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package com.itextpdf.barcodes.qrcode;

/**
 * This class contains utility methods for performing mathematical operations over
 * the Galois Field GF(256). Operations use a given primitive polynomial in calculations.
 * 

* Throughout this package, elements of GF(256) are represented as an int * for convenience and speed (but at the cost of memory). * Only the bottom 8 bits are really used. * * @author Sean Owen */ final class GF256 { // x^8 + x^4 + x^3 + x^2 + 1 public static final GF256 QR_CODE_FIELD = new GF256(0x011D); // x^8 + x^5 + x^3 + x^2 + 1 public static final GF256 DATA_MATRIX_FIELD = new GF256(0x012D); private final int[] expTable; private final int[] logTable; private final GF256Poly zero; private final GF256Poly one; /** * Create a representation of GF(256) using the given primitive polynomial. * * @param primitive irreducible polynomial whose coefficients are represented by * the bits of an int, where the least-significant bit represents the constant * coefficient */ private GF256(int primitive) { expTable = new int[256]; logTable = new int[256]; int x = 1; for (int i = 0; i < 256; i++) { expTable[i] = x; // x = x * 2; we're assuming the generator alpha is 2 x <<= 1; if (x >= 0x100) { x ^= primitive; } } for (int i = 0; i < 255; i++) { logTable[expTable[i]] = i; } // logTable[0] == 0 but this should never be used zero = new GF256Poly(this, new int[]{0}); one = new GF256Poly(this, new int[]{1}); } GF256Poly getZero() { return zero; } GF256Poly getOne() { return one; } /** * @return the monomial representing coefficient * x^degree */ GF256Poly buildMonomial(int degree, int coefficient) { if (degree < 0) { throw new IllegalArgumentException(); } if (coefficient == 0) { return zero; } int[] coefficients = new int[degree + 1]; coefficients[0] = coefficient; return new GF256Poly(this, coefficients); } /** * Implements both addition and subtraction -- they are the same in GF(256). * * @return sum/difference of a and b */ static int addOrSubtract(int a, int b) { return a ^ b; } /** * @return 2 to the power of a in GF(256) */ int exp(int a) { return expTable[a]; } /** * @return base 2 log of a in GF(256) */ int log(int a) { if (a == 0) { throw new IllegalArgumentException(); } return logTable[a]; } /** * @return multiplicative inverse of a */ int inverse(int a) { if (a == 0) { throw new ArithmeticException(); } return expTable[255 - logTable[a]]; } /** * @param a * @param b * @return product of a and b in GF(256) */ int multiply(int a, int b) { if (a == 0 || b == 0) { return 0; } if (a == 1) { return b; } if (b == 1) { return a; } return expTable[(logTable[a] + logTable[b]) % 255]; } }





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