private GenericGFPoly[] runEuclideanAlgorithm(GenericGFPoly a, GenericGFPoly b, int R) throws ReedSolomonException { // Assume a's degree is >= b's if (a.getDegree() < b.getDegree()) { GenericGFPoly temp = a; a = b; b = temp; } GenericGFPoly rLast = a; GenericGFPoly r = b; GenericGFPoly tLast = field.getZero(); GenericGFPoly t = field.getOne(); // Run Euclidean algorithm until r's degree is less than R/2 while (r.getDegree() >= R / 2) { GenericGFPoly rLastLast = rLast; GenericGFPoly tLastLast = tLast; rLast = r; 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; GenericGFPoly 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)); } t = q.multiply(tLast).addOrSubtract(tLastLast); if (r.getDegree() >= rLast.getDegree()) { throw new IllegalStateException("Division algorithm failed to reduce polynomial?"); } } int sigmaTildeAtZero = t.getCoefficient(0); if (sigmaTildeAtZero == 0) { throw new ReedSolomonException("sigmaTilde(0) was zero"); } int inverse = field.inverse(sigmaTildeAtZero); GenericGFPoly sigma = t.multiply(inverse); GenericGFPoly omega = r.multiply(inverse); return new GenericGFPoly[] {sigma, omega}; }