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- /*
- * Copyright 2007 ZXing authors
- *
- * Licensed under the Apache License, Version 2.0 (the "License");
- * you may not use this file except in compliance with the License.
- * You may obtain a copy of the License at
- *
- * http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
- using System;
-
- namespace ZXing.Common.ReedSolomon
- {
- /// <summary>
- /// <p>This class contains utility methods for performing mathematical operations over
- /// the Galois Fields. Operations use a given primitive polynomial in calculations.</p>
- /// <p>Throughout this package, elements of the GF are represented as an {@code int}
- /// for convenience and speed (but at the cost of memory).
- /// </p>
- /// </summary>
- /// <author>Sean Owen</author>
- public sealed class GenericGF
- {
- public static GenericGF QR_CODE_FIELD_256 = new GenericGF(0x011D, 256, 0); // x^8 + x^4 + x^3 + x^2 + 1
-
- private int[] expTable;
- private int[] logTable;
- private GenericGFPoly zero;
- private GenericGFPoly one;
- private readonly int size;
- private readonly int primitive;
- private readonly int generatorBase;
-
- /// <summary>
- /// Create a representation of GF(size) using the given primitive polynomial.
- /// </summary>
- /// <param name="primitive">irreducible polynomial whose coefficients are represented by
- /// * the bits of an int, where the least-significant bit represents the constant
- /// * coefficient</param>
- /// <param name="size">the size of the field</param>
- /// <param name="genBase">the factor b in the generator polynomial can be 0- or 1-based
- /// * (g(x) = (x+a^b)(x+a^(b+1))...(x+a^(b+2t-1))).
- /// * In most cases it should be 1, but for QR code it is 0.</param>
- public GenericGF(int primitive, int size, int genBase)
- {
- this.primitive = primitive;
- this.size = size;
- this.generatorBase = genBase;
-
- expTable = new int[size];
- logTable = new int[size];
- int x = 1;
- for (int i = 0; i < size; i++)
- {
- expTable[i] = x;
- x <<= 1; // x = x * 2; we're assuming the generator alpha is 2
- if (x >= size)
- {
- x ^= primitive;
- x &= size - 1;
- }
- }
- for (int i = 0; i < size - 1; i++)
- {
- logTable[expTable[i]] = i;
- }
- // logTable[0] == 0 but this should never be used
- zero = new GenericGFPoly(this, new int[] { 0 });
- one = new GenericGFPoly(this, new int[] { 1 });
- }
-
- internal GenericGFPoly Zero
- {
- get
- {
- return zero;
- }
- }
-
- /// <summary>
- /// Builds the monomial.
- /// </summary>
- /// <param name="degree">The degree.</param>
- /// <param name="coefficient">The coefficient.</param>
- /// <returns>the monomial representing coefficient * x^degree</returns>
- internal GenericGFPoly buildMonomial(int degree, int coefficient)
- {
- if (degree < 0)
- {
- throw new ArgumentException();
- }
- if (coefficient == 0)
- {
- return zero;
- }
- int[] coefficients = new int[degree + 1];
- coefficients[0] = coefficient;
- return new GenericGFPoly(this, coefficients);
- }
-
- /// <summary>
- /// Implements both addition and subtraction -- they are the same in GF(size).
- /// </summary>
- /// <returns>sum/difference of a and b</returns>
- static internal int addOrSubtract(int a, int b)
- {
- return a ^ b;
- }
-
- /// <summary>
- /// Exps the specified a.
- /// </summary>
- /// <returns>2 to the power of a in GF(size)</returns>
- internal int exp(int a)
- {
- return expTable[a];
- }
-
-
- /// <summary>
- /// Inverses the specified a.
- /// </summary>
- /// <returns>multiplicative inverse of a</returns>
- internal int inverse(int a)
- {
- if (a == 0)
- {
- throw new ArithmeticException();
- }
- return expTable[size - logTable[a] - 1];
- }
-
- /// <summary>
- /// Multiplies the specified a with b.
- /// </summary>
- /// <param name="a">A.</param>
- /// <param name="b">The b.</param>
- /// <returns>product of a and b in GF(size)</returns>
- internal int multiply(int a, int b)
- {
- if (a == 0 || b == 0)
- {
- return 0;
- }
- return expTable[(logTable[a] + logTable[b]) % (size - 1)];
- }
-
- /// <summary>
- /// Gets the generator base.
- /// </summary>
- public int GeneratorBase
- {
- get { return generatorBase; }
- }
- }
- }
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