001/* 002 * Copyright 2007 ZXing authors 003 * 004 * Licensed under the Apache License, Version 2.0 (the "License"); 005 * you may not use this file except in compliance with the License. 006 * You may obtain a copy of the License at 007 * 008 * http://www.apache.org/licenses/LICENSE-2.0 009 * 010 * Unless required by applicable law or agreed to in writing, software 011 * distributed under the License is distributed on an "AS IS" BASIS, 012 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 013 * See the License for the specific language governing permissions and 014 * limitations under the License. 015 */ 016 017package com.itextpdf.text.pdf.qrcode; 018 019/** 020 * <p>This class contains utility methods for performing mathematical operations over 021 * the Galois Field GF(256). Operations use a given primitive polynomial in calculations.</p> 022 * 023 * <p>Throughout this package, elements of GF(256) are represented as an <code>int</code> 024 * for convenience and speed (but at the cost of memory). 025 * Only the bottom 8 bits are really used.</p> 026 * 027 * @author Sean Owen 028 * @since 5.0.2 029 */ 030public final class GF256 { 031 032 public static final GF256 QR_CODE_FIELD = new GF256(0x011D); // x^8 + x^4 + x^3 + x^2 + 1 033 public static final GF256 DATA_MATRIX_FIELD = new GF256(0x012D); // x^8 + x^5 + x^3 + x^2 + 1 034 035 private final int[] expTable; 036 private final int[] logTable; 037 private final GF256Poly zero; 038 private final GF256Poly one; 039 040 /** 041 * Create a representation of GF(256) using the given primitive polynomial. 042 * 043 * @param primitive irreducible polynomial whose coefficients are represented by 044 * the bits of an int, where the least-significant bit represents the constant 045 * coefficient 046 */ 047 private GF256(int primitive) { 048 expTable = new int[256]; 049 logTable = new int[256]; 050 int x = 1; 051 for (int i = 0; i < 256; i++) { 052 expTable[i] = x; 053 x <<= 1; // x = x * 2; we're assuming the generator alpha is 2 054 if (x >= 0x100) { 055 x ^= primitive; 056 } 057 } 058 for (int i = 0; i < 255; i++) { 059 logTable[expTable[i]] = i; 060 } 061 // logTable[0] == 0 but this should never be used 062 zero = new GF256Poly(this, new int[]{0}); 063 one = new GF256Poly(this, new int[]{1}); 064 } 065 066 GF256Poly getZero() { 067 return zero; 068 } 069 070 GF256Poly getOne() { 071 return one; 072 } 073 074 /** 075 * @return the monomial representing coefficient * x^degree 076 */ 077 GF256Poly buildMonomial(int degree, int coefficient) { 078 if (degree < 0) { 079 throw new IllegalArgumentException(); 080 } 081 if (coefficient == 0) { 082 return zero; 083 } 084 int[] coefficients = new int[degree + 1]; 085 coefficients[0] = coefficient; 086 return new GF256Poly(this, coefficients); 087 } 088 089 /** 090 * Implements both addition and subtraction -- they are the same in GF(256). 091 * 092 * @return sum/difference of a and b 093 */ 094 static int addOrSubtract(int a, int b) { 095 return a ^ b; 096 } 097 098 /** 099 * @return 2 to the power of a in GF(256) 100 */ 101 int exp(int a) { 102 return expTable[a]; 103 } 104 105 /** 106 * @return base 2 log of a in GF(256) 107 */ 108 int log(int a) { 109 if (a == 0) { 110 throw new IllegalArgumentException(); 111 } 112 return logTable[a]; 113 } 114 115 /** 116 * @return multiplicative inverse of a 117 */ 118 int inverse(int a) { 119 if (a == 0) { 120 throw new ArithmeticException(); 121 } 122 return expTable[255 - logTable[a]]; 123 } 124 125 /** 126 * @param a 127 * @param b 128 * @return product of a and b in GF(256) 129 */ 130 int multiply(int a, int b) { 131 if (a == 0 || b == 0) { 132 return 0; 133 } 134 if (a == 1) { 135 return b; 136 } 137 if (b == 1) { 138 return a; 139 } 140 return expTable[(logTable[a] + logTable[b]) % 255]; 141 } 142 143}