public GF256Poly multiply(GF256Poly other) { if (!field.Equals(other.field)) { throw new ArgumentException("GF256Polys do not have same GF256 field"); } if (isZero() || other.isZero()) { return(field.getZero()); } 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)); }
public GF256Poly[] divide(GF256Poly other) { if (!field.Equals(other.field)) { throw new ArgumentException("GF256Polys do not have same GF256 field"); } if (other.isZero()) { throw new ArgumentException("Divide by 0"); } GF256Poly quotient = field.getZero(); GF256Poly remainder = this; int denominatorLeadingTerm = other.getCoefficient(other.getDegree()); int inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm); while (remainder.getDegree() >= other.getDegree() && !remainder.isZero()) { int degreeDifference = remainder.getDegree() - other.getDegree(); int scale = field.multiply(remainder.getCoefficient(remainder.getDegree()), 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 GF256Poly addOrSubtract(GF256Poly other) { if (!field.Equals(other.field)) { throw new ArgumentException("GF256Polys do not have same GF256 field"); } if (isZero()) { return(other); } if (other.isZero()) { 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 System.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)); }
public GF256Poly[] divide(GF256Poly other) { if (!field.Equals(other.field)) { throw new ArgumentException("GF256Polys do not have same GF256 field"); } if (other.isZero()) { throw new ArgumentException("Divide by 0"); } GF256Poly quotient = field.getZero(); GF256Poly remainder = this; int denominatorLeadingTerm = other.getCoefficient(other.getDegree()); int inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm); while (remainder.getDegree() >= other.getDegree() && !remainder.isZero()) { int degreeDifference = remainder.getDegree() - other.getDegree(); int scale = field.multiply(remainder.getCoefficient(remainder.getDegree()), 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 GF256Poly multiply(GF256Poly other) { if (!field.Equals(other.field)) { throw new ArgumentException("GF256Polys do not have same GF256 field"); } if (isZero() || other.isZero()) { return field.getZero(); } 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); }
public GF256Poly addOrSubtract(GF256Poly other) { if (!field.Equals(other.field)) { throw new ArgumentException("GF256Polys do not have same GF256 field"); } if (isZero()) { return other; } if (other.isZero()) { 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 System.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); }
private GF256Poly[] runEuclideanAlgorithm(GF256Poly a, GF256Poly b, int R) { // Assume a's degree is >= b's if (a.getDegree() < b.getDegree()) { GF256Poly temp = a; a = b; b = temp; } GF256Poly rLast = a; GF256Poly r = b; GF256Poly sLast = field.getOne(); GF256Poly s = field.getZero(); GF256Poly tLast = field.getZero(); GF256Poly t = field.getOne(); // Run Euclidean algorithm until r's degree is less than R/2 while (r.getDegree() >= R / 2) { GF256Poly rLastLast = rLast; GF256Poly sLastLast = sLast; GF256Poly tLastLast = tLast; rLast = r; sLast = s; tLast = t; // Divide rLastLast by rLast, with quotient in q and remainder in r if (rLast.isZero()) { // Oops, Euclidean algorithm already terminated? throw new ReedSolomonException("r_{i-1} was zero"); } r = rLastLast; GF256Poly q = field.getZero(); int denominatorLeadingTerm = rLast.getCoefficient(rLast.getDegree()); int dltInverse = field.inverse(denominatorLeadingTerm); while (r.getDegree() >= rLast.getDegree() && !r.isZero()) { int degreeDiff = r.getDegree() - rLast.getDegree(); int scale = field.multiply(r.getCoefficient(r.getDegree()), dltInverse); q = q.addOrSubtract(field.buildMonomial(degreeDiff, scale)); r = r.addOrSubtract(rLast.multiplyByMonomial(degreeDiff, scale)); } s = q.multiply(sLast).addOrSubtract(sLastLast); t = q.multiply(tLast).addOrSubtract(tLastLast); } int sigmaTildeAtZero = t.getCoefficient(0); if (sigmaTildeAtZero == 0) { throw new ReedSolomonException("sigmaTilde(0) was zero"); } int inverse = field.inverse(sigmaTildeAtZero); GF256Poly sigma = t.multiply(inverse); GF256Poly omega = r.multiply(inverse); return(new GF256Poly[] { sigma, omega }); }