internal GenericGFPoly[] Divide(GenericGFPoly other)
{
if (field.Equals(other.field) == false)
{
throw new ArgumentException("GenericGFPolys do not have same GenericGF field");
}
if (other.IsZero)
{
throw new ArgumentException("Divide by 0");
}
GenericGFPoly quotient = field.Zero;
GenericGFPoly remainder = this;
int denominatorLeadingTerm = other.GetCoefficient(other.Degree);
int inverseDenominatorLeadingTerm = field.Inverse(denominatorLeadingTerm);
while (remainder.Degree >= other.Degree && !remainder.IsZero)
{
int degreeDifference = remainder.Degree - other.Degree;
int scale = field.Multiply(remainder.GetCoefficient(remainder.Degree), inverseDenominatorLeadingTerm);
GenericGFPoly term = other.MultiplyByMonomial(degreeDifference, scale);
GenericGFPoly iterationQuotient = field.BuildMonomial(degreeDifference, scale);
quotient = quotient.AddOrSubtract(iterationQuotient);
remainder = remainder.AddOrSubtract(term);
}
return(new GenericGFPoly[] { quotient, remainder });
}
internal GenericGFPoly[] RunEuclideanAlgorithm(GenericGFPoly a, GenericGFPoly b, int R)
{
// Assume a's degree is >= b's
if (a.Degree < b.Degree)
{
GenericGFPoly temp = a;
a = b;
b = temp;
}
GenericGFPoly rLast = a;
GenericGFPoly r = b;
GenericGFPoly tLast = field.Zero;
GenericGFPoly t = field.One;
int halfR = R / 2;
// Run Euclidean algorithm until r's degree is less than R/2
while (r.Degree >= halfR)
{
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");
return(null);
}
r = rLastLast;
GenericGFPoly q = field.Zero;
int denominatorLeadingTerm = rLast.GetCoefficient(rLast.Degree);
int dltInverse = field.Inverse(denominatorLeadingTerm);
while (r.Degree >= rLast.Degree && !r.IsZero)
{
int degreeDiff = r.Degree - rLast.Degree;
int scale = field.Multiply(r.GetCoefficient(r.Degree), dltInverse);
q = q.AddOrSubtract(field.BuildMonomial(degreeDiff, scale));
r = r.AddOrSubtract(rLast.MultiplyByMonomial(degreeDiff, scale));
}
t = q.Multiply(tLast).AddOrSubtract(tLastLast);
if (r.Degree >= rLast.Degree)
{
// throw new IllegalStateException("Division algorithm failed to reduce polynomial?");
return(null);
}
}
int sigmaTildeAtZero = t.GetCoefficient(0);
if (sigmaTildeAtZero == 0)
{
// throw new ReedSolomonException("sigmaTilde(0) was zero");
return(null);
}
int inverse = field.Inverse(sigmaTildeAtZero);
GenericGFPoly sigma = t.Multiply(inverse);
GenericGFPoly omega = r.Multiply(inverse);
return(new GenericGFPoly[] { sigma, omega });
}