Bit reversed order rearrangement of array in O(n) time.

bit_reversed_order.c

/*
For Fast Fourier Transformations an important step is the rearrangement of the
data in a bit reversed order.

The implemention below shows how to do this inplace or as copy in O(n) runtime.
*/

/*
The MIT License (MIT)

Copyright (c) 2015, Heinrich Schuchardt <xypron.glpk@gmx.de>

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/


#include <malloc.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/**
 * Rearranges array in bit reversed order.
 *
 * @param a data
 * @param n number of elements, must be power of two
 *
 * Runtime is O(n).
 */
void bro(int *a, int n)
{
	int i;
	int lowbit;
	int carry;
	int counter = 0;
	int buf;

	lowbit = n >> 1;

	for (i = 1; i < n; i++) {
		/*
		 * Increment bit reversed counter.
		 */
		carry = lowbit;
		while(counter & carry) {
			counter ^= carry;
			carry >>= 1;
		}
		counter ^= carry;

		if (counter > i) {
			/*
			 * Swap
			 */
			buf        = a[i];
			a[i]       = a[counter];
			a[counter] = buf;
		}
	}
}

/**
 * Copy array in bit reversed order.
 *
 * @param a input
 * @param b output
 * @param n number of elements, must be power of two
 *
 * Runtime is O(n).
 */
void brocopy(int *a, int *b, int n)
{
	int i;
	int lowbit;
	int carry;
	int counter = 0;

	lowbit = n >> 1;

	b[0] = a[0];
	for (i = 1; i < n; i++) {
		/*
		 * Increment bit reversed counter.
		 */
		carry = lowbit;
		while(counter & carry) {
			counter ^= carry;
			carry >>= 1;
		}
		counter ^= carry;

		/*
		 * Copy.
		 */
		b[counter] = a[i];
		b[i] = a[counter];
	}
}

/**
 * Rearranges array in bit reversed order using merge sort.
 *
 * @param a data
 * @param b work area
 * @param n number of elements, must be power of two
 *
 * Runtime is O(n log(n)).
 * The algorithm is optimized to profit from caching,
 * furthermore it can easily be parallelized.
 */
void bromerge(int *a, int *b, int n)
{
	int o, m, i;
	int n2 = n >> 1;
	int *c[3];
	int *p1, *p2, *p3;

	c[0] = b;
	c[1] = a;

	for(o = 1; o < n2; o <<= 1) {
		c[2] = c[1];
		c[1] = c[0];
		c[0] = c[2];
		p1 = c[0];
		p2 = c[1];
		p3 = p1 + n2;
		for(m = 0; m < n; m += (o << 1)) {
			memcpy(p2, p1, o * sizeof(int));
			p2 += o;
			p1 += o;
			memcpy(p2, p3, o * sizeof(int));
			p2 += o;
			p3 += o;
		}
	}
	if (c[0] == a)
		memcpy(a, b, n * sizeof(int));
}

/**
 * Prints array.
 *
 * @param a array
 * @param n number of elements
 */
static void print(int *a, int n)
{
	int m = -1;
	int i, j;
	int mask = 1;
	int b;

	for (i = n; i != 0; i >>= 1)
		++m;

	for (i = 1; i < m; ++i)
		mask <<= 1;


	for (i = 0; i < n; ++i) {
		printf("%08x ", i);
		b = a[i];
		for (j = 0; j < m; ++j) {
			printf("%1x", (b & mask) ? 1 : 0);
			b <<= 1;
		}
		printf("\n");
	}
	printf("\n");

}

/**
 * Fills an array with numbers 0..n-1.
 * Then the array is rearranged in bit reversed order.
 * The array is output before and after the rearrangement.
 */
int main(int argc, char *argv[])
{

	int m = 6;
	int n = 1 << m;
	int i;

	int *a = malloc(n * sizeof(int));
	int *b = malloc(n * sizeof(int));

	for (i = 0; i < n; ++i) {
		a[i] = i;
	}

	print(a, n);

	bromerge(a, b, n);

	print(a, n);
	free(a);
	free(b);

	return EXIT_SUCCESS;
}