@zxing/library
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TypeScript port of ZXing multi-format 1D/2D barcode image processing library.
179 lines (178 loc) • 7.71 kB
JavaScript
/*
* 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 com.google.zxing.common.reedsolomon {*/
import GenericGF from './GenericGF';
import GenericGFPoly from './GenericGFPoly';
import ReedSolomonException from '../../ReedSolomonException';
import IllegalStateException from '../../IllegalStateException';
/**
* <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
*/
export default class ReedSolomonDecoder {
constructor(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
*/
decode(received, twoS /*int*/) {
const field = this.field;
const poly = new GenericGFPoly(field, received);
const syndromeCoefficients = new Int32Array(twoS);
let noError = true;
for (let i = 0; i < twoS; i++) {
const evalResult = poly.evaluateAt(field.exp(i + field.getGeneratorBase()));
syndromeCoefficients[syndromeCoefficients.length - 1 - i] = evalResult;
if (evalResult !== 0) {
noError = false;
}
}
if (noError) {
return;
}
const syndrome = new GenericGFPoly(field, syndromeCoefficients);
const sigmaOmega = this.runEuclideanAlgorithm(field.buildMonomial(twoS, 1), syndrome, twoS);
const sigma = sigmaOmega[0];
const omega = sigmaOmega[1];
const errorLocations = this.findErrorLocations(sigma);
const errorMagnitudes = this.findErrorMagnitudes(omega, errorLocations);
for (let i = 0; i < errorLocations.length; i++) {
const 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]);
}
}
runEuclideanAlgorithm(a, b, R /*int*/) {
// Assume a's degree is >= b's
if (a.getDegree() < b.getDegree()) {
const temp = a;
a = b;
b = temp;
}
const field = this.field;
let rLast = a;
let r = b;
let tLast = field.getZero();
let t = field.getOne();
// Run Euclidean algorithm until r's degree is less than R/2
while (r.getDegree() >= (R / 2 | 0)) {
let rLastLast = rLast;
let 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;
let q = field.getZero();
const denominatorLeadingTerm = rLast.getCoefficient(rLast.getDegree());
const dltInverse = field.inverse(denominatorLeadingTerm);
while (r.getDegree() >= rLast.getDegree() && !r.isZero()) {
const degreeDiff = r.getDegree() - rLast.getDegree();
const scale = field.multiply(r.getCoefficient(r.getDegree()), dltInverse);
q = q.addOrSubtract(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?');
}
}
const sigmaTildeAtZero = t.getCoefficient(0);
if (sigmaTildeAtZero === 0) {
throw new ReedSolomonException('sigmaTilde(0) was zero');
}
const inverse = field.inverse(sigmaTildeAtZero);
const sigma = t.multiplyScalar(inverse);
const omega = r.multiplyScalar(inverse);
return [sigma, omega];
}
findErrorLocations(errorLocator) {
// This is a direct application of Chien's search
const numErrors = errorLocator.getDegree();
if (numErrors === 1) { // shortcut
return Int32Array.from([errorLocator.getCoefficient(1)]);
}
const result = new Int32Array(numErrors);
let e = 0;
const field = this.field;
for (let 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;
}
findErrorMagnitudes(errorEvaluator, errorLocations) {
// This is directly applying Forney's Formula
const s = errorLocations.length;
const result = new Int32Array(s);
const field = this.field;
for (let i = 0; i < s; i++) {
const xiInverse = field.inverse(errorLocations[i]);
let denominator = 1;
for (let 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
const term = field.multiply(errorLocations[j], xiInverse);
const termPlus1 = (term & 0x1) === 0 ? term | 1 : term & ~1;
denominator = field.multiply(denominator, termPlus1);
}
}
result[i] = field.multiply(errorEvaluator.evaluateAt(xiInverse), field.inverse(denominator));
if (field.getGeneratorBase() !== 0) {
result[i] = field.multiply(result[i], xiInverse);
}
}
return result;
}
}