cuetools.net/CUETools.Parity/Galois.cs

<EFBFBD><EFBFBD>using System;
using System.Collections.Generic;
using System.Text;

namespace CUETools.Parity
{
	public class Galois
	{
		private ushort[] expTbl; // <EFBFBD>N͑k0<EFBFBD>0d0S0h0k0<EFBFBD>0<EFBFBD>0mul, divI{<EFBFBD>0!|euS
		private ushort[] logTbl;
		private int w;
		private int max;
		private int symStart = 0;

		/**
		 * <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0n0<EFBFBD>v<EFBFBD>N	Y<EFBFBD>c<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0n0\Ob
		 */
		public Galois(int polynomial, int _w)
		{
			w = _w;
			max = (1 << _w) - 1;

			expTbl = new ushort[max * 2];
			logTbl = new ushort[max + 1];

			int d = 1;
			for (int i = 0; i < max; i++)
			{
				//if (d == 0)
				//    throw new Exception("oops");
				expTbl[i] = expTbl[max + i] = (ushort)d;
				logTbl[d] = (ushort)i;
				d <<= 1;
				if (((d >> _w) & 1) != 0)
					d = (d ^ polynomial) & max;
			}
		}

		public int Max
		{
			get
			{
				return max;
			}
		}

		public ushort[] ExpTbl
		{
			get
			{
				return expTbl;
			}
		}

		public ushort[] LogTbl
		{
			get
			{
				return logTbl;
			}
		}

		/**
		 * <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0 -> <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0	Y<EFBFBD>c
		 *
		 * @param a int
		 * @return int
		 */
		public int toExp(int a)
		{
			return expTbl[a];
		}

		/**
		 * <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0 -> <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0	Y<EFBFBD>c
		 *
		 * @param a int
		 * @return int
		 */
		public int toLog(int a)
		{
			return logTbl[a];
		}

		/**
		 * <EFBFBD><EFBFBD><EFBFBD>0MOn<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0n0<EFBFBD><EFBFBD>{
		 *
		 * @param length int
		 * 		<EFBFBD>0<EFBFBD>0<EFBFBD>0w<EFBFBD>
		 * @param a int
		 * 		<EFBFBD><EFBFBD><EFBFBD>0MOn<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
		 * @return int
		 * 		<EFBFBD><EFBFBD><EFBFBD>0MOn<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
		 */
		public int toPos(int length, int a)
		{
			return length - 1 - logTbl[a];
		}

		/**
		 * <EFBFBD>cQ0<EFBFBD>{
		 *
		 * @param a int
		 * @param b int
		 * @return int
		 * 		= a * b
		 */
		public int mul(int a, int b)
		{
			return (a == 0 || b == 0) ? 0 : expTbl[(int)logTbl[a] + logTbl[b]];
		}

		/**
		 * <EFBFBD>cQ0<EFBFBD>{
		 *
		 * @param a int
		 * @param b int
		 * @return int
		 * 		= a * <EFBFBD>^b
		 */
		public int mulExp(int a, int b)
		{
			return (a == 0) ? 0 : expTbl[logTbl[a] + b];
		}

		/**
		 * rR<EFBFBD>0<EFBFBD>{
		 *
		 * @param a int
		 * @param b int
		 * @return int
		 * 		= a / b
		 */
		public int div(int a, int b)
		{
			return (a == 0) ? 0 : expTbl[logTbl[a] - logTbl[b] + max];
		}

		/**
		 * rR<EFBFBD>0<EFBFBD>{
		 *
		 * @param a int
		 * @param b int
		 * @return int
		 * 		= a / <EFBFBD>^b
		 */
		public int divExp(int a, int b)
		{
			return (a == 0) ? 0 : expTbl[logTbl[a] - b + max];
		}

		/**
		 * <EFBFBD>pe
		 *
		 * @param a int
		 * @return int
		 * 		= 1/a
		 */
		public int inv(int a)
		{
			return expTbl[max - logTbl[a]];
		}

		/**
		 * pe_n0<EFBFBD>cQ0<EFBFBD>{
		 *
		 * @param seki int[]
		 * 		seki = a * b
		 * @param a int[]
		 * @param b int[]
		 */
		public void mulPoly(int[] seki, int[] a, int[] b)
		{
			Array.Clear(seki, 0, seki.Length);
			for (int ia = 0; ia < a.Length; ia++)
			{
				if (a[ia] != 0)
				{
					int loga = logTbl[a[ia]];
					int ib2 = Math.Min(b.Length, seki.Length - ia);
					for (int ib = 0; ib < ib2; ib++)
					{
						if (b[ib] != 0)
						{
							seki[ia + ib] ^= expTbl[loga + logTbl[b[ib]]];	// = a[ia] * b[ib]
						}
					}
				}
			}
		}

		public unsafe void mulPoly(int* seki, int* a, int* b, int lenS, int lenA, int lenB)
		{
			for (int i = 0; i < lenS; i++)
				seki[i] = 0;
			for (int ia = 0; ia < lenA; ia++)
			{
				if (a[ia] != 0)
				{
					int loga = logTbl[a[ia]];
					int ib2 = Math.Min(lenB, lenS - ia);
					for (int ib = 0; ib < ib2; ib++)
					{
						if (b[ib] != 0)
						{
							seki[ia + ib] ^= expTbl[loga + logTbl[b[ib]]];	// = a[ia] * b[ib]
						}
					}
				}
			}
		}

		/**
		 * ubY<EFBFBD>_M<EFBFBD>Rn0\Ob
		 *		G(x)=<EFBFBD>[k=0,n-1](x + <EFBFBD>^k)
		 *		encodeGxn0<EFBFBD>mH0W[h0!kpen0&Ns0L0<EFBFBD>j0n0k0<EFBFBD>la
		 *		encodeGx[0]        = x^(npar - 1)n0<EFBFBD>
		 *		encodeGx[1]        = x^(npar - 2)n0<EFBFBD>
		 *		...
		 *		encodeGx[npar - 1] = x^0n0<EFBFBD>
		 */
		public int[] makeEncodeGx(int npar)
		{
			int[] encodeGx = new int[npar];
			encodeGx[npar - 1] = 1;
			for (int i = 0, kou = symStart; i < npar; i++, kou++)
			{
				int ex = toExp(kou); // ex = <EFBFBD>^kou
				// (x + <EFBFBD>^kou)<EFBFBD>0<EFBFBD>c<EFBFBD>0
				for (int j = 0; j < npar - 1; j++)
				{
					// <EFBFBD>s(Wn0<EFBFBD> * <EFBFBD>^kou + Nd0Nn0!kpen0<EFBFBD>
					encodeGx[j] = mul(encodeGx[j], ex) ^ encodeGx[j + 1];
				}
				encodeGx[npar - 1] = mul(encodeGx[npar - 1], ex);// gNMO<EFBFBD>n0<EFBFBD><EFBFBD>{
			}
			return encodeGx;
		}

		public int[] makeEncodeGxLog(int npar)
		{
			int[] encodeGx = makeEncodeGx(npar);
			for (int i = 0; i < npar; i++)
			{
				if (encodeGx[i] == 0)
					throw new Exception("0 in encodeGx");
				encodeGx[i] = toLog(encodeGx[i]);
			}
			return encodeGx;
		}

		/**
		 * <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0n0<EFBFBD><EFBFBD>{
		 * @param data int[]
		 *		eQ<EFBFBD>R<EFBFBD>0<EFBFBD>0<EFBFBD>0M<EFBFBD>R
		 * @param length int
		 *		<EFBFBD>0<EFBFBD>0<EFBFBD>0w<EFBFBD>
		 * @param syn int[]
		 *		(x - <EFBFBD>^0) (x - <EFBFBD>^1) (x - <EFBFBD>^2) ...n0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
		 * @return boolean
		 *		true: <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0o0<EFBFBD>}f00
		 */
		public bool calcSyndrome(byte[] data, int length, int[] syn)
		{
			int hasErr = 0;
			for (int i = 0; i < syn.Length; i++)
			{
				int wk = 0;
				for (int idx = 0; idx < length; idx++)
				{
					//wk = data[idx] ^ ((wk == 0) ? 0 : expTbl[logTbl[wk] + i + symStart]);		// wk = data + wk * <EFBFBD>^i
					wk = data[idx] ^ ((wk == 0) ? 0 : expTbl[logTbl[wk] + i]);		// wk = data + wk * <EFBFBD>^i
				}
				syn[i] = wk;
				hasErr |= wk;
			}
			return hasErr == 0;
		}

		/**
		 * <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0n0<EFBFBD><EFBFBD>{
		 * @param data int[]
		 *		eQ<EFBFBD>R<EFBFBD>0<EFBFBD>0<EFBFBD>0M<EFBFBD>R
		 * @param length int
		 *		<EFBFBD>0<EFBFBD>0<EFBFBD>0w<EFBFBD>
		 * @param syn int[]
		 *		(x - <EFBFBD>^0) (x - <EFBFBD>^1) (x - <EFBFBD>^2) ...n0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
		 * @return boolean
		 *		true: <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0o0<EFBFBD>}f00
		 */
		public unsafe bool calcSyndrome(ushort* data, int length, int[] syn)
		{
			int hasErr = 0;
			for (int i = 0; i < syn.Length; i++)
			{
				int wk = 0;
				for (int idx = 0; idx < length; idx++)
				{
					//wk = data[idx] ^ ((wk == 0) ? 0 : expTbl[logTbl[wk] + i + symStart]);		// wk = data + wk * <EFBFBD>^i
					wk = data[idx] ^ ((wk == 0) ? 0 : expTbl[logTbl[wk] + i]);		// wk = data + wk * <EFBFBD>^i
				}
				syn[i] = wk;
				hasErr |= wk;
			}
			return hasErr == 0;
		}
	}

	public class Galois81D: Galois
	{
		public const int POLYNOMIAL = 0x1d;

		public static Galois81D instance = new Galois81D();

		Galois81D()
			: base(POLYNOMIAL, 8)
		{
		}
	}

	public class Galois16 : Galois
	{
		public const int POLYNOMIAL = 0x1100B;

		public static Galois16 instance = new Galois16();

		Galois16()
			: base(POLYNOMIAL, 16)
		{
		}
	}
}