/* * 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 #include #include #include #include #include #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 segs = QrSegment::makeSegments(text); return encodeSegments(segs, ecl); } QrCode QrCode::encodeBinary(const vector &data, Ecc ecl) { vector segs{QrSegment::makeBytes(data)}; return encodeSegments(segs, ecl); } QrCode QrCode::encodeSegments(const vector &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::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(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(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 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 &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 >(size, vector(size)); // Initially all white isFunction = vector >(size, vector(size)); // Compute ECC, draw modules drawFunctionPatterns(); const vector 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 << "\n"; sb << "\n"; sb << "\n"; sb << "\t\n"; sb << "\t\n"; sb << "\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 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 QrCode::addEccAndInterleave(const vector &data) const { if (data.size() != static_cast(getNumDataCodewords(version, errorCorrectionLevel))) throw std::invalid_argument("Invalid argument"); // Calculate parameter numbers int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[static_cast(errorCorrectionLevel)][version]; int blockEccLen = ECC_CODEWORDS_PER_BLOCK [static_cast(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 > blocks; const vector rsDiv = reedSolomonComputeDivisor(blockEccLen); for (int i = 0, k = 0; i < numBlocks; i++) { vector dat(data.cbegin() + k, data.cbegin() + (k + shortBlockLen - blockEccLen + (i < numShortBlocks ? 0 : 1))); k += dat.size(); const vector ecc = reedSolomonComputeRemainder(dat, rsDiv); 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 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(shortBlockLen - blockEccLen) || j >= static_cast(numShortBlocks)) result.push_back(blocks.at(j).at(i)); } } if (result.size() != static_cast(rawCodewords)) throw std::logic_error("Assertion error"); return result; } void QrCode::drawCodewords(const vector &data) { if (data.size() != static_cast(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(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++) { bool runColor = false; int runX = 0; std::array runHistory = {}; int padRun = size; // Add white border to initial run for (int x = 0; x < size; x++) { if (module(x, y) == runColor) { runX++; if (runX == 5) result += PENALTY_N1; else if (runX > 5) result++; } else { finderPenaltyAddHistory(runX + padRun, runHistory); padRun = 0; if (!runColor) result += finderPenaltyCountPatterns(runHistory) * PENALTY_N3; runColor = module(x, y); runX = 1; } } result += finderPenaltyTerminateAndCount(runColor, runX + padRun, runHistory) * PENALTY_N3; } // Adjacent modules in column having same color, and finder-like patterns for (int x = 0; x < size; x++) { bool runColor = false; int runY = 0; std::array runHistory = {}; int padRun = size; // Add white border to initial run for (int y = 0; y < size; y++) { if (module(x, y) == runColor) { runY++; if (runY == 5) result += PENALTY_N1; else if (runY > 5) result++; } else { finderPenaltyAddHistory(runY + padRun, runHistory); padRun = 0; if (!runColor) result += finderPenaltyCountPatterns(runHistory) * PENALTY_N3; runColor = module(x, y); runY = 1; } } result += finderPenaltyTerminateAndCount(runColor, runY + padRun, runHistory) * 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 &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((std::abs(black * 20L - total * 10L) + total - 1) / total) - 1; result += k * PENALTY_N4; return result; } vector QrCode::getAlignmentPatternPositions() const { if (version == 1) return vector(); else { int numAlign = version / 7 + 2; int step = (version == 32) ? 26 : (version*4 + numAlign*2 + 1) / (numAlign*2 - 2) * 2; vector 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(ecl)][ver] * NUM_ERROR_CORRECTION_BLOCKS[static_cast(ecl)][ver]; } vector QrCode::reedSolomonComputeDivisor(int degree) { if (degree < 1 || degree > 255) throw std::domain_error("Degree out of range"); // Polynomial coefficients are stored from highest to lowest power, excluding the leading term which is always 1. // For example the polynomial x^3 + 255x^2 + 8x + 93 is stored as the uint8 array {255, 8, 93}. vector result(degree); result.at(degree - 1) = 1; // Start off with the monomial x^0 // Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}), // and drop the highest monomial term which is always 1x^degree. // 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 < result.size(); j++) { result.at(j) = reedSolomonMultiply(result.at(j), root); if (j + 1 < result.size()) result.at(j) ^= result.at(j + 1); } root = reedSolomonMultiply(root, 0x02); } return result; } vector QrCode::reedSolomonComputeRemainder(const vector &data, const vector &divisor) { vector result(divisor.size()); for (uint8_t b : data) { // Polynomial division uint8_t factor = b ^ result.at(0); result.erase(result.begin()); result.push_back(0); for (size_t i = 0; i < result.size(); i++) result.at(i) ^= reedSolomonMultiply(divisor.at(i), factor); } return result; } uint8_t QrCode::reedSolomonMultiply(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(z); } int QrCode::finderPenaltyCountPatterns(const std::array &runHistory) const { int n = runHistory.at(1); if (n > size * 3) throw std::logic_error("Assertion error"); bool core = n > 0 && runHistory.at(2) == n && runHistory.at(3) == n * 3 && runHistory.at(4) == n && runHistory.at(5) == n; return (core && runHistory.at(0) >= n * 4 && runHistory.at(6) >= n ? 1 : 0) + (core && runHistory.at(6) >= n * 4 && runHistory.at(0) >= n ? 1 : 0); } int QrCode::finderPenaltyTerminateAndCount(bool currentRunColor, int currentRunLength, std::array &runHistory) const { if (currentRunColor) { // Terminate black run finderPenaltyAddHistory(currentRunLength, runHistory); currentRunLength = 0; } currentRunLength += size; // Add white border to final run finderPenaltyAddHistory(currentRunLength, runHistory); return finderPenaltyCountPatterns(runHistory); } void QrCode::finderPenaltyAddHistory(int currentRunLength, std::array &runHistory) { std::copy_backward(runHistory.cbegin(), runHistory.cend() - 1, runHistory.end()); runHistory.at(0) = currentRunLength; } 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 }; data_too_long::data_too_long(const std::string &msg) : std::length_error(msg) {} }