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/*
* QR Code generator library (C++)
*
* Copyright (c) Project Nayuki. (MIT License)
* https://www.nayuki.io/page/qr-code-generator-library
*
* 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 <cstddef>
#include <cstdlib>
#include <sstream>
#include <stdexcept>
#include <utility>
#include "BitBuffer.hpp"
#include "QrCode.hpp"
using std::int8_t;
using std::uint8_t;
using std::size_t;
using std::vector;
namespace qrcodegen {
int QrCode::getFormatBits(Ecc ecl) {
switch (ecl) {
case Ecc::LOW : return 1;
case Ecc::MEDIUM : return 0;
case Ecc::QUARTILE: return 3;
case Ecc::HIGH : return 2;
default: throw std::logic_error("Assertion error");
}
}
QrCode QrCode::encodeText(const char *text, Ecc ecl) {
vector<QrSegment> segs = QrSegment::makeSegments(text);
return encodeSegments(segs, ecl);
}
QrCode QrCode::encodeBinary(const vector<uint8_t> &data, Ecc ecl) {
vector<QrSegment> segs{QrSegment::makeBytes(data)};
return encodeSegments(segs, ecl);
}
QrCode QrCode::encodeSegments(const vector<QrSegment> &segs, Ecc ecl,
int minVersion, int maxVersion, int mask, bool boostEcl) {
if (!(MIN_VERSION <= minVersion && minVersion <= maxVersion && maxVersion <= MAX_VERSION) || mask < -1 || mask > 7)
throw std::invalid_argument("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
std::ostringstream sb;
if (dataUsedBits == -1)
sb << "Segment too long";
else {
sb << "Data length = " << dataUsedBits << " bits, ";
sb << "Max capacity = " << dataCapacityBits << " bits";
}
throw data_too_long(sb.str());
}
}
if (dataUsedBits == -1)
throw std::logic_error("Assertion error");
// Increase the error correction level while the data still fits in the current version number
for (Ecc newEcl : vector<Ecc>{Ecc::MEDIUM, Ecc::QUARTILE, Ecc::HIGH}) { // From low to high
if (boostEcl && dataUsedBits <= getNumDataCodewords(version, newEcl) * 8)
ecl = newEcl;
}
// Concatenate all segments to create the data bit string
BitBuffer bb;
for (const QrSegment &seg : segs) {
bb.appendBits(seg.getMode().getModeBits(), 4);
bb.appendBits(seg.getNumChars(), seg.getMode().numCharCountBits(version));
bb.insert(bb.end(), seg.getData().begin(), seg.getData().end());
}
if (bb.size() != static_cast<unsigned int>(dataUsedBits))
throw std::logic_error("Assertion error");
// Add terminator and pad up to a byte if applicable
size_t dataCapacityBits = getNumDataCodewords(version, ecl) * 8;
if (bb.size() > dataCapacityBits)
throw std::logic_error("Assertion error");
bb.appendBits(0, std::min<size_t>(4, dataCapacityBits - bb.size()));
bb.appendBits(0, (8 - bb.size() % 8) % 8);
if (bb.size() % 8 != 0)
throw std::logic_error("Assertion error");
// Pad with alternating bytes until data capacity is reached
for (uint8_t padByte = 0xEC; bb.size() < dataCapacityBits; padByte ^= 0xEC ^ 0x11)
bb.appendBits(padByte, 8);
// Pack bits into bytes in big endian
vector<uint8_t> dataCodewords(bb.size() / 8);
for (size_t i = 0; i < bb.size(); i++)
dataCodewords[i >> 3] |= (bb.at(i) ? 1 : 0) << (7 - (i & 7));
// Create the QR Code object
return QrCode(version, ecl, dataCodewords, mask);
}
QrCode::QrCode(int ver, Ecc ecl, const vector<uint8_t> &dataCodewords, int mask) :
// Initialize fields and check arguments
version(ver),
errorCorrectionLevel(ecl) {
if (ver < MIN_VERSION || ver > MAX_VERSION)
throw std::domain_error("Version value out of range");
if (mask < -1 || mask > 7)
throw std::domain_error("Mask value out of range");
size = ver * 4 + 17;
modules = vector<vector<bool> >(size, vector<bool>(size)); // Initially all white
isFunction = vector<vector<bool> >(size, vector<bool>(size));
// Compute ECC, draw modules
drawFunctionPatterns();
const vector<uint8_t> allCodewords = addEccAndInterleave(dataCodewords);
drawCodewords(allCodewords);
// Do masking
if (mask == -1) { // Automatically choose best mask
long minPenalty = LONG_MAX;
for (int i = 0; i < 8; i++) {
applyMask(i);
drawFormatBits(i);
long penalty = getPenaltyScore();
if (penalty < minPenalty) {
mask = i;
minPenalty = penalty;
}
applyMask(i); // Undoes the mask due to XOR
}
}
if (mask < 0 || mask > 7)
throw std::logic_error("Assertion error");
this->mask = mask;
applyMask(mask); // Apply the final choice of mask
drawFormatBits(mask); // Overwrite old format bits
isFunction.clear();
isFunction.shrink_to_fit();
}
int QrCode::getVersion() const {
return version;
}
int QrCode::getSize() const {
return size;
}
QrCode::Ecc QrCode::getErrorCorrectionLevel() const {
return errorCorrectionLevel;
}
int QrCode::getMask() const {
return mask;
}
bool QrCode::getModule(int x, int y) const {
return 0 <= x && x < size && 0 <= y && y < size && module(x, y);
}
std::string QrCode::toSvgString(int border) const {
if (border < 0)
throw std::domain_error("Border must be non-negative");
if (border > INT_MAX / 2 || border * 2 > INT_MAX - size)
throw std::overflow_error("Border too large");
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) << "\" stroke=\"none\">\n";
sb << "\t<rect width=\"100%\" height=\"100%\" fill=\"#FFFFFF\"/>\n";
sb << "\t<path d=\"";
for (int y = 0; y < size; y++) {
for (int x = 0; x < size; x++) {
if (getModule(x, y)) {
if (x != 0 || y != 0)
sb << " ";
sb << "M" << (x + border) << "," << (y + border) << "h1v1h-1z";
}
}
}
sb << "\" fill=\"#000000\"/>\n";
sb << "</svg>\n";
return sb.str();
}
void QrCode::drawFunctionPatterns() {
// Draw 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 numerous alignment patterns
const vector<int> alignPatPos = getAlignmentPatternPositions();
int numAlign = alignPatPos.size();
for (int i = 0; i < numAlign; i++) {
for (int j = 0; j < numAlign; j++) {
// Don't draw on the three finder corners
if (!((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0)))
drawAlignmentPattern(alignPatPos.at(i), alignPatPos.at(j));
}
}
// Draw configuration data
drawFormatBits(0); // Dummy mask value; overwritten later in the constructor
drawVersion();
}
void QrCode::drawFormatBits(int mask) {
// Calculate error correction code and pack bits
int data = getFormatBits(errorCorrectionLevel) << 3 | mask; // errCorrLvl is uint2, mask is uint3
int rem = data;
for (int i = 0; i < 10; i++)
rem = (rem << 1) ^ ((rem >> 9) * 0x537);
int bits = (data << 10 | rem) ^ 0x5412; // uint15
if (bits >> 15 != 0)
throw std::logic_error("Assertion error");
// Draw first copy
for (int i = 0; i <= 5; i++)
setFunctionModule(8, i, getBit(bits, i));
setFunctionModule(8, 7, getBit(bits, 6));
setFunctionModule(8, 8, getBit(bits, 7));
setFunctionModule(7, 8, getBit(bits, 8));
for (int i = 9; i < 15; i++)
setFunctionModule(14 - i, 8, getBit(bits, i));
// Draw second copy
for (int i = 0; i < 8; i++)
setFunctionModule(size - 1 - i, 8, getBit(bits, i));
for (int i = 8; i < 15; i++)
setFunctionModule(8, size - 15 + i, getBit(bits, i));
setFunctionModule(8, size - 8, true); // Always black
}
void 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);
long bits = (long)version << 12 | rem; // uint18
if (bits >> 18 != 0)
throw std::logic_error("Assertion error");
// Draw two copies
for (int i = 0; i < 18; i++) {
bool bit = getBit(bits, i);
int a = size - 11 + i % 3;
int b = i / 3;
setFunctionModule(a, b, bit);
setFunctionModule(b, a, bit);
}
}
void QrCode::drawFinderPattern(int x, int y) {
for (int dy = -4; dy <= 4; dy++) {
for (int dx = -4; dx <= 4; dx++) {
int dist = std::max(std::abs(dx), std::abs(dy)); // Chebyshev/infinity norm
int xx = x + dx, yy = y + dy;
if (0 <= xx && xx < size && 0 <= yy && yy < size)
setFunctionModule(xx, yy, dist != 2 && dist != 4);
}
}
}
void QrCode::drawAlignmentPattern(int x, int y) {
for (int dy = -2; dy <= 2; dy++) {
for (int dx = -2; dx <= 2; dx++)
setFunctionModule(x + dx, y + dy, std::max(std::abs(dx), std::abs(dy)) != 1);
}
}
void QrCode::setFunctionModule(int x, int y, bool isBlack) {
modules.at(y).at(x) = isBlack;
isFunction.at(y).at(x) = true;
}
bool QrCode::module(int x, int y) const {
return modules.at(y).at(x);
}
vector<uint8_t> QrCode::addEccAndInterleave(const vector<uint8_t> &data) const {
if (data.size() != static_cast<unsigned int>(getNumDataCodewords(version, errorCorrectionLevel)))
throw std::invalid_argument("Invalid argument");
// Calculate parameter numbers
int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[static_cast<int>(errorCorrectionLevel)][version];
int blockEccLen = ECC_CODEWORDS_PER_BLOCK [static_cast<int>(errorCorrectionLevel)][version];
int rawCodewords = getNumRawDataModules(version) / 8;
int numShortBlocks = numBlocks - rawCodewords % numBlocks;
int shortBlockLen = rawCodewords / numBlocks;
// Split data into blocks and append ECC to each block
vector<vector<uint8_t> > blocks;
const ReedSolomonGenerator rs(blockEccLen);
for (int i = 0, k = 0; i < numBlocks; i++) {
vector<uint8_t> dat(data.cbegin() + k, data.cbegin() + (k + shortBlockLen - blockEccLen + (i < numShortBlocks ? 0 : 1)));
k += dat.size();
const vector<uint8_t> ecc = rs.getRemainder(dat);
if (i < numShortBlocks)
dat.push_back(0);
dat.insert(dat.end(), ecc.cbegin(), ecc.cend());
blocks.push_back(std::move(dat));
}
// Interleave (not concatenate) the bytes from every block into a single sequence
vector<uint8_t> result;
for (size_t i = 0; i < blocks.at(0).size(); i++) {
for (size_t j = 0; j < blocks.size(); j++) {
// Skip the padding byte in short blocks
if (i != static_cast<unsigned int>(shortBlockLen - blockEccLen) || j >= static_cast<unsigned int>(numShortBlocks))
result.push_back(blocks.at(j).at(i));
}
}
if (result.size() != static_cast<unsigned int>(rawCodewords))
throw std::logic_error("Assertion error");
return result;
}
void QrCode::drawCodewords(const vector<uint8_t> &data) {
if (data.size() != static_cast<unsigned int>(getNumRawDataModules(version) / 8))
throw std::invalid_argument("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 upward = ((right + 1) & 2) == 0;
int y = upward ? size - 1 - vert : vert; // Actual y coordinate
if (!isFunction.at(y).at(x) && i < data.size() * 8) {
modules.at(y).at(x) = getBit(data.at(i >> 3), 7 - static_cast<int>(i & 7));
i++;
}
// If this QR Code has any remainder bits (0 to 7), they were assigned as
// 0/false/white by the constructor and are left unchanged by this method
}
}
}
if (i != data.size() * 8)
throw std::logic_error("Assertion error");
}
void QrCode::applyMask(int mask) {
if (mask < 0 || mask > 7)
throw std::domain_error("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 std::logic_error("Assertion error");
}
modules.at(y).at(x) = modules.at(y).at(x) ^ (invert & !isFunction.at(y).at(x));
}
}
}
long QrCode::getPenaltyScore() const {
long result = 0;
// Adjacent modules in row having same color, and finder-like patterns
for (int y = 0; y < size; y++) {
std::deque<int> runHistory(7, 0);
bool color = false;
int runX = 0;
for (int x = 0; x < size; x++) {
if (module(x, y) == color) {
runX++;
if (runX == 5)
result += PENALTY_N1;
else if (runX > 5)
result++;
} else {
addRunToHistory(runX, runHistory);
if (!color && hasFinderLikePattern(runHistory))
result += PENALTY_N3;
color = module(x, y);
runX = 1;
}
}
addRunToHistory(runX, runHistory);
if (color)
addRunToHistory(0, runHistory); // Dummy run of white
if (hasFinderLikePattern(runHistory))
result += PENALTY_N3;
}
// Adjacent modules in column having same color, and finder-like patterns
for (int x = 0; x < size; x++) {
std::deque<int> runHistory(7, 0);
bool color = false;
int runY = 0;
for (int y = 0; y < size; y++) {
if (module(x, y) == color) {
runY++;
if (runY == 5)
result += PENALTY_N1;
else if (runY > 5)
result++;
} else {
addRunToHistory(runY, runHistory);
if (!color && hasFinderLikePattern(runHistory))
result += PENALTY_N3;
color = module(x, y);
runY = 1;
}
}
addRunToHistory(runY, runHistory);
if (color)
addRunToHistory(0, runHistory); // Dummy run of white
if (hasFinderLikePattern(runHistory))
result += PENALTY_N3;
}
// 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 = module(x, y);
if ( color == module(x + 1, y) &&
color == module(x, y + 1) &&
color == module(x + 1, y + 1))
result += PENALTY_N2;
}
}
// Balance of black and white modules
int black = 0;
for (const vector<bool> &row : modules) {
for (bool color : row) {
if (color)
black++;
}
}
int total = size * size; // Note that size is odd, so black/total != 1/2
// Compute the smallest integer k >= 0 such that (45-5k)% <= black/total <= (55+5k)%
int k = static_cast<int>((std::abs(black * 20L - total * 10L) + total - 1) / total) - 1;
result += k * PENALTY_N4;
return result;
}
vector<int> QrCode::getAlignmentPatternPositions() const {
if (version == 1)
return vector<int>();
else {
int numAlign = version / 7 + 2;
int step = (version == 32) ? 26 :
(version*4 + numAlign*2 + 1) / (numAlign*2 - 2) * 2;
vector<int> result;
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 QrCode::getNumRawDataModules(int ver) {
if (ver < MIN_VERSION || ver > MAX_VERSION)
throw std::domain_error("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 -= 36;
}
return result;
}
int QrCode::getNumDataCodewords(int ver, Ecc ecl) {
return getNumRawDataModules(ver) / 8
- ECC_CODEWORDS_PER_BLOCK [static_cast<int>(ecl)][ver]
* NUM_ERROR_CORRECTION_BLOCKS[static_cast<int>(ecl)][ver];
}
void QrCode::addRunToHistory(int run, std::deque<int> &history) {
history.pop_back();
history.push_front(run);
}
bool QrCode::hasFinderLikePattern(const std::deque<int> &runHistory) {
int n = runHistory.at(1);
return n > 0 && runHistory.at(2) == n && runHistory.at(4) == n && runHistory.at(5) == n
&& runHistory.at(3) == n * 3 && std::max(runHistory.at(0), runHistory.at(6)) >= n * 4;
}
bool QrCode::getBit(long x, int i) {
return ((x >> i) & 1) != 0;
}
/*---- Tables of constants ----*/
const int QrCode::PENALTY_N1 = 3;
const int QrCode::PENALTY_N2 = 3;
const int QrCode::PENALTY_N3 = 40;
const int QrCode::PENALTY_N4 = 10;
const int8_t QrCode::ECC_CODEWORDS_PER_BLOCK[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, 18, 20, 24, 30, 18, 20, 24, 26, 30, 22, 24, 28, 30, 28, 28, 28, 28, 30, 30, 26, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30}, // Low
{-1, 10, 16, 26, 18, 24, 16, 18, 22, 22, 26, 30, 22, 22, 24, 24, 28, 28, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28}, // Medium
{-1, 13, 22, 18, 26, 18, 24, 18, 22, 20, 24, 28, 26, 24, 20, 30, 24, 28, 28, 26, 30, 28, 30, 30, 30, 30, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30}, // Quartile
{-1, 17, 28, 22, 16, 22, 28, 26, 26, 24, 28, 24, 28, 22, 24, 24, 30, 28, 28, 26, 28, 30, 24, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30}, // High
};
const int8_t 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
};
QrCode::ReedSolomonGenerator::ReedSolomonGenerator(int degree) :
coefficients() {
if (degree < 1 || degree > 255)
throw std::domain_error("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).
uint8_t 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), root);
if (j + 1 < coefficients.size())
coefficients.at(j) ^= coefficients.at(j + 1);
}
root = multiply(root, 0x02);
}
}
vector<uint8_t> QrCode::ReedSolomonGenerator::getRemainder(const vector<uint8_t> &data) const {
// Compute the remainder by performing polynomial division
vector<uint8_t> result(coefficients.size());
for (uint8_t b : data) {
uint8_t factor = b ^ 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 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 std::logic_error("Assertion error");
return static_cast<uint8_t>(z);
}
data_too_long::data_too_long(const std::string &msg) :
std::length_error(msg) {}
}