/// <summary>
/// evaluation of this polynomial at a given point
/// </summary>
/// <param name="a">A.</param>
/// <returns>evaluation of this polynomial at a given point</returns>
internal int EvaluateAt(int a)
{
int result = 0;
if (a == 0)
{
// Just return the x^0 coefficient
return(GetCoefficient(0));
}
int size = coefficients.Length;
if (a == 1)
{
// Just the sum of the coefficients
foreach (var coefficient in coefficients)
{
result = GenericGF.AddOrSubtract(result, coefficient);
}
return(result);
}
result = coefficients[0];
for (int i = 1; i < size; i++)
{
result = GenericGF.AddOrSubtract(field.Multiply(a, result), coefficients[i]);
}
return(result);
}
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 });
}