public GF256Poly multiply(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GF256Polys do not have same GF256 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] = GF256.addOrSubtract(product[i + j],
field.multiply(aCoeff, bCoefficients[j]));
}
}
return(new GF256Poly(field, product));
}
public GF256Poly[] divide(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GF256Polys do not have same GF256 field");
}
if (other.isZero())
{
throw new ArgumentException("Divide by 0");
}
GF256Poly quotient = field.getZero();
GF256Poly remainder = this;
int denominatorLeadingTerm = other.getCoefficient(other.getDegree());
int inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm);
while (remainder.getDegree() >= other.getDegree() && !remainder.isZero())
{
int degreeDifference = remainder.getDegree() - other.getDegree();
int scale = field.multiply(remainder.getCoefficient(remainder.getDegree()), 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 GF256Poly addOrSubtract(GF256Poly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GF256Polys do not have same GF256 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
System.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));
}
public GF256Poly[] divide(GF256Poly other)
{
if (!field.Equals(other.field)) {
throw new ArgumentException("GF256Polys do not have same GF256 field");
}
if (other.isZero()) {
throw new ArgumentException("Divide by 0");
}
GF256Poly quotient = field.getZero();
GF256Poly remainder = this;
int denominatorLeadingTerm = other.getCoefficient(other.getDegree());
int inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm);
while (remainder.getDegree() >= other.getDegree() && !remainder.isZero()) {
int degreeDifference = remainder.getDegree() - other.getDegree();
int scale = field.multiply(remainder.getCoefficient(remainder.getDegree()), 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 GF256Poly multiply(GF256Poly other)
{
if (!field.Equals(other.field)) {
throw new ArgumentException("GF256Polys do not have same GF256 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] = GF256.addOrSubtract(product[i + j],
field.multiply(aCoeff, bCoefficients[j]));
}
}
return new GF256Poly(field, product);
}
public GF256Poly addOrSubtract(GF256Poly other)
{
if (!field.Equals(other.field)) {
throw new ArgumentException("GF256Polys do not have same GF256 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
System.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);
}
private GF256Poly[] runEuclideanAlgorithm(GF256Poly a, GF256Poly b, int R)
{
// Assume a's degree is >= b's
if (a.getDegree() < b.getDegree())
{
GF256Poly temp = a;
a = b;
b = temp;
}
GF256Poly rLast = a;
GF256Poly r = b;
GF256Poly sLast = field.getOne();
GF256Poly s = field.getZero();
GF256Poly tLast = field.getZero();
GF256Poly t = field.getOne();
// Run Euclidean algorithm until r's degree is less than R/2
while (r.getDegree() >= R / 2)
{
GF256Poly rLastLast = rLast;
GF256Poly sLastLast = sLast;
GF256Poly tLastLast = tLast;
rLast = r;
sLast = s;
tLast = t;
// Divide rLastLast by rLast, with quotient in q and remainder in r
if (rLast.isZero())
{
// Oops, Euclidean algorithm already terminated?
throw new ReedSolomonException("r_{i-1} was zero");
}
r = rLastLast;
GF256Poly q = field.getZero();
int denominatorLeadingTerm = rLast.getCoefficient(rLast.getDegree());
int dltInverse = field.inverse(denominatorLeadingTerm);
while (r.getDegree() >= rLast.getDegree() && !r.isZero())
{
int degreeDiff = r.getDegree() - rLast.getDegree();
int scale = field.multiply(r.getCoefficient(r.getDegree()), dltInverse);
q = q.addOrSubtract(field.buildMonomial(degreeDiff, scale));
r = r.addOrSubtract(rLast.multiplyByMonomial(degreeDiff, scale));
}
s = q.multiply(sLast).addOrSubtract(sLastLast);
t = q.multiply(tLast).addOrSubtract(tLastLast);
}
int sigmaTildeAtZero = t.getCoefficient(0);
if (sigmaTildeAtZero == 0)
{
throw new ReedSolomonException("sigmaTilde(0) was zero");
}
int inverse = field.inverse(sigmaTildeAtZero);
GF256Poly sigma = t.multiply(inverse);
GF256Poly omega = r.multiply(inverse);
return(new GF256Poly[] { sigma, omega });
}
