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 }); }
private int[] findErrorLocations(GF256Poly errorLocator) { // This is a direct application of Chien's search int numErrors = errorLocator.getDegree(); if (numErrors == 1) // shortcut { return(new int[] { errorLocator.getCoefficient(1) }); } int[] result = new int[numErrors]; int e = 0; for (int i = 1; i < 256 && e < numErrors; i++) { if (errorLocator.evaluateAt(i) == 0) { result[e] = field.inverse(i); e++; } } if (e != numErrors) { throw new ReedSolomonException("Error locator degree does not match number of roots"); } return(result); }
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}; }
private int[] findErrorLocations(GF256Poly errorLocator){ // This is a direct application of Chien's search int numErrors = errorLocator.getDegree(); if (numErrors == 1) { // shortcut return new int[] { errorLocator.getCoefficient(1) }; } int[] result = new int[numErrors]; int e = 0; for (int i = 1; i < 256 && e < numErrors; i++) { if (errorLocator.evaluateAt(i) == 0) { result[e] = field.inverse(i); e++; } } if (e != numErrors) { throw new ReedSolomonException("Error locator degree does not match number of roots"); } return result; }
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 }; }
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 }); }