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diff --git a/libraries/zxing/src/com/google/zxing/common/reedsolomon/ReedSolomonDecoder.java b/libraries/zxing/src/com/google/zxing/common/reedsolomon/ReedSolomonDecoder.java
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+/*
+ * 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.
+ */
+
+package com.google.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
+ */
+public final class ReedSolomonDecoder {
+
+ private final GenericGF field;
+
+ public ReedSolomonDecoder(GenericGF 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 void decode(int[] received, int twoS) throws ReedSolomonException {
+ GenericGFPoly poly = new GenericGFPoly(field, received);
+ int[] syndromeCoefficients = new int[twoS];
+ boolean dataMatrix = field.equals(GenericGF.DATA_MATRIX_FIELD_256);
+ boolean noError = true;
+ for (int i = 0; i < twoS; i++) {
+ // Thanks to sanfordsquires for this fix:
+ int eval = poly.evaluateAt(field.exp(dataMatrix ? i + 1 : i));
+ syndromeCoefficients[syndromeCoefficients.length - 1 - i] = eval;
+ if (eval != 0) {
+ noError = false;
+ }
+ }
+ if (noError) {
+ return;
+ }
+ GenericGFPoly syndrome = new GenericGFPoly(field, syndromeCoefficients);
+ GenericGFPoly[] sigmaOmega =
+ runEuclideanAlgorithm(field.buildMonomial(twoS, 1), syndrome, twoS);
+ GenericGFPoly sigma = sigmaOmega[0];
+ GenericGFPoly omega = sigmaOmega[1];
+ int[] errorLocations = findErrorLocations(sigma);
+ int[] errorMagnitudes = findErrorMagnitudes(omega, errorLocations, dataMatrix);
+ for (int i = 0; i < errorLocations.length; i++) {
+ int position = received.length - 1 - field.log(errorLocations[i]);
+ if (position < 0) {
+ throw new ReedSolomonException("Bad error location");
+ }
+ received[position] = GenericGF.addOrSubtract(received[position], errorMagnitudes[i]);
+ }
+ }
+
+ private GenericGFPoly[] runEuclideanAlgorithm(GenericGFPoly a, GenericGFPoly b, int R)
+ throws ReedSolomonException {
+ // Assume a's degree is >= b's
+ if (a.getDegree() < b.getDegree()) {
+ GenericGFPoly temp = a;
+ a = b;
+ b = temp;
+ }
+
+ GenericGFPoly rLast = a;
+ GenericGFPoly r = b;
+ GenericGFPoly sLast = field.getOne();
+ GenericGFPoly s = field.getZero();
+ GenericGFPoly tLast = field.getZero();
+ GenericGFPoly t = field.getOne();
+
+ // Run Euclidean algorithm until r's degree is less than R/2
+ while (r.getDegree() >= R / 2) {
+ GenericGFPoly rLastLast = rLast;
+ GenericGFPoly sLastLast = sLast;
+ GenericGFPoly 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;
+ 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 new ReedSolomonException("sigmaTilde(0) was zero");
+ }
+
+ int inverse = field.inverse(sigmaTildeAtZero);
+ GenericGFPoly sigma = t.multiply(inverse);
+ GenericGFPoly omega = r.multiply(inverse);
+ return new GenericGFPoly[]{sigma, omega};
+ }
+
+ private int[] findErrorLocations(GenericGFPoly errorLocator) throws ReedSolomonException {
+ // This is a direct application of Chien's search
+ int numErrors = errorLocator.getDegree();
+ if (numErrors == 1) { // shortcut
+ return new int[] { errorLocator.getCoefficient(1) };
+ }
+ int[] result = new int[numErrors];
+ int e = 0;
+ for (int i = 1; i < field.getSize() && e < numErrors; i++) {
+ if (errorLocator.evaluateAt(i) == 0) {
+ result[e] = field.inverse(i);
+ e++;
+ }
+ }
+ if (e != numErrors) {
+ throw new ReedSolomonException("Error locator degree does not match number of roots");
+ }
+ return result;
+ }
+
+ private int[] findErrorMagnitudes(GenericGFPoly errorEvaluator, int[] errorLocations, boolean dataMatrix) {
+ // This is directly applying Forney's Formula
+ int s = errorLocations.length;
+ int[] result = new int[s];
+ for (int i = 0; i < s; i++) {
+ int xiInverse = field.inverse(errorLocations[i]);
+ int denominator = 1;
+ for (int 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
+ int term = field.multiply(errorLocations[j], xiInverse);
+ int termPlus1 = (term & 0x1) == 0 ? term | 1 : term & ~1;
+ denominator = field.multiply(denominator, termPlus1);
+ }
+ }
+ result[i] = field.multiply(errorEvaluator.evaluateAt(xiInverse),
+ field.inverse(denominator));
+ // Thanks to sanfordsquires for this fix:
+ if (dataMatrix) {
+ result[i] = field.multiply(result[i], xiInverse);
+ }
+ }
+ return result;
+ }
+
+}