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vendor/khanamiryan/qrcode-detector-decoder/lib/common/reedsolomon/ReedSolomonDecoder.php 0000777 00000016703 14711072547 0034251 0 ustar 00 home/lakoyani/e-learn.mltcfiji.com <?php /* * Copyright 2007 ZXing authors * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ namespace Zxing\Common\Reedsolomon; /** * <p>Implements Reed-Solomon decoding, as the name implies.</p> * * <p>The algorithm will not be explained here, but the following references were helpful * in creating this implementation:</p> * * <ul> * <li>Bruce Maggs. * <a href="http://www.cs.cmu.edu/afs/cs.cmu.edu/project/pscico-guyb/realworld/www/rs_decode.ps"> * "Decoding Reed-Solomon Codes"</a> (see discussion of Forney's Formula)</li> * <li>J.I. Hall. <a href="www.mth.msu.edu/~jhall/classes/codenotes/GRS.pdf"> * "Chapter 5. Generalized Reed-Solomon Codes"</a> * (see discussion of Euclidean algorithm)</li> * </ul> * * <p>Much credit is due to William Rucklidge since portions of this code are an indirect * port of his C++ Reed-Solomon implementation.</p> * * @author Sean Owen * @author William Rucklidge * @author sanfordsquires */ final class ReedSolomonDecoder { private $field; public function __construct($field) { $this->field = $field; } /** * <p>Decodes given set of received codewords, which include both data and error-correction * codewords. Really, this means it uses Reed-Solomon to detect and correct errors, in-place, * in the input.</p> * * @param received data and error-correction codewords * @param twoS number of error-correction codewords available * @throws ReedSolomonException if decoding fails for any reason */ public function decode(&$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]); } } private function runEuclideanAlgorithm($a, $b, $R) { // Assume a's degree is >= b's if ($a->getDegree() < $b->getDegree()) { $temp = $a; $a = $b; $b = $temp; } $rLast = $a; $r = $b; $tLast = $this->field->getZero(); $t = $this->field->getOne(); // Run Euclidean algorithm until r's degree is less than R/2 while ($r->getDegree() >= $R / 2) { $rLastLast = $rLast; $tLastLast = $tLast; $rLast = $r; $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; $q = $this->field->getZero(); $denominatorLeadingTerm = $rLast->getCoefficient($rLast->getDegree()); $dltInverse = $this->field->inverse($denominatorLeadingTerm); while ($r->getDegree() >= $rLast->getDegree() && !$r->isZero()) { $degreeDiff = $r->getDegree() - $rLast->getDegree(); $scale = $this->field->multiply($r->getCoefficient($r->getDegree()), $dltInverse); $q = $q->addOrSubtract($this->field->buildMonomial($degreeDiff, $scale)); $r = $r->addOrSubtract($rLast->multiplyByMonomial($degreeDiff, $scale)); } $t = $q->multiply($tLast)->addOrSubtract($tLastLast); if ($r->getDegree() >= $rLast->getDegree()) { throw new IllegalStateException("Division algorithm failed to reduce polynomial?"); } } $sigmaTildeAtZero = $t->getCoefficient(0); if ($sigmaTildeAtZero == 0) { throw new ReedSolomonException("sigmaTilde(0) was zero"); } $inverse = $this->field->inverse($sigmaTildeAtZero); $sigma = $t->multiply($inverse); $omega = $r->multiply($inverse); return array($sigma, $omega); } private function findErrorLocations($errorLocator) { // This is a direct application of Chien's search $numErrors = $errorLocator->getDegree(); if ($numErrors == 1) { // shortcut return array($errorLocator->getCoefficient(1) ); } $result = fill_array(0,$numErrors,0); $e = 0; for ($i = 1; $i < $this->field->getSize() && $e < $numErrors; $i++) { if ($errorLocator->evaluateAt($i) == 0) { $result[$e] = $this->field->inverse($i); $e++; } } if ($e != $numErrors) { throw new ReedSolomonException("Error locator degree does not match number of roots"); } return $result; } private function findErrorMagnitudes($errorEvaluator, $errorLocations) { // This is directly applying Forney's Formula $s = count($errorLocations); $result = fill_array(0,$s,0); for ($i = 0; $i < $s; $i++) { $xiInverse = $this->field->inverse($errorLocations[$i]); $denominator = 1; for ($j = 0; $j < $s; $j++) { if ($i != $j) { //denominator = field.multiply(denominator, // GenericGF.addOrSubtract(1, field.multiply(errorLocations[j], xiInverse))); // Above should work but fails on some Apple and Linux JDKs due to a Hotspot bug. // Below is a funny-looking workaround from Steven Parkes $term = $this->field->multiply($errorLocations[$j], $xiInverse); $termPlus1 = ($term & 0x1) == 0 ? $term | 1 : $term & ~1; $denominator = $this->field->multiply($denominator, $termPlus1); } } $result[$i] = $this->field->multiply($errorEvaluator->evaluateAt($xiInverse), $this->field->inverse($denominator)); if ($this->field->getGeneratorBase() != 0) { $result[$i] = $this->field->multiply($result[$i], $xiInverse); } } return $result; } } vendor/khanamiryan/qrcode-detector-decoder/lib/Common/Reedsolomon/ReedSolomonDecoder.php 0000777 00000017377 14711072713 0034154 0 ustar 00 home/lakoyani/e-learn.mltcfiji.com <?php /* * Copyright 2007 ZXing authors * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ namespace Zxing\Common\Reedsolomon; /** * <p>Implements Reed-Solomon decoding, as the name implies.</p> * * <p>The algorithm will not be explained here, but the following references were helpful * in creating this implementation:</p> * * <ul> * <li>Bruce Maggs. * <a href="http://www.cs.cmu.edu/afs/cs.cmu.edu/project/pscico-guyb/realworld/www/rs_decode.ps"> * "Decoding Reed-Solomon Codes"</a> (see discussion of Forney's Formula)</li> * <li>J.I. Hall. <a href="www.mth.msu.edu/~jhall/classes/codenotes/GRS.pdf"> * "Chapter 5. Generalized Reed-Solomon Codes"</a> * (see discussion of Euclidean algorithm)</li> * </ul> * * <p>Much credit is due to William Rucklidge since portions of this code are an indirect * port of his C++ Reed-Solomon implementation.</p> * * @author Sean Owen * @author William Rucklidge * @author sanfordsquires */ final class ReedSolomonDecoder { private $field; public function __construct($field) { $this->field = $field; } /** * <p>Decodes given set of received codewords, which include both data and error-correction * codewords. Really, this means it uses Reed-Solomon to detect and correct errors, in-place, * in the input.</p> * * @param received data and error-correction codewords * @param twoS number of error-correction codewords available * * @throws ReedSolomonException if decoding fails for any reason */ public function decode(&$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); $errorLocationsCount = count($errorLocations); for ($i = 0; $i < $errorLocationsCount; $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]); } } private function runEuclideanAlgorithm($a, $b, $R) { // Assume a's degree is >= b's if ($a->getDegree() < $b->getDegree()) { $temp = $a; $a = $b; $b = $temp; } $rLast = $a; $r = $b; $tLast = $this->field->getZero(); $t = $this->field->getOne(); // Run Euclidean algorithm until r's degree is less than R/2 while ($r->getDegree() >= $R / 2) { $rLastLast = $rLast; $tLastLast = $tLast; $rLast = $r; $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; $q = $this->field->getZero(); $denominatorLeadingTerm = $rLast->getCoefficient($rLast->getDegree()); $dltInverse = $this->field->inverse($denominatorLeadingTerm); while ($r->getDegree() >= $rLast->getDegree() && !$r->isZero()) { $degreeDiff = $r->getDegree() - $rLast->getDegree(); $scale = $this->field->multiply($r->getCoefficient($r->getDegree()), $dltInverse); $q = $q->addOrSubtract($this->field->buildMonomial($degreeDiff, $scale)); $r = $r->addOrSubtract($rLast->multiplyByMonomial($degreeDiff, $scale)); } $t = $q->multiply($tLast)->addOrSubtract($tLastLast); if ($r->getDegree() >= $rLast->getDegree()) { throw new ReedSolomonException("Division algorithm failed to reduce polynomial?"); } } $sigmaTildeAtZero = $t->getCoefficient(0); if ($sigmaTildeAtZero == 0) { throw new ReedSolomonException("sigmaTilde(0) was zero"); } $inverse = $this->field->inverse($sigmaTildeAtZero); $sigma = $t->multiply($inverse); $omega = $r->multiply($inverse); return [$sigma, $omega]; } private function findErrorLocations($errorLocator) { // This is a direct application of Chien's search $numErrors = $errorLocator->getDegree(); if ($numErrors == 1) { // shortcut return [$errorLocator->getCoefficient(1)]; } $result = fill_array(0, $numErrors, 0); $e = 0; for ($i = 1; $i < $this->field->getSize() && $e < $numErrors; $i++) { if ($errorLocator->evaluateAt($i) == 0) { $result[$e] = $this->field->inverse($i); $e++; } } if ($e != $numErrors) { throw new ReedSolomonException("Error locator degree does not match number of roots"); } return $result; } private function findErrorMagnitudes($errorEvaluator, $errorLocations) { // This is directly applying Forney's Formula $s = count($errorLocations); $result = fill_array(0, $s, 0); for ($i = 0; $i < $s; $i++) { $xiInverse = $this->field->inverse($errorLocations[$i]); $denominator = 1; for ($j = 0; $j < $s; $j++) { if ($i != $j) { //denominator = field.multiply(denominator, // GenericGF.addOrSubtract(1, field.multiply(errorLocations[j], xiInverse))); // Above should work but fails on some Apple and Linux JDKs due to a Hotspot bug. // Below is a funny-looking workaround from Steven Parkes $term = $this->field->multiply($errorLocations[$j], $xiInverse); $termPlus1 = ($term & 0x1) == 0 ? $term | 1 : $term & ~1; $denominator = $this->field->multiply($denominator, $termPlus1); } } $result[$i] = $this->field->multiply($errorEvaluator->evaluateAt($xiInverse), $this->field->inverse($denominator)); if ($this->field->getGeneratorBase() != 0) { $result[$i] = $this->field->multiply($result[$i], $xiInverse); } } return $result; } }
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