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 });
}
private int[] findErrorLocations(GF256Poly errorLocator)
{
// This is a direct application of Chien's search
int numErrors = errorLocator.getDegree();
if (numErrors == 1) // shortcut
{
return(new int[] { errorLocator.getCoefficient(1) });
}
int[] result = new int[numErrors];
int e = 0;
for (int i = 1; i < 256 && e < numErrors; i++)
{
if (errorLocator.evaluateAt(i) == 0)
{
result[e] = field.inverse(i);
e++;
}
}
if (e != numErrors)
{
throw new ReedSolomonException("Error locator degree does not match number of roots");
}
return(result);
}
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};
}
private int[] findErrorLocations(GF256Poly errorLocator){
// This is a direct application of Chien's search
int numErrors = errorLocator.getDegree();
if (numErrors == 1) { // shortcut
return new int[] { errorLocator.getCoefficient(1) };
}
int[] result = new int[numErrors];
int e = 0;
for (int i = 1; i < 256 && e < numErrors; i++) {
if (errorLocator.evaluateAt(i) == 0) {
result[e] = field.inverse(i);
e++;
}
}
if (e != numErrors) {
throw new ReedSolomonException("Error locator degree does not match number of roots");
}
return result;
}
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 };
}
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 });
}
