@zxing/library
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TypeScript port of ZXing multi-format 1D/2D barcode image processing library.
175 lines (174 loc) • 7.1 kB
JavaScript
/*
* Copyright 2012 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.pdf417.decoder.ec;
// import com.google.zxing.ChecksumException;
import ChecksumException from '../../../ChecksumException';
import ModulusPoly from './ModulusPoly';
import ModulusGF from './ModulusGF';
/**
* <p>PDF417 error correction implementation.</p>
*
* <p>This <a href="http://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction#Example">example</a>
* is quite useful in understanding the algorithm.</p>
*
* @author Sean Owen
* @see com.google.zxing.common.reedsolomon.ReedSolomonDecoder
*/
export default /*public final*/ class ErrorCorrection {
constructor() {
this.field = ModulusGF.PDF417_GF;
}
/**
* @param received received codewords
* @param numECCodewords number of those codewords used for EC
* @param erasures location of erasures
* @return number of errors
* @throws ChecksumException if errors cannot be corrected, maybe because of too many errors
*/
decode(received, numECCodewords, erasures) {
let poly = new ModulusPoly(this.field, received);
let S = new Int32Array(numECCodewords);
let error = false;
for (let i /*int*/ = numECCodewords; i > 0; i--) {
let evaluation = poly.evaluateAt(this.field.exp(i));
S[numECCodewords - i] = evaluation;
if (evaluation !== 0) {
error = true;
}
}
if (!error) {
return 0;
}
let knownErrors = this.field.getOne();
if (erasures != null) {
for (const erasure of erasures) {
let b = this.field.exp(received.length - 1 - erasure);
// Add (1 - bx) term:
let term = new ModulusPoly(this.field, new Int32Array([this.field.subtract(0, b), 1]));
knownErrors = knownErrors.multiply(term);
}
}
let syndrome = new ModulusPoly(this.field, S);
// syndrome = syndrome.multiply(knownErrors);
let sigmaOmega = this.runEuclideanAlgorithm(this.field.buildMonomial(numECCodewords, 1), syndrome, numECCodewords);
let sigma = sigmaOmega[0];
let omega = sigmaOmega[1];
// sigma = sigma.multiply(knownErrors);
let errorLocations = this.findErrorLocations(sigma);
let errorMagnitudes = this.findErrorMagnitudes(omega, sigma, errorLocations);
for (let i /*int*/ = 0; i < errorLocations.length; i++) {
let position = received.length - 1 - this.field.log(errorLocations[i]);
if (position < 0) {
throw ChecksumException.getChecksumInstance();
}
received[position] = this.field.subtract(received[position], errorMagnitudes[i]);
}
return errorLocations.length;
}
/**
*
* @param ModulusPoly
* @param a
* @param ModulusPoly
* @param b
* @param int
* @param R
* @throws ChecksumException
*/
runEuclideanAlgorithm(a, b, R) {
// Assume a's degree is >= b's
if (a.getDegree() < b.getDegree()) {
let temp = a;
a = b;
b = temp;
}
let rLast = a;
let r = b;
let tLast = this.field.getZero();
let t = this.field.getOne();
// Run Euclidean algorithm until r's degree is less than R/2
while (r.getDegree() >= Math.round(R / 2)) {
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 ChecksumException.getChecksumInstance();
}
r = rLastLast;
let q = this.field.getZero();
let denominatorLeadingTerm = rLast.getCoefficient(rLast.getDegree());
let dltInverse = this.field.inverse(denominatorLeadingTerm);
while (r.getDegree() >= rLast.getDegree() && !r.isZero()) {
let degreeDiff = r.getDegree() - rLast.getDegree();
let scale = this.field.multiply(r.getCoefficient(r.getDegree()), dltInverse);
q = q.add(this.field.buildMonomial(degreeDiff, scale));
r = r.subtract(rLast.multiplyByMonomial(degreeDiff, scale));
}
t = q.multiply(tLast).subtract(tLastLast).negative();
}
let sigmaTildeAtZero = t.getCoefficient(0);
if (sigmaTildeAtZero === 0) {
throw ChecksumException.getChecksumInstance();
}
let inverse = this.field.inverse(sigmaTildeAtZero);
let sigma = t.multiply(inverse);
let omega = r.multiply(inverse);
return [sigma, omega];
}
/**
*
* @param errorLocator
* @throws ChecksumException
*/
findErrorLocations(errorLocator) {
// This is a direct application of Chien's search
let numErrors = errorLocator.getDegree();
let result = new Int32Array(numErrors);
let e = 0;
for (let i /*int*/ = 1; i < this.field.getSize() && e < numErrors; i++) {
if (errorLocator.evaluateAt(i) === 0) {
result[e] = this.field.inverse(i);
e++;
}
}
if (e !== numErrors) {
throw ChecksumException.getChecksumInstance();
}
return result;
}
findErrorMagnitudes(errorEvaluator, errorLocator, errorLocations) {
let errorLocatorDegree = errorLocator.getDegree();
let formalDerivativeCoefficients = new Int32Array(errorLocatorDegree);
for (let i /*int*/ = 1; i <= errorLocatorDegree; i++) {
formalDerivativeCoefficients[errorLocatorDegree - i] =
this.field.multiply(i, errorLocator.getCoefficient(i));
}
let formalDerivative = new ModulusPoly(this.field, formalDerivativeCoefficients);
// This is directly applying Forney's Formula
let s = errorLocations.length;
let result = new Int32Array(s);
for (let i /*int*/ = 0; i < s; i++) {
let xiInverse = this.field.inverse(errorLocations[i]);
let numerator = this.field.subtract(0, errorEvaluator.evaluateAt(xiInverse));
let denominator = this.field.inverse(formalDerivative.evaluateAt(xiInverse));
result[i] = this.field.multiply(numerator, denominator);
}
return result;
}
}