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506 lines
20 KiB
506 lines
20 KiB
/*
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* QR Code generator library (C)
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*
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* Copyright (c) Project Nayuki
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* https://www.nayuki.io/page/qr-code-generator-library
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*
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* (MIT License)
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* Permission is hereby granted, free of charge, to any person obtaining a copy of
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* this software and associated documentation files (the "Software"), to deal in
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* the Software without restriction, including without limitation the rights to
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* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
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* the Software, and to permit persons to whom the Software is furnished to do so,
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* subject to the following conditions:
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* - The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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* - The Software is provided "as is", without warranty of any kind, express or
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* implied, including but not limited to the warranties of merchantability,
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* fitness for a particular purpose and noninfringement. In no event shall the
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* authors or copyright holders be liable for any claim, damages or other
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* liability, whether in an action of contract, tort or otherwise, arising from,
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* out of or in connection with the Software or the use or other dealings in the
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* Software.
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*/
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#include <assert.h>
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#include <stdlib.h>
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#include <string.h>
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#include "qrcodegen.h"
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/*---- Forward declarations for private functions ----*/
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static bool getModule(const uint8_t qrcode[], int size, int x, int y);
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static void setModule(uint8_t qrcode[], int size, int x, int y, bool isBlack);
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static void setModuleBounded(uint8_t qrcode[], int size, int x, int y, bool isBlack);
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static void initializeFunctionalModules(int version, uint8_t qrcode[]);
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static void drawWhiteFunctionModules(uint8_t qrcode[], int version);
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static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[], int size);
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static int getAlignmentPatternPositions(int version, uint8_t result[7]);
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static void appendErrorCorrection(uint8_t data[], int version, enum qrcodegen_Ecc ecl, uint8_t result[]);
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static int getNumRawDataModules(int version);
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static void drawCodewords(const uint8_t data[], int dataLen, uint8_t qrcode[], int version);
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static void applyMask(const uint8_t functionModules[], uint8_t qrcode[], int size, int mask);
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static void calcReedSolomonGenerator(int degree, uint8_t result[]);
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static void calcReedSolomonRemainder(const uint8_t data[], int dataLen, const uint8_t generator[], int degree, uint8_t result[]);
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static uint8_t finiteFieldMultiply(uint8_t x, uint8_t y);
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/*---- Private tables of constants ----*/
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static const int16_t NUM_ERROR_CORRECTION_CODEWORDS[4][41] = {
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// Version: (note that index 0 is for padding, and is set to an illegal value)
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//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
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{-1, 7, 10, 15, 20, 26, 36, 40, 48, 60, 72, 80, 96, 104, 120, 132, 144, 168, 180, 196, 224, 224, 252, 270, 300, 312, 336, 360, 390, 420, 450, 480, 510, 540, 570, 570, 600, 630, 660, 720, 750}, // Low
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{-1, 10, 16, 26, 36, 48, 64, 72, 88, 110, 130, 150, 176, 198, 216, 240, 280, 308, 338, 364, 416, 442, 476, 504, 560, 588, 644, 700, 728, 784, 812, 868, 924, 980, 1036, 1064, 1120, 1204, 1260, 1316, 1372}, // Medium
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{-1, 13, 22, 36, 52, 72, 96, 108, 132, 160, 192, 224, 260, 288, 320, 360, 408, 448, 504, 546, 600, 644, 690, 750, 810, 870, 952, 1020, 1050, 1140, 1200, 1290, 1350, 1440, 1530, 1590, 1680, 1770, 1860, 1950, 2040}, // Quartile
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{-1, 17, 28, 44, 64, 88, 112, 130, 156, 192, 224, 264, 308, 352, 384, 432, 480, 532, 588, 650, 700, 750, 816, 900, 960, 1050, 1110, 1200, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2100, 2220, 2310, 2430}, // High
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};
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const int8_t NUM_ERROR_CORRECTION_BLOCKS[4][41] = {
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// Version: (note that index 0 is for padding, and is set to an illegal value)
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//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
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{-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
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{-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
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{-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
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{-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
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};
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/*---- Function implementations ----*/
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// Public function - see documentation comment in header file.
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bool qrcodegen_isAlphanumeric(const char *text) {
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for (; *text != '\0'; text++) {
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char c = *text;
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if (('0' <= c && c <= '9') || ('A' <= c && c <= 'Z'))
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continue;
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else switch (c) {
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case ' ':
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case '$':
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case '%':
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case '*':
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case '+':
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case '-':
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case '.':
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case '/':
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case ':':
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continue;
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default:
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return false;
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}
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return false;
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}
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return true;
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}
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// Public function - see documentation comment in header file.
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bool qrcodegen_isNumeric(const char *text) {
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for (; *text != '\0'; text++) {
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char c = *text;
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if (c < '0' || c > '9')
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return false;
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}
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return true;
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}
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// Public function - see documentation comment in header file.
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int qrcodegen_getSize(int version) {
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assert(1 <= version && version <= 40);
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return version * 4 + 17;
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}
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// Public function - see documentation comment in header file.
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bool qrcodegen_getModule(const uint8_t qrcode[], int version, int x, int y) {
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int size = qrcodegen_getSize(version);
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return (0 <= x && x < size && 0 <= y && y < size) && getModule(qrcode, size, x, y);
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}
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// Gets the module at the given coordinates, which must be in bounds.
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static bool getModule(const uint8_t qrcode[], int size, int x, int y) {
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assert(21 <= size && size <= 177 && 0 <= x && x < size && 0 <= y && y < size);
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int index = y * size + x;
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int bitIndex = index & 7;
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int byteIndex = index >> 3;
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return ((qrcode[byteIndex] >> bitIndex) & 1) != 0;
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}
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// Sets the module at the given coordinates, which must be in bounds.
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static void setModule(uint8_t qrcode[], int size, int x, int y, bool isBlack) {
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assert(21 <= size && size <= 177 && 0 <= x && x < size && 0 <= y && y < size);
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int index = y * size + x;
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int bitIndex = index & 7;
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int byteIndex = index >> 3;
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if (isBlack)
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qrcode[byteIndex] |= 1 << bitIndex;
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else
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qrcode[byteIndex] &= (1 << bitIndex) ^ 0xFF;
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}
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// Sets the module at the given coordinates, doing nothing if out of bounds.
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static void setModuleBounded(uint8_t qrcode[], int size, int x, int y, bool isBlack) {
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if (0 <= x && x < size && 0 <= y && y < size)
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setModule(qrcode, size, x, y, isBlack);
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}
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// Fills the given QR Code grid with white modules for the given version's size,
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// then marks every function module in the QR Code as black.
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static void initializeFunctionalModules(int version, uint8_t qrcode[]) {
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// Initialize QR Code
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int size = qrcodegen_getSize(version);
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memset(qrcode, 0, (size * size + 7) / 8 * sizeof(qrcode[0]));
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// Fill horizontal and vertical timing patterns
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for (int i = 0; i < size; i++) {
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setModule(qrcode, size, 6, i, true);
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setModule(qrcode, size, i, 6, true);
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}
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// Fill 3 finder patterns (all corners except bottom right)
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for (int i = 0; i < 8; i++) {
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for (int j = 0; j < 8; j++) {
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setModule(qrcode, size, j, i, true);
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setModule(qrcode, size, size - 1 - j, i, true);
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setModule(qrcode, size, j, size - 1 - i, true);
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}
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}
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// Fill numerous alignment patterns
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uint8_t alignPatPos[7] = {0};
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int numAlign = getAlignmentPatternPositions(version, alignPatPos);
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for (int i = 0; i < numAlign; i++) {
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for (int j = 0; j < numAlign; j++) {
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if ((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0))
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continue; // Skip the three finder corners
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else {
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for (int k = -2; k <= 2; k++) {
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for (int l = -2; l <= 2; l++)
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setModule(qrcode, size, alignPatPos[i] + l, alignPatPos[j] + k, true);
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}
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}
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}
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}
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// Fill format bits
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for (int i = 0; i < 8; i++) {
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setModule(qrcode, size, i, 8, true);
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setModule(qrcode, size, 8, i, true);
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setModule(qrcode, size, size - 1 - i, 8, true);
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setModule(qrcode, size, 8, size - 1 - i, true);
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}
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setModule(qrcode, size, 8, 8, true);
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// Fill version
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if (version >= 7) {
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 6; j++) {
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int k = size - 11 + i;
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setModule(qrcode, size, k, j, true);
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setModule(qrcode, size, j, k, true);
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}
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}
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}
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}
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// Draws white function modules and possibly some black modules onto the given QR Code, without changing
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// non-function modules. This does not draw the format bits. This requires all function modules to be previously
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// marked black (namely by initializeFunctionalModules()), because this may skip redrawing black function modules.
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static void drawWhiteFunctionModules(uint8_t qrcode[], int version) {
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// Draw horizontal and vertical timing patterns
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int size = qrcodegen_getSize(version);
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for (int i = 7; i < size - 7; i += 2) {
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setModule(qrcode, size, 6, i, false);
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setModule(qrcode, size, i, 6, false);
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}
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// Draw 3 finder patterns
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for (int i = -4; i <= 4; i++) {
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for (int j = -4; j <= 4; j++) {
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int dist = abs(i);
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if (abs(j) > dist)
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dist = abs(j);
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if (dist == 2 || dist == 4) {
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setModuleBounded(qrcode, size, 3 + j, 3 + i, false);
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setModuleBounded(qrcode, size, size - 4 + j, 3 + i, false);
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setModuleBounded(qrcode, size, 3 + j, size - 4 + i, false);
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}
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}
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}
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// Draw numerous alignment patterns
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uint8_t alignPatPos[7] = {0};
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int numAlign = getAlignmentPatternPositions(version, alignPatPos);
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for (int i = 0; i < numAlign; i++) {
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for (int j = 0; j < numAlign; j++) {
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if ((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0))
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continue; // Skip the three finder corners
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else {
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for (int k = -1; k <= 1; k++) {
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for (int l = -1; l <= 1; l++)
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setModule(qrcode, size, alignPatPos[i] + l, alignPatPos[j] + k, k == 0 && l == 0);
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}
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}
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}
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}
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// Draw version block
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if (version >= 7) {
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// Calculate error correction code and pack bits
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int rem = version; // version is uint6, in the range [7, 40]
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for (int i = 0; i < 12; i++)
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rem = (rem << 1) ^ ((rem >> 11) * 0x1F25);
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long data = (long)version << 12 | rem; // uint18
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assert(data >> 18 == 0);
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// Draw two copies
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for (int i = 0; i < 3; i++) {
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for (int j = 0; j < 6; j++) {
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int k = size - 11 + i;
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setModule(qrcode, size, k, j, (data & 1) != 0);
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setModule(qrcode, size, j, k, (data & 1) != 0);
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data >>= 1;
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}
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}
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}
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}
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// Based on the given ECC level and mask, this calculates the format bits
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// and draws their black and white modules onto the given QR Code.
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static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[], int size) {
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// Calculate error correction code and pack bits
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assert(0 <= (int)mask && (int)mask <= 7);
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int data;
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switch (ecl) {
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case qrcodegen_Ecc_LOW : data = 1; break;
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case qrcodegen_Ecc_MEDIUM : data = 0; break;
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case qrcodegen_Ecc_QUARTILE: data = 3; break;
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case qrcodegen_Ecc_HIGH : data = 2; break;
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default: assert(false);
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}
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data = data << 3 | (int)mask; // ecl-derived value is uint2, mask is uint3
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int rem = data;
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for (int i = 0; i < 10; i++)
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rem = (rem << 1) ^ ((rem >> 9) * 0x537);
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data = data << 10 | rem;
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data ^= 0x5412; // uint15
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assert(data >> 15 == 0);
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// Draw first copy
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for (int i = 0; i <= 5; i++)
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setModule(qrcode, size, 8, i, ((data >> i) & 1) != 0);
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setModule(qrcode, size, 8, 7, ((data >> 6) & 1) != 0);
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setModule(qrcode, size, 8, 8, ((data >> 7) & 1) != 0);
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setModule(qrcode, size, 7, 8, ((data >> 8) & 1) != 0);
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for (int i = 9; i < 15; i++)
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setModule(qrcode, size, 14 - i, 8, ((data >> i) & 1) != 0);
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// Draw second copy
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for (int i = 0; i <= 7; i++)
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setModule(qrcode, size, size - 1 - i, 8, ((data >> i) & 1) != 0);
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for (int i = 8; i < 15; i++)
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setModule(qrcode, size, 8, size - 15 + i, ((data >> i) & 1) != 0);
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setModule(qrcode, size, 8, size - 8, true);
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}
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// Calculates the positions of alignment patterns in ascending order for the given version number,
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// storing them to the given array and returning an array length in the range [0, 7].
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static int getAlignmentPatternPositions(int version, uint8_t result[7]) {
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if (version == 1)
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return 0;
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int size = qrcodegen_getSize(version);
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int numAlign = version / 7 + 2;
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int step;
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if (version != 32)
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step = (version * 4 + numAlign * 2 + 1) / (2 * numAlign - 2) * 2; // ceil((size - 13) / (2*numAlign - 2)) * 2
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else // C-C-C-Combo breaker!
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step = 26;
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for (int i = numAlign - 1, pos = size - 7; i >= 1; i--, pos -= step)
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result[i] = pos;
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result[0] = 6;
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return numAlign;
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}
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// Appends error correction bytes to each block of the given data array, then interleaves bytes
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// from the blocks and stores them in the result array. data[0 : rawCodewords - totalEcc] contains
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// the input data. data[rawCodewords - totalEcc : rawCodewords] is used as a temporary work area
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// and will be clobbered by this function. The final answer is stored in result[0 : rawCodewords].
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static void appendErrorCorrection(uint8_t data[], int version, enum qrcodegen_Ecc ecl, uint8_t result[]) {
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// Calculate parameter numbers
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assert(0 <= (int)ecl && (int)ecl < 4 && 1 <= version && version <= 40);
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int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[(int)ecl][version];
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int totalEcc = NUM_ERROR_CORRECTION_CODEWORDS[(int)ecl][version];
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assert(totalEcc % numBlocks == 0);
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int blockEccLen = totalEcc / numBlocks;
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int rawCodewords = getNumRawDataModules(version) / 8;
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int dataLen = rawCodewords - totalEcc;
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int numShortBlocks = numBlocks - rawCodewords % numBlocks;
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int shortBlockDataLen = rawCodewords / numBlocks - blockEccLen;
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// Split data into blocks and append ECC after all data
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uint8_t generator[30];
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calcReedSolomonGenerator(blockEccLen, generator);
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for (int i = 0, j = dataLen, k = 0; i < numBlocks; i++) {
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int blockLen = shortBlockDataLen;
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if (i >= numShortBlocks)
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blockLen++;
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calcReedSolomonRemainder(&data[k], blockLen, generator, blockEccLen, &data[j]);
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j += blockEccLen;
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k += blockLen;
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}
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// Interleave (not concatenate) the bytes from every block into a single sequence
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for (int i = 0, k = 0; i < numBlocks; i++) {
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for (int j = 0, l = i; j < shortBlockDataLen; j++, k++, l += numBlocks)
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result[l] = data[k];
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if (i >= numShortBlocks)
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k++;
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}
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for (int i = numShortBlocks, l = numBlocks * shortBlockDataLen, k = (numShortBlocks + 1) * shortBlockDataLen;
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i < numBlocks; i++, k += shortBlockDataLen + 1, l++)
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result[l] = data[k];
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for (int i = 0, k = dataLen; i < numBlocks; i++) {
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for (int j = 0, l = dataLen + i; j < blockEccLen; j++, k++, l += numBlocks)
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result[l] = data[k];
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}
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}
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// Returns the number of data bits that can be stored in a QR Code of the given version number, after
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// all function modules are excluded. This includes remainder bits, so it may not be a multiple of 8.
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static int getNumRawDataModules(int version) {
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assert(1 <= version && version <= 40);
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int result = (16 * version + 128) * version + 64;
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if (version >= 2) {
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int numAlign = version / 7 + 2;
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result -= (25 * numAlign - 10) * numAlign - 55;
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if (version >= 7)
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result -= 18 * 2; // Subtract version information
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}
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return result;
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}
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// Draws the raw codewords (including data and ECC) onto the given QR Code. This requires the initial state of
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// the QR Code to be black at function modules and white at codeword modules (including unused remainder bits).
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static void drawCodewords(const uint8_t data[], int dataLen, uint8_t qrcode[], int version) {
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int size = qrcodegen_getSize(version);
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int i = 0; // Bit index into the data
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// Do the funny zigzag scan
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for (int right = size - 1; right >= 1; right -= 2) { // Index of right column in each column pair
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if (right == 6)
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right = 5;
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for (int vert = 0; vert < size; vert++) { // Vertical counter
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for (int j = 0; j < 2; j++) {
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int x = right - j; // Actual x coordinate
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bool upwards = ((right & 2) == 0) ^ (x < 6);
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int y = upwards ? size - 1 - vert : vert; // Actual y coordinate
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if (!getModule(qrcode, size, x, y) && i < dataLen * 8) {
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bool black = ((data[i >> 3] >> (7 - (i & 7))) & 1) != 0;
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setModule(qrcode, size, x, y, black);
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i++;
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}
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// If there are any remainder bits (0 to 7), they are already
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// set to 0/false/white when the grid of modules was initialized
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}
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}
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}
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assert(i == dataLen * 8);
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}
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// XORs the data modules in this QR Code with the given mask pattern. Due to XOR's mathematical
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// properties, calling applyMask(m) twice with the same value is equivalent to no change at all.
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// This means it is possible to apply a mask, undo it, and try another mask. Note that a final
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// well-formed QR Code symbol needs exactly one mask applied (not zero, not two, etc.).
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static void applyMask(const uint8_t functionModules[], uint8_t qrcode[], int size, int mask) {
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assert(0 <= mask && mask <= 7);
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for (int y = 0; y < size; y++) {
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for (int x = 0; x < size; x++) {
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if (getModule(functionModules, size, x, y))
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continue;
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bool invert;
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switch (mask) {
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case 0: invert = (x + y) % 2 == 0; break;
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case 1: invert = y % 2 == 0; break;
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case 2: invert = x % 3 == 0; break;
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case 3: invert = (x + y) % 3 == 0; break;
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case 4: invert = (x / 3 + y / 2) % 2 == 0; break;
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case 5: invert = x * y % 2 + x * y % 3 == 0; break;
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case 6: invert = (x * y % 2 + x * y % 3) % 2 == 0; break;
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case 7: invert = ((x + y) % 2 + x * y % 3) % 2 == 0; break;
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default: assert(false);
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}
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bool val = getModule(qrcode, size, x, y);
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setModule(qrcode, size, x, y, val ^ invert);
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}
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}
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}
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// Calculates the Reed-Solomon generator polynomial of the given degree, storing in result[0 : degree].
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static void calcReedSolomonGenerator(int degree, uint8_t result[]) {
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// Start with the monomial x^0
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assert(1 <= degree && degree <= 30);
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memset(result, 0, degree * sizeof(result[0]));
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result[degree - 1] = 1;
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// Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}),
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// drop the highest term, and store the rest of the coefficients in order of descending powers.
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// Note that r = 0x02, which is a generator element of this field GF(2^8/0x11D).
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int root = 1;
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for (int i = 0; i < degree; i++) {
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// Multiply the current product by (x - r^i)
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for (int j = 0; j < degree; j++) {
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result[j] = finiteFieldMultiply(result[j], (uint8_t)root);
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if (j + 1 < degree)
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result[j] ^= result[j + 1];
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}
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root = (root << 1) ^ ((root >> 7) * 0x11D); // Multiply by 0x02 mod GF(2^8/0x11D)
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}
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}
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// Calculates the remainder of the polynomial data[0 : dataLen] when divided by the generator[0 : degree], where all
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// polynomials are in big endian and the generator has an implicit leading 1 term, storing the result in result[0 : degree].
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static void calcReedSolomonRemainder(const uint8_t data[], int dataLen, const uint8_t generator[], int degree, uint8_t result[]) {
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// Perform polynomial division
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assert(1 <= degree && degree <= 30);
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memset(result, 0, degree * sizeof(result[0]));
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for (int i = 0; i < dataLen; i++) {
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uint8_t factor = data[i] ^ result[0];
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memmove(&result[0], &result[1], (degree - 1) * sizeof(result[0]));
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result[degree - 1] = 0;
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for (int j = 0; j < degree; j++)
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result[j] ^= finiteFieldMultiply(generator[j], factor);
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}
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}
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// Returns the product of the two given field elements modulo GF(2^8/0x11D). All argument values are valid.
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static uint8_t finiteFieldMultiply(uint8_t x, uint8_t y) {
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// Russian peasant multiplication
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uint8_t z = 0;
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for (int i = 7; i >= 0; i--) {
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z = (z << 1) ^ ((z >> 7) * 0x11D);
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z ^= ((y >> i) & 1) * x;
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}
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return z;
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}
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