/// <summary>
/// Create a representation of GF(size) 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>
/// <param name="size">the size of the field</param>
/// <param name="genBase">the factor b in the generator polynomial can be 0- or 1-based
/// * (g(x) = (x+a^b)(x+a^(b+1))...(x+a^(b+2t-1))).
/// * In most cases it should be 1, but for QR code it is 0.</param>
public GenericGF(int primitive, int size, int genBase)
{
this.primitive = primitive;
this.size = size;
this.generatorBase = genBase;
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 });
}
public void encode(int[] toEncode, int ecBytes)
{
if (ecBytes == 0)
{
throw new ArgumentException("No error correction bytes");
}
var dataBytes = toEncode.Length - ecBytes;
if (dataBytes <= 0)
{
throw new ArgumentException("No data bytes provided");
}
var 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);
var remainder = info.divide(generator)[1];
var coefficients = remainder.Coefficients;
var numZeroCoefficients = ecBytes - coefficients.Length;
for (var i = 0; i < numZeroCoefficients; i++)
{
toEncode[dataBytes + i] = 0;
}
Array.Copy(coefficients, 0, toEncode, dataBytes + numZeroCoefficients, coefficients.Length);
}
internal GenericGFPoly multiply(GenericGFPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GenericGFPolys do not have same GenericGF 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] = 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))
{
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 });
}
internal GenericGFPoly addOrSubtract(GenericGFPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GenericGFPolys do not have same GenericGF 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] = GenericGF.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return(new GenericGFPoly(field, sumDiff));
}