/**
* <p>Decodes given set of received codewords, which include both data and error-correction
* codewords. Really, this means it uses Reed-Solomon to detect and correct errors, in-place,
* in the input.</p>
*
* @param received data and error-correction codewords
* @param twoS number of error-correction codewords available
* @throws ReedSolomonException if decoding fails for any reason
*/
public function decode(&$received, $twoS)
{
$poly = new GenericGFPoly($this->field, $received);
$syndromeCoefficients = fill_array(0, $twoS, 0);
$noError = true;
for ($i = 0; $i < $twoS; $i++) {
$eval = $poly->evaluateAt($this->field->exp($i + $this->field->getGeneratorBase()));
$syndromeCoefficients[count($syndromeCoefficients) - 1 - $i] = $eval;
if ($eval != 0) {
$noError = false;
}
}
if ($noError) {
return;
}
$syndrome = new GenericGFPoly($this->field, $syndromeCoefficients);
$sigmaOmega = $this->runEuclideanAlgorithm($this->field->buildMonomial($twoS, 1), $syndrome, $twoS);
$sigma = $sigmaOmega[0];
$omega = $sigmaOmega[1];
$errorLocations = $this->findErrorLocations($sigma);
$errorMagnitudes = $this->findErrorMagnitudes($omega, $errorLocations);
for ($i = 0; $i < count($errorLocations); $i++) {
$position = count($received) - 1 - $this->field->log($errorLocations[$i]);
if ($position < 0) {
throw new ReedSolomonException("Bad error location");
}
$received[$position] = GenericGF::addOrSubtract($received[$position], $errorMagnitudes[$i]);
}
}
public function divide(GenericGFPoly $other)
{
if ($other->getField() != $this->field) {
throw new \InvalidArgumentException('GenericGFPolys do not have same GenericGF field');
}
if ($other->isZero()) {
throw new \InvalidArgumentException('Divide by 0');
}
$quotient = $this->field->getZero();
$remainder = $this;
$denominatorLeadingTerm = $other->getCoefficient($other->getDegree());
$inverseDenominatorLeadingTerm = $this->field->inverse($denominatorLeadingTerm);
while ($remainder->getDegree() >= $other->getDegree() && !$remainder->isZero()) {
$degreeDifference = $remainder->getDegree() - $other->getDegree();
$scale = $this->field->multiply($remainder->getCoefficient($remainder->getDegree()), $inverseDenominatorLeadingTerm);
$term = $other->multiplyByMonomial($degreeDifference, $scale);
$iterationQuotient = $this->field->buildMonomial($degreeDifference, $scale);
$quotient = $quotient->addOrSubtract($iterationQuotient);
$remainder = $remainder->addOrSubtract($term);
}
return new DivisionResult($quotient, $remainder);
}
