internal GF256Poly[] divide(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new System.ArgumentException("GF256Polys do not have same GF256 field");
}
if (other.Zero)
{
throw new System.ArgumentException("Divide by 0");
}
GF256Poly quotient = field.Zero;
GF256Poly remainder = this;
int denominatorLeadingTerm = other.getCoefficient(other.Degree);
int inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm);
while (remainder.Degree >= other.Degree && !remainder.Zero)
{
int degreeDifference = remainder.Degree - other.Degree;
int scale = field.multiply(remainder.getCoefficient(remainder.Degree), 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 });
}
public void encode(int[] toEncode, int ecBytes)
{
if (ecBytes == 0)
{
throw new System.ArgumentException("No error correction bytes");
}
int dataBytes = toEncode.Length - ecBytes;
if (dataBytes <= 0)
{
throw new System.ArgumentException("No data bytes provided");
}
GF256Poly generator = buildGenerator(ecBytes);
int[] infoCoefficients = new int[dataBytes];
Array.Copy(toEncode, 0, infoCoefficients, 0, dataBytes);
GF256Poly info = new GF256Poly(field, infoCoefficients);
info = info.multiplyByMonomial(ecBytes, 1);
GF256Poly remainder = info.divide(generator)[1];
int[] coefficients = remainder.Coefficients;
int numZeroCoefficients = ecBytes - coefficients.Length;
for (int i = 0; i < numZeroCoefficients; i++)
{
toEncode[dataBytes + i] = 0;
}
Array.Copy(coefficients, 0, toEncode, dataBytes + numZeroCoefficients, coefficients.Length);
}
internal GF256Poly multiply(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new System.ArgumentException("GF256Polys do not have same GF256 field");
}
if (Zero || other.Zero)
{
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] = GF256.addOrSubtract(product[i + j], field.multiply(aCoeff, bCoefficients[j]));
}
}
return(new GF256Poly(field, product));
}
public void encode(int[] toEncode, int ecBytes)
{
if (ecBytes == 0)
{
throw new System.ArgumentException("No error correction bytes");
}
int dataBytes = toEncode.Length - ecBytes;
if (dataBytes <= 0)
{
throw new System.ArgumentException("No data bytes provided");
}
GF256Poly generator = buildGenerator(ecBytes);
int[] infoCoefficients = new int[dataBytes];
Array.Copy(toEncode, 0, infoCoefficients, 0, dataBytes);
GF256Poly info = new GF256Poly(field, infoCoefficients);
info = info.multiplyByMonomial(ecBytes, 1);
GF256Poly remainder = info.divide(generator)[1];
int[] coefficients = remainder.Coefficients;
int numZeroCoefficients = ecBytes - coefficients.Length;
for (int i = 0; i < numZeroCoefficients; i++)
{
toEncode[dataBytes + i] = 0;
}
Array.Copy(coefficients, 0, toEncode, dataBytes + numZeroCoefficients, coefficients.Length);
}
private GF256Poly buildGenerator(int degree)
{
if (degree >= cachedGenerators.Count)
{
GF256Poly lastGenerator = (GF256Poly)cachedGenerators[cachedGenerators.Count - 1];
for (int d = cachedGenerators.Count; d <= degree; d++)
{
GF256Poly nextGenerator = lastGenerator.multiply(new GF256Poly(field, new int[] { 1, field.exp(d - 1) }));
cachedGenerators.Add(nextGenerator);
lastGenerator = nextGenerator;
}
}
return((GF256Poly)cachedGenerators[degree]);
}
/// <summary> Create a representation of GF(256) using the given primitive polynomial.
///
/// </summary>
/// <param name="primitive">irreducible polynomial whose coefficients are represented by
/// the bits of an int, where the least-significant bit represents the constant
/// coefficient
/// </param>
private GF256(int primitive)
{
expTable = new int[256];
logTable = new int[256];
int x = 1;
for (int i = 0; i < 256; i++)
{
expTable[i] = x;
x <<= 1; // x = x * 2; we're assuming the generator alpha is 2
if (x >= 0x100)
{
x ^= primitive;
}
}
for (int i = 0; i < 255; i++)
{
logTable[expTable[i]] = i;
}
// logTable[0] == 0 but this should never be used
zero = new GF256Poly(this, new int[]{0});
one = new GF256Poly(this, new int[]{1});
}
/// <summary> Create a representation of GF(256) using the given primitive polynomial.
///
/// </summary>
/// <param name="primitive">irreducible polynomial whose coefficients are represented by
/// the bits of an int, where the least-significant bit represents the constant
/// coefficient
/// </param>
private GF256(int primitive)
{
expTable = new int[256];
logTable = new int[256];
int x = 1;
for (int i = 0; i < 256; i++)
{
expTable[i] = x;
x <<= 1; // x = x * 2; we're assuming the generator alpha is 2
if (x >= 0x100)
{
x ^= primitive;
}
}
for (int i = 0; i < 255; i++)
{
logTable[expTable[i]] = i;
}
// logTable[0] == 0 but this should never be used
zero = new GF256Poly(this, new int[] { 0 });
one = new GF256Poly(this, new int[] { 1 });
}
internal GF256Poly addOrSubtract(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new System.ArgumentException("GF256Polys do not have same GF256 field");
}
if (Zero)
{
return(other);
}
if (other.Zero)
{
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] = GF256.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return(new GF256Poly(field, sumDiff));
}
internal GF256Poly[] divide(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new System.ArgumentException("GF256Polys do not have same GF256 field");
}
if (other.Zero)
{
throw new System.ArgumentException("Divide by 0");
}
GF256Poly quotient = field.Zero;
GF256Poly remainder = this;
int denominatorLeadingTerm = other.getCoefficient(other.Degree);
int inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm);
while (remainder.Degree >= other.Degree && !remainder.Zero)
{
int degreeDifference = remainder.Degree - other.Degree;
int scale = field.multiply(remainder.getCoefficient(remainder.Degree), 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 multiply(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new System.ArgumentException("GF256Polys do not have same GF256 field");
}
if (Zero || other.Zero)
{
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] = GF256.addOrSubtract(product[i + j], field.multiply(aCoeff, bCoefficients[j]));
}
}
return new GF256Poly(field, product);
}
internal GF256Poly addOrSubtract(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new System.ArgumentException("GF256Polys do not have same GF256 field");
}
if (Zero)
{
return other;
}
if (other.Zero)
{
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] = GF256.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return new GF256Poly(field, sumDiff);
}