com.itextpdf.barcodes.qrcode.GF256 Maven / Gradle / Ivy
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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];
}
}