QrCode.cpp

#include "stdafx.h"

#include <algorithm>
#include <climits>
#include <cstddef>
#include <cstdlib>
#include <sstream>
#include <utility>
#include "BitBuffer.hpp"
#include "QrCode.hpp"

using namespace std;
using std::int8_t;
using std::uint8_t;
using std::size_t;
using std::vector;


namespace qrcodegen {

	// Returns a value in the range 0 to 3
	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");
		}
	}

	// Returns a QR Code representing the given Unicode text string at the given error correction level
	QrCode QrCode::encodeText(const char *text, Ecc ecl) 
	{
		vector<QrSegment> segs = QrSegment::makeSegments(text); // 가장 효율적인 encoding을 자동으로 선택
		return encodeSegments(segs, ecl);
	}

	// Returns a QR Code representing the given binary data at the given error correction level.
	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) // used bits < capacity bits 이면 사용 가능
			{
				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) // boostEcl이 뭐지
				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 = max(abs(dx), 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, max(abs(dx), 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<vector<bool> > 형식. 
									// The modules of this QR Code (false = white, true = black).
	}


	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 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 && 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) {}

}