public void Divide(GaloisPolynomial divider, out GaloisPolynomial quotient, out GaloisPolynomial remainder)
{
if (!m_Field.Equals(divider.m_Field))
{
throw new AzosException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Div(divider: different field)");
}
if (divider.IsPolynomial0)
{
throw new AzosException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Div(divider: div zero is undefined)");
}
quotient = m_Field.Polynomial0;
remainder = this;
int dividerLeadingCoefficient = divider.coefficientAt(divider.Degree);//divider.Coefficients.Last();
int inversedDividerLeadingCoefficient = m_Field.Inverse(dividerLeadingCoefficient);
while (remainder.Degree >= divider.Degree && !remainder.IsPolynomial0)
{
int deltaDegree = remainder.Degree - divider.Degree;
int scale = m_Field.Multiply(remainder.coefficientAt(remainder.Degree), inversedDividerLeadingCoefficient);
GaloisPolynomial term = divider.Multiply(deltaDegree, scale);
GaloisPolynomial iterationQuotient = m_Field.GenerateMonomial(deltaDegree, scale);
quotient = quotient.Add(iterationQuotient);
remainder = remainder.Add(term);
}
}
public GaloisPolynomial Multiply(GaloisPolynomial factorPolynomial)
{
if (!m_Field.Equals(factorPolynomial.m_Field))
{
throw new AzosException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Mult(factor: different field)");
}
if (IsPolynomial0 || factorPolynomial.IsPolynomial0)
{
return(m_Field.Polynomial0);
}
int[] multiplicand = m_Coefficients;
int[] factor = factorPolynomial.m_Coefficients;
int[] product = new int[m_Coefficients.Length + factorPolynomial.m_Coefficients.Length - 1];
for (int i = 0; i < multiplicand.Length; i++)
{
int multiplicandCoefficient = multiplicand[i];
for (int j = 0; j < factor.Length; j++)
{
product[i + j] = GaloisField.Add(product[i + j], m_Field.Multiply(multiplicandCoefficient, factor[j]));
}
}
return(new GaloisPolynomial(m_Field, product));
}
private GaloisPolynomial getPolySet(int degree)
{
if (degree >= m_PolySet.Count)
{
GaloisPolynomial lastPoly = m_PolySet.Last();
for (int i = m_PolySet.Count; i <= degree; i++)
{
GaloisPolynomial newPoly = lastPoly.Multiply(new GaloisPolynomial(m_Field, new int[] { 1, m_Field.Exp(i - 1 + m_Field.GeneratorBase) }));
m_PolySet.Add(newPoly);
lastPoly = newPoly;
}
}
return(m_PolySet[degree]);
}
public GaloisPolynomial Add(GaloisPolynomial summand)
{
if (!m_Field.Equals(summand.m_Field))
{
throw new AzosException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Add(summand: different field)");
}
if (IsPolynomial0)
{
return(summand);
}
if (summand.IsPolynomial0)
{
return(this);
}
int[] shorterPolynomialCoefficients;
int[] longerPolynomialCoefficients;
if (m_Coefficients.Length < summand.m_Coefficients.Length)
{
shorterPolynomialCoefficients = m_Coefficients;
longerPolynomialCoefficients = summand.m_Coefficients;
}
else
{
shorterPolynomialCoefficients = summand.m_Coefficients;
longerPolynomialCoefficients = m_Coefficients;
}
int[] resultCoefficients = new int[longerPolynomialCoefficients.Length];
int deltaLength = (int)(longerPolynomialCoefficients.Length - shorterPolynomialCoefficients.Length);
for (int i = 0; i < longerPolynomialCoefficients.Length; i++)
{
if (i < deltaLength)
{
resultCoefficients[i] = longerPolynomialCoefficients[i];
}
else
{
resultCoefficients[i] = GaloisField.Add(longerPolynomialCoefficients[i], shorterPolynomialCoefficients[i - deltaLength]);
}
}
return(new GaloisPolynomial(m_Field, resultCoefficients));
}
public void Encode(int[] src, int errorCorrectionLength)
{
if (errorCorrectionLength <= 0)
{
throw new AzosException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Encode(errorCorrectionLength)");
}
int dataLength = src.Length - errorCorrectionLength;
if (dataLength <= 0)
{
throw new AzosException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Encode: No data bytes provided");
}
GaloisPolynomial generationPoly = getPolySet(errorCorrectionLength);
int[] infoCoefficients = new int[dataLength];
Array.Copy(src, 0, infoCoefficients, 0, dataLength);
GaloisPolynomial infoPoly = new GaloisPolynomial(m_Field, infoCoefficients);
infoPoly = infoPoly.Multiply(errorCorrectionLength, 1);
GaloisPolynomial remainder, quotient;
infoPoly.Divide(generationPoly, out quotient, out remainder);
int[] coefficients = remainder.Coefficients;
int numZeroCoefficients = errorCorrectionLength - coefficients.Length;
for (var i = 0; i < numZeroCoefficients; i++)
{
src[dataLength + i] = 0;
}
Array.Copy(coefficients, 0, src, dataLength + numZeroCoefficients, coefficients.Length);
}
