/*******************************************************************
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		3.141592653589793238462643383279502884197F	// pi
#define MYROOT2 	1.414213562373095048801688724209698078569F	// sqrt(2)
#define MYCOSPID8	0.9238795325112867561281831893967882868224F	// cos(pi/8)
#define MYSINPID8	0.3826834323650897717284599840303988667613F	// 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] = (float) 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] = (short) 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 = 1.0F/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;
long 	Uinc;
long 	Uinc2;
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;
long 	Uinc;
long 	Uinc2;
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 = 1.0F/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 = 1.0F/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 = 1.0F/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 = 1.0F/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 = 1.0F/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 = 1.0F/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);
	}
}
}

