/* * 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 #include #include #include "qrcodegen.h" /*---- Forward declarations for private functions ----*/ static bool getModule(const uint8_t qrcode[], int size, int x, int y); static void setModule(uint8_t qrcode[], int size, int x, int y, bool isBlack); static void setModuleBounded(uint8_t qrcode[], int size, int x, int y, bool isBlack); static void initializeFunctionalModules(int version, uint8_t qrcode[]); static void drawWhiteFunctionModules(uint8_t qrcode[], int version); static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[], int size); static int getAlignmentPatternPositions(int version, uint8_t result[7]); static void calcReedSolomonGenerator(int degree, uint8_t result[]); static void calcReedSolomonRemainder(const uint8_t data[], int dataLen, const uint8_t generator[], int degree, uint8_t result[]); static uint8_t finiteFieldMultiply(uint8_t x, uint8_t y); /*---- Function implementations ----*/ // Public function - see documentation comment in header file. bool qrcodegen_isAlphanumeric(const char *text) { for (; *text != '\0'; text++) { char c = *text; if (('0' <= c && c <= '9') || ('A' <= c && c <= 'Z')) continue; else switch (c) { case ' ': case '$': case '%': case '*': case '+': case '-': case '.': case '/': case ':': continue; default: return false; } return false; } return true; } // Public function - see documentation comment in header file. bool qrcodegen_isNumeric(const char *text) { for (; *text != '\0'; text++) { char c = *text; if (c < '0' || c > '9') return false; } return true; } // Public function - see documentation comment in header file. int qrcodegen_getSize(int version) { assert(1 <= version && version <= 40); return version * 4 + 17; } // Public function - see documentation comment in header file. bool qrcodegen_getModule(const uint8_t qrcode[], int version, int x, int y) { int size = qrcodegen_getSize(version); return (0 <= x && x < size && 0 <= y && y < size) && getModule(qrcode, size, x, y); } // Gets the module at the given coordinates, which must be in bounds. static bool getModule(const uint8_t qrcode[], int size, int x, int y) { assert(21 <= size && size <= 177 && 0 <= x && x < size && 0 <= y && y < size); int index = y * size + x; int bitIndex = index & 7; int byteIndex = index >> 3; return ((qrcode[byteIndex] >> bitIndex) & 1) != 0; } // Sets the module at the given coordinates, which must be in bounds. static void setModule(uint8_t qrcode[], int size, int x, int y, bool isBlack) { assert(21 <= size && size <= 177 && 0 <= x && x < size && 0 <= y && y < size); int index = y * size + x; int bitIndex = index & 7; int byteIndex = index >> 3; if (isBlack) qrcode[byteIndex] |= 1 << bitIndex; else qrcode[byteIndex] &= (1 << bitIndex) ^ 0xFF; } // Sets the module at the given coordinates, doing nothing if out of bounds. static void setModuleBounded(uint8_t qrcode[], int size, int x, int y, bool isBlack) { if (0 <= x && x < size && 0 <= y && y < size) setModule(qrcode, size, x, y, isBlack); } // Fills the given QR Code grid with white modules for the given version's size, // then marks every function module in the QR Code as black. static void initializeFunctionalModules(int version, uint8_t qrcode[]) { // Initialize QR Code int size = qrcodegen_getSize(version); memset(qrcode, 0, (size * size + 7) / 8 * sizeof(qrcode[0])); // Fill horizontal and vertical timing patterns for (int i = 0; i < size; i++) { setModule(qrcode, size, 6, i, true); setModule(qrcode, size, i, 6, true); } // Fill 3 finder patterns (all corners except bottom right) for (int i = 0; i < 8; i++) { for (int j = 0; j < 8; j++) { setModule(qrcode, size, j, i, true); setModule(qrcode, size, size - 1 - j, i, true); setModule(qrcode, size, j, size - 1 - i, true); } } // Fill numerous alignment patterns uint8_t alignPatPos[7] = {0}; int numAlign = getAlignmentPatternPositions(version, alignPatPos); 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 { for (int k = -2; k <= 2; k++) { for (int l = -2; l <= 2; l++) setModule(qrcode, size, alignPatPos[i] + l, alignPatPos[j] + k, true); } } } } // Fill format bits for (int i = 0; i < 8; i++) { setModule(qrcode, size, i, 8, true); setModule(qrcode, size, 8, i, true); setModule(qrcode, size, size - 1 - i, 8, true); setModule(qrcode, size, 8, size - 1 - i, true); } setModule(qrcode, size, 8, 8, true); // Fill version if (version >= 7) { for (int i = 0; i < 3; i++) { for (int j = 0; j < 6; j++) { int k = size - 11 + i; setModule(qrcode, size, k, j, true); setModule(qrcode, size, j, k, true); } } } } // Draws white function modules and possibly some black modules onto the given QR Code, without changing // non-function modules. This does not draw the format bits. This requires all function modules to be previously // marked black (namely by initializeFunctionalModules()), because this may skip redrawing black function modules. static void drawWhiteFunctionModules(uint8_t qrcode[], int version) { // Draw horizontal and vertical timing patterns int size = qrcodegen_getSize(version); for (int i = 7; i < size - 7; i += 2) { setModule(qrcode, size, 6, i, false); setModule(qrcode, size, i, 6, false); } // Draw 3 finder patterns for (int i = -4; i <= 4; i++) { for (int j = -4; j <= 4; j++) { int dist = abs(i); if (abs(j) > dist) dist = abs(j); if (dist == 2 || dist == 4) { setModuleBounded(qrcode, size, 3 + j, 3 + i, false); setModuleBounded(qrcode, size, size - 4 + j, 3 + i, false); setModuleBounded(qrcode, size, 3 + j, size - 4 + i, false); } } } // Draw numerous alignment patterns uint8_t alignPatPos[7] = {0}; int numAlign = getAlignmentPatternPositions(version, alignPatPos); 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 { for (int k = -1; k <= 1; k++) { for (int l = -1; l <= 1; l++) setModule(qrcode, size, alignPatPos[i] + l, alignPatPos[j] + k, k == 0 && l == 0); } } } } // Draw version block if (version >= 7) { // 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 data = (long)version << 12 | rem; // uint18 assert(data >> 18 == 0); // Draw two copies for (int i = 0; i < 3; i++) { for (int j = 0; j < 6; j++) { int k = size - 11 + i; setModule(qrcode, size, k, j, (data & 1) != 0); setModule(qrcode, size, j, k, (data & 1) != 0); data >>= 1; } } } } // Based on the given ECC level and mask, this calculates the format bits // and draws their black and white modules onto the given QR Code. static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[], int size) { // Calculate error correction code and pack bits assert(0 <= (int)mask && (int)mask <= 7); int data; switch (ecl) { case qrcodegen_Ecc_LOW : data = 1; break; case qrcodegen_Ecc_MEDIUM : data = 0; break; case qrcodegen_Ecc_QUARTILE: data = 3; break; case qrcodegen_Ecc_HIGH : data = 2; break; default: assert(false); } data = data << 3 | (int)mask; // ecl-derived value 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 assert(data >> 15 == 0); // Draw first copy for (int i = 0; i <= 5; i++) setModule(qrcode, size, 8, i, ((data >> i) & 1) != 0); setModule(qrcode, size, 8, 7, ((data >> 6) & 1) != 0); setModule(qrcode, size, 8, 8, ((data >> 7) & 1) != 0); setModule(qrcode, size, 7, 8, ((data >> 8) & 1) != 0); for (int i = 9; i < 15; i++) setModule(qrcode, size, 14 - i, 8, ((data >> i) & 1) != 0); // Draw second copy for (int i = 0; i <= 7; i++) setModule(qrcode, size, size - 1 - i, 8, ((data >> i) & 1) != 0); for (int i = 8; i < 15; i++) setModule(qrcode, size, 8, size - 15 + i, ((data >> i) & 1) != 0); setModule(qrcode, size, 8, size - 8, true); } // Calculates the positions of alignment patterns in ascending order for the given version number, // storing them to the given array and returning an array length in the range [0, 7]. static int getAlignmentPatternPositions(int version, uint8_t result[7]) { if (version == 1) return 0; int size = qrcodegen_getSize(version); int numAlign = version / 7 + 2; int step; if (version != 32) step = (version * 4 + numAlign * 2 + 1) / (2 * numAlign - 2) * 2; // ceil((size - 13) / (2*numAlign - 2)) * 2 else // C-C-C-Combo breaker! step = 26; for (int i = numAlign - 1, pos = size - 7; i >= 1; i--, pos -= step) result[i] = pos; result[0] = 6; return numAlign; } // Calculates the Reed-Solomon generator polynomial of the given degree, storing in result[0 : degree]. static void calcReedSolomonGenerator(int degree, uint8_t result[]) { // Start with the monomial x^0 assert(1 <= degree && degree <= 30); memset(result, 0, degree * sizeof(result[0])); result[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 (int j = 0; j < degree; j++) { result[j] = finiteFieldMultiply(result[j], (uint8_t)root); if (j + 1 < degree) result[j] ^= result[j + 1]; } root = (root << 1) ^ ((root >> 7) * 0x11D); // Multiply by 0x02 mod GF(2^8/0x11D) } } // Calculates the remainder of the polynomial data[0 : dataLen] when divided by the generator[0 : degree], where all // polynomials are in big endian and the generator has an implicit leading 1 term, storing the result in result[0 : degree]. static void calcReedSolomonRemainder(const uint8_t data[], int dataLen, const uint8_t generator[], int degree, uint8_t result[]) { // Perform polynomial division assert(1 <= degree && degree <= 30); memset(result, 0, degree * sizeof(result[0])); for (int i = 0; i < dataLen; i++) { uint8_t factor = data[i] ^ result[0]; memmove(&result[0], &result[1], (degree - 1) * sizeof(result[0])); result[degree - 1] = 0; for (int j = 0; j < degree; j++) result[j] ^= finiteFieldMultiply(generator[j], factor); } } // Returns the product of the two given field elements modulo GF(2^8/0x11D). All argument values are valid. static uint8_t finiteFieldMultiply(uint8_t x, uint8_t y) { // Russian peasant multiplication uint8_t z = 0; for (int i = 7; i >= 0; i--) { z = (z << 1) ^ ((z >> 7) * 0x11D); z ^= ((y >> i) & 1) * x; } return z; }