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long dFFTInit(long *fftMptr, long fftN, double *Utbl);
/* Compute cosine table and check size for complex ffts */
/* INPUTS */
/* fftN = size of fft */
/* OUTPUTS */
/* *fftMptr = log2 of fft size */
/* *Utbl = cosine table with fftN/4 + 1 entries (angles = 0 to pi/2 inclusive) */
/* RETURNS */
/* 1 if fftN is invalid, 0 otherwise */
long drFFTInit(long *fftMptr, long fftN, double *Utbl);
/* Compute cosine table and check size for a real input fft */
/* INPUTS */
/* fftN = size of fft */
/* OUTPUTS */
/* *fftMptr = log2 of fft size */
/* *Utbl = cosine table with fftN/4 + 1 entries (angles = 0 to pi/2 inclusive) */
/* RETURNS */
/* 1 if fftN is invalid, 0 otherwise */
void dffts(double *ioptr, long M, long Rows, double *Utbl);
/* Compute in-place complex fft on the rows of the input array */
/* INPUTS */
/* M = log2 of fft size */
/* *ioptr = input data array */
/* *Utbl = cosine table */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* OUTPUTS */
/* *ioptr = output data array */
void diffts(double *ioptr, long M, long Rows, double *Utbl);
/* Compute in-place inverse complex fft on the rows of the input array */
/* INPUTS */
/* M = log2 of fft size */
/* *ioptr = input data array */
/* *Utbl = cosine table */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* OUTPUTS */
/* *ioptr = output data array */
void drffts(double *ioptr, long M, long Rows, double *Utbl);
/* Compute in-place real fft on the rows of the input array */
/* INPUTS */
/* M = log2 of fft size */
/* *ioptr = real input data array */
/* *Utbl = cosine table */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* OUTPUTS */
/* *ioptr = output data array 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 driffts(double *ioptr, long M, long Rows, double *Utbl);
/* Compute in-place real ifft on the rows of the input array */
/* INPUTS */
/* M = log2 of fft size */
/* *ioptr = input 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]). */
/* *Utbl = cosine table */
/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */
/* OUTPUTS */
/* *ioptr = real output data array */
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