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89 lines
3.6 KiB
89 lines
3.6 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 <stdint.h>
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#include <string.h>
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/*---- Forward declarations for private functions ----*/
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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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/*---- Function implementations ----*/
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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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