/* * Copyright 2016 Huy Cuong Nguyen * Copyright 2016 ZXing authors */ // SPDX-License-Identifier: Apache-2.0 #include "QRMatrixUtil.h" #include "BitArray.h" #include "BitHacks.h" #include "QRDataMask.h" #include "QRErrorCorrectionLevel.h" #include "QRVersion.h" #include #include namespace ZXing::QRCode { // From Appendix D in JISX0510:2004 (p. 67) static const int VERSION_INFO_POLY = 0x1f25; // 1 1111 0010 0101 // From Appendix C in JISX0510:2004 (p.65). static const int TYPE_INFO_POLY = 0x537; static const int TYPE_INFO_MASK_PATTERN = 0x5412; static void EmbedTimingPatterns(TritMatrix& matrix) { // -8 is for skipping position detection patterns (size 7), and two horizontal/vertical // separation patterns (size 1). Thus, 8 = 7 + 1. for (int i = 8; i < matrix.width() - 8; ++i) { bool bit = (i + 1) % 2; // Horizontal line. matrix.set(i, 6, bit); // Vertical line. matrix.set(6, i, bit); } } // Note that we cannot unify the function with embedPositionDetectionPattern() despite they are // almost identical, since we cannot write a function that takes 2D arrays in different sizes in // C/C++. We should live with the fact. static void EmbedPositionAdjustmentPattern(int xStart, int yStart, TritMatrix& matrix) { for (int y = 0; y < 5; ++y) for (int x = 0; x < 5; ++x) matrix.set(xStart + x, yStart + y, maxAbsComponent(PointI(x, y) - PointI(2, 2)) != 1); } // Embed position adjustment patterns if need be. static void EmbedPositionAdjustmentPatterns(const Version& version, TritMatrix& matrix) { if (version.versionNumber() < 2) { // The patterns appear if version >= 2 return; } auto& coordinates = version.alignmentPatternCenters(); for (int y : coordinates) { for (int x : coordinates) { // Check x/y is valid: don't place alignment patterns intersecting with the 3 finder patterns if ((x == 6 && y == 6) || (x == 6 && y == matrix.height() - 7) || (x == matrix.width() - 7 && y == 6)) continue; // -2 is necessary since the x/y coordinates point to the center of the pattern, not the // left top corner. EmbedPositionAdjustmentPattern(x - 2, y - 2, matrix); } } } static void EmbedPositionDetectionPattern(int xStart, int yStart, TritMatrix& matrix) { for (int y = 0; y < 7; ++y) for (int x = 0; x < 7; ++x) matrix.set(xStart + x, yStart + y, maxAbsComponent(PointI(x, y) - PointI(3, 3)) != 2); // Surround the 7x7 pattern with one line of white space (separation pattern) auto setIfInside = [&](int x, int y) { if( x >= 0 && x < matrix.width() && y >= 0 && y < matrix.height()) matrix.set(x, y, 0); }; for (int i = -1; i < 8; ++i) { setIfInside(xStart + i, yStart - 1); // top setIfInside(xStart + i, yStart + 7); // bottom setIfInside(xStart - 1, yStart + i); // left setIfInside(xStart + 7, yStart + i); // right } } // Embed position detection patterns and surrounding vertical/horizontal separators. static void EmbedPositionDetectionPatternsAndSeparators(TritMatrix& matrix) { // Left top corner. EmbedPositionDetectionPattern(0, 0, matrix); // Right top corner. EmbedPositionDetectionPattern(matrix.width() - 7, 0, matrix); // Left bottom corner. EmbedPositionDetectionPattern(0, matrix.width() - 7, matrix); } // Embed the lonely dark dot at left bottom corner. JISX0510:2004 (p.46) static void EmbedDarkDotAtLeftBottomCorner(TritMatrix& matrix) { matrix.set(8, matrix.height() - 8, 1); } // Return the position of the most significant bit set (to one) in the "value". The most // significant bit is position 32. If there is no bit set, return 0. Examples: // - findMSBSet(0) => 0 // - findMSBSet(1) => 1 // - findMSBSet(255) => 8 static int FindMSBSet(unsigned value) { return 32 - BitHacks::NumberOfLeadingZeros(value); } // Calculate BCH (Bose-Chaudhuri-Hocquenghem) code for "value" using polynomial "poly". The BCH // code is used for encoding type information and version information. // Example: Calculation of version information of 7. // f(x) is created from 7. // - 7 = 000111 in 6 bits // - f(x) = x^2 + x^1 + x^0 // g(x) is given by the standard (p. 67) // - g(x) = x^12 + x^11 + x^10 + x^9 + x^8 + x^5 + x^2 + 1 // Multiply f(x) by x^(18 - 6) // - f'(x) = f(x) * x^(18 - 6) // - f'(x) = x^14 + x^13 + x^12 // Calculate the remainder of f'(x) / g(x) // x^2 // __________________________________________________ // g(x) )x^14 + x^13 + x^12 // x^14 + x^13 + x^12 + x^11 + x^10 + x^7 + x^4 + x^2 // -------------------------------------------------- // x^11 + x^10 + x^7 + x^4 + x^2 // // The remainder is x^11 + x^10 + x^7 + x^4 + x^2 // Encode it in binary: 110010010100 // The return value is 0xc94 (1100 1001 0100) // // Since all coefficients in the polynomials are 1 or 0, we can do the calculation by bit // operations. We don't care if cofficients are positive or negative. static int CalculateBCHCode(int value, int poly) { // If poly is "1 1111 0010 0101" (version info poly), msbSetInPoly is 13. We'll subtract 1 // from 13 to make it 12. int msbSetInPoly = FindMSBSet(poly); value <<= msbSetInPoly - 1; // Do the division business using exclusive-or operations. while (FindMSBSet(value) >= msbSetInPoly) { value ^= poly << (FindMSBSet(value) - msbSetInPoly); } // Now the "value" is the remainder (i.e. the BCH code) return value; } // Make bit vector of type information. On success, store the result in "bits" and return true. // Encode error correction level and mask pattern. See 8.9 of // JISX0510:2004 (p.45) for details. static BitArray MakeTypeInfoBits(ErrorCorrectionLevel ecLevel, int maskPattern) { if (maskPattern < 0 || maskPattern >= NUM_MASK_PATTERNS) { throw std::invalid_argument("Invalid mask pattern"); } BitArray bits; int typeInfo = (BitsFromECLevel(ecLevel) << 3) | maskPattern; bits.appendBits(typeInfo, 5); int bchCode = CalculateBCHCode(typeInfo, TYPE_INFO_POLY); bits.appendBits(bchCode, 10); BitArray maskBits; maskBits.appendBits(TYPE_INFO_MASK_PATTERN, 15); bits.bitwiseXOR(maskBits); if (bits.size() != 15) { // Just in case. throw std::logic_error("Should not happen but we got: " + std::to_string(bits.size())); } return bits; } // Embed type information. On success, modify the matrix. static void EmbedTypeInfo(ErrorCorrectionLevel ecLevel, int maskPattern, TritMatrix& matrix) { // Type info cells at the left top corner. constexpr PointI TYPE_INFO_COORDINATES[] = { {8, 0}, {8, 1}, {8, 2}, {8, 3}, {8, 4}, {8, 5}, {8, 7}, {8, 8}, {7, 8}, {5, 8}, {4, 8}, {3, 8}, {2, 8}, {1, 8}, {0, 8} }; BitArray typeInfoBits = MakeTypeInfoBits(ecLevel, maskPattern); for (int i = 0; i < typeInfoBits.size(); ++i) { // Place bits in LSB to MSB order. LSB (least significant bit) is the last value in // "typeInfoBits". bool bit = typeInfoBits.get(typeInfoBits.size() - 1 - i); // Type info bits at the left top corner. See 8.9 of JISX0510:2004 (p.46). matrix.set(TYPE_INFO_COORDINATES[i], bit); if (i < 8) { // Right top corner. matrix.set(matrix.width() - i - 1, 8, bit); } else { // Left bottom corner. matrix.set(8, matrix.height() - 7 + (i - 8), bit); } } } // Make bit vector of version information. On success, store the result in "bits" and return true. // See 8.10 of JISX0510:2004 (p.45) for details. static BitArray MakeVersionInfoBits(const Version& version) { BitArray bits; bits.appendBits(version.versionNumber(), 6); int bchCode = CalculateBCHCode(version.versionNumber(), VERSION_INFO_POLY); bits.appendBits(bchCode, 12); if (bits.size() != 18) { // Just in case. throw std::logic_error("Should not happen but we got: " + std::to_string(bits.size())); } return bits; } // Embed version information if need be. On success, modify the matrix and return true. // See 8.10 of JISX0510:2004 (p.47) for how to embed version information. static void EmbedVersionInfo(const Version& version, TritMatrix& matrix) { if (version.versionNumber() < 7) { // Version info is necessary if version >= 7. return; // Don't need version info. } BitArray versionInfoBits = MakeVersionInfoBits(version); int bitIndex = 6 * 3 - 1; // It will decrease from 17 to 0. for (int i = 0; i < 6; ++i) { for (int j = 0; j < 3; ++j) { // Place bits in LSB (least significant bit) to MSB order. bool bit = versionInfoBits.get(bitIndex); bitIndex--; // Left bottom corner. matrix.set(i, matrix.height() - 11 + j, bit); // Right bottom corner. matrix.set(matrix.height() - 11 + j, i, bit); } } } // Embed "dataBits" using "getMaskPattern". On success, modify the matrix and return true. // For debugging purposes, it skips masking process if "getMaskPattern" is -1. // See 8.7 of JISX0510:2004 (p.38) for how to embed data bits. static void EmbedDataBits(const BitArray& dataBits, int maskPattern, TritMatrix& matrix) { int bitIndex = 0; int direction = -1; // Start from the right bottom cell. int x = matrix.width() - 1; int y = matrix.height() - 1; while (x > 0) { // Skip the vertical timing pattern. if (x == 6) { x -= 1; } while (y >= 0 && y < matrix.height()) { for (int xx = x; xx > x - 2; --xx) { // Skip the cell if it's not empty. if (!matrix.get(xx, y).isEmpty()) { continue; } // Padding bit. If there is no bit left, we'll fill the left cells with 0, as described // in 8.4.9 of JISX0510:2004 (p. 24). bool bit = bitIndex < dataBits.size() ? dataBits.get(bitIndex) : false; ++bitIndex; // Skip masking if mask_pattern is -1. if (maskPattern != -1 && GetDataMaskBit(maskPattern, xx, y)) { bit = !bit; } matrix.set(xx, y, bit); } y += direction; } direction = -direction; // Reverse the direction. y += direction; x -= 2; // Move to the left. } // All bits should be consumed. if (bitIndex < dataBits.size()) { throw std::invalid_argument("Not all bits consumed: " + std::to_string(bitIndex) + '/' + std::to_string(dataBits.size())); } } // Build 2D matrix of QR Code from "dataBits" with "ecLevel", "version" and "getMaskPattern". On // success, store the result in "matrix" and return true. void BuildMatrix(const BitArray& dataBits, ErrorCorrectionLevel ecLevel, const Version& version, int maskPattern, TritMatrix& matrix) { matrix.clear(); // Let's get started with embedding big squares at corners. EmbedPositionDetectionPatternsAndSeparators(matrix); // Then, embed the dark dot at the left bottom corner. EmbedDarkDotAtLeftBottomCorner(matrix); // Position adjustment patterns appear if version >= 2. EmbedPositionAdjustmentPatterns(version, matrix); // Timing patterns should be embedded after position adj. patterns. EmbedTimingPatterns(matrix); // Type information appear with any version. EmbedTypeInfo(ecLevel, maskPattern, matrix); // Version info appear if version >= 7. EmbedVersionInfo(version, matrix); // Data should be embedded at end. EmbedDataBits(dataBits, maskPattern, matrix); } } // namespace ZXing::QRCode