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));
}
/**
* @param field the {@link GF256} instance representing the field to use
* to perform computations
* @param coefficients coefficients as ints representing elements of GF(256), arranged
* from most significant (highest-power term) coefficient to least significant
* @throws ArgumentException if argument is null or empty,
* or if leading coefficient is 0 and this is not a
* constant polynomial (that is, it is not the monomial "0")
*/
public GF256Poly(GF256 field, int[] coefficients)
{
if (coefficients == null || coefficients.Length == 0)
{
throw new ArgumentException();
}
this.field = field;
int coefficientsLength = coefficients.Length;
if (coefficientsLength > 1 && coefficients[0] == 0)
{
// Leading term must be non-zero for anything except the constant polynomial "0"
int firstNonZero = 1;
while (firstNonZero < coefficientsLength && coefficients[firstNonZero] == 0)
{
firstNonZero++;
}
if (firstNonZero == coefficientsLength)
{
this.coefficients = field.getZero().coefficients;
}
else
{
this.coefficients = new int[coefficientsLength - firstNonZero];
System.Array.Copy(coefficients, firstNonZero, this.coefficients, 0, this.coefficients.Length);
}
}
else
{
this.coefficients = coefficients;
}
}
/**
* @param field the {@link GF256} instance representing the field to use
* to perform computations
* @param coefficients coefficients as ints representing elements of GF(256), arranged
* from most significant (highest-power term) coefficient to least significant
* @throws ArgumentException if argument is null or empty,
* or if leading coefficient is 0 and this is not a
* constant polynomial (that is, it is not the monomial "0")
*/
public GF256Poly(GF256 field, int[] coefficients) {
if (coefficients == null || coefficients.Length == 0) {
throw new ArgumentException();
}
this.field = field;
int coefficientsLength = coefficients.Length;
if (coefficientsLength > 1 && coefficients[0] == 0) {
// Leading term must be non-zero for anything except the constant polynomial "0"
int firstNonZero = 1;
while (firstNonZero < coefficientsLength && coefficients[firstNonZero] == 0) {
firstNonZero++;
}
if (firstNonZero == coefficientsLength) {
this.coefficients = field.getZero().coefficients;
} else {
this.coefficients = new int[coefficientsLength - firstNonZero];
System.Array.Copy(coefficients,firstNonZero,this.coefficients,0,this.coefficients.Length);
}
} else {
this.coefficients = coefficients;
}
}
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 });
}
