/*
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* Copyright 2007 ZXing authors
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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/*namespace com.google.zxing.common.reedsolomon {*/
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import GenericGF from './GenericGF';
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import GenericGFPoly from './GenericGFPoly';
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import ReedSolomonException from '../../ReedSolomonException';
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import IllegalStateException from '../../IllegalStateException';
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/**
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* <p>Implements Reed-Solomon decoding, as the name implies.</p>
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*
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* <p>The algorithm will not be explained here, but the following references were helpful
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* in creating this implementation:</p>
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*
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* <ul>
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* <li>Bruce Maggs.
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* <a href="http://www.cs.cmu.edu/afs/cs.cmu.edu/project/pscico-guyb/realworld/www/rs_decode.ps">
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* "Decoding Reed-Solomon Codes"</a> (see discussion of Forney's Formula)</li>
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* <li>J.I. Hall. <a href="www.mth.msu.edu/~jhall/classes/codenotes/GRS.pdf">
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* "Chapter 5. Generalized Reed-Solomon Codes"</a>
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* (see discussion of Euclidean algorithm)</li>
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* </ul>
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*
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* <p>Much credit is due to William Rucklidge since portions of this code are an indirect
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* port of his C++ Reed-Solomon implementation.</p>
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*
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* @author Sean Owen
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* @author William Rucklidge
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* @author sanfordsquires
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*/
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export default class ReedSolomonDecoder {
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constructor(field) {
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this.field = field;
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}
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/**
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* <p>Decodes given set of received codewords, which include both data and error-correction
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* codewords. Really, this means it uses Reed-Solomon to detect and correct errors, in-place,
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* in the input.</p>
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*
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* @param received data and error-correction codewords
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* @param twoS number of error-correction codewords available
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* @throws ReedSolomonException if decoding fails for any reason
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*/
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decode(received, twoS /*int*/) {
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const field = this.field;
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const poly = new GenericGFPoly(field, received);
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const syndromeCoefficients = new Int32Array(twoS);
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let noError = true;
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for (let i = 0; i < twoS; i++) {
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const evalResult = poly.evaluateAt(field.exp(i + field.getGeneratorBase()));
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syndromeCoefficients[syndromeCoefficients.length - 1 - i] = evalResult;
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if (evalResult !== 0) {
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noError = false;
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}
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}
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if (noError) {
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return;
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}
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const syndrome = new GenericGFPoly(field, syndromeCoefficients);
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const sigmaOmega = this.runEuclideanAlgorithm(field.buildMonomial(twoS, 1), syndrome, twoS);
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const sigma = sigmaOmega[0];
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const omega = sigmaOmega[1];
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const errorLocations = this.findErrorLocations(sigma);
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const errorMagnitudes = this.findErrorMagnitudes(omega, errorLocations);
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for (let i = 0; i < errorLocations.length; i++) {
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const position = received.length - 1 - field.log(errorLocations[i]);
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if (position < 0) {
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throw new ReedSolomonException('Bad error location');
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}
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received[position] = GenericGF.addOrSubtract(received[position], errorMagnitudes[i]);
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}
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}
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runEuclideanAlgorithm(a, b, R /*int*/) {
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// Assume a's degree is >= b's
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if (a.getDegree() < b.getDegree()) {
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const temp = a;
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a = b;
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b = temp;
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}
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const field = this.field;
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let rLast = a;
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let r = b;
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let tLast = field.getZero();
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let t = field.getOne();
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// Run Euclidean algorithm until r's degree is less than R/2
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while (r.getDegree() >= (R / 2 | 0)) {
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let rLastLast = rLast;
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let tLastLast = tLast;
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rLast = r;
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tLast = t;
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// Divide rLastLast by rLast, with quotient in q and remainder in r
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if (rLast.isZero()) {
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// Oops, Euclidean algorithm already terminated?
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throw new ReedSolomonException('r_{i-1} was zero');
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}
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r = rLastLast;
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let q = field.getZero();
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const denominatorLeadingTerm = rLast.getCoefficient(rLast.getDegree());
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const dltInverse = field.inverse(denominatorLeadingTerm);
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while (r.getDegree() >= rLast.getDegree() && !r.isZero()) {
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const degreeDiff = r.getDegree() - rLast.getDegree();
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const scale = field.multiply(r.getCoefficient(r.getDegree()), dltInverse);
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q = q.addOrSubtract(field.buildMonomial(degreeDiff, scale));
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r = r.addOrSubtract(rLast.multiplyByMonomial(degreeDiff, scale));
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}
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t = q.multiply(tLast).addOrSubtract(tLastLast);
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if (r.getDegree() >= rLast.getDegree()) {
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throw new IllegalStateException('Division algorithm failed to reduce polynomial?');
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}
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}
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const sigmaTildeAtZero = t.getCoefficient(0);
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if (sigmaTildeAtZero === 0) {
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throw new ReedSolomonException('sigmaTilde(0) was zero');
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}
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const inverse = field.inverse(sigmaTildeAtZero);
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const sigma = t.multiplyScalar(inverse);
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const omega = r.multiplyScalar(inverse);
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return [sigma, omega];
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}
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findErrorLocations(errorLocator) {
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// This is a direct application of Chien's search
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const numErrors = errorLocator.getDegree();
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if (numErrors === 1) { // shortcut
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return Int32Array.from([errorLocator.getCoefficient(1)]);
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}
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const result = new Int32Array(numErrors);
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let e = 0;
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const field = this.field;
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for (let i = 1; i < field.getSize() && e < numErrors; i++) {
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if (errorLocator.evaluateAt(i) === 0) {
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result[e] = field.inverse(i);
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e++;
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}
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}
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if (e !== numErrors) {
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throw new ReedSolomonException('Error locator degree does not match number of roots');
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}
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return result;
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}
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findErrorMagnitudes(errorEvaluator, errorLocations) {
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// This is directly applying Forney's Formula
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const s = errorLocations.length;
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const result = new Int32Array(s);
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const field = this.field;
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for (let i = 0; i < s; i++) {
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const xiInverse = field.inverse(errorLocations[i]);
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let denominator = 1;
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for (let j = 0; j < s; j++) {
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if (i !== j) {
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// denominator = field.multiply(denominator,
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// GenericGF.addOrSubtract(1, field.multiply(errorLocations[j], xiInverse)))
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// Above should work but fails on some Apple and Linux JDKs due to a Hotspot bug.
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// Below is a funny-looking workaround from Steven Parkes
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const term = field.multiply(errorLocations[j], xiInverse);
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const termPlus1 = (term & 0x1) === 0 ? term | 1 : term & ~1;
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denominator = field.multiply(denominator, termPlus1);
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}
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}
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result[i] = field.multiply(errorEvaluator.evaluateAt(xiInverse), field.inverse(denominator));
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if (field.getGeneratorBase() !== 0) {
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result[i] = field.multiply(result[i], xiInverse);
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}
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}
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return result;
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}
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}
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