ref: 0df3039072e1eb47d710348117063fa45cfaf2dd
dir: /lib/fft/fftlib.c/
/* Public domain FFT implementation in C by John Green */
#include <stdint.h>
#include <stdlib.h>
#include <math.h>
#include "base.h"
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
#define LOG2(n) (log(n) / log(2))
#define POW2(m) ((uint32_t) 1 << (m)) /* integer power of 2 for m<32 */
/* fft's with M bigger than this bust primary cache */
#undef MCACHE
#define MCACHE (11 - (sizeof(SPFLOAT) / 8))
/* 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 *
*****************************************************/
static void fftCosInit(int M, SPFLOAT *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 int fftN = POW2(M);
unsigned int i1;
Utbl[0] = 1.0;
for (i1 = 1; i1 < fftN/4; i1++)
Utbl[i1] = cos((2.0 * M_PI * (SPFLOAT)i1) / (SPFLOAT)fftN);
Utbl[fftN/4] = 0.0;
}
void fftBRInit(int M, int16_t *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 */
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 *
*****************/
static void bitrevR2(SPFLOAT *ioptr, int M, int16_t *BRLow)
{
/*** bit reverse and first radix 2 stage of forward or inverse fft ***/
SPFLOAT f0r;
SPFLOAT f0i;
SPFLOAT f1r;
SPFLOAT f1i;
SPFLOAT f2r;
SPFLOAT f2i;
SPFLOAT f3r;
SPFLOAT f3i;
SPFLOAT f4r;
SPFLOAT f4i;
SPFLOAT f5r;
SPFLOAT f5i;
SPFLOAT f6r;
SPFLOAT f6i;
SPFLOAT f7r;
SPFLOAT f7i;
SPFLOAT t0r;
SPFLOAT t0i;
SPFLOAT t1r;
SPFLOAT t1i;
SPFLOAT *p0r;
SPFLOAT *p1r;
SPFLOAT *IOP;
SPFLOAT *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 + 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;
}
}
}
static void fft2pt(SPFLOAT *ioptr)
{
/*** RADIX 2 fft ***/
SPFLOAT f0r, f0i, f1r, f1i;
SPFLOAT 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;
}
static void fft4pt(SPFLOAT *ioptr)
{
/*** RADIX 4 fft ***/
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT 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;
}
static void fft8pt(SPFLOAT *ioptr)
{
/*** RADIX 8 fft ***/
SPFLOAT w0r = (SPFLOAT)(1.0 / MYROOT2); /* cos(pi/4) */
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
SPFLOAT t0r, t0i, t1r, t1i;
const SPFLOAT 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;
}
static void bfR2(SPFLOAT *ioptr, int M, int NDiffU)
{
/*** 2nd radix 2 stage ***/
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int NSameU;
unsigned int SameUCnt;
SPFLOAT *pstrt;
SPFLOAT *p0r, *p1r, *p2r, *p3r;
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT 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;
}
}
static void bfR4(SPFLOAT *ioptr, int M, int NDiffU)
{
/*** 1 radix 4 stage ***/
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int pnexti;
unsigned int NSameU;
unsigned int SameUCnt;
SPFLOAT *pstrt;
SPFLOAT *p0r, *p1r, *p2r, *p3r;
SPFLOAT w1r = 1.0 / MYROOT2; /* cos(pi/4) */
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
SPFLOAT t1r, t1i;
const SPFLOAT 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;
}
static void bfstages(SPFLOAT *ioptr, int M, SPFLOAT *Utbl, int Ustride,
int NDiffU, int StageCnt)
{
/*** RADIX 8 Stages ***/
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;
SPFLOAT *pstrt;
SPFLOAT *p0r, *p1r, *p2r, *p3r;
SPFLOAT *u0r, *u0i, *u1r, *u1i, *u2r, *u2i;
SPFLOAT w0r, w0i, w1r, w1i, w2r, w2i, w3r, w3i;
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
SPFLOAT t0r, t0i, t1r, t1i;
const SPFLOAT 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 = &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 ((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;
}
}
static void fftrecurs(SPFLOAT *ioptr, int M, SPFLOAT *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 */
}
}
static void ffts1(SPFLOAT *ioptr, int M, SPFLOAT *Utbl, int16_t *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) */
/* *Utbl = cosine table */
/* *BRLow = bit reversed counter table */
/* OUTPUTS */
/* *ioptr = output data array */
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 *
******************/
static void scbitrevR2(SPFLOAT *ioptr, int M, int16_t *BRLow, SPFLOAT scale)
{
/*** scaled bit reverse and first radix 2 stage forward or inverse fft ***/
SPFLOAT f0r;
SPFLOAT f0i;
SPFLOAT f1r;
SPFLOAT f1i;
SPFLOAT f2r;
SPFLOAT f2i;
SPFLOAT f3r;
SPFLOAT f3i;
SPFLOAT f4r;
SPFLOAT f4i;
SPFLOAT f5r;
SPFLOAT f5i;
SPFLOAT f6r;
SPFLOAT f6i;
SPFLOAT f7r;
SPFLOAT f7i;
SPFLOAT t0r;
SPFLOAT t0i;
SPFLOAT t1r;
SPFLOAT t1i;
SPFLOAT *p0r;
SPFLOAT *p1r;
SPFLOAT *IOP;
SPFLOAT *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 + 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;
}
}
}
/* static void ifft2pt(SPFLOAT *ioptr, SPFLOAT scale) */
/* { */
/* /\*** RADIX 2 ifft ***\/ */
/* SPFLOAT f0r, f0i, f1r, f1i; */
/* SPFLOAT 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; */
/* } */
/* static void ifft4pt(SPFLOAT *ioptr, SPFLOAT scale) */
/* { */
/* /\*** RADIX 4 ifft ***\/ */
/* SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i; */
/* SPFLOAT 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; */
/* } */
/* static void ifft8pt(SPFLOAT *ioptr, SPFLOAT scale) */
/* { */
/* /\*** RADIX 8 ifft ***\/ */
/* SPFLOAT w0r = 1.0 / MYROOT2; /\* cos(pi/4) *\/ */
/* SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i; */
/* SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i; */
/* SPFLOAT t0r, t0i, t1r, t1i; */
/* const SPFLOAT 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; */
/* } */
static void ibfR2(SPFLOAT *ioptr, int M, int NDiffU)
{
/*** 2nd radix 2 stage ***/
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int NSameU;
unsigned int SameUCnt;
SPFLOAT *pstrt;
SPFLOAT *p0r, *p1r, *p2r, *p3r;
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT 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;
}
}
static void ibfR4(SPFLOAT *ioptr, int M, int NDiffU)
{
/*** 1 radix 4 stage ***/
unsigned int pos;
unsigned int posi;
unsigned int pinc;
unsigned int pnext;
unsigned int pnexti;
unsigned int NSameU;
unsigned int SameUCnt;
SPFLOAT *pstrt;
SPFLOAT *p0r, *p1r, *p2r, *p3r;
SPFLOAT w1r = 1.0 / MYROOT2; /* cos(pi/4) */
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
SPFLOAT t1r, t1i;
const SPFLOAT 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;
}
static void ibfstages(SPFLOAT *ioptr, int M, SPFLOAT *Utbl, int Ustride,
int NDiffU, int StageCnt)
{
/*** RADIX 8 Stages ***/
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;
SPFLOAT *pstrt;
SPFLOAT *p0r, *p1r, *p2r, *p3r;
SPFLOAT *u0r, *u0i, *u1r, *u1i, *u2r, *u2i;
SPFLOAT w0r, w0i, w1r, w1i, w2r, w2i, w3r, w3i;
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
SPFLOAT t0r, t0i, t1r, t1i;
const SPFLOAT 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 = &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 ((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;
}
}
static void ifftrecurs(SPFLOAT *ioptr, int M, SPFLOAT *Utbl, int Ustride,
int NDiffU, int StageCnt)
{
/* recursive bfstages calls to maximize on chip cache efficiency */
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 */
}
}
/* Paul: not currently used, so commented out */
/* static void iffts1(SPFLOAT *ioptr, int M, SPFLOAT *Utbl, int16_t *BRLow) */
/* { */
/* /\* 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 *\/ */
/* int StageCnt; */
/* int NDiffU; */
/* const SPFLOAT 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 *
******************/
static void rfft1pt(SPFLOAT *ioptr)
{
/*** RADIX 2 rfft ***/
SPFLOAT f0r, f0i;
SPFLOAT 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;
}
static void rfft2pt(SPFLOAT *ioptr)
{
/*** RADIX 4 rfft ***/
SPFLOAT f0r, f0i, f1r, f1i;
SPFLOAT 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;
}
static void rfft4pt(SPFLOAT *ioptr)
{
/*** RADIX 8 rfft ***/
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT t0r, t0i, t1r, t1i;
SPFLOAT w0r = 1.0 / MYROOT2; /* cos(pi/4) */
const SPFLOAT Two = 2.0;
const SPFLOAT 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;
}
static void rfft8pt(SPFLOAT *ioptr)
{
/*** RADIX 16 rfft ***/
SPFLOAT w0r = 1.0 / MYROOT2; /* cos(pi/4) */
SPFLOAT w1r = MYCOSPID8; /* cos(pi/8) */
SPFLOAT w1i = MYSINPID8; /* sin(pi/8) */
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
SPFLOAT t0r, t0i, t1r, t1i;
const SPFLOAT Two = 2.0;
const SPFLOAT 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;
}
static void frstage(SPFLOAT *ioptr, int M, SPFLOAT *Utbl)
{
/* Finish RFFT */
unsigned int pos;
unsigned int posi;
unsigned int diffUcnt;
SPFLOAT *p0r, *p1r;
SPFLOAT *u0r, *u0i;
SPFLOAT w0r, w0i;
SPFLOAT f0r, f0i, f1r, f1i, f4r, f4i, f5r, f5i;
SPFLOAT t0r, t0i, t1r, t1i;
const SPFLOAT 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;
}
}
static void rffts1(SPFLOAT *ioptr, int M, SPFLOAT *Utbl, int16_t *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 */
/* *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]). */
SPFLOAT 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 *
*******************/
static void rifft1pt(SPFLOAT *ioptr, SPFLOAT scale)
{
/*** RADIX 2 rifft ***/
SPFLOAT f0r, f0i;
SPFLOAT 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;
}
static void rifft2pt(SPFLOAT *ioptr, SPFLOAT scale)
{
/*** RADIX 4 rifft ***/
SPFLOAT f0r, f0i, f1r, f1i;
SPFLOAT t0r, t0i;
const SPFLOAT 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;
}
static void rifft4pt(SPFLOAT *ioptr, SPFLOAT scale)
{
/*** RADIX 8 rifft ***/
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT t0r, t0i, t1r, t1i;
SPFLOAT w0r = 1.0 / MYROOT2; /* cos(pi/4) */
const SPFLOAT 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;
}
static void rifft8pt(SPFLOAT *ioptr, SPFLOAT scale)
{
/*** RADIX 16 rifft ***/
SPFLOAT w0r = (SPFLOAT) (1.0 / MYROOT2); /* cos(pi/4) */
SPFLOAT w1r = MYCOSPID8; /* cos(pi/8) */
SPFLOAT w1i = MYSINPID8; /* sin(pi/8) */
SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i;
SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i;
SPFLOAT t0r, t0i, t1r, t1i;
const SPFLOAT 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;
}
static void ifrstage(SPFLOAT *ioptr, int M, SPFLOAT *Utbl)
{
/* Start RIFFT */
unsigned int pos;
unsigned int posi;
unsigned int diffUcnt;
SPFLOAT *p0r, *p1r;
SPFLOAT *u0r, *u0i;
SPFLOAT w0r, w0i;
SPFLOAT f0r, f0i, f1r, f1i, f4r, f4i, f5r, f5i;
SPFLOAT t0r, t0i, t1r, t1i;
const SPFLOAT 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;
}
}
static void riffts1(SPFLOAT *ioptr, int M, SPFLOAT *Utbl, int16_t *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]). */
/* *Utbl = cosine table */
/* *BRLow = bit reversed counter table */
/* OUTPUTS */
/* *ioptr = real output data array */
SPFLOAT scale;
int StageCnt;
int NDiffU;
scale = (SPFLOAT)(1.0 / (double)((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 */
}
}