vector<Ref<GenericGFPoly> > ReedSolomonDecoder::runEuclideanAlgorithm(Ref<GenericGFPoly> a,
Ref<GenericGFPoly> b,
int R) {
// Assume a's degree is >= b's
if (a->getDegree() < b->getDegree()) {
Ref<GenericGFPoly> tmp = a;
a = b;
b = tmp;
}
Ref<GenericGFPoly> rLast(a);
Ref<GenericGFPoly> r(b);
Ref<GenericGFPoly> sLast(field->getOne());
Ref<GenericGFPoly> s(field->getZero());
Ref<GenericGFPoly> tLast(field->getZero());
Ref<GenericGFPoly> t(field->getOne());
// Run Euclidean algorithm until r's degree is less than R/2
while (r->getDegree() >= R / 2) {
Ref<GenericGFPoly> rLastLast(rLast);
Ref<GenericGFPoly> sLastLast(sLast);
Ref<GenericGFPoly> tLastLast(tLast);
rLast = r;
sLast = s;
tLast = t;
// Divide rLastLast by rLast, with quotient q and remainder r
if (rLast->isZero()) {
// Oops, Euclidean algorithm already terminated?
throw ReedSolomonException("r_{i-1} was zero");
}
r = rLastLast;
Ref<GenericGFPoly> 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 ReedSolomonException("sigmaTilde(0) was zero");
}
int inverse = field->inverse(sigmaTildeAtZero);
Ref<GenericGFPoly> sigma(t->multiply(inverse));
Ref<GenericGFPoly> omega(r->multiply(inverse));
#ifdef DEBUG
cout << "t = " << *t << "\n";
cout << "r = " << *r << "\n";
cout << "sigma = " << *sigma << "\n";
cout << "omega = " << *omega << "\n";
#endif
vector<Ref<GenericGFPoly> > result(2);
result[0] = sigma;
result[1] = omega;
return result;
}
CFX_PtrArray* CBC_ReedSolomonDecoder::RunEuclideanAlgorithm(
CBC_ReedSolomonGF256Poly* a,
CBC_ReedSolomonGF256Poly* b,
int32_t R,
int32_t& e) {
if (a->GetDegree() < b->GetDegree()) {
CBC_ReedSolomonGF256Poly* temp = a;
a = b;
b = temp;
}
CBC_ReedSolomonGF256Poly* rsg1 = a->Clone(e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> rLast(rsg1);
CBC_ReedSolomonGF256Poly* rsg2 = b->Clone(e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> r(rsg2);
CBC_ReedSolomonGF256Poly* rsg3 = m_field->GetOne()->Clone(e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> sLast(rsg3);
CBC_ReedSolomonGF256Poly* rsg4 = m_field->GetZero()->Clone(e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> s(rsg4);
CBC_ReedSolomonGF256Poly* rsg5 = m_field->GetZero()->Clone(e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> tLast(rsg5);
CBC_ReedSolomonGF256Poly* rsg6 = m_field->GetOne()->Clone(e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> t(rsg6);
while (r->GetDegree() >= R / 2) {
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> rLastLast = rLast;
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> sLastLast = sLast;
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> tLastlast = tLast;
rLast = r;
sLast = s;
tLast = t;
if (rLast->IsZero()) {
e = BCExceptionR_I_1IsZero;
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
}
CBC_ReedSolomonGF256Poly* rsg7 = rLastLast->Clone(e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> rTemp(rsg7);
r = rTemp;
CBC_ReedSolomonGF256Poly* rsg8 = m_field->GetZero()->Clone(e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> q(rsg8);
int32_t denominatorLeadingTerm = rLast->GetCoefficients(rLast->GetDegree());
int32_t dltInverse = m_field->Inverse(denominatorLeadingTerm, e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
while (r->GetDegree() >= rLast->GetDegree() && !(r->IsZero())) {
int32_t degreeDiff = r->GetDegree() - rLast->GetDegree();
int32_t scale =
m_field->Multiply(r->GetCoefficients(r->GetDegree()), dltInverse);
CBC_ReedSolomonGF256Poly* rsgp1 =
m_field->BuildMonomial(degreeDiff, scale, e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> build(rsgp1);
CBC_ReedSolomonGF256Poly* rsgp2 = q->AddOrSubtract(build.get(), e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> temp(rsgp2);
q = temp;
CBC_ReedSolomonGF256Poly* rsgp3 =
rLast->MultiplyByMonomial(degreeDiff, scale, e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> multiply(rsgp3);
CBC_ReedSolomonGF256Poly* rsgp4 = r->AddOrSubtract(multiply.get(), e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> temp3(rsgp4);
r = temp3;
}
CBC_ReedSolomonGF256Poly* rsg9 = q->Multiply(sLast.get(), e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> temp1(rsg9);
CBC_ReedSolomonGF256Poly* rsg10 = temp1->AddOrSubtract(sLastLast.get(), e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> temp2(rsg10);
s = temp2;
CBC_ReedSolomonGF256Poly* rsg11 = q->Multiply(tLast.get(), e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> temp5(rsg11);
CBC_ReedSolomonGF256Poly* rsg12 = temp5->AddOrSubtract(tLastlast.get(), e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> temp6(rsg12);
t = temp6;
}
int32_t sigmaTildeAtZero = t->GetCoefficients(0);
if (sigmaTildeAtZero == 0) {
e = BCExceptionIsZero;
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
}
int32_t inverse = m_field->Inverse(sigmaTildeAtZero, e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_ReedSolomonGF256Poly* rsg13 = t->Multiply(inverse, e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> sigma(rsg13);
CBC_ReedSolomonGF256Poly* rsg14 = r->Multiply(inverse, e);
BC_EXCEPTION_CHECK_ReturnValue(e, NULL);
CBC_AutoPtr<CBC_ReedSolomonGF256Poly> omega(rsg14);
CFX_PtrArray* temp = new CFX_PtrArray;
temp->Add(sigma.release());
temp->Add(omega.release());
return temp;
}
