/// <summary>
/// The multiply.
/// </summary>
/// <param name="other">
/// The other.
/// </param>
/// <returns>
/// The <see cref="QrGaloisFieldPoly"/>.
/// </returns>
public QrGaloisFieldPoly Multiply(QrGaloisFieldPoly other)
{
if (this.IsZero() || other.IsZero())
{
return(this.field.Zero);
}
int[] galoisACoefficients = this.coefficients;
int galoisALength = galoisACoefficients.Length;
int[] galoisBCoefficients = other.coefficients;
int galoisBLength = galoisBCoefficients.Length;
int[] product = new int[galoisALength + galoisBLength - 1];
for (int i = 0; i < galoisALength; i++)
{
int galoisACoeff = galoisACoefficients[i];
for (int j = 0; j < galoisBLength; j++)
{
product[i + j] = QrGaloisField.AddOrSubtract(product[i + j], this.field.Multiply(galoisACoeff, galoisBCoefficients[j]));
}
}
return(new QrGaloisFieldPoly(this.field, product));
}
/// <summary>
/// The initialization method.
/// </summary>
private void Init()
{
this.antiLogTable = new int[this.size];
this.logTable = new int[this.size];
int x = 1;
for (int i = 0; i < this.size; i++)
{
this.antiLogTable[i] = x;
x = x << 1;
if (x >= this.size)
{
x ^= this.primitive;
x &= this.size - 1;
}
}
for (int i = 0; i < this.size - 1; i++)
{
this.logTable[this.antiLogTable[i]] = i;
}
// LogTable[0] should never be used
this.Zero = new QrGaloisFieldPoly(this, new[] { 0 });
this.One = new QrGaloisFieldPoly(this, new[] { 1 });
}
/// <summary>
/// The calculate method.
/// </summary>
/// <param name="message">
/// The message.
/// </param>
/// <param name="numEcc">
/// The number of <c>ecc</c> codes.
/// </param>
/// <returns>
/// The <see cref="byte"/> array.
/// </returns>
public byte[] Calculate(Poly message, int numEcc)
{
// Get message poly coefficients
int[] messageCoefficients = new int[message.Terms.Length];
for (int i = 0; i < message.Terms.Length; i++)
{
messageCoefficients[i] = message.Terms[i].Coefficient;
}
// Convert message poly coefficients into Galois Field (get a coefficients from numbers)
QrGaloisFieldPoly info = new QrGaloisFieldPoly(this.field, messageCoefficients);
// Increase level of the poly by number of ECC
info = info.MultiplyByMonomial(numEcc, 1);
// Get generator poly
QrGaloisFieldPoly generatorPoly = this.BuildGeneratorPolynomial(numEcc);
// Divite by generator poly
QrGaloisFieldPoly remainder = info.Divide(generatorPoly)[1];
// Return remainder coefficients in bytes
int[] coefficients = remainder.GetCoefficients();
byte[] eccCodes = new byte[coefficients.Length];
for (int i = 0; i < coefficients.Length; i++)
{
eccCodes[i] = Convert.ToByte(coefficients[i]);
}
return(eccCodes);
}
/// <summary>
/// The calculate method.
/// </summary>
/// <param name="message">
/// The message.
/// </param>
/// <param name="numEcc">
/// The number of <c>ecc</c> codes.
/// </param>
/// <returns>
/// The <see cref="byte"/> array.
/// </returns>
public byte[] Calculate(Poly message, int numEcc)
{
// Get message poly coefficients
int[] messageCoefficients = new int[message.Terms.Length];
for (int i = 0; i < message.Terms.Length; i++)
{
messageCoefficients[i] = message.Terms[i].Coefficient;
}
// Convert message poly coefficients into Galois Field (get a coefficients from numbers)
QrGaloisFieldPoly info = new QrGaloisFieldPoly(this.field, messageCoefficients);
// Increase level of the poly by number of ECC
info = info.MultiplyByMonomial(numEcc, 1);
// Get generator poly
QrGaloisFieldPoly generatorPoly = this.BuildGeneratorPolynomial(numEcc);
// Divite by generator poly
QrGaloisFieldPoly remainder = info.Divide(generatorPoly)[1];
// Return remainder coefficients in bytes
int[] coefficients = remainder.GetCoefficients();
byte[] eccCodes = new byte[coefficients.Length];
for (int i = 0; i < coefficients.Length; i++)
{
eccCodes[i] = Convert.ToByte(coefficients[i]);
}
return eccCodes;
}
/// <summary>
/// The divide.
/// </summary>
/// <param name="other">
/// The other.
/// </param>
/// <returns>
/// The <see cref="QrGaloisFieldPoly" /> array.
/// </returns>
/// <exception cref="ArgumentException">
/// Exception if division by zero.
/// </exception>
public QrGaloisFieldPoly[] Divide(QrGaloisFieldPoly other)
{
if (other.IsZero())
{
throw new ArgumentException("Divide by 0");
}
QrGaloisFieldPoly quotient = this.field.Zero;
QrGaloisFieldPoly remainder = this;
int denominatorLeadingTerm = other.GetCoefficient(other.GetPower());
int inverseDenominatorLeadingTerm = this.field.Inverse(denominatorLeadingTerm);
while ((remainder.GetPower() >= other.GetPower()) && !remainder.IsZero())
{
int powerDifference = remainder.GetPower() - other.GetPower();
int scale = this.field.Multiply(
remainder.GetCoefficient(remainder.GetPower()), inverseDenominatorLeadingTerm);
QrGaloisFieldPoly term = other.MultiplyByMonomial(powerDifference, scale);
QrGaloisFieldPoly iterationQuotient = this.field.BuildMonomial(powerDifference, scale);
quotient = quotient.AddOrSubtract(iterationQuotient);
remainder = remainder.AddOrSubtract(term);
}
return(new[] { quotient, remainder });
}
/// <summary>
/// The add or subtract.
/// </summary>
/// <param name="other">
/// The other.
/// </param>
/// <returns>
/// The <see cref="QrGaloisFieldPoly"/>.
/// </returns>
public QrGaloisFieldPoly AddOrSubtract(QrGaloisFieldPoly other)
{
if (this.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-power polynomial's coefficients
Array.Copy(largerCoefficients, 0, sumDiff, 0, lengthDiff);
for (int i = lengthDiff; i < largerCoefficients.Length; i++)
{
sumDiff[i] = QrGaloisField.AddOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return(new QrGaloisFieldPoly(this.field, sumDiff));
}
/// <summary>
/// The build generator polynomial.
/// </summary>
/// <param name="power">
/// The power.
/// </param>
/// <returns>
/// The <see cref="QrGaloisFieldPoly"/>.
/// </returns>
private QrGaloisFieldPoly BuildGeneratorPolynomial(int power)
{
if (power >= this.generatorCache.Count)
{
QrGaloisFieldPoly lastGenerator = this.generatorCache[this.generatorCache.Count - 1];
for (int i = this.generatorCache.Count; i <= power; i++)
{
QrGaloisFieldPoly nextGenerator =
lastGenerator.Multiply(
new QrGaloisFieldPoly(this.field, new[] { 1, this.field.GetExponent(i - 1) }));
this.generatorCache.Add(nextGenerator);
lastGenerator = nextGenerator;
}
}
return(this.generatorCache[power]);
}
/// <summary>
/// The initialization method.
/// </summary>
private void Init()
{
this.antiLogTable = new int[this.size];
this.logTable = new int[this.size];
int x = 1;
for (int i = 0; i < this.size; i++)
{
this.antiLogTable[i] = x;
x = x << 1;
if (x >= this.size)
{
x ^= this.primitive;
x &= this.size - 1;
}
}
for (int i = 0; i < this.size - 1; i++)
{
this.logTable[this.antiLogTable[i]] = i;
}
// LogTable[0] should never be used
this.Zero = new QrGaloisFieldPoly(this, new[] { 0 });
this.One = new QrGaloisFieldPoly(this, new[] { 1 });
}
/// <summary>
/// The multiply.
/// </summary>
/// <param name="other">
/// The other.
/// </param>
/// <returns>
/// The <see cref="QrGaloisFieldPoly"/>.
/// </returns>
public QrGaloisFieldPoly Multiply(QrGaloisFieldPoly other)
{
if (this.IsZero() || other.IsZero())
{
return this.field.Zero;
}
int[] galoisACoefficients = this.coefficients;
int galoisALength = galoisACoefficients.Length;
int[] galoisBCoefficients = other.coefficients;
int galoisBLength = galoisBCoefficients.Length;
int[] product = new int[galoisALength + galoisBLength - 1];
for (int i = 0; i < galoisALength; i++)
{
int galoisACoeff = galoisACoefficients[i];
for (int j = 0; j < galoisBLength; j++)
{
product[i + j] = QrGaloisField.AddOrSubtract(product[i + j], this.field.Multiply(galoisACoeff, galoisBCoefficients[j]));
}
}
return new QrGaloisFieldPoly(this.field, product);
}
/// <summary>
/// The divide.
/// </summary>
/// <param name="other">
/// The other.
/// </param>
/// <returns>
/// The <see cref="QrGaloisFieldPoly" /> array.
/// </returns>
/// <exception cref="ArgumentException">
/// Exception if division by zero.
/// </exception>
public QrGaloisFieldPoly[] Divide(QrGaloisFieldPoly other)
{
if (other.IsZero())
{
throw new ArgumentException("Divide by 0");
}
QrGaloisFieldPoly quotient = this.field.Zero;
QrGaloisFieldPoly remainder = this;
int denominatorLeadingTerm = other.GetCoefficient(other.GetPower());
int inverseDenominatorLeadingTerm = this.field.Inverse(denominatorLeadingTerm);
while ((remainder.GetPower() >= other.GetPower()) && !remainder.IsZero())
{
int powerDifference = remainder.GetPower() - other.GetPower();
int scale = this.field.Multiply(
remainder.GetCoefficient(remainder.GetPower()), inverseDenominatorLeadingTerm);
QrGaloisFieldPoly term = other.MultiplyByMonomial(powerDifference, scale);
QrGaloisFieldPoly iterationQuotient = this.field.BuildMonomial(powerDifference, scale);
quotient = quotient.AddOrSubtract(iterationQuotient);
remainder = remainder.AddOrSubtract(term);
}
return new[] { quotient, remainder };
}
/// <summary>
/// The add or subtract.
/// </summary>
/// <param name="other">
/// The other.
/// </param>
/// <returns>
/// The <see cref="QrGaloisFieldPoly"/>.
/// </returns>
public QrGaloisFieldPoly AddOrSubtract(QrGaloisFieldPoly other)
{
if (this.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-power polynomial's coefficients
Array.Copy(largerCoefficients, 0, sumDiff, 0, lengthDiff);
for (int i = lengthDiff; i < largerCoefficients.Length; i++)
{
sumDiff[i] = QrGaloisField.AddOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return new QrGaloisFieldPoly(this.field, sumDiff);
}
