/* * Copyright 2007 ZXing authors * * 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. */ using System; namespace com.google.zxing.common.reedsolomon { ///

Represents a polynomial whose coefficients are elements of GF(256). /// Instances of this class are immutable.

/// ///

Much credit is due to William Rucklidge since portions of this code are an indirect /// port of his C++ Reed-Solomon implementation.

/// ///
/// Sean Owen /// /// www.Redivivus.in (suraj.supekar@redivivus.in) - Ported from ZXING Java Source /// sealed class GF256Poly { internal int[] Coefficients { get { return coefficients; } } /// degree of this polynomial /// internal int Degree { get { return coefficients.Length - 1; } } /// true iff this polynomial is the monomial "0" /// internal bool Zero { get { return coefficients[0] == 0; } } //UPGRADE_NOTE: Final was removed from the declaration of 'field '. "ms-help://MS.VSCC.v80/dv_commoner/local/redirect.htm?index='!DefaultContextWindowIndex'&keyword='jlca1003'" private GF256 field; //UPGRADE_NOTE: Final was removed from the declaration of 'coefficients '. "ms-help://MS.VSCC.v80/dv_commoner/local/redirect.htm?index='!DefaultContextWindowIndex'&keyword='jlca1003'" private int[] coefficients; /// the {@link GF256} instance representing the field to use /// to perform computations /// /// coefficients as ints representing elements of GF(256), arranged /// from most significant (highest-power term) coefficient to least significant /// /// IllegalArgumentException if argument is null or empty, /// or if leading coefficient is 0 and this is not a /// constant polynomial (that is, it is not the monomial "0") /// internal GF256Poly(GF256 field, int[] coefficients) { if (coefficients == null || coefficients.Length == 0) { throw new System.ArgumentException(); } this.field = field; int coefficientsLength = coefficients.Length; if (coefficientsLength > 1 && coefficients[0] == 0) { // Leading term must be non-zero for anything except the constant polynomial "0" int firstNonZero = 1; while (firstNonZero < coefficientsLength && coefficients[firstNonZero] == 0) { firstNonZero++; } if (firstNonZero == coefficientsLength) { this.coefficients = field.Zero.coefficients; } else { this.coefficients = new int[coefficientsLength - firstNonZero]; Array.Copy(coefficients, firstNonZero, this.coefficients, 0, this.coefficients.Length); } } else { this.coefficients = coefficients; } } /// coefficient of x^degree term in this polynomial /// internal int getCoefficient(int degree) { return coefficients[coefficients.Length - 1 - degree]; } /// evaluation of this polynomial at a given point /// internal int evaluateAt(int a) { if (a == 0) { // Just return the x^0 coefficient return getCoefficient(0); } int size = coefficients.Length; if (a == 1) { // Just the sum of the coefficients int result = 0; for (int i = 0; i < size; i++) { result = GF256.addOrSubtract(result, coefficients[i]); } return result; } int result2 = coefficients[0]; for (int i = 1; i < size; i++) { result2 = GF256.addOrSubtract(field.multiply(a, result2), coefficients[i]); } return result2; } internal GF256Poly addOrSubtract(GF256Poly other) { if (!field.Equals(other.field)) { throw new System.ArgumentException("GF256Polys do not have same GF256 field"); } if (Zero) { return other; } if (other.Zero) { return this; } int[] smallerCoefficients = this.coefficients; int[] largerCoefficients = other.coefficients; if (smallerCoefficients.Length > largerCoefficients.Length) { int[] temp = smallerCoefficients; smallerCoefficients = largerCoefficients; largerCoefficients = temp; } int[] sumDiff = new int[largerCoefficients.Length]; int lengthDiff = largerCoefficients.Length - smallerCoefficients.Length; // Copy high-order terms only found in higher-degree polynomial's coefficients Array.Copy(largerCoefficients, 0, sumDiff, 0, lengthDiff); for (int i = lengthDiff; i < largerCoefficients.Length; i++) { sumDiff[i] = GF256.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]); } return new GF256Poly(field, sumDiff); } internal GF256Poly multiply(GF256Poly other) { if (!field.Equals(other.field)) { throw new System.ArgumentException("GF256Polys do not have same GF256 field"); } if (Zero || other.Zero) { return field.Zero; } int[] aCoefficients = this.coefficients; int aLength = aCoefficients.Length; int[] bCoefficients = other.coefficients; int bLength = bCoefficients.Length; int[] product = new int[aLength + bLength - 1]; for (int i = 0; i < aLength; i++) { int aCoeff = aCoefficients[i]; for (int j = 0; j < bLength; j++) { product[i + j] = GF256.addOrSubtract(product[i + j], field.multiply(aCoeff, bCoefficients[j])); } } return new GF256Poly(field, product); } internal GF256Poly multiply(int scalar) { if (scalar == 0) { return field.Zero; } if (scalar == 1) { return this; } int size = coefficients.Length; int[] product = new int[size]; for (int i = 0; i < size; i++) { product[i] = field.multiply(coefficients[i], scalar); } return new GF256Poly(field, product); } internal GF256Poly multiplyByMonomial(int degree, int coefficient) { if (degree < 0) { throw new System.ArgumentException(); } if (coefficient == 0) { return field.Zero; } int size = coefficients.Length; int[] product = new int[size + degree]; for (int i = 0; i < size; i++) { product[i] = field.multiply(coefficients[i], coefficient); } return new GF256Poly(field, product); } internal GF256Poly[] divide(GF256Poly other) { if (!field.Equals(other.field)) { throw new System.ArgumentException("GF256Polys do not have same GF256 field"); } if (other.Zero) { throw new System.ArgumentException("Divide by 0"); } GF256Poly quotient = field.Zero; GF256Poly remainder = this; int denominatorLeadingTerm = other.getCoefficient(other.Degree); int inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm); while (remainder.Degree >= other.Degree && !remainder.Zero) { int degreeDifference = remainder.Degree - other.Degree; int scale = field.multiply(remainder.getCoefficient(remainder.Degree), inverseDenominatorLeadingTerm); GF256Poly term = other.multiplyByMonomial(degreeDifference, scale); GF256Poly iterationQuotient = field.buildMonomial(degreeDifference, scale); quotient = quotient.addOrSubtract(iterationQuotient); remainder = remainder.addOrSubtract(term); } return new GF256Poly[]{quotient, remainder}; } public override System.String ToString() { System.Text.StringBuilder result = new System.Text.StringBuilder(8 * Degree); for (int degree = Degree; degree >= 0; degree--) { int coefficient = getCoefficient(degree); if (coefficient != 0) { if (coefficient < 0) { result.Append(" - "); coefficient = - coefficient; } else { if (result.Length > 0) { result.Append(" + "); } } if (degree == 0 || coefficient != 1) { int alphaPower = field.log(coefficient); if (alphaPower == 0) { result.Append('1'); } else if (alphaPower == 1) { result.Append('a'); } else { result.Append("a^"); result.Append(alphaPower); } } if (degree != 0) { if (degree == 1) { result.Append('x'); } else { result.Append("x^"); result.Append(degree); } } } } return result.ToString(); } } }