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#define MYRECIPLN2 1.442695040888963407359924681001892137426 // 1.0/log(2)
/* some useful conversions between a number and its power of 2 */
#define LOG2(a) (MYRECIPLN2*log(a)) // floating point logarithm base 2
#define POW2(m) ((unsigned long) 1 << (m)) // integer power of 2 for m<32
/*******************************************************************
lower level fft stuff called by routines in fftext.c and fft2d.c
*******************************************************************/
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 */
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 */
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 */
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 */
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]). */
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 */
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