ANSLibs/QRCode/ReedSolomonDecoder.cpp

/*
* Copyright 2016 Nu-book Inc.
* Copyright 2016 ZXing authors
* Copyright 2017 Axel Waggershauser
*/
// SPDX-License-Identifier: Apache-2.0

#include "ReedSolomonDecoder.h"

#include "GenericGF.h"
#include "ZXConfig.h"

#include <algorithm>
#include <stdexcept>
#include <utility>

namespace ZXing {

static bool
RunEuclideanAlgorithm(const GenericGF& field, std::vector<int>&& rCoefs, GenericGFPoly& sigma, GenericGFPoly& omega)
{
	int R = Size(rCoefs); // == numECCodeWords
	GenericGFPoly r(field, std::move(rCoefs));
	GenericGFPoly& tLast = omega.setField(field);
	GenericGFPoly& t = sigma.setField(field);
	ZX_THREAD_LOCAL GenericGFPoly q, rLast;

	rLast.setField(field);
	q.setField(field);

	rLast.setMonomial(1, R);
	tLast.setMonomial(0);
	t.setMonomial(1);

	// Assume r's degree is < rLast's
	if (r.degree() >= rLast.degree())
		swap(r, rLast);

	// Run Euclidean algorithm until r's degree is less than R/2
	while (r.degree() >= R / 2) {
		swap(tLast, t);
		swap(rLast, r);

		// Divide rLastLast by rLast, with quotient in q and remainder in r
		if (rLast.isZero())
			return false; // Oops, Euclidean algorithm already terminated?

		r.divide(rLast, q);

		q.multiply(tLast);
		q.addOrSubtract(t);
		swap(t, q); // t = q

		if (r.degree() >= rLast.degree())
			throw std::runtime_error("Division algorithm failed to reduce polynomial?");
	}

	int sigmaTildeAtZero = t.constant();
	if (sigmaTildeAtZero == 0)
		return false;

	int inverse = field.inverse(sigmaTildeAtZero);
	t.multiplyByMonomial(inverse);
	r.multiplyByMonomial(inverse);

	// sigma is t
	omega = std::move(r);
	return true;
}

static std::vector<int>
FindErrorLocations(const GenericGF& field, const GenericGFPoly& errorLocator)
{
	// This is a direct application of Chien's search
	int numErrors = errorLocator.degree();
	std::vector<int> res;
	res.reserve(numErrors);

	for (int i = 1; i < field.size() && Size(res) < numErrors; i++)
		if (errorLocator.evaluateAt(i) == 0)
			res.push_back(field.inverse(i));

	if (Size(res) != numErrors)
		return {}; // Error locator degree does not match number of roots

	return res;
}

static std::vector<int>
FindErrorMagnitudes(const GenericGF& field, const GenericGFPoly& errorEvaluator, const std::vector<int>& errorLocations)
{
	// This is directly applying Forney's Formula
	int s = Size(errorLocations);
	std::vector<int> res(s);
	for (int i = 0; i < s; ++i) {
		int xiInverse = field.inverse(errorLocations[i]);
		int denom = 1;
		for (int j = 0; j < s; ++j)
			if (i != j)
				denom = field.multiply(denom, 1 ^ field.multiply(errorLocations[j], xiInverse));
		res[i] = field.multiply(errorEvaluator.evaluateAt(xiInverse), field.inverse(denom));
		if (field.generatorBase() != 0)
			res[i] = field.multiply(res[i], xiInverse);
	}
	return res;
}

bool
ReedSolomonDecode(const GenericGF& field, std::vector<int>& message, int numECCodeWords)
{
	GenericGFPoly poly(field, message);

	std::vector<int> syndromes(numECCodeWords);
	for (int i = 0; i < numECCodeWords; i++)
		syndromes[numECCodeWords - 1 - i] = poly.evaluateAt(field.exp(i + field.generatorBase()));

	// if all syndromes are 0 there is no error to correct
	if (std::all_of(syndromes.begin(), syndromes.end(), [](int c) { return c == 0; }))
		return true;

	ZX_THREAD_LOCAL GenericGFPoly sigma, omega;

	if (!RunEuclideanAlgorithm(field, std::move(syndromes), sigma, omega))
		return false;

	auto errorLocations = FindErrorLocations(field, sigma);
	if (errorLocations.empty())
		return false;

	auto errorMagnitudes = FindErrorMagnitudes(field, omega, errorLocations);

	int msgLen = Size(message);
	for (int i = 0; i < Size(errorLocations); ++i) {
		int position = msgLen - 1 - field.log(errorLocations[i]);
		if (position < 0)
			return false;

		message[position] ^= errorMagnitudes[i];
	}
	return true;
}

} // namespace ZXing