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};
}
