boofcv.alg.fiducial.qrcode.GaliosFieldTableOps Maven / Gradle / Ivy

/*
 * Copyright (c) 2022, Peter Abeles. All Rights Reserved.
 *
 * This file is part of BoofCV (http://boofcv.org).
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package boofcv.alg.fiducial.qrcode;

/**
 * Precomputed look up table for performing operations on GF polynomials of the specified degree.
 *
 * Code and code comments based on the tutorial at [1].
 *
 * [1] Reed-Solomon Codes for Coders
 * Viewed on September 28, 2017
 *
 * @author Peter Abeles
 */
public class GaliosFieldTableOps {
	protected int max_value; // maximum possible
	protected int num_values; // number of values in the field
	protected int numBits;
	protected int primitive;

	protected int[] exp;
	protected int[] log;

	/**
	 * Specifies the GF polynomial
	 *
	 * @param numBits Number of bits needed to describe the polynomial. GF(2**8) = 8 bits
	 * @param primitive The primitive polynomial
	 */
	public GaliosFieldTableOps( int numBits, int primitive ) {
		if (numBits < 1 || numBits > 16)
			throw new IllegalArgumentException("Degree must be more than 1 and less than or equal to 16");

		this.numBits = numBits;
		this.primitive = primitive;
		max_value = 0;
		for (int i = 0; i < numBits; i++) {
			max_value |= 1 << i;
		}
		num_values = max_value + 1;

		log = new int[num_values];
		exp = new int[num_values*2]; // make it twice as long to avoid a modulus operation

		// exhaustively compute all values
		int x = 1;
		for (int i = 0; i < max_value; i++) {
			exp[i] = x;
			log[x] = i;
			x = GaliosFieldOps.multiply(x, 2, primitive, num_values);
		}

		for (int i = 0; i < num_values; i++) {
			exp[i + max_value] = exp[i];
		}
	}

	/**
	 * Computes the following (x*y) mod primitive. This is done by
	 */
	public int multiply( int x, int y ) {
		if (x == 0 || y == 0)
			return 0;
		return exp[log[x] + log[y]];
	}

	/**
	 * Computes the following the value of output such that:

	 * divide(multiply(x,y),y)==x for any x and any nonzero y.
	 */
	public int divide( int x, int y ) {
		if (y == 0)
			throw new ArithmeticException("Divide by zero");
		if (x == 0)
			return 0;

		return exp[log[x] + max_value - log[y]];
	}

	/**
	 * Computes the following x**power mod primitive
	 */
	public int power( int x, int power ) {
		return exp[(log[x]*power)%max_value];
	}

	public int power_n( int x, int power ) {
		int a = (log[x]*power)%max_value;
		if (a < 0)
			a = max_value*2 + a;
		return exp[a];
	}

	/**
	 * Computes the following 2**(max-x) mod primitive
	 */
	public int inverse( int x ) {
		return exp[max_value - log[x]];
	}
}