mirror of
https://github.com/claunia/cuetools.net.git
synced 2025-12-16 18:14:25 +00:00
536 lines
22 KiB
C#
536 lines
22 KiB
C#
using System;
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using System.Collections.Generic;
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using System.Text;
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namespace CUETools.Parity
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{
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public class Galois
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{
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private ushort[] expTbl; // 二重にもつことによりmul, div等を簡略化
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private ushort[] logTbl;
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private int w;
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private int max;
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private int symStart = 0;
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/**
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* スカラー、ベクターの相互変換テーブルの作成
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*/
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public Galois(int polynomial, int _w)
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{
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w = _w;
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max = (1 << _w) - 1;
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expTbl = new ushort[max * 2];
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logTbl = new ushort[max + 1];
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int d = 1;
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for (int i = 0; i < max; i++)
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{
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//if (d == 0)
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// throw new Exception("oops");
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expTbl[i] = expTbl[max + i] = (ushort)d;
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logTbl[d] = (ushort)i;
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d <<= 1;
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if (((d >> _w) & 1) != 0)
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d = (d ^ polynomial) & max;
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}
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}
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public int Max
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{
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get
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{
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return max;
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}
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}
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public ushort[] ExpTbl
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{
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get
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{
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return expTbl;
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}
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}
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public ushort[] LogTbl
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{
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get
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{
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return logTbl;
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}
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}
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/**
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* スカラー -> ベクター変換
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*
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* @param a int
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* @return int
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*/
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public int toExp(int a)
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{
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return expTbl[a];
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}
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/**
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* ベクター -> スカラー変換
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*
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* @param a int
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* @return int
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*/
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public int toLog(int a)
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{
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return logTbl[a];
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}
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/**
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* 誤り位置インデックスの計算
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*
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* @param length int
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* データ長
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* @param a int
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* 誤り位置ベクター
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* @return int
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* 誤り位置インデックス
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*/
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public int toPos(int length, int a)
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{
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return length - 1 - logTbl[a];
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}
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/**
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* 掛け算
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*
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* @param a int
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* @param b int
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* @return int
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* = a * b
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*/
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public int mul(int a, int b)
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{
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return (a == 0 || b == 0) ? 0 : expTbl[(int)logTbl[a] + logTbl[b]];
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}
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/**
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* 掛け算
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*
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* @param a int
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* @param b int
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* @return int
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* = a * α^b
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*/
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public int mulExp(int a, int b)
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{
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return (a == 0) ? 0 : expTbl[logTbl[a] + b];
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}
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/**
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* 割り算
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*
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* @param a int
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* @param b int
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* @return int
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* = a / b
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*/
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public int div(int a, int b)
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{
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return (a == 0) ? 0 : expTbl[logTbl[a] - logTbl[b] + max];
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}
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/**
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* 割り算
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*
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* @param a int
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* @param b int
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* @return int
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* = a / α^b
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*/
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public int divExp(int a, int b)
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{
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return (a == 0) ? 0 : expTbl[logTbl[a] - b + max];
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}
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/**
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* 逆数
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*
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* @param a int
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* @return int
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* = 1/a
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*/
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public int inv(int a)
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{
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return expTbl[max - logTbl[a]];
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}
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public int[] toLog(int[] a)
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{
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var res = new int[a.Length];
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for (int i = 0; i < a.Length; i++)
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res[i] = a[i] == 0 ? - 1 : toLog(a[i]);
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return res;
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}
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public int[] toLog(ushort[] a)
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{
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var res = new int[a.Length];
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for (int i = 0; i < a.Length; i++)
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res[i] = a[i] == 0 ? -1 : toLog(a[i]);
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return res;
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}
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public int[] toExp(int[] a)
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{
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var res = new int[a.Length];
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for (int i = 0; i < a.Length; i++)
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res[i] = a[i] == -1 ? 0 : toExp(a[i]);
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return res;
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}
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public int gfadd(int a, int b)
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{
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var a_exp = a == -1 ? 0 : toExp(a);
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var b_exp = b == -1 ? 0 : toExp(b);
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var res_exp = a_exp ^ b_exp;
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return res_exp == 0 ? -1 : toLog(res_exp);
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}
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public int[] gfadd(int[] a, int b)
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{
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var res = new int[a.Length];
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var a_exp = toExp(a);
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var b_exp = b == -1 ? 0 : toExp(b);
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for (int i = 0; i < a.Length; i++)
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res[i] = a_exp[i] ^ b_exp;
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return toLog(res);
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}
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public int[] gfdiff(int[] a)
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{
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//l = length(polynomial);
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//for cc = 2:l
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// %cc-1 represents the power of x
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// if mod(cc-1,2) == 0 %all the even powers are zero because of GF(2)
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// diff(cc-1) = -Inf;
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// else
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// diff(cc-1) = polynomial(cc);
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// end
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//end
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var res = new int[a.Length - 1];
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for (int i = 0; i < res.Length; i++)
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res[i] = (i % 2) == 0 ? a[i + 1] : -1;
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return res;
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}
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public int gfmul(int a, int b)
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{
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return a < 0 || b < 0 ? -1 : ((a + b) % max);
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}
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public int gfdiv(int a, int b)
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{
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return a < 0 ? -1 : ((max + a - b) % max);
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}
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public int gfpow(int value, int p)
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{
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return (value * p) % max;
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}
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public int gfsubstitute(int[] polynomial, int value, int terms)
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{
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var sum = 0;
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if (value != -1)
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for (int p = 0; p < terms; p++)
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if (polynomial[p] != -1)
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{
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var pow = polynomial[p] + value * p;
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sum ^= expTbl[(pow & max) + (pow >> w)];
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}
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return sum == 0 ? -1 : logTbl[sum];
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}
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public int[] gfconv(int[] a, int[] b)
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{
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return gfconv(a, b, a.Length + b.Length - 1);
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}
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public int[] gfconv(int[] a, int[] b, int len)
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{
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var seki = new int[len];
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for (int ia = 0; ia < a.Length; ia++)
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{
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var loga = a[ia];
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if (loga != -1)
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{
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int ib2 = Math.Min(b.Length, len - ia);
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for (int ib = 0; ib < ib2; ib++)
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{
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var logb = b[ib];
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if (logb != -1)
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seki[ia + ib] ^= expTbl[loga + logb]; // = a[ia] * b[ib]
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}
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}
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}
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for (int i = 0; i < len; i++)
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seki[i] = seki[i] == 0 ? -1 : logTbl[seki[i]];
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return seki;
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}
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public unsafe void gfconv(int* a, int alen, int* b, int blen, int* c, int clen)
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{
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for (int i = 0; i < clen; i++)
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c[i] = 0;
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for (int ia = 0; ia < alen; ia++)
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{
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var loga = a[ia];
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if (loga != -1)
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{
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int ib2 = Math.Min(blen, clen - ia);
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for (int ib = 0; ib < ib2; ib++)
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{
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var logb = b[ib];
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if (logb != -1)
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c[ia + ib] ^= expTbl[loga + logb]; // = a[ia] * b[ib]
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}
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}
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}
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for (int i = 0; i < clen; i++)
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c[i] = c[i] == 0 ? -1 : logTbl[c[i]];
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}
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public int[] mulPoly(int[] a, int[] b)
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{
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return mulPoly(a, b, a.Length + b.Length - 1);
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}
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public int[] mulPoly(int[] a, int[] b, int len)
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{
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var res = new int[len];
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mulPoly(res, a, b);
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return res;
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}
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/**
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* 数式の掛け算
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*
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* @param seki int[]
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* seki = a * b
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* @param a int[]
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* @param b int[]
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*/
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public void mulPoly(int[] seki, int[] a, int[] b)
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{
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Array.Clear(seki, 0, seki.Length);
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for (int ia = 0; ia < a.Length; ia++)
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{
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if (a[ia] != 0)
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{
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int loga = logTbl[a[ia]];
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int ib2 = Math.Min(b.Length, seki.Length - ia);
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for (int ib = 0; ib < ib2; ib++)
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{
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if (b[ib] != 0)
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{
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seki[ia + ib] ^= expTbl[loga + logTbl[b[ib]]]; // = a[ia] * b[ib]
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}
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}
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}
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}
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}
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public unsafe void mulPoly(int* seki, int* a, int* b, int lenS, int lenA, int lenB)
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{
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for (int i = 0; i < lenS; i++)
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seki[i] = 0;
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for (int ia = 0; ia < lenA; ia++)
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{
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if (a[ia] != 0)
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{
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int loga = logTbl[a[ia]];
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int ib2 = Math.Min(lenB, lenS - ia);
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for (int ib = 0; ib < ib2; ib++)
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{
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if (b[ib] != 0)
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{
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seki[ia + ib] ^= expTbl[loga + logTbl[b[ib]]]; // = a[ia] * b[ib]
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}
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}
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}
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}
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}
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/**
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* 生成多項式配列の作成
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* G(x)=Π[k=0,n-1](x + α^k)
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* encodeGxの添え字と次数の並びが逆なのに注意
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* encodeGx[0] = x^(npar - 1)の項
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* encodeGx[1] = x^(npar - 2)の項
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* ...
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* encodeGx[npar - 1] = x^0の項
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*/
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public int[] makeEncodeGx(int npar)
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{
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int[] encodeGx = new int[npar];
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encodeGx[npar - 1] = 1;
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for (int i = 0, kou = symStart; i < npar; i++, kou++)
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{
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int ex = toExp(kou); // ex = α^kou
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// (x + α^kou)を掛る
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for (int j = 0; j < npar - 1; j++)
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{
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// 現在の項 * α^kou + 一つ下の次数の項
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encodeGx[j] = mul(encodeGx[j], ex) ^ encodeGx[j + 1];
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}
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encodeGx[npar - 1] = mul(encodeGx[npar - 1], ex);// 最下位項の計算
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}
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return encodeGx;
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}
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public int[] makeEncodeGxLog(int npar)
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{
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int[] encodeGx = makeEncodeGx(npar);
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for (int i = 0; i < npar; i++)
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{
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if (encodeGx[i] == 0)
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throw new Exception("0 in encodeGx");
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encodeGx[i] = toLog(encodeGx[i]);
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}
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return encodeGx;
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}
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/// <summary>
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/// parityTable[xx, 0, i] = mul(00xx, encodeGx[i])
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/// parityTable[xx, 1, i] = mul(xx00, encodeGx[i])
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/// </summary>
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/// <param name="npar"></param>
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/// <returns></returns>
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public ushort[,,] makeEncodeTable(int npar)
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{
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var loggx = makeEncodeGxLog(npar);
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var parityTable = new ushort[256, 2, npar];
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for (int i = 0; i < npar; i++)
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{
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parityTable[0, 0, i] = 0;
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parityTable[0, 1, i] = 0;
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}
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for (int ib = 1; ib < 256; ib++)
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{
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int logib0 = LogTbl[ib];
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int logib1 = LogTbl[ib << 8];
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for (int i = 0; i < npar; i++)
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{
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parityTable[ib, 0, i] = ExpTbl[logib0 + loggx[i]];
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parityTable[ib, 1, i] = ExpTbl[logib1 + loggx[i]];
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}
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}
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return parityTable;
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}
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/// <summary>
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/// parityTable[xx, 0, i] = mul(00xx, α^i)
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/// parityTable[xx, 1, i] = mul(xx00, α^i)
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/// </summary>
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/// <param name="npar"></param>
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/// <returns></returns>
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public ushort[,,] makeDecodeTable(int npar)
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{
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var parityTable = new ushort[256, 2, npar];
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for (int i = 0; i < npar; i++)
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{
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parityTable[0, 0, i] = 0;
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parityTable[0, 1, i] = 0;
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}
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for (int ib = 1; ib < 256; ib++)
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{
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int logib0 = LogTbl[ib];
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int logib1 = LogTbl[ib << 8];
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for (int i = 0; i < npar; i++)
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{
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parityTable[ib, 0, i] = ExpTbl[logib0 + i];
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parityTable[ib, 1, i] = ExpTbl[logib1 + i];
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}
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}
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return parityTable;
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}
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/**
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* シンドロームの計算
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* @param data int[]
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* 入力データ配列
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* @param length int
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* データ長
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* @param syn int[]
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* (x - α^0) (x - α^1) (x - α^2) ...のシンドローム
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* @return boolean
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* true: シンドロームは総て0
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*/
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public bool calcSyndrome(byte[] data, int length, int[] syn)
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{
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int hasErr = 0;
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for (int i = 0; i < syn.Length; i++)
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{
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int wk = 0;
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for (int idx = 0; idx < length; idx++)
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{
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//wk = data[idx] ^ ((wk == 0) ? 0 : expTbl[logTbl[wk] + i + symStart]); // wk = data + wk * α^i
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wk = data[idx] ^ ((wk == 0) ? 0 : expTbl[logTbl[wk] + i]); // wk = data + wk * α^i
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}
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syn[i] = wk;
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hasErr |= wk;
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}
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return hasErr == 0;
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}
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/**
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* シンドロームの計算
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* @param data int[]
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* 入力データ配列
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* @param length int
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* データ長
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* @param syn int[]
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* (x - α^0) (x - α^1) (x - α^2) ...のシンドローム
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* @return boolean
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* true: シンドロームは総て0
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*/
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public unsafe bool calcSyndrome(ushort* data, int length, int[] syn)
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{
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int hasErr = 0;
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for (int i = 0; i < syn.Length; i++)
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{
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int wk = 0;
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for (int idx = 0; idx < length; idx++)
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{
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//wk = data[idx] ^ ((wk == 0) ? 0 : expTbl[logTbl[wk] + i + symStart]); // wk = data + wk * α^i
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wk = data[idx] ^ ((wk == 0) ? 0 : expTbl[logTbl[wk] + i]); // wk = data + wk * α^i
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}
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syn[i] = wk;
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hasErr |= wk;
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}
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return hasErr == 0;
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}
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}
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public class Galois81D: Galois
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{
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public const int POLYNOMIAL = 0x1d;
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public static Galois81D instance = new Galois81D();
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Galois81D()
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: base(POLYNOMIAL, 8)
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{
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}
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}
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public class Galois16 : Galois
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{
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public const int POLYNOMIAL = 0x1100B;
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public static Galois16 instance = new Galois16();
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Galois16()
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: base(POLYNOMIAL, 16)
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{
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}
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}
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}
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