internal GF256Poly Multiply(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GF256Polys do not have same GF256 field");
}
if (IsZero() || other.IsZero())
{
return(field.GetZero());
}
int[] aCoefficients = this.coefficients;
int aLength = aCoefficients.Length;
int[] bCoefficients = other.coefficients;
int bLength = bCoefficients.Length;
int[] product = new int[aLength + bLength - 1];
for (int i = 0; i < aLength; i++)
{
int aCoeff = aCoefficients[i];
for (int j = 0; j < bLength; j++)
{
product[i + j] = GF256.AddOrSubtract(product[i + j],
field.Multiply(aCoeff, bCoefficients[j]));
}
}
return(new GF256Poly(field, product));
}
internal GF256Poly[] Divide(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GF256Polys do not have same GF256 field");
}
if (other.IsZero())
{
throw new DivideByZeroException("Divide by 0");
}
GF256Poly quotient = field.GetZero();
GF256Poly remainder = this;
int denominatorLeadingTerm = other.GetCoefficient(other.GetDegree());
int inverseDenominatorLeadingTerm = field.Inverse(denominatorLeadingTerm);
while (remainder.GetDegree() >= other.GetDegree() && !remainder.IsZero())
{
int degreeDifference = remainder.GetDegree() - other.GetDegree();
int scale = field.Multiply(remainder.GetCoefficient(remainder.GetDegree()), inverseDenominatorLeadingTerm);
GF256Poly term = other.MultiplyByMonomial(degreeDifference, scale);
GF256Poly iterationQuotient = field.BuildMonomial(degreeDifference, scale);
quotient = quotient.AddOrSubtract(iterationQuotient);
remainder = remainder.AddOrSubtract(term);
}
return(new GF256Poly[] { quotient, remainder });
}
internal GF256Poly AddOrSubtract(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GF256Polys do not have same GF256 field");
}
if (IsZero())
{
return(other);
}
if (other.IsZero())
{
return(this);
}
int[] smallerCoefficients = this.coefficients;
int[] largerCoefficients = other.coefficients;
if (smallerCoefficients.Length > largerCoefficients.Length)
{
int[] temp = smallerCoefficients;
smallerCoefficients = largerCoefficients;
largerCoefficients = temp;
}
int[] sumDiff = new int[largerCoefficients.Length];
int lengthDiff = largerCoefficients.Length - smallerCoefficients.Length;
// Copy high-order terms only found in higher-degree polynomial's coefficients
System.Array.Copy(largerCoefficients, 0, sumDiff, 0, lengthDiff);
for (int i = lengthDiff; i < largerCoefficients.Length; i++)
{
sumDiff[i] = GF256.AddOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return(new GF256Poly(field, sumDiff));
}