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/* Fast Fourier Transformation (FFT)
 *
 * (C) 2016 by Andreas Eversberg <jolly@eversberg.eu>
 * All Rights Reserved
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

#include <math.h>
#include <string.h>
#include "fft.h"

/*
 * Code based closely to work by Paul Bourke
 *
 * This computes an in-place complex-to-complex FFT 
 * x and y are the real and imaginary arrays of 2^m points.
 * dir =  1 gives forward transform
 * dir = -1 gives reverse transform 
 */
void fft_process(int dir, int m, double *x, double *y)
{
	int	n, i, i1, j, k, i2, l, l1, l2;
	double	c1, c2, tx, ty, t1, t2, u1, u2, z;

	/* Calculate the number of points */
	n = 1 << m;

	/* Do the bit reversal */
	i2 = n >> 1;
	j = 0;
	for (i = 0; i < n - 1; i++) {
		if (i < j) {
			tx = x[i];
			ty = y[i];
			x[i] = x[j];
			y[i] = y[j];
			x[j] = tx;
			y[j] = ty;
		}
		k = i2;
		while (k <= j) {
			j -= k;
			k >>= 1;
		}
		j += k;
	}

	/* Compute the FFT */
	c1 = -1.0; 
	c2 = 0.0;
	l2 = 1;
	for (l = 0; l < m; l++) {
		l1 = l2;
		l2 <<= 1;
		u1 = 1.0; 
		u2 = 0.0;
		for (j = 0; j < l1; j++) {
			for (i = j; i < n; i += l2) {
				i1 = i + l1;
				t1 = u1 * x[i1] - u2 * y[i1];
				t2 = u1 * y[i1] + u2 * x[i1];
				x[i1] = x[i] - t1; 
				y[i1] = y[i] - t2;
				x[i] += t1;
				y[i] += t2;
			}
			z =  u1 * c1 - u2 * c2;
			u2 = u1 * c2 + u2 * c1;
			u1 = z;
		}
		c2 = sqrt((1.0 - c1) / 2.0);
		if (dir == 1) 
			c2 = -c2;
		c1 = sqrt((1.0 + c1) / 2.0);
	}

	/* Scaling for forward transform */
	if (dir == 1) {
		for (i = 0; i < n; i++) {
			x[i] /= n;
			y[i] /= n;
		}
	}
}