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608 lines
21 KiB
608 lines
21 KiB
/*
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* QR Code generator library (C++)
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*
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* Copyright (c) 2016 Project Nayuki
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* https://www.nayuki.io/page/qr-code-generator-library
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*
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* (MIT License)
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* Permission is hereby granted, free of charge, to any person obtaining a copy of
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* this software and associated documentation files (the "Software"), to deal in
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* the Software without restriction, including without limitation the rights to
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* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
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* the Software, and to permit persons to whom the Software is furnished to do so,
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* subject to the following conditions:
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* - The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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* - The Software is provided "as is", without warranty of any kind, express or
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* implied, including but not limited to the warranties of merchantability,
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* fitness for a particular purpose and noninfringement. In no event shall the
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* authors or copyright holders be liable for any claim, damages or other
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* liability, whether in an action of contract, tort or otherwise, arising from,
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* out of or in connection with the Software or the use or other dealings in the
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* Software.
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*/
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#include <algorithm>
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#include <climits>
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#include <cmath>
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#include <cstddef>
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#include <sstream>
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#include "BitBuffer.hpp"
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#include "QrCode.hpp"
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qrcodegen::QrCode::Ecc::Ecc(int ord, int fb) :
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ordinal(ord),
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formatBits(fb) {}
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const qrcodegen::QrCode::Ecc qrcodegen::QrCode::Ecc::LOW (0, 1);
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const qrcodegen::QrCode::Ecc qrcodegen::QrCode::Ecc::MEDIUM (1, 0);
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const qrcodegen::QrCode::Ecc qrcodegen::QrCode::Ecc::QUARTILE(2, 3);
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const qrcodegen::QrCode::Ecc qrcodegen::QrCode::Ecc::HIGH (3, 2);
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qrcodegen::QrCode qrcodegen::QrCode::encodeText(const char *text, const Ecc &ecl) {
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std::vector<QrSegment> segs(QrSegment::makeSegments(text));
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return encodeSegments(segs, ecl);
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}
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qrcodegen::QrCode qrcodegen::QrCode::encodeBinary(const std::vector<uint8_t> &data, const Ecc &ecl) {
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std::vector<QrSegment> segs;
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segs.push_back(QrSegment::makeBytes(data));
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return encodeSegments(segs, ecl);
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}
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qrcodegen::QrCode qrcodegen::QrCode::encodeSegments(const std::vector<QrSegment> &segs, const Ecc &ecl,
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int minVersion, int maxVersion, int mask, bool boostEcl) {
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if (!(1 <= minVersion && minVersion <= maxVersion && maxVersion <= 40) || mask < -1 || mask > 7)
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throw "Invalid value";
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// Find the minimal version number to use
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int version, dataUsedBits;
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for (version = minVersion; ; version++) {
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int dataCapacityBits = getNumDataCodewords(version, ecl) * 8; // Number of data bits available
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dataUsedBits = QrSegment::getTotalBits(segs, version);
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if (dataUsedBits != -1 && dataUsedBits <= dataCapacityBits)
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break; // This version number is found to be suitable
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if (version >= maxVersion) // All versions in the range could not fit the given data
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throw "Data too long";
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}
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if (dataUsedBits == -1)
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throw "Assertion error";
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// Increase the error correction level while the data still fits in the current version number
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const Ecc *newEcl = &ecl;
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if (boostEcl) {
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if (dataUsedBits <= getNumDataCodewords(version, Ecc::MEDIUM ) * 8) newEcl = &Ecc::MEDIUM ;
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if (dataUsedBits <= getNumDataCodewords(version, Ecc::QUARTILE) * 8) newEcl = &Ecc::QUARTILE;
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if (dataUsedBits <= getNumDataCodewords(version, Ecc::HIGH ) * 8) newEcl = &Ecc::HIGH ;
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}
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// Create the data bit string by concatenating all segments
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int dataCapacityBits = getNumDataCodewords(version, *newEcl) * 8;
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BitBuffer bb;
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for (size_t i = 0; i < segs.size(); i++) {
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const QrSegment &seg(segs.at(i));
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bb.appendBits(seg.mode.modeBits, 4);
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bb.appendBits(seg.numChars, seg.mode.numCharCountBits(version));
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bb.appendData(seg);
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}
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// Add terminator and pad up to a byte if applicable
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bb.appendBits(0, std::min(4, dataCapacityBits - bb.getBitLength()));
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bb.appendBits(0, (8 - bb.getBitLength() % 8) % 8);
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// Pad with alternate bytes until data capacity is reached
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for (uint8_t padByte = 0xEC; bb.getBitLength() < dataCapacityBits; padByte ^= 0xEC ^ 0x11)
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bb.appendBits(padByte, 8);
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if (bb.getBitLength() % 8 != 0)
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throw "Assertion error";
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// Create the QR Code symbol
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return QrCode(version, *newEcl, bb.getBytes(), mask);
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}
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qrcodegen::QrCode::QrCode(int ver, const Ecc &ecl, const std::vector<uint8_t> &dataCodewords, int mask) :
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// Initialize scalar fields
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version(ver),
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size(1 <= ver && ver <= 40 ? ver * 4 + 17 : -1), // Avoid signed overflow undefined behavior
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errorCorrectionLevel(ecl) {
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// Check arguments
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if (ver < 1 || ver > 40 || mask < -1 || mask > 7)
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throw "Value out of range";
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std::vector<bool> row(size);
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for (int i = 0; i < size; i++) {
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modules.push_back(row);
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isFunction.push_back(row);
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}
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// Draw function patterns, draw all codewords, do masking
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drawFunctionPatterns();
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const std::vector<uint8_t> allCodewords(appendErrorCorrection(dataCodewords));
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drawCodewords(allCodewords);
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this->mask = handleConstructorMasking(mask);
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}
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qrcodegen::QrCode::QrCode(const QrCode &qr, int mask) :
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// Copy scalar fields
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version(qr.version),
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size(qr.size),
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errorCorrectionLevel(qr.errorCorrectionLevel) {
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// Check arguments
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if (mask < -1 || mask > 7)
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throw "Mask value out of range";
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// Handle grid fields
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modules = qr.modules;
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isFunction = qr.isFunction;
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// Handle masking
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applyMask(qr.mask); // Undo old mask
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this->mask = handleConstructorMasking(mask);
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}
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int qrcodegen::QrCode::getMask() const {
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return mask;
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}
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int qrcodegen::QrCode::getModule(int x, int y) const {
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if (0 <= x && x < size && 0 <= y && y < size)
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return modules.at(y).at(x) ? 1 : 0;
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else
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return 0; // Infinite white border
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}
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std::string qrcodegen::QrCode::toSvgString(int border) const {
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if (border < 0)
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throw "Border must be non-negative";
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std::ostringstream sb;
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sb << "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n";
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sb << "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n";
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sb << "<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\" viewBox=\"0 0 ";
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sb << (size + border * 2) << " " << (size + border * 2) << "\">\n";
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sb << "\t<rect width=\"100%\" height=\"100%\" fill=\"#FFFFFF\" stroke-width=\"0\"/>\n";
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sb << "\t<path d=\"";
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bool head = true;
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for (int y = -border; y < size + border; y++) {
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for (int x = -border; x < size + border; x++) {
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if (getModule(x, y) == 1) {
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if (head)
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head = false;
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else
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sb << " ";
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sb << "M" << (x + border) << "," << (y + border) << "h1v1h-1z";
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}
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}
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}
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sb << "\" fill=\"#000000\" stroke-width=\"0\"/>\n";
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sb << "</svg>\n";
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return sb.str();
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}
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void qrcodegen::QrCode::drawFunctionPatterns() {
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// Draw the horizontal and vertical timing patterns
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for (int i = 0; i < size; i++) {
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setFunctionModule(6, i, i % 2 == 0);
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setFunctionModule(i, 6, i % 2 == 0);
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}
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// Draw 3 finder patterns (all corners except bottom right; overwrites some timing modules)
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drawFinderPattern(3, 3);
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drawFinderPattern(size - 4, 3);
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drawFinderPattern(3, size - 4);
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// Draw the numerous alignment patterns
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const std::vector<int> alignPatPos(getAlignmentPatternPositions(version));
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int numAlign = alignPatPos.size();
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for (int i = 0; i < numAlign; i++) {
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for (int j = 0; j < numAlign; j++) {
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if ((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0))
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continue; // Skip the three finder corners
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else
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drawAlignmentPattern(alignPatPos.at(i), alignPatPos.at(j));
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}
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}
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// Draw configuration data
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drawFormatBits(0); // Dummy mask value; overwritten later in the constructor
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drawVersion();
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}
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void qrcodegen::QrCode::drawFormatBits(int mask) {
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// Calculate error correction code and pack bits
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int data = errorCorrectionLevel.formatBits << 3 | mask; // errCorrLvl is uint2, mask is uint3
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int rem = data;
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for (int i = 0; i < 10; i++)
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rem = (rem << 1) ^ ((rem >> 9) * 0x537);
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data = data << 10 | rem;
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data ^= 0x5412; // uint15
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if (data >> 15 != 0)
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throw "Assertion error";
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// Draw first copy
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for (int i = 0; i <= 5; i++)
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setFunctionModule(8, i, ((data >> i) & 1) != 0);
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setFunctionModule(8, 7, ((data >> 6) & 1) != 0);
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setFunctionModule(8, 8, ((data >> 7) & 1) != 0);
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setFunctionModule(7, 8, ((data >> 8) & 1) != 0);
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for (int i = 9; i < 15; i++)
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setFunctionModule(14 - i, 8, ((data >> i) & 1) != 0);
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// Draw second copy
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for (int i = 0; i <= 7; i++)
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setFunctionModule(size - 1 - i, 8, ((data >> i) & 1) != 0);
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for (int i = 8; i < 15; i++)
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setFunctionModule(8, size - 15 + i, ((data >> i) & 1) != 0);
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setFunctionModule(8, size - 8, true);
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}
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void qrcodegen::QrCode::drawVersion() {
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if (version < 7)
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return;
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// Calculate error correction code and pack bits
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int rem = version; // version is uint6, in the range [7, 40]
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for (int i = 0; i < 12; i++)
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rem = (rem << 1) ^ ((rem >> 11) * 0x1F25);
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int data = version << 12 | rem; // uint18
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if (data >> 18 != 0)
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throw "Assertion error";
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// Draw two copies
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for (int i = 0; i < 18; i++) {
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bool bit = ((data >> i) & 1) != 0;
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int a = size - 11 + i % 3, b = i / 3;
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setFunctionModule(a, b, bit);
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setFunctionModule(b, a, bit);
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}
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}
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void qrcodegen::QrCode::drawFinderPattern(int x, int y) {
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for (int i = -4; i <= 4; i++) {
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for (int j = -4; j <= 4; j++) {
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int dist = std::max(std::abs(i), std::abs(j)); // Chebyshev/infinity norm
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int xx = x + j, yy = y + i;
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if (0 <= xx && xx < size && 0 <= yy && yy < size)
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setFunctionModule(xx, yy, dist != 2 && dist != 4);
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}
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}
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}
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void qrcodegen::QrCode::drawAlignmentPattern(int x, int y) {
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for (int i = -2; i <= 2; i++) {
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for (int j = -2; j <= 2; j++)
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setFunctionModule(x + j, y + i, std::max(std::abs(i), std::abs(j)) != 1);
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}
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}
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void qrcodegen::QrCode::setFunctionModule(int x, int y, bool isBlack) {
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modules.at(y).at(x) = isBlack;
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isFunction.at(y).at(x) = true;
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}
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std::vector<uint8_t> qrcodegen::QrCode::appendErrorCorrection(const std::vector<uint8_t> &data) const {
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if (data.size() != static_cast<unsigned int>(getNumDataCodewords(version, errorCorrectionLevel)))
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throw "Invalid argument";
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int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[errorCorrectionLevel.ordinal][version];
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int numEcc = NUM_ERROR_CORRECTION_CODEWORDS[errorCorrectionLevel.ordinal][version];
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if (numEcc % numBlocks != 0)
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throw "Assertion error";
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int eccLen = numEcc / numBlocks;
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int numShortBlocks = numBlocks - getNumRawDataModules(version) / 8 % numBlocks;
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int shortBlockLen = getNumRawDataModules(version) / 8 / numBlocks;
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std::vector<std::vector<uint8_t>> blocks;
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const ReedSolomonGenerator rs(eccLen);
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for (int i = 0, k = 0; i < numBlocks; i++) {
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std::vector<uint8_t> dat;
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dat.insert(dat.begin(), data.begin() + k, data.begin() + (k + shortBlockLen - eccLen + (i < numShortBlocks ? 0 : 1)));
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k += dat.size();
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const std::vector<uint8_t> ecc(rs.getRemainder(dat));
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if (i < numShortBlocks)
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dat.push_back(0);
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dat.insert(dat.end(), ecc.begin(), ecc.end());
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blocks.push_back(dat);
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}
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std::vector<uint8_t> result;
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for (int i = 0; static_cast<unsigned int>(i) < blocks.at(0).size(); i++) {
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for (int j = 0; static_cast<unsigned int>(j) < blocks.size(); j++) {
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if (i != shortBlockLen - eccLen || j >= numShortBlocks)
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result.push_back(blocks.at(j).at(i));
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}
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}
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return result;
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}
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void qrcodegen::QrCode::drawCodewords(const std::vector<uint8_t> &data) {
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if (data.size() != static_cast<unsigned int>(getNumRawDataModules(version) / 8))
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throw "Invalid argument";
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size_t i = 0; // Bit index into the data
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// Do the funny zigzag scan
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for (int right = size - 1; right >= 1; right -= 2) { // Index of right column in each column pair
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if (right == 6)
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right = 5;
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for (int vert = 0; vert < size; vert++) { // Vertical counter
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for (int j = 0; j < 2; j++) {
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int x = right - j; // Actual x coordinate
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bool upwards = ((right & 2) == 0) ^ (x < 6);
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int y = upwards ? size - 1 - vert : vert; // Actual y coordinate
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if (!isFunction.at(y).at(x) && i < data.size() * 8) {
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modules.at(y).at(x) = ((data[i >> 3] >> (7 - (i & 7))) & 1) != 0;
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i++;
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}
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}
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}
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}
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if (static_cast<unsigned int>(i) != data.size() * 8)
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throw "Assertion error";
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}
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void qrcodegen::QrCode::applyMask(int mask) {
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if (mask < 0 || mask > 7)
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throw "Mask value out of range";
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for (int y = 0; y < size; y++) {
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for (int x = 0; x < size; x++) {
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bool invert;
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switch (mask) {
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case 0: invert = (x + y) % 2 == 0; break;
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case 1: invert = y % 2 == 0; break;
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case 2: invert = x % 3 == 0; break;
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case 3: invert = (x + y) % 3 == 0; break;
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case 4: invert = (x / 3 + y / 2) % 2 == 0; break;
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case 5: invert = x * y % 2 + x * y % 3 == 0; break;
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case 6: invert = (x * y % 2 + x * y % 3) % 2 == 0; break;
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case 7: invert = ((x + y) % 2 + x * y % 3) % 2 == 0; break;
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default: throw "Assertion error";
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}
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modules.at(y).at(x) = modules.at(y).at(x) ^ (invert & !isFunction.at(y).at(x));
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}
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}
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}
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int qrcodegen::QrCode::handleConstructorMasking(int mask) {
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if (mask == -1) { // Automatically choose best mask
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int32_t minPenalty = INT32_MAX;
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for (int i = 0; i < 8; i++) {
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drawFormatBits(i);
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applyMask(i);
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int penalty = getPenaltyScore();
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if (penalty < minPenalty) {
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mask = i;
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minPenalty = penalty;
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}
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applyMask(i); // Undoes the mask due to XOR
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}
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}
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if (mask < 0 || mask > 7)
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throw "Assertion error";
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drawFormatBits(mask); // Overwrite old format bits
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applyMask(mask); // Apply the final choice of mask
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return mask; // The caller shall assign this value to the final-declared field
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}
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int qrcodegen::QrCode::getPenaltyScore() const {
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int result = 0;
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// Adjacent modules in row having same color
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for (int y = 0; y < size; y++) {
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bool colorX = modules.at(y).at(0);
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for (int x = 1, runX = 1; x < size; x++) {
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if (modules.at(y).at(x) != colorX) {
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colorX = modules.at(y).at(x);
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runX = 1;
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} else {
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runX++;
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if (runX == 5)
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result += PENALTY_N1;
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else if (runX > 5)
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result++;
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}
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}
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}
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// Adjacent modules in column having same color
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for (int x = 0; x < size; x++) {
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bool colorY = modules.at(0).at(x);
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for (int y = 1, runY = 1; y < size; y++) {
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if (modules.at(y).at(x) != colorY) {
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colorY = modules.at(y).at(x);
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runY = 1;
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} else {
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runY++;
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if (runY == 5)
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result += PENALTY_N1;
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else if (runY > 5)
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result++;
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}
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}
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}
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// 2*2 blocks of modules having same color
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for (int y = 0; y < size - 1; y++) {
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for (int x = 0; x < size - 1; x++) {
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bool color = modules.at(y).at(x);
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if ( color == modules.at(y).at(x + 1) &&
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color == modules.at(y + 1).at(x) &&
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color == modules.at(y + 1).at(x + 1))
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result += PENALTY_N2;
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}
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}
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|
|
|
// Finder-like pattern in rows
|
|
for (int y = 0; y < size; y++) {
|
|
for (int x = 0, bits = 0; x < size; x++) {
|
|
bits = ((bits << 1) & 0x7FF) | (modules.at(y).at(x) ? 1 : 0);
|
|
if (x >= 10 && (bits == 0x05D || bits == 0x5D0)) // Needs 11 bits accumulated
|
|
result += PENALTY_N3;
|
|
}
|
|
}
|
|
// Finder-like pattern in columns
|
|
for (int x = 0; x < size; x++) {
|
|
for (int y = 0, bits = 0; y < size; y++) {
|
|
bits = ((bits << 1) & 0x7FF) | (modules.at(y).at(x) ? 1 : 0);
|
|
if (y >= 10 && (bits == 0x05D || bits == 0x5D0)) // Needs 11 bits accumulated
|
|
result += PENALTY_N3;
|
|
}
|
|
}
|
|
|
|
// Balance of black and white modules
|
|
int black = 0;
|
|
for (int y = 0; y < size; y++) {
|
|
for (int x = 0; x < size; x++) {
|
|
if (modules.at(y).at(x))
|
|
black++;
|
|
}
|
|
}
|
|
int total = size * size;
|
|
// Find smallest k such that (45-5k)% <= dark/total <= (55+5k)%
|
|
for (int k = 0; black*20 < (9-k)*total || black*20 > (11+k)*total; k++)
|
|
result += PENALTY_N4;
|
|
return result;
|
|
}
|
|
|
|
|
|
std::vector<int> qrcodegen::QrCode::getAlignmentPatternPositions(int ver) {
|
|
if (ver < 1 || ver > 40)
|
|
throw "Version number out of range";
|
|
else if (ver == 1)
|
|
return std::vector<int>();
|
|
else {
|
|
int numAlign = ver / 7 + 2;
|
|
int step;
|
|
if (ver != 32)
|
|
step = (ver * 4 + numAlign * 2 + 1) / (2 * numAlign - 2) * 2; // ceil((size - 13) / (2*numAlign - 2)) * 2
|
|
else // C-C-C-Combo breaker!
|
|
step = 26;
|
|
|
|
std::vector<int> result(numAlign);
|
|
int size = ver * 4 + 17;
|
|
result.at(0) = 6;
|
|
for (int i = numAlign - 1, pos = size - 7; i >= 1; i--, pos -= step)
|
|
result.at(i) = pos;
|
|
return result;
|
|
}
|
|
}
|
|
|
|
|
|
int qrcodegen::QrCode::getNumRawDataModules(int ver) {
|
|
if (ver < 1 || ver > 40)
|
|
throw "Version number out of range";
|
|
int result = (16 * ver + 128) * ver + 64;
|
|
if (ver >= 2) {
|
|
int numAlign = ver / 7 + 2;
|
|
result -= (25 * numAlign - 10) * numAlign - 55;
|
|
if (ver >= 7)
|
|
result -= 18 * 2; // Subtract version information
|
|
}
|
|
return result;
|
|
}
|
|
|
|
|
|
int qrcodegen::QrCode::getNumDataCodewords(int ver, const Ecc &ecl) {
|
|
if (ver < 1 || ver > 40)
|
|
throw "Version number out of range";
|
|
return getNumRawDataModules(ver) / 8 - NUM_ERROR_CORRECTION_CODEWORDS[ecl.ordinal][ver];
|
|
}
|
|
|
|
|
|
/*---- Tables of constants ----*/
|
|
|
|
const int qrcodegen::QrCode::PENALTY_N1 = 3;
|
|
const int qrcodegen::QrCode::PENALTY_N2 = 3;
|
|
const int qrcodegen::QrCode::PENALTY_N3 = 40;
|
|
const int qrcodegen::QrCode::PENALTY_N4 = 10;
|
|
|
|
|
|
const int16_t qrcodegen::QrCode::NUM_ERROR_CORRECTION_CODEWORDS[4][41] = {
|
|
// Version: (note that index 0 is for padding, and is set to an illegal value)
|
|
//0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 Error correction level
|
|
{-1, 7, 10, 15, 20, 26, 36, 40, 48, 60, 72, 80, 96, 104, 120, 132, 144, 168, 180, 196, 224, 224, 252, 270, 300, 312, 336, 360, 390, 420, 450, 480, 510, 540, 570, 570, 600, 630, 660, 720, 750}, // Low
|
|
{-1, 10, 16, 26, 36, 48, 64, 72, 88, 110, 130, 150, 176, 198, 216, 240, 280, 308, 338, 364, 416, 442, 476, 504, 560, 588, 644, 700, 728, 784, 812, 868, 924, 980, 1036, 1064, 1120, 1204, 1260, 1316, 1372}, // Medium
|
|
{-1, 13, 22, 36, 52, 72, 96, 108, 132, 160, 192, 224, 260, 288, 320, 360, 408, 448, 504, 546, 600, 644, 690, 750, 810, 870, 952, 1020, 1050, 1140, 1200, 1290, 1350, 1440, 1530, 1590, 1680, 1770, 1860, 1950, 2040}, // Quartile
|
|
{-1, 17, 28, 44, 64, 88, 112, 130, 156, 192, 224, 264, 308, 352, 384, 432, 480, 532, 588, 650, 700, 750, 816, 900, 960, 1050, 1110, 1200, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2100, 2220, 2310, 2430}, // High
|
|
};
|
|
|
|
const int8_t qrcodegen::QrCode::NUM_ERROR_CORRECTION_BLOCKS[4][41] = {
|
|
// Version: (note that index 0 is for padding, and is set to an illegal value)
|
|
//0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 Error correction level
|
|
{-1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 7, 8, 8, 9, 9, 10, 12, 12, 12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 21, 22, 24, 25}, // Low
|
|
{-1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5, 5, 8, 9, 9, 10, 10, 11, 13, 14, 16, 17, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 33, 35, 37, 38, 40, 43, 45, 47, 49}, // Medium
|
|
{-1, 1, 1, 2, 2, 4, 4, 6, 6, 8, 8, 8, 10, 12, 16, 12, 17, 16, 18, 21, 20, 23, 23, 25, 27, 29, 34, 34, 35, 38, 40, 43, 45, 48, 51, 53, 56, 59, 62, 65, 68}, // Quartile
|
|
{-1, 1, 1, 2, 4, 4, 4, 5, 6, 8, 8, 11, 11, 16, 16, 18, 16, 19, 21, 25, 25, 25, 34, 30, 32, 35, 37, 40, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 77, 81}, // High
|
|
};
|
|
|
|
|
|
qrcodegen::QrCode::ReedSolomonGenerator::ReedSolomonGenerator(int degree) :
|
|
coefficients() {
|
|
if (degree < 1 || degree > 255)
|
|
throw "Degree out of range";
|
|
|
|
// Start with the monomial x^0
|
|
coefficients.resize(degree);
|
|
coefficients.at(degree - 1) = 1;
|
|
|
|
// Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}),
|
|
// drop the highest term, and store the rest of the coefficients in order of descending powers.
|
|
// Note that r = 0x02, which is a generator element of this field GF(2^8/0x11D).
|
|
int root = 1;
|
|
for (int i = 0; i < degree; i++) {
|
|
// Multiply the current product by (x - r^i)
|
|
for (size_t j = 0; j < coefficients.size(); j++) {
|
|
coefficients.at(j) = multiply(coefficients.at(j), static_cast<uint8_t>(root));
|
|
if (j + 1 < coefficients.size())
|
|
coefficients.at(j) ^= coefficients.at(j + 1);
|
|
}
|
|
root = (root << 1) ^ ((root >> 7) * 0x11D); // Multiply by 0x02 mod GF(2^8/0x11D)
|
|
}
|
|
}
|
|
|
|
|
|
std::vector<uint8_t> qrcodegen::QrCode::ReedSolomonGenerator::getRemainder(const std::vector<uint8_t> &data) const {
|
|
// Compute the remainder by performing polynomial division
|
|
std::vector<uint8_t> result(coefficients.size());
|
|
for (size_t i = 0; i < data.size(); i++) {
|
|
uint8_t factor = data.at(i) ^ result.at(0);
|
|
result.erase(result.begin());
|
|
result.push_back(0);
|
|
for (size_t j = 0; j < result.size(); j++)
|
|
result.at(j) ^= multiply(coefficients.at(j), factor);
|
|
}
|
|
return result;
|
|
}
|
|
|
|
|
|
uint8_t qrcodegen::QrCode::ReedSolomonGenerator::multiply(uint8_t x, uint8_t y) {
|
|
// Russian peasant multiplication
|
|
int z = 0;
|
|
for (int i = 7; i >= 0; i--) {
|
|
z = (z << 1) ^ ((z >> 7) * 0x11D);
|
|
z ^= ((y >> i) & 1) * x;
|
|
}
|
|
if (z >> 8 != 0)
|
|
throw "Assertion error";
|
|
return static_cast<uint8_t>(z);
|
|
}
|