 147, 83, 211,
51, 179, 115, 243, 11, 139, 75, 203, 43, 171, 107, 235,
27, 155, 91, 219, 59, 187, 123, 251, 7, 135, 71, 199,
39, 167, 103, 231, 23, 151, 87, 215, 55, 183, 119, 247,
15, 143, 79, 207, 47, 175, 111, 239, 31, 159, 95, 223,
63, 191, 127, 255 };
/* Table of powers of 2 */
static const long Ntbl[21] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048,
4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576};
long FFTInit(long *fftMptr, long fftN, float *Utbl){
/* Compute cosine table and check size for complex ffts */
/* INPUTS */
/* fftN = size of fft */
/* OUTPUTS */
/* *fftMptr = log2 of fft size */
/* *Utbl = cosine table with fftN/4 + 1 entries (angles = 0 to pi/2 inclusive) */
/* RETURNS */
/* 1 if fftN is invalid, 0 otherwise */
long i1, ErrVal;
ErrVal = 0;
*fftMptr = (long)(log(fftN)/log(2.0) + 0.5);
if ((*fftMptr >= 3) & (*fftMptr <= 19) & (int)(pow(2,*fftMptr)+.5) == fftN)
for (i1 = 0; i1 <= fftN/4; i1++)
Utbl[i1] = cos( ( 3.1415926535897932384626433832795 * 2.0 * i1 ) / fftN );
else
ErrVal = 1;
return ErrVal;
}
long rFFTInit(long *fftMptr, long fftN, float *Utbl){
/* Compute cosine table and check size for a real input fft */
/* INPUTS */
/* fftN = size of fft */
/* OUTPUTS */
/* *fftMptr = log2 of fft size */
/* *Utbl = cosine table with fftN/4 + 1 entries (angles = 0 to pi/2 inclusive) */
/* RETURNS */
/* 1 if fftN is invalid, 0 otherwise */
long i1, ErrVal;
ErrVal = 0;
*fftMptr = (long)(log(fftN)/log(2.0) + 0.5);
if ((*fftMptr >= 4) & (*fftMptr <= 20) & (int)(pow(2,*fftMptr)+.5) == fftN)
for (i1 = 0; i1 <= fftN/4; i1++)
Utbl[i1] = cos( ( 3.1415926535897932384626433832795 * 2.0 * i1 ) / fftN );
else
ErrVal = 1;
return ErrVal;
}
void ffts(float *ioptr, long M, long Rows, float *Utbl){
/* Compute in-place complex fft on the rows of the input array */
/* INPUTS */
/* M = log2 of fft size */
/* *ioptr = input data array */
/* *Utbl = cosine table */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* OUTPUTS */
/* *ioptr = output data array */
long Flyinc;
long FlyOffsetA;
long FlyOffsetAIm;
long FlyOffsetB;
long FlyOffsetBIm;
long NsameU1;
long NsameU2;
long NsameU4;
long diffUcnt;
long LoopCnt;
float scale;
float fly0r;
float fly0i;
float fly1r;
float fly1i;
float fly2r;
float fly2i;
float fly3r;
float fly3i;
float fly4r;
float fly4i;
float fly5r;
float fly5i;
float fly6r;
float fly6i;
float fly7r;
float fly7i;
float U0r;
float U0i;
float U1r;
float U1i;
float U2r;
float U2i;
float U3r;
float U3i;
float t0r;
float t0i;
float t1r;
float t1i;
float *fly0P;
float *fly1P;
float *fly2P;
float *fly3P;
float *U0rP;
float *U0iP;
float *U1rP;
float *U1iP;
float *U2rP;
float *U2iP;
float *IOP;
long U3offset;
long stage;
long NdiffU;
long LoopN;
const long BRshift = MAXMROOT - (M>>1);
const long Nrems2 = Ntbl[M-(M>>1)+1];
const long Nroot_1_ColInc = (Ntbl[M-1]-Ntbl[M-(M>>1)])*2;
scale = 2.0;
for (;Rows>0;Rows--){
FlyOffsetA = Ntbl[M] * (2/2);
FlyOffsetAIm = FlyOffsetA + 1;
FlyOffsetB = FlyOffsetA + 2;
FlyOffsetBIm = FlyOffsetB + 1;
/* BitrevR2 ** bit reverse and first radix 2 stage ******/
for (stage = 0; stage < Ntbl[M-(M>>1)]*2; stage += Ntbl[M>>1]*2){
for (LoopN = (Ntbl[(M>>1)-1]-1); LoopN >= 0; LoopN--){
LoopCnt = (Ntbl[(M>>1)-1]-1);
fly0P = ioptr+ Nroot_1_ColInc + ((int)BRcnt[LoopN] >> BRshift)*(2*2) + stage;
IOP = ioptr + (LoopN<<(M+1)/2) * 2 + stage;
fly1P = IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2);
fly0r = *(fly0P);
fly0i = *(fly0P+1);
fly1r = *(fly0P+FlyOffsetA);
fly1i = *(fly0P+FlyOffsetAIm);
for (; LoopCnt > LoopN;){
fly2r = *(fly0P+2);
fly2i = *(fly0P+(2+1));
fly3r = *(fly0P+FlyOffsetB);
fly3i = *(fly0P+FlyOffsetBIm);
fly4r = *(fly1P);
fly4i = *(fly1P+1);
fly5r = *(fly1P+FlyOffsetA);
fly5i = *(fly1P+FlyOffsetAIm);
fly6r = *(fly1P+2);
fly6i = *(fly1P+(2+1));
fly7r = *(fly1P+FlyOffsetB);
fly7i = *(fly1P+FlyOffsetBIm);
t0r = fly0r + fly1r;
t0i = fly0i + fly1i;
fly1r = fly0r - fly1r;
fly1i = fly0i - fly1i;
t1r = fly2r + fly3r;
t1i = fly2i + fly3i;
fly3r = fly2r - fly3r;
fly3i = fly2i - fly3i;
fly0r = fly4r + fly5r;
fly0i = fly4i + fly5i;
fly5r = fly4r - fly5r;
fly5i = fly4i - fly5i;
fly2r = fly6r + fly7r;
fly2i = fly6i + fly7i;
fly7r = fly6r - fly7r;
fly7i = fly6i - fly7i;
*(fly1P) = t0r;
*(fly1P+1) = t0i;
*(fly1P+2) = fly1r;
*(fly1P+(2+1)) = fly1i;
*(fly1P+FlyOffsetA) = t1r;
*(fly1P+FlyOffsetAIm) = t1i;
*(fly1P+FlyOffsetB) = fly3r;
*(fly1P+FlyOffsetBIm) = fly3i;
*(fly0P) = fly0r;
*(fly0P+1) = fly0i;
*(fly0P+2) = fly5r;
*(fly0P+(2+1)) = fly5i;
*(fly0P+FlyOffsetA) = fly2r;
*(fly0P+FlyOffsetAIm) = fly2i;
*(fly0P+FlyOffsetB) = fly7r;
*(fly0P+FlyOffsetBIm) = fly7i;
fly0P -= Nrems2;
fly0r = *(fly0P);
fly0i = *(fly0P+1);
fly1r = *(fly0P+FlyOffsetA);
fly1i = *(fly0P+FlyOffsetAIm);
LoopCnt -= 1;
fly1P = (IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2));
};
fly2r = *(fly0P+2);
fly2i = *(fly0P+(2+1));
fly3r = *(fly0P+FlyOffsetB);
fly3i = *(fly0P+FlyOffsetBIm);
t0r = fly0r + fly1r;
t0i = fly0i + fly1i;
fly1r = fly0r - fly1r;
fly1i = fly0i - fly1i;
t1r = fly2r + fly3r;
t1i = fly2i + fly3i;
fly3r = fly2r - fly3r;
fly3i = fly2i - fly3i;
*(fly0P) = t0r;
*(fly0P+1) = t0i;
*(fly0P+2) = fly1r;
*(fly0P+(2+1)) = fly1i;
*(fly0P+FlyOffsetA) = t1r;
*(fly0P+FlyOffsetAIm) = t1i;
*(fly0P+FlyOffsetB) = fly3r;
*(fly0P+FlyOffsetBIm) = fly3i;
};
};
/**** FFTC **************/
NdiffU = 2;
Flyinc = (NdiffU);
NsameU4 = Ntbl[M]/4;
LoopN = Ntbl[M-3];
stage = ((M-1)/3);
if ( (M-1-(stage * 3)) != 0 ){
FlyOffsetA = Flyinc << 2;
FlyOffsetB = FlyOffsetA << 1;
FlyOffsetAIm = FlyOffsetA + 1;
FlyOffsetBIm = FlyOffsetB + 1;
if ( (M-1-(stage * 3)) == 1 ){
/* 1 radix 2 stage */
IOP = ioptr;
fly0P = IOP;
fly1P = (IOP+Flyinc);
fly2P = (fly1P+Flyinc);
fly3P = (fly2P+Flyinc);
/* Butterflys */
/*
t0 - - t0
t1 - - t1
f2 - 1- f5
f1 - -i- f7
f4 - - f4
f0 - - f0
f6 - 1- f2
f3 - -i- f1
*/
for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){
t0r = *(fly0P);
t0i = *(fly0P + 1);
t1r = *(fly1P);
t1i = *(fly1P + 1);
fly2r = *(fly2P);
fly2i = *(fly2P + 1);
fly1r = *(fly3P);
fly1i = *(fly3P + 1);
fly4r = *(fly0P + FlyOffsetA);
fly4i = *(fly0P + FlyOffsetAIm);
fly0r = *(fly1P + FlyOffsetA);
fly0i = *(fly1P + FlyOffsetAIm);
fly6r = *(fly2P + FlyOffsetA);
fly6i = *(fly2P + FlyOffsetAIm);
fly3r = *(fly3P + FlyOffsetA);
fly3i = *(fly3P + FlyOffsetAIm);
fly5r = t0r - fly2r;
fly5i = t0i - fly2i;
t0r = t0r + fly2r;
t0i = t0i + fly2i;
fly7r = t1r - fly1i;
fly7i = t1i + fly1r;
t1r = t1r + fly1i;
t1i = t1i - fly1r;
fly2r = fly4r - fly6r;
fly2i = fly4i - fly6i;
fly4r = fly4r + fly6r;
fly4i = fly4i + fly6i;
fly1r = fly0r - fly3i;
fly1i = fly0i + fly3r;
fly0r = fly0r + fly3i;
fly0i = fly0i - fly3r;
*(fly2P) = fly5r;
*(fly2P + 1) = fly5i;
*(fly0P) = t0r;
*(fly0P + 1) = t0i;
*(fly3P) = fly7r;
*(fly3P + 1) = fly7i;
*(fly1P) = t1r;
*(fly1P + 1) = t1i;
*(fly2P + FlyOffsetA) = fly2r;
*(fly2P + FlyOffsetAIm) = fly2i;
*(fly0P + FlyOffsetA) = fly4r;
*(fly0P + FlyOffsetAIm) = fly4i;
*(fly3P + FlyOffsetA) = fly1r;
*(fly3P + FlyOffsetAIm) = fly1i;
*(fly1P + FlyOffsetA) = fly0r;
*(fly1P + FlyOffsetAIm) = fly0i;
fly0P = (fly0P + FlyOffsetB);
fly1P = (fly1P + FlyOffsetB);
fly2P = (fly2P + FlyOffsetB);
fly3P = (fly3P + FlyOffsetB);
};
NsameU4 >>= 1;
LoopN >>= 1;
NdiffU <<= 1;
Flyinc = Flyinc << 1;
}
else{
/* 1 radix 4 stage */
IOP = ioptr;
U3r = 0.7071067811865475244008443621; /* sqrt(0.5); */
U3i = U3r;
fly0P = IOP;
fly1P = (IOP+Flyinc);
fly2P = (fly1P+Flyinc);
fly3P = (fly2P+Flyinc);
/* Butterflys */
/*
t0 - - t0 - - t0
t1 - - t1 - - t1
f2 - 1- f5 - - f5
f1 - -i- f7 - - f7
f4 - - f4 - 1- f6
f0 - - f0 -U3 - f3
f6 - 1- f2 - -i- f4
f3 - -i- f1 -U3a- f2
*/
for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){
t0r = *(fly0P);
t0i = *(fly0P + 1);
t1r = *(fly1P);
t1i = *(fly1P + 1);
fly2r = *(fly2P);
fly2i = *(fly2P + 1);
fly1r = *(fly3P);
fly1i = *(fly3P + 1);
fly4r = *(fly0P + FlyOffsetA);
fly4i = *(fly0P + FlyOffsetAIm);
fly0r = *(fly1P + FlyOffsetA);
fly0i = *(fly1P + FlyOffsetAIm);
fly6r = *(fly2P + FlyOffsetA);
fly6i = *(fly2P + FlyOffsetAIm);
fly3r = *(fly3P + FlyOffsetA);
fly3i = *(fly3P + FlyOffsetAIm);
fly5r = t0r - fly2r;
fly5i = t0i - fly2i;
t0r = t0r + fly2r;
t0i = t0i + fly2i;
fly7r = t1r - fly1i;
fly7i = t1i + fly1r;
t1r = t1r + fly1i;
t1i = t1i - fly1r;
fly2r = fly4r - fly6r;
fly2i = fly4i - fly6i;
fly4r = fly4r + fly6r;
fly4i = fly4i + fly6i;
fly1r = fly0r - fly3i;
fly1i = fly0i + fly3r;
fly0r = fly0r + fly3i;
fly0i = fly0i - fly3r;
fly6r = t0r - fly4r;
fly6i = t0i - fly4i;
t0r = t0r + fly4r;
t0i = t0i + fly4i;
fly3r = fly5r - fly2i;
fly3i = fly5i + fly2r;
fly5r = fly5r + fly2i;
fly5i = fly5i - fly2r;
fly4r = t1r - U3r * fly0r;
fly4r = fly4r - U3i * fly0i;
fly4i = t1i + U3i * fly0r;
fly4i = fly4i - U3r * fly0i;
t1r = scale * t1r - fly4r;
t1i = scale * t1i - fly4i;
fly2r = fly7r + U3i * fly1r;
fly2r = fly2r - U3r * fly1i;
fly2i = fly7i + U3r * fly1r;
fly2i = fly2i + U3i * fly1i;
fly7r = scale * fly7r - fly2r;
fly7i = scale * fly7i - fly2i;
*(fly0P + FlyOffsetA) = fly6r;
*(fly0P + FlyOffsetAIm) = fly6i;
*(fly0P) = t0r;
*(fly0P + 1) = t0i;
*(fly2P + FlyOffsetA) = fly3r;
*(fly2P + FlyOffsetAIm) = fly3i;
*(fly2P) = fly5r;
*(fly2P + 1) = fly5i;
*(fly1P + FlyOffsetA) = fly4r;
*(fly1P + FlyOffsetAIm) = fly4i;
*(fly1P) = t1r;
*(fly1P + 1) = t1i;
*(fly3P + FlyOffsetA) = fly2r;
*(fly3P + FlyOffsetAIm) = fly2i;
*(fly3P) = fly7r;
*(fly3P + 1) = fly7i;
fly0P = (fly0P + FlyOffsetB);
fly1P = (fly1P + FlyOffsetB);
fly2P = (fly2P + FlyOffsetB);
fly3P = (fly3P + FlyOffsetB);
};
NsameU4 >>= 2;
LoopN >>= 2;
NdiffU <<= 2;
Flyinc = Flyinc << 2;
};
};
NsameU2 = NsameU4 >> 1;
NsameU1 = NsameU2 >> 1;
Flyinc <<= 1;
FlyOffsetA = Flyinc << 2;
FlyOffsetB = FlyOffsetA << 1;
FlyOffsetAIm = FlyOffsetA + 1;
FlyOffsetBIm = FlyOffsetB + 1;
LoopN >>= 1;
/* ****** RADIX 8 Stages */
for (stage = stage<<1; stage > 0 ; stage--){
/* an fft stage is done in two parts to ease use of the single quadrant cos table */
/* fftcalc1(iobuf, Utbl, N, NdiffU, LoopN); */
if(!(stage&1)){
U0rP = &Utbl[0];
U0iP = &Utbl[Ntbl[M-2]];
U1rP = U0rP;
U1iP = U0iP;
U2rP = U0rP;
U2iP = U0iP;
U3offset = (Ntbl[M]) / 8;
IOP = ioptr;
U0r = *U0rP,
U0i = *U0iP;
U1r = *U1rP,
U1i = *U1iP;
U2r = *U2rP,
U2i = *U2iP;
U3r = *( U2rP + U3offset);
U3i = *( U2iP - U3offset);
}
fly0P = IOP;
fly1P = (IOP+Flyinc);
fly2P = (fly1P+Flyinc);
fly3P = (fly2P+Flyinc);
for (diffUcnt = (NdiffU)>>1; diffUcnt != 0; diffUcnt--){
/* Butterflys */
/*
f0 - - t0 - - t0 - - t0
f1 -U0 - t1 - - t1 - - t1
f2 - - f2 -U1 - f5 - - f3
f3 -U0 - f1 -U1a- f7 - - f7
f4 - - f4 - - f4 -U2 - f6
f5 -U0 - f0 - - f0 -U3 - f4
f6 - - f6 -U1 - f2 -U2a- f2
f7 -U0 - f3 -U1a- f1 -U3a- f5
*/
fly0r = *(IOP);
fly0i = *(IOP+1);
fly1r = *(fly1P);
fly1i = *(fly1P+1);
for (LoopCnt = LoopN-1; LoopCnt > 0 ; LoopCnt--){
fly2r = *(fly2P);
fly2i = *(fly2P + 1);
fly3r = *(fly3P);
fly3i = *(fly3P + 1);
fly4r = *(fly0P + FlyOffsetA);
fly4i = *(fly0P + FlyOffsetAIm);
fly5r = *(fly1P + FlyOffsetA);
fly5i = *(fly1P + FlyOffsetAIm);
fly6r = *(fly2P + FlyOffsetA);
fly6i = *(fly2P + FlyOffsetAIm);
fly7r = *(fly3P + FlyOffsetA);
fly7i = *(fly3P + FlyOffsetAIm);
t1r = fly0r - U0r * fly1r;
t1r = t1r - U0i * fly1i;
t1i = fly0i + U0i * fly1r;
t1i = t1i - U0r * fly1i;
t0r = scale * fly0r - t1r;
t0i = scale * fly0i - t1i;
fly1r = fly2r - U0r * fly3r;
fly1r = fly1r - U0i * fly3i;
fly1i = fly2i + U0i * fly3r;
fly1i = fly1i - U0r * fly3i;
fly2r = scale * fly2r - fly1r;
fly2i = scale * fly2i - fly1i;
fly0r = fly4r - U0r * fly5r;
fly0r = fly0r - U0i * fly5i;
fly0i = fly4i + U0i * fly5r;
fly0i = fly0i - U0r * fly5i;
fly4r = scale * fly4r - fly0r;
fly4i = scale * fly4i - fly0i;
fly3r = fly6r - U0r * fly7r;
fly3r = fly3r - U0i * fly7i;
fly3i = fly6i + U0i * fly7r;
fly3i = fly3i - U0r * fly7i;
fly6r = scale * fly6r - fly3r;
fly6i = scale * fly6i - fly3i;
fly5r = t0r - U1r * fly2r;
fly5r = fly5r - U1i * fly2i;
fly5i = t0i + U1i * fly2r;
fly5i = fly5i - U1r * fly2i;
t0r = scale * t0r - fly5r;
t0i = scale * t0i - fly5i;
fly7r = t1r + U1i * fly1r;
fly7r = fly7r - U1r * fly1i;
fly7i = t1i + U1r * fly1r;
fly7i = fly7i + U1i * fly1i;
t1r = scale * t1r - fly7r;
t1i = scale * t1i - fly7i;
fly2r = fly4r - U1r * fly6r;
fly2r = fly2r - U1i * fly6i;
fly2i = fly4i + U1i * fly6r;
fly2i = fly2i - U1r * fly6i;
fly4r = scale * fly4r - fly2r;
fly4i = scale * fly4i - fly2i;
fly1r = fly0r + U1i * fly3r;
fly1r = fly1r - U1r * fly3i;
fly1i = fly0i + U1r * fly3r;
fly1i = fly1i + U1i * fly3i;
fly0r = scale * fly0r - fly1r;
fly0i = scale * fly0i - fly1i;
fly6r = t0r - U2r * fly4r;
fly6r = fly6r - U2i * fly4i;
fly6i = t0i + U2i * fly4r;
fly6i = fly6i - U2r * fly4i;
t0r = scale * t0r - fly6r;
t0i = scale * t0i - fly6i;
fly3r = fly5r - U2i * fly2r;
fly3r = fly3r + U2r * fly2i;
fly3i = fly5i - U2r * fly2r;
fly3i = fly3i - U2i * fly2i;
fly2r = scale * fly5r - fly3r;
fly2i = scale * fly5i - fly3i;
fly4r = t1r - U3r * fly0r;
fly4r = fly4r - U3i * fly0i;
fly4i = t1i + U3i * fly0r;
fly4i = fly4i - U3r * fly0i;
t1r = scale * t1r - fly4r;
t1i = scale * t1i - fly4i;
fly5r = fly7r + U3i * fly1r;
fly5r = fly5r - U3r * fly1i;
fly5i = fly7i + U3r * fly1r;
fly5i = fly5i + U3i * fly1i;
fly7r = scale * fly7r - fly5r;
fly7i = scale * fly7i - fly5i;
*(fly0P + FlyOffsetA) = fly6r;
*(fly0P + FlyOffsetAIm) = fly6i;
*(fly0P) = t0r;
*(fly0P + 1) = t0i;
*(fly2P) = fly3r;
*(fly2P + 1) = fly3i;
*(fly2P + FlyOffsetA) = fly2r;
*(fly2P + FlyOffsetAIm) = fly2i;
fly0r = *(fly0P + FlyOffsetB);
fly0i = *(fly0P + FlyOffsetBIm);
*(fly1P + FlyOffsetA) = fly4r;
*(fly1P + FlyOffsetAIm) = fly4i;
*(fly1P) = t1r;
*(fly1P + 1) = t1i;
fly1r = *(fly1P + FlyOffsetB);
fly1i = *(fly1P + FlyOffsetBIm);
*(fly3P + FlyOffsetA) = fly5r;
*(fly3P + FlyOffsetAIm) = fly5i;
*(fly3P) = fly7r;
*(fly3P + 1) = fly7i;
fly0P = (fly0P + FlyOffsetB);
fly1P = (fly1P + FlyOffsetB);
fly2P = (fly2P + FlyOffsetB);
fly3P = (fly3P + FlyOffsetB);
};
fly2r = *(fly2P);
fly2i = *(fly2P + 1);
fly3r = *(fly3P);
fly3i = *(fly3P + 1);
fly4r = *(fly0P + FlyOffsetA);
fly4i = *(fly0P + FlyOffsetAIm);
fly5r = *(fly1P + FlyOffsetA);
fly5i = *(fly1P + FlyOffsetAIm);
fly6r = *(fly2P + FlyOffsetA);
fly6i = *(fly2P + FlyOffsetAIm);
fly7r = *(fly3P + FlyOffsetA);
fly7i = *(fly3P + FlyOffsetAIm);
t1r = fly0r - U0r * fly1r;
t1r = t1r - U0i * fly1i;
t1i = fly0i + U0i * fly1r;
t1i = t1i - U0r * fly1i;
t0r = scale * fly0r - t1r;
t0i = scale * fly0i - t1i;
fly1r = fly2r - U0r * fly3r;
fly1r = fly1r - U0i * fly3i;
fly1i = fly2i + U0i * fly3r;
fly1i = fly1i - U0r * fly3i;
fly2r = scale * fly2r - fly1r;
fly2i = scale * fly2i - fly1i;
fly0r = fly4r - U0r * fly5r;
fly0r = fly0r - U0i * fly5i;
fly0i = fly4i + U0i * fly5r;
fly0i = fly0i - U0r * fly5i;
fly4r = scale * fly4r - fly0r;
fly4i = scale * fly4i - fly0i;
fly3r = fly6r - U0r * fly7r;
fly3r = fly3r - U0i * fly7i;
fly3i = fly6i + U0i * fly7r;
fly3i = fly3i - U0r * fly7i;
fly6r = scale * fly6r - fly3r;
fly6i = scale * fly6i - fly3i;
fly5r = t0r - U1r * fly2r;
fly5r = fly5r - U1i * fly2i;
fly5i = t0i + U1i * fly2r;
fly5i = fly5i - U1r * fly2i;
t0r = scale * t0r - fly5r;
t0i = scale * t0i - fly5i;
fly7r = t1r + U1i * fly1r;
fly7r = fly7r - U1r * fly1i;
fly7i = t1i + U1r * fly1r;
fly7i = fly7i + U1i * fly1i;
t1r = scale * t1r - fly7r;
t1i = scale * t1i - fly7i;
fly2r = fly4r - U1r * fly6r;
fly2r = fly2r - U1i * fly6i;
fly2i = fly4i + U1i * fly6r;
fly2i = fly2i - U1r * fly6i;
fly4r = scale * fly4r - fly2r;
fly4i = scale * fly4i - fly2i;
fly1r = fly0r + U1i * fly3r;
fly1r = fly1r - U1r * fly3i;
fly1i = fly0i + U1r * fly3r;
fly1i = fly1i + U1i * fly3i;
fly0r = scale * fly0r - fly1r;
fly0i = scale * fly0i - fly1i;
U0i = *(U0iP = (U0iP - NsameU4));
U0r = *(U0rP = (U0rP + NsameU4));
U1r = *(U1rP = (U1rP + NsameU2));
U1i = *(U1iP = (U1iP - NsameU2));
if(stage&1)
U0r = -U0r;
fly6r = t0r - U2r * fly4r;
fly6r = fly6r - U2i * fly4i;
fly6i = t0i + U2i * fly4r;
fly6i = fly6i - U2r * fly4i;
t0r = scale * t0r - fly6r;
t0i = scale * t0i - fly6i;
fly3r = fly5r - U2i * fly2r;
fly3r = fly3r + U2r * fly2i;
fly3i = fly5i - U2r * fly2r;
fly3i = fly3i - U2i * fly2i;
fly2r = scale * fly5r - fly3r;
fly2i = scale * fly5i - fly3i;
fly4r = t1r - U3r * fly0r;
fly4r = fly4r - U3i * fly0i;
fly4i = t1i + U3i * fly0r;
fly4i = fly4i - U3r * fly0i;
t1r = scale * t1r - fly4r;
t1i = scale * t1i - fly4i;
fly5r = fly7r + U3i * fly1r;
fly5r = fly5r - U3r * fly1i;
fly5i = fly7i + U3r * fly1r;
fly5i = fly5i + U3i * fly1i;
fly7r = scale * fly7r - fly5r;
fly7i = scale * fly7i - fly5i;
*(fly0P + FlyOffsetA) = fly6r;
*(fly0P + FlyOffsetAIm) = fly6i;
*(fly0P) = t0r;
*(fly0P + 1) = t0i;
U2r = *(U2rP = (U2rP + NsameU1));
U2i = *(U2iP = (U2iP - NsameU1));
*(fly2P) = fly3r;
*(fly2P + 1) = fly3i;
*(fly2P + FlyOffsetA) = fly2r;
*(fly2P + FlyOffsetAIm) = fly2i;
*(fly1P + FlyOffsetA) = fly4r;
*(fly1P + FlyOffsetAIm) = fly4i;
*(fly1P) = t1r;
*(fly1P + 1) = t1i;
U3r = *( U2rP + U3offset);
U3i = *( U2iP - U3offset);
*(fly3P + FlyOffsetA) = fly5r;
*(fly3P + FlyOffsetAIm) = fly5i;
*(fly3P) = fly7r;
*(fly3P + 1) = fly7i;
IOP = IOP + 2;
fly0P = IOP;
fly1P = (IOP+Flyinc);
fly2P = (fly1P+Flyinc);
fly3P = (fly2P+Flyinc);
};
NsameU4 = -NsameU4;
if(stage&1){
LoopN >>= 3;
NsameU1 >>= 3;
NsameU2 >>= 3;
NsameU4 >>= 3;
NdiffU <<= 3;
Flyinc <<= 3;
FlyOffsetA <<= 3;
FlyOffsetB <<= 3;
FlyOffsetAIm = FlyOffsetA + 1;
FlyOffsetBIm = FlyOffsetB + 1;
}
}
ioptr += 2*Ntbl[M];
}
}
void iffts(float *ioptr, long M, long Rows, float *Utbl){
/* Compute in-place inverse complex fft on the rows of the input array */
/* INPUTS */
/* M = log2 of fft size */
/* *ioptr = input data array */
/* *Utbl = cosine table */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* OUTPUTS */
/* *ioptr = output data array */
long Flyinc;
long FlyOffsetA;
long FlyOffsetAIm;
long FlyOffsetB;
long FlyOffsetBIm;
long NsameU1;
long NsameU2;
long NsameU4;
long diffUcnt;
long LoopCnt;
float scale;
float fly0r;
float fly0i;
float fly1r;
float fly1i;
float fly2r;
float fly2i;
float fly3r;
float fly3i;
float fly4r;
float fly4i;
float fly5r;
float fly5i;
float fly6r;
float fly6i;
float fly7r;
float fly7i;
float U0r;
float U0i;
float U1r;
float U1i;
float U2r;
float U2i;
float U3r;
float U3i;
float t0r;
float t0i;
float t1r;
float t1i;
float *fly0P;
float *fly1P;
float *fly2P;
float *fly3P;
float *U0rP;
float *U0iP;
float *U1rP;
float *U1iP;
float *U2rP;
float *U2iP;
float *IOP;
long U3offset;
long stage;
long NdiffU;
long LoopN;
const long BRshift = MAXMROOT - (M>>1);
const long Nrems2 = Ntbl[M-(M>>1)+1];
const long Nroot_1_ColInc = (Ntbl[M-1]-Ntbl[M-(M>>1)])*2;
for (;Rows>0;Rows--){
FlyOffsetA = Ntbl[M] * 2/2;
FlyOffsetAIm = FlyOffsetA + 1;
FlyOffsetB = FlyOffsetA + 2;
FlyOffsetBIm = FlyOffsetB + 1;
/* BitrevR2 ** bit reverse and first radix 2 stage ******/
scale = 1./Ntbl[M];
for (stage = 0; stage < Ntbl[M-(M>>1)]*2; stage += Ntbl[M>>1]*2){
for (LoopN = (Ntbl[(M>>1)-1]-1); LoopN >= 0; LoopN--){
LoopCnt = (Ntbl[(M>>1)-1]-1);
fly0P = ioptr + Nroot_1_ColInc + ((int)BRcnt[LoopN] >> BRshift)*(2*2) + stage;
IOP = ioptr + (LoopN<<(M+1)/2) * 2 + stage;
fly1P = IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2);
fly0r = *(fly0P);
fly0i = *(fly0P+1);
fly1r = *(fly0P+FlyOffsetA);
fly1i = *(fly0P+FlyOffsetAIm);
for (; LoopCnt > LoopN;){
fly2r = *(fly0P+2);
fly2i = *(fly0P+(2+1));
fly3r = *(fly0P+FlyOffsetB);
fly3i = *(fly0P+FlyOffsetBIm);
fly4r = *(fly1P);
fly4i = *(fly1P+1);
fly5r = *(fly1P+FlyOffsetA);
fly5i = *(fly1P+FlyOffsetAIm);
fly6r = *(fly1P+2);
fly6i = *(fly1P+(2+1));
fly7r = *(fly1P+FlyOffsetB);
fly7i = *(fly1P+FlyOffsetBIm);
t0r = fly0r + fly1r;
t0i = fly0i + fly1i;
fly1r = fly0r - fly1r;
fly1i = fly0i - fly1i;
t1r = fly2r + fly3r;
t1i = fly2i + fly3i;
fly3r = fly2r - fly3r;
fly3i = fly2i - fly3i;
fly0r = fly4r + fly5r;
fly0i = fly4i + fly5i;
fly5r = fly4r - fly5r;
fly5i = fly4i - fly5i;
fly2r = fly6r + fly7r;
fly2i = fly6i + fly7i;
fly7r = fly6r - fly7r;
fly7i = fly6i - fly7i;
*(fly1P) = scale*t0r;
*(fly1P+1) = scale*t0i;
*(fly1P+2) = scale*fly1r;
*(fly1P+(2+1)) = scale*fly1i;
*(fly1P+FlyOffsetA) = scale*t1r;
*(fly1P+FlyOffsetAIm) = scale*t1i;
*(fly1P+FlyOffsetB) = scale*fly3r;
*(fly1P+FlyOffsetBIm) = scale*fly3i;
*(fly0P) = scale*fly0r;
*(fly0P+1) = scale*fly0i;
*(fly0P+2) = scale*fly5r;
*(fly0P+(2+1)) = scale*fly5i;
*(fly0P+FlyOffsetA) = scale*fly2r;
*(fly0P+FlyOffsetAIm) = scale*fly2i;
*(fly0P+FlyOffsetB) = scale*fly7r;
*(fly0P+FlyOffsetBIm) = scale*fly7i;
fly0P -= Nrems2;
fly0r = *(fly0P);
fly0i = *(fly0P+1);
fly1r = *(fly0P+FlyOffsetA);
fly1i = *(fly0P+FlyOffsetAIm);
LoopCnt -= 1;
fly1P = (IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2));
};
fly2r = *(fly0P+2);
fly2i = *(fly0P+(2+1));
fly3r = *(fly0P+FlyOffsetB);
fly3i = *(fly0P+FlyOffsetBIm);
t0r = fly0r + fly1r;
t0i = fly0i + fly1i;
fly1r = fly0r - fly1r;
fly1i = fly0i - fly1i;
t1r = fly2r + fly3r;
t1i = fly2i + fly3i;
fly3r = fly2r - fly3r;
fly3i = fly2i - fly3i;
*(fly0P) = scale*t0r;
*(fly0P+1) = scale*t0i;
*(fly0P+2) = scale*fly1r;
*(fly0P+(2+1)) = scale*fly1i;
*(fly0P+FlyOffsetA) = scale*t1r;
*(fly0P+FlyOffsetAIm) = scale*t1i;
*(fly0P+FlyOffsetB) = scale*fly3r;
*(fly0P+FlyOffsetBIm) = scale*fly3i;
};
};
/**** FFTC **************/