QrCode.cpp

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/* 
 * QR Code generator library (C++)
 * 
 * Copyright (c) Project Nayuki
 * https://www.nayuki.io/page/qr-code-generator-library
 * 
 * (MIT License)
 * Permission is hereby granted, free of charge, to any person obtaining a copy of
 * this software and associated documentation files (the "Software"), to deal in
 * the Software without restriction, including without limitation the rights to
 * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
 * the Software, and to permit persons to whom the Software is furnished to do so,
 * subject to the following conditions:
 * - The above copyright notice and this permission notice shall be included in
 *   all copies or substantial portions of the Software.
 * - The Software is provided "as is", without warranty of any kind, express or
 *   implied, including but not limited to the warranties of merchantability,
 *   fitness for a particular purpose and noninfringement. In no event shall the
 *   authors or copyright holders be liable for any claim, damages or other
 *   liability, whether in an action of contract, tort or otherwise, arising from,
 *   out of or in connection with the Software or the use or other dealings in the
 *   Software.
 */
 
#include <algorithm>
#include <climits>
#include <cmath>
#include <cstddef>
#include <sstream>
#include "BitBuffer.hpp"
#include "QrCode.hpp"
 
 
qrcodegen::QrCode::Ecc::Ecc(int ord, int fb) :
    ordinal(ord),
    formatBits(fb) {}
 
 
const qrcodegen::QrCode::Ecc qrcodegen::QrCode::Ecc::LOW     (0, 1);
const qrcodegen::QrCode::Ecc qrcodegen::QrCode::Ecc::MEDIUM  (1, 0);
const qrcodegen::QrCode::Ecc qrcodegen::QrCode::Ecc::QUARTILE(2, 3);
const qrcodegen::QrCode::Ecc qrcodegen::QrCode::Ecc::HIGH    (3, 2);
 
 
qrcodegen::QrCode qrcodegen::QrCode::encodeText(const char *text, int version, const Ecc &ecl) {
    std::vector<QrSegment> segs(QrSegment::makeSegments(text));
    return encodeSegments(segs, ecl, version, version, -1, false);
}
 
 
qrcodegen::QrCode qrcodegen::QrCode::encodeBinary(const std::vector<uint8_t> &data, const Ecc &ecl) {
    std::vector<QrSegment> segs;
    segs.push_back(QrSegment::makeBytes(data));
    return encodeSegments(segs, ecl);
}
 
 
qrcodegen::QrCode qrcodegen::QrCode::encodeSegments(const std::vector<QrSegment> &segs, const Ecc &ecl,
        int minVersion, int maxVersion, int mask, bool boostEcl) {
    if (!(1 <= minVersion && minVersion <= maxVersion && maxVersion <= 40) || mask < -1 || mask > 7)
        throw "Invalid value";
    
    // Find the minimal version number to use
    int version, dataUsedBits;
    for (version = minVersion; ; version++) {
        int dataCapacityBits = getNumDataCodewords(version, ecl) * 8;  // Number of data bits available
        dataUsedBits = QrSegment::getTotalBits(segs, version);
        if (dataUsedBits != -1 && dataUsedBits <= dataCapacityBits)
            break;  // This version number is found to be suitable
        if (version >= maxVersion)  // All versions in the range could not fit the given data
            throw "Data too long";
    }
    if (dataUsedBits == -1)
        throw "Assertion error";
    
    // Increase the error correction level while the data still fits in the current version number
    const Ecc *newEcl = &ecl;
    if (boostEcl) {
        if (dataUsedBits <= getNumDataCodewords(version, Ecc::MEDIUM  ) * 8)  newEcl = &Ecc::MEDIUM  ;
        if (dataUsedBits <= getNumDataCodewords(version, Ecc::QUARTILE) * 8)  newEcl = &Ecc::QUARTILE;
        if (dataUsedBits <= getNumDataCodewords(version, Ecc::HIGH    ) * 8)  newEcl = &Ecc::HIGH    ;
    }
    
    // Create the data bit string by concatenating all segments
    int dataCapacityBits = getNumDataCodewords(version, *newEcl) * 8;
    BitBuffer bb;
    for (size_t i = 0; i < segs.size(); i++) {
        const QrSegment &seg(segs.at(i));
        bb.appendBits(seg.mode.modeBits, 4);
        bb.appendBits(seg.numChars, seg.mode.numCharCountBits(version));
        bb.appendData(seg);
    }
    
    // Add terminator and pad up to a byte if applicable
    bb.appendBits(0, std::min(4, dataCapacityBits - bb.getBitLength()));
    bb.appendBits(0, (8 - bb.getBitLength() % 8) % 8);
    
    // Pad with alternate bytes until data capacity is reached
    for (uint8_t padByte = 0xEC; bb.getBitLength() < dataCapacityBits; padByte ^= 0xEC ^ 0x11)
        bb.appendBits(padByte, 8);
    if (bb.getBitLength() % 8 != 0)
        throw "Assertion error";
    
    // Create the QR Code symbol
    return QrCode(version, *newEcl, bb.getBytes(), mask);
}
 
 
qrcodegen::QrCode::QrCode(int ver, const Ecc &ecl, const std::vector<uint8_t> &dataCodewords, int mask) :
        // Initialize scalar fields
        version(ver),
        size(1 <= ver && ver <= 40 ? ver * 4 + 17 : -1),  // Avoid signed overflow undefined behavior
        errorCorrectionLevel(ecl) {
    
    // Check arguments
    if (ver < 1 || ver > 40 || mask < -1 || mask > 7)
        throw "Value out of range";
    
    std::vector<bool> row(size);
    for (int i = 0; i < size; i++) {
        modules.push_back(row);
        isFunction.push_back(row);
    }
    
    // Draw function patterns, draw all codewords, do masking
    drawFunctionPatterns();
    const std::vector<uint8_t> allCodewords(appendErrorCorrection(dataCodewords));
    drawCodewords(allCodewords);
    this->mask = handleConstructorMasking(mask);
}
 
 
qrcodegen::QrCode::QrCode(const QrCode &qr, int mask) :
        // Copy scalar fields
        version(qr.version),
        size(qr.size),
        errorCorrectionLevel(qr.errorCorrectionLevel) {
    
    // Check arguments
    if (mask < -1 || mask > 7)
        throw "Mask value out of range";
    
    // Handle grid fields
    modules = qr.modules;
    isFunction = qr.isFunction;
    
    // Handle masking
    applyMask(qr.mask);  // Undo old mask
    this->mask = handleConstructorMasking(mask);
}
 
 
int qrcodegen::QrCode::getMask() const {
    return mask;
}
 
 
int qrcodegen::QrCode::getModule(int x, int y) const {
    if (0 <= x && x < size && 0 <= y && y < size)
        return modules.at(y).at(x) ? 1 : 0;
    else
        return 0;  // Infinite white border
}
 
 
std::string qrcodegen::QrCode::toSvgString(int border) const {
    if (border < 0)
        throw "Border must be non-negative";
    std::ostringstream sb;
    sb << "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n";
    sb << "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n";
    sb << "<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\" viewBox=\"0 0 ";
    sb << (size + border * 2) << " " << (size + border * 2) << "\">\n";
    sb << "\t<rect width=\"100%\" height=\"100%\" fill=\"#FFFFFF\" stroke-width=\"0\"/>\n";
    sb << "\t<path d=\"";
    bool head = true;
    for (int y = -border; y < size + border; y++) {
        for (int x = -border; x < size + border; x++) {
            if (getModule(x, y) == 1) {
                if (head)
                    head = false;
                else
                    sb << " ";
                sb << "M" << (x + border) << "," << (y + border) << "h1v1h-1z";
            }
        }
    }
    sb << "\" fill=\"#000000\" stroke-width=\"0\"/>\n";
    sb << "</svg>\n";
    return sb.str();
}
 
 
void qrcodegen::QrCode::drawFunctionPatterns() {
    // Draw the horizontal and vertical timing patterns
    for (int i = 0; i < size; i++) {
        setFunctionModule(6, i, i % 2 == 0);
        setFunctionModule(i, 6, i % 2 == 0);
    }
    
    // Draw 3 finder patterns (all corners except bottom right; overwrites some timing modules)
    drawFinderPattern(3, 3);
    drawFinderPattern(size - 4, 3);
    drawFinderPattern(3, size - 4);
    
    // Draw the numerous alignment patterns
    const std::vector<int> alignPatPos(getAlignmentPatternPositions(version));
    int numAlign = alignPatPos.size();
    for (int i = 0; i < numAlign; i++) {
        for (int j = 0; j < numAlign; j++) {
            if ((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0))
                continue;  // Skip the three finder corners
            else
                drawAlignmentPattern(alignPatPos.at(i), alignPatPos.at(j));
        }
    }
    
    // Draw configuration data
    drawFormatBits(0);  // Dummy mask value; overwritten later in the constructor
    drawVersion();
}
 
 
void qrcodegen::QrCode::drawFormatBits(int mask) {
    // Calculate error correction code and pack bits
    int data = errorCorrectionLevel.formatBits << 3 | mask;  // errCorrLvl is uint2, mask is uint3
    int rem = data;
    for (int i = 0; i < 10; i++)
        rem = (rem << 1) ^ ((rem >> 9) * 0x537);
    data = data << 10 | rem;
    data ^= 0x5412;  // uint15
    if (data >> 15 != 0)
        throw "Assertion error";
    
    // Draw first copy
    for (int i = 0; i <= 5; i++)
        setFunctionModule(8, i, ((data >> i) & 1) != 0);
    setFunctionModule(8, 7, ((data >> 6) & 1) != 0);
    setFunctionModule(8, 8, ((data >> 7) & 1) != 0);
    setFunctionModule(7, 8, ((data >> 8) & 1) != 0);
    for (int i = 9; i < 15; i++)
        setFunctionModule(14 - i, 8, ((data >> i) & 1) != 0);
    
    // Draw second copy
    for (int i = 0; i <= 7; i++)
        setFunctionModule(size - 1 - i, 8, ((data >> i) & 1) != 0);
    for (int i = 8; i < 15; i++)
        setFunctionModule(8, size - 15 + i, ((data >> i) & 1) != 0);
    setFunctionModule(8, size - 8, true);
}
 
 
void qrcodegen::QrCode::drawVersion() {
    if (version < 7)
        return;
    
    // Calculate error correction code and pack bits
    int rem = version;  // version is uint6, in the range [7, 40]
    for (int i = 0; i < 12; i++)
        rem = (rem << 1) ^ ((rem >> 11) * 0x1F25);
    int data = version << 12 | rem;  // uint18
    if (data >> 18 != 0)
        throw "Assertion error";
    
    // Draw two copies
    for (int i = 0; i < 18; i++) {
        bool bit = ((data >> i) & 1) != 0;
        int a = size - 11 + i % 3, b = i / 3;
        setFunctionModule(a, b, bit);
        setFunctionModule(b, a, bit);
    }
}
 
 
void qrcodegen::QrCode::drawFinderPattern(int x, int y) {
    for (int i = -4; i <= 4; i++) {
        for (int j = -4; j <= 4; j++) {
            int dist = std::max(std::abs(i), std::abs(j));  // Chebyshev/infinity norm
            int xx = x + j, yy = y + i;
            if (0 <= xx && xx < size && 0 <= yy && yy < size)
                setFunctionModule(xx, yy, dist != 2 && dist != 4);
        }
    }
}
 
 
void qrcodegen::QrCode::drawAlignmentPattern(int x, int y) {
    for (int i = -2; i <= 2; i++) {
        for (int j = -2; j <= 2; j++)
            setFunctionModule(x + j, y + i, std::max(std::abs(i), std::abs(j)) != 1);
    }
}
 
 
void qrcodegen::QrCode::setFunctionModule(int x, int y, bool isBlack) {
    modules.at(y).at(x) = isBlack;
    isFunction.at(y).at(x) = true;
}
 
 
std::vector<uint8_t> qrcodegen::QrCode::appendErrorCorrection(const std::vector<uint8_t> &data) const {
    if (data.size() != static_cast<unsigned int>(getNumDataCodewords(version, errorCorrectionLevel)))
        throw "Invalid argument";
    
    // Calculate parameter numbers
    int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[errorCorrectionLevel.ordinal][version];
    int totalEcc = NUM_ERROR_CORRECTION_CODEWORDS[errorCorrectionLevel.ordinal][version];
    if (totalEcc % numBlocks != 0)
        throw "Assertion error";
    int blockEccLen = totalEcc / numBlocks;
    int numShortBlocks = numBlocks - getNumRawDataModules(version) / 8 % numBlocks;
    int shortBlockLen = getNumRawDataModules(version) / 8 / numBlocks;
    
    // Split data into blocks and append ECC to each block
    std::vector<std::vector<uint8_t> > blocks;
    const ReedSolomonGenerator rs(blockEccLen);
    for (int i = 0, k = 0; i < numBlocks; i++) {
        std::vector<uint8_t> dat;
        dat.insert(dat.begin(), data.begin() + k, data.begin() + (k + shortBlockLen - blockEccLen + (i < numShortBlocks ? 0 : 1)));
        k += dat.size();
        const std::vector<uint8_t> ecc(rs.getRemainder(dat));
        if (i < numShortBlocks)
            dat.push_back(0);
        dat.insert(dat.end(), ecc.begin(), ecc.end());
        blocks.push_back(dat);
    }
    
    // Interleave (not concatenate) the bytes from every block into a single sequence
    std::vector<uint8_t> result;
    for (int i = 0; static_cast<unsigned int>(i) < blocks.at(0).size(); i++) {
        for (int j = 0; static_cast<unsigned int>(j) < blocks.size(); j++) {
            // Skip the padding byte in short blocks
            if (i != shortBlockLen - blockEccLen || j >= numShortBlocks)
                result.push_back(blocks.at(j).at(i));
        }
    }
    if (result.size() != static_cast<unsigned int>(getNumRawDataModules(version) / 8))
        throw "Assertion error";
    return result;
}
 
 
void qrcodegen::QrCode::drawCodewords(const std::vector<uint8_t> &data) {
    if (data.size() != static_cast<unsigned int>(getNumRawDataModules(version) / 8))
        throw "Invalid argument";
    
    size_t i = 0;  // Bit index into the data
    // Do the funny zigzag scan
    for (int right = size - 1; right >= 1; right -= 2) {  // Index of right column in each column pair
        if (right == 6)
            right = 5;
        for (int vert = 0; vert < size; vert++) {  // Vertical counter
            for (int j = 0; j < 2; j++) {
                int x = right - j;  // Actual x coordinate
                bool upwards = ((right & 2) == 0) ^ (x < 6);
                int y = upwards ? size - 1 - vert : vert;  // Actual y coordinate
                if (!isFunction.at(y).at(x) && i < data.size() * 8) {
                    modules.at(y).at(x) = ((data.at(i >> 3) >> (7 - (i & 7))) & 1) != 0;
                    i++;
                }
                // If there are any remainder bits (0 to 7), they are already
                // set to 0/false/white when the grid of modules was initialized
            }
        }
    }
    if (static_cast<unsigned int>(i) != data.size() * 8)
        throw "Assertion error";
}
 
 
void qrcodegen::QrCode::applyMask(int mask) {
    if (mask < 0 || mask > 7)
        throw "Mask value out of range";
    for (int y = 0; y < size; y++) {
        for (int x = 0; x < size; x++) {
            bool invert;
            switch (mask) {
                case 0:  invert = (x + y) % 2 == 0;                    break;
                case 1:  invert = y % 2 == 0;                          break;
                case 2:  invert = x % 3 == 0;                          break;
                case 3:  invert = (x + y) % 3 == 0;                    break;
                case 4:  invert = (x / 3 + y / 2) % 2 == 0;            break;
                case 5:  invert = x * y % 2 + x * y % 3 == 0;          break;
                case 6:  invert = (x * y % 2 + x * y % 3) % 2 == 0;    break;
                case 7:  invert = ((x + y) % 2 + x * y % 3) % 2 == 0;  break;
                default:  throw "Assertion error";
            }
            modules.at(y).at(x) = modules.at(y).at(x) ^ (invert & !isFunction.at(y).at(x));
        }
    }
}
 
 
int qrcodegen::QrCode::handleConstructorMasking(int mask) {
    if (mask == -1) {  // Automatically choose best mask
        int32_t minPenalty = INT32_MAX;
        for (int i = 0; i < 8; i++) {
            drawFormatBits(i);
            applyMask(i);
            int penalty = getPenaltyScore();
            if (penalty < minPenalty) {
                mask = i;
                minPenalty = penalty;
            }
            applyMask(i);  // Undoes the mask due to XOR
        }
    }
    if (mask < 0 || mask > 7)
        throw "Assertion error";
    drawFormatBits(mask);  // Overwrite old format bits
    applyMask(mask);  // Apply the final choice of mask
    return mask;  // The caller shall assign this value to the final-declared field
}
 
 
int qrcodegen::QrCode::getPenaltyScore() const {
    int result = 0;
    
    // Adjacent modules in row having same color
    for (int y = 0; y < size; y++) {
        bool colorX = modules.at(y).at(0);
        for (int x = 1, runX = 1; x < size; x++) {
            if (modules.at(y).at(x) != colorX) {
                colorX = modules.at(y).at(x);
                runX = 1;
            } else {
                runX++;
                if (runX == 5)
                    result += PENALTY_N1;
                else if (runX > 5)
                    result++;
            }
        }
    }
    // Adjacent modules in column having same color
    for (int x = 0; x < size; x++) {
        bool colorY = modules.at(0).at(x);
        for (int y = 1, runY = 1; y < size; y++) {
            if (modules.at(y).at(x) != colorY) {
                colorY = modules.at(y).at(x);
                runY = 1;
            } else {
                runY++;
                if (runY == 5)
                    result += PENALTY_N1;
                else if (runY > 5)
                    result++;
            }
        }
    }
    
    // 2*2 blocks of modules having same color
    for (int y = 0; y < size - 1; y++) {
        for (int x = 0; x < size - 1; x++) {
            bool  color = modules.at(y).at(x);
            if (  color == modules.at(y).at(x + 1) &&
                  color == modules.at(y + 1).at(x) &&
                  color == modules.at(y + 1).at(x + 1))
                result += PENALTY_N2;
        }
    }
    
    // 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;
        int size = ver * 4 + 17;
        for (int i = 0, pos = size - 7; i < numAlign - 1; i++, pos -= step)
            result.insert(result.begin(), pos);
        result.insert(result.begin(), 6);
        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);
}