internal GenericGFPoly Multiply(GenericGFPoly other)
{
if (field.Equals(other.field) == false)
{
throw new ArgumentException("GenericGFPolys do not have same GenericGF field");
}
if (IsZero || other.IsZero)
{
return(field.Zero);
}
int[] aCoefficients = 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] = GenericGF.AddOrSubtract(product[i + j], field.Multiply(aCoeff, bCoefficients[j]));
}
}
return(new GenericGFPoly(field, product));
}
internal GenericGFPoly[] Divide(GenericGFPoly other)
{
if (field.Equals(other.field) == false)
{
throw new ArgumentException("GenericGFPolys do not have same GenericGF field");
}
if (other.IsZero)
{
throw new ArgumentException("Divide by 0");
}
GenericGFPoly quotient = field.Zero;
GenericGFPoly 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);
GenericGFPoly term = other.MultiplyByMonomial(degreeDifference, scale);
GenericGFPoly iterationQuotient = field.BuildMonomial(degreeDifference, scale);
quotient = quotient.AddOrSubtract(iterationQuotient);
remainder = remainder.AddOrSubtract(term);
}
return(new GenericGFPoly[] { quotient, remainder });
}
// this method has been added by Sebastien ROBERT
// this implementation makes the mathematician-friendly approach programmer-friendly
public byte[] EncodeEx(byte[] toEncode, int ecBytes)
{
if (ecBytes == 0)
{
throw new ArgumentException("No error correction bytes");
}
int dataBytes = toEncode.Length - ecBytes;
if (dataBytes <= 0)
{
throw new ArgumentException("No data bytes provided");
}
GenericGFPoly generator = BuildGenerator(ecBytes);
int[] infoCoefficients = toEncode.Select(x => (int)x).ToArray();
var info = new GenericGFPoly(field, infoCoefficients);
info = info.MultiplyByMonomial(ecBytes, 1);
GenericGFPoly remainder = info.Divide(generator)[1];
int[] coefficients = remainder.Coefficients;
int numZeroCoefficients = ecBytes - coefficients.Length;
return(Enumerable.Repeat <byte>(0, numZeroCoefficients)
.Concat(coefficients.Select(x => (byte)x))
.ToArray());
}
public void Encode(int[] toEncode, int ecBytes)
{
if (ecBytes == 0)
{
throw new ArgumentException("No error correction bytes");
}
int dataBytes = toEncode.Length - ecBytes;
if (dataBytes <= 0)
{
throw new ArgumentException("No data bytes provided");
}
GenericGFPoly generator = BuildGenerator(ecBytes);
var infoCoefficients = new int[dataBytes];
Array.Copy(toEncode, 0, infoCoefficients, 0, dataBytes);
var info = new GenericGFPoly(field, infoCoefficients);
info = info.MultiplyByMonomial(ecBytes, 1);
GenericGFPoly remainder = info.Divide(generator)[1];
int[] coefficients = remainder.Coefficients;
int numZeroCoefficients = ecBytes - coefficients.Length;
for (var i = 0; i < numZeroCoefficients; i++)
{
toEncode[dataBytes + i] = 0;
}
Array.Copy(coefficients, 0, toEncode, dataBytes + numZeroCoefficients, coefficients.Length);
}
private void Initialize()
{
expTable = new int[size];
logTable = new int[size];
int x = 1;
for (int i = 0; i < size; i++)
{
expTable[i] = x;
x <<= 1; // x = x * 2; we're assuming the generator alpha is 2
if (x >= size)
{
x ^= primitive;
x &= size - 1;
}
}
for (int i = 0; i < size - 1; i++)
{
logTable[expTable[i]] = i;
}
// logTable[0] == 0 but this should never be used
zero = new GenericGFPoly(this, new int[] { 0 });
one = new GenericGFPoly(this, new int[] { 1 });
initialized = true;
}
private GenericGFPoly BuildGenerator(int degree)
{
if (degree >= cachedGenerators.Count)
{
GenericGFPoly lastGenerator = cachedGenerators[cachedGenerators.Count - 1];
for (int d = cachedGenerators.Count; d <= degree; d++)
{
var nextGenerator = lastGenerator.Multiply(new GenericGFPoly(field, new int[] { 1, field.Exp(d - 1 + field.GeneratorBase) }));
cachedGenerators.Add(nextGenerator);
lastGenerator = nextGenerator;
}
}
return(cachedGenerators[degree]);
}
internal GenericGFPoly AddOrSubtract(GenericGFPoly other)
{
if (field.Equals(other.field) == false)
{
throw new ArgumentException("GenericGFPolys do not have same GenericGF field");
}
if (IsZero)
{
return(other);
}
if (other.IsZero)
{
return(this);
}
int[] smallerCoefficients = 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] = GenericGF.AddOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return(new GenericGFPoly(field, sumDiff));
}
