public void Divide()
{
//System.Diagnostics.Debugger.Launch();
GaloisField field = new GaloisField(285, 256, 0);
GaloisPolynomial divident = new GaloisPolynomial(field, new int[] {32, 49, 205, 69, 42, 20, 0, 236, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0});
GaloisPolynomial divider = new GaloisPolynomial(field, new int[] {1, 119, 66, 83, 120, 119, 22, 197, 83, 249, 41, 143, 134, 85, 53, 125, 99, 79});
GaloisPolynomial quotient, remainder;
divident.Divide(divider, out quotient, out remainder);
int[] expectedQuotientCoefficients = new int[] { 32, 119, 212, 254, 109, 212, 30, 95, 117};
int[] expectedRemainderCoefficients = new int[] { 3, 130, 179, 194, 0, 55, 211, 110, 79, 98, 72, 170, 96, 211, 137, 213};
Assert.AreEqual(expectedQuotientCoefficients.Length, quotient.Coefficients.Length);
Assert.AreEqual(expectedRemainderCoefficients.Length, remainder.Coefficients.Length);
for (int i = 0; i < quotient.Coefficients.Length; i++)
Assert.AreEqual(expectedQuotientCoefficients[i], quotient.Coefficients[i]);
for (int i = 0; i < remainder.Coefficients.Length; i++)
Assert.AreEqual(expectedRemainderCoefficients[i], remainder.Coefficients[i]);
}
public GaloisPolynomial Multiply(GaloisPolynomial factorPolynomial)
{
if (!m_Field.Equals(factorPolynomial.m_Field))
{
throw new NFXException(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));
}
public void Divide(GaloisPolynomial divider, out GaloisPolynomial quotient, out GaloisPolynomial remainder)
{
if (!m_Field.Equals(divider.m_Field))
{
throw new NFXException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Div(divider: different field)");
}
if (divider.IsPolynomial0)
{
throw new NFXException(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);
}
}
private void initialize()
{
m_ExpTable = new int[m_Size];
m_LogTable = new int[m_Size];
int x = 1;
for (int i = 0; i < m_Size; i++)
{
m_ExpTable[i] = x;
x <<= 1;
if (x >= m_Size)
{
x ^= m_Primitive;
x &= m_Size - 1;
}
}
for (int i = 0; i < m_Size - 1; i++)
{
m_LogTable[m_ExpTable[i]] = i;
}
m_Polynomial0 = new GaloisPolynomial(this, new int[] { 0 });
m_Polynomial1 = new GaloisPolynomial(this, new int[] { 1 });
m_Initialized = true;
}
public void Encode(int[] src, int errorCorrectionLength)
{
if (errorCorrectionLength <= 0)
throw new NFXException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Encode(errorCorrectionLength)");
int dataLength = src.Length - errorCorrectionLength;
if (dataLength <= 0)
throw new NFXException(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);
}
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 NFXException(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 GaloisPolynomial GenerateMonomial(int degree, int coefficient)
{
ensureInitialized();
if (coefficient == 0)
{
return(m_Polynomial0);
}
int[] coefficients = new int[degree + 1];
coefficients[0] = coefficient;
GaloisPolynomial polynomial = new GaloisPolynomial(this, coefficients);
return(polynomial);
}
public void Encode(int[] src, int errorCorrectionLength)
{
if (errorCorrectionLength <= 0)
{
throw new NFXException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Encode(errorCorrectionLength)");
}
int dataLength = src.Length - errorCorrectionLength;
if (dataLength <= 0)
{
throw new NFXException(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);
}
private void initialize()
{
m_ExpTable = new int[m_Size];
m_LogTable = new int[m_Size];
int x = 1;
for (int i = 0; i < m_Size; i++)
{
m_ExpTable[i] = x;
x <<= 1;
if (x >= m_Size)
{
x ^= m_Primitive;
x &= m_Size - 1;
}
}
for (int i = 0; i < m_Size-1; i++)
{
m_LogTable[m_ExpTable[i]] = i;
}
m_Polynomial0 = new GaloisPolynomial(this, new int[] { 0 });
m_Polynomial1 = new GaloisPolynomial(this, new int[] { 1 });
m_Initialized = true;
}
public GaloisPolynomial GenerateMonomial( int degree, int coefficient)
{
ensureInitialized();
if (coefficient == 0)
return m_Polynomial0;
int[] coefficients = new int[degree + 1];
coefficients[0] = coefficient;
GaloisPolynomial polynomial = new GaloisPolynomial(this, coefficients);
return polynomial;
}
public GaloisPolynomial Add(GaloisPolynomial summand)
{
if (!m_Field.Equals(summand.m_Field))
throw new NFXException(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 GaloisPolynomial Multiply(GaloisPolynomial factorPolynomial)
{
if (!m_Field.Equals(factorPolynomial.m_Field))
throw new NFXException(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);
}
public void Divide(GaloisPolynomial divider, out GaloisPolynomial quotient, out GaloisPolynomial remainder)
{
if (!m_Field.Equals(divider.m_Field))
throw new NFXException(StringConsts.ARGUMENT_ERROR + GetType().Name + ".Div(divider: different field)");
if (divider.IsPolynomial0)
throw new NFXException(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);
}
}