/// <summary>
/// Divide by another modulus
/// </summary>
/// <param name="other">Other.</param>
internal ModulusPoly[] divide(ModulusPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("ModulusPolys do not have same ModulusGF field");
}
if (other.isZero)
{
throw new DivideByZeroException();
}
ModulusPoly quotient = field.Zero;
ModulusPoly 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);
ModulusPoly term = other.multiplyByMonomial(degreeDifference, scale);
ModulusPoly iterationQuotient = field.buildMonomial(degreeDifference, scale);
quotient = quotient.add(iterationQuotient);
remainder = remainder.subtract(term);
}
return(new ModulusPoly[] { quotient, remainder });
}
/// <summary>
/// Multiply by another Modulus
/// </summary>
/// <param name="other">Other.</param>
internal ModulusPoly multiply(ModulusPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("ModulusPolys do not have same ModulusGF field");
}
if (isZero || other.isZero)
{
return(field.Zero);
}
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] = field.add(product[i + j], field.multiply(aCoeff, bCoefficients[j]));
}
}
return(new ModulusPoly(field, product));
}
/// <summary>
/// Subtract another Modulus
/// </summary>
/// <param name="other">Other.</param>
internal ModulusPoly subtract(ModulusPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("ModulusPolys do not have same ModulusGF field");
}
if (other.isZero)
{
return(this);
}
return(add(other.getNegative()));
}
public ModulusGF(int modulus, int generator)
{
this.Modulus = modulus;
expTable = new int[modulus];
logTable = new int[modulus];
int x = 1;
for (int i = 0; i < modulus; i++)
{
expTable[i] = x;
x = (x * generator) % modulus;
}
for (int i = 0; i < modulus - 1; i++)
{
logTable[expTable[i]] = i;
}
// logTable[0] == 0 but this should never be used
Zero = new ModulusPoly(this, new int[] { 0 });
One = new ModulusPoly(this, new int[] { 1 });
}
public ModulusGF(int modulus, int generator)
{
this.modulus = modulus;
expTable = new int[modulus];
logTable = new int[modulus];
int x = 1;
for (int i = 0; i < modulus; i++)
{
expTable[i] = x;
x = (x * generator) % modulus;
}
for (int i = 0; i < modulus - 1; i++)
{
logTable[expTable[i]] = i;
}
// logTable[0] == 0 but this should never be used
Zero = new ModulusPoly(this, new int[] { 0 });
One = new ModulusPoly(this, new int[] { 1 });
}
/// <summary>
/// Adds another Modulus
/// </summary>
/// <param name="other">Other.</param>
internal ModulusPoly add(ModulusPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("ModulusPolys do not have same ModulusGF 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
Array.Copy(largerCoefficients, 0, sumDiff, 0, lengthDiff);
for (int i = lengthDiff; i < largerCoefficients.Length; i++)
{
sumDiff[i] = field.add(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return(new ModulusPoly(field, sumDiff));
}
internal ModulusPoly[] divide(ModulusPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("ModulusPolys do not have same ModulusGF field");
}
if (other.isZero)
{
throw new ArgumentException("Divide by 0");
}
ModulusPoly quotient = field.getZero();
ModulusPoly 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);
ModulusPoly term = other.multiplyByMonomial(degreeDifference, scale);
ModulusPoly iterationQuotient = field.buildMonomial(degreeDifference, scale);
quotient = quotient.add(iterationQuotient);
remainder = remainder.subtract(term);
}
return new ModulusPoly[] { quotient, remainder };
}
internal ModulusPoly multiply(ModulusPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("ModulusPolys do not have same ModulusGF 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] = field.add(product[i + j], field.multiply(aCoeff, bCoefficients[j]));
}
}
return new ModulusPoly(field, product);
}
internal ModulusPoly subtract(ModulusPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("ModulusPolys do not have same ModulusGF field");
}
if (other.isZero)
{
return this;
}
return add(other.negative());
}
internal ModulusPoly add(ModulusPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("ModulusPolys do not have same ModulusGF 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
Array.Copy(largerCoefficients, 0, sumDiff, 0, lengthDiff);
for (int i = lengthDiff; i < largerCoefficients.Length; i++)
{
sumDiff[i] = field.add(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return new ModulusPoly(field, sumDiff);
}
