cuetools.net/CUETools.Parity/RsDecode.cs

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

namespace CUETools.Parity
{
	/**
	 * <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0: RS<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
	 *
	 * @author Masayuki Miyazaki
	 * http://sourceforge.jp/projects/reedsolomon/
	 */
	public class RsDecode
	{
		protected Galois galois;
		protected int npar;

		public RsDecode(int npar, Galois galois)
		{
			this.npar = npar;
			this.galois = galois;
		}

		/// <summary>
		/// Modified Berlekamp-Massey 
		/// </summary>
		/// <param name="sigma">
		/// <EFBFBD>(z)<h
}(uM<EFBFBD>R
0g'Ynpar/2 + 2Pn0<EFBFBD><EFBFBD>WL0<EFBFBD>_<EFBFBD><EFBFBD>
		/// <EFBFBD>0,<EFBFBD>1,<EFBFBD>2, ... <EFBFBD>[jisu]
		/// </param>
		/// <param name="omega">
		/// <EFBFBD>(z)<h
}(uM<EFBFBD>R
0g'Ynpar/2 + 1Pn0<EFBFBD><EFBFBD>WL0<EFBFBD>_<EFBFBD><EFBFBD>
		/// <EFBFBD>0,<EFBFBD>1,<EFBFBD>2, ... <EFBFBD>[jisu-1]
		/// </param>
		/// <param name="syn">
		/// <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0M<EFBFBD>R
		/// s0,s1,s2, ... s[npar-1]
		/// </param>
		/// <returns>
		/// >= 0: <EFBFBD>n0!kpe
		/// else: <EFBFBD>0<EFBFBD>0<EFBFBD>0
		/// </returns>
		public unsafe int calcSigmaMBM(int* sigma, int* syn)
		{
			int* sg0 = stackalloc int[npar + 1];
			int* sg1 = stackalloc int[npar + 1];
			int* wk = stackalloc int[npar + 1];

			sg0[1] = 1;
			sg1[0] = 1;
			int jisu0 = 1;
			int jisu1 = 0;
			int m = -1;

			for (int n = 0; n < npar; n++)
			{
				// $R%R_<EFBFBD>0<EFBFBD><EFBFBD>{
				int d = syn[n];
				for (int i = 1; i <= jisu1; i++)
					d ^= galois.mul(sg1[i], syn[n - i]);

				if (d != 0)
				{
					int logd = galois.toLog(d);
					for (int i = 0; i <= n; i++)
						wk[i] = sg1[i] ^ galois.mulExp(sg0[i], logd);
					int js = n - m;
					if (js > jisu1)
					{
						for (int i = 0; i <= jisu0; i++)
							sg0[i] = galois.divExp(sg1[i], logd);
						m = n - jisu1;
						jisu1 = js;
						jisu0 = js;
					}
					for (int i = 0; i < npar; i++)
						sg1[i] = wk[i];
				}
				for (int i = jisu0; i > 0; i--)
					sg0[i] = sg0[i - 1];
				sg0[0] = 0;
				jisu0++;
			}
			if (sg1[jisu1] == 0)
				return -1;
			//galois.mulPoly(omega, sg1, syn, npar / 2 + 1, npar, npar);
			for (int i = 0; i < Math.Min(npar / 2 + 2, npar); i++)
				sigma[i] = sg1[i];
			return jisu1;
		}

		public unsafe int calcSigmaMBM(int[] sigma, int[] omega, int[] syn)
		{
			fixed (int* s = sigma, o = omega, y = syn)
			{
				int res = calcSigmaMBM(s, y);
				if (res >= 0) galois.mulPoly(o, s, y, npar / 2 + 1, npar, npar);
				return res;
			}
		}

		/**
		 * gB}<EFBFBD>0<EFBFBD>0<EFBFBD>0MOnn0<EFBFBD>0<EFBFBD>0<EFBFBD>0
		 * @param pos
		 * 		<EFBFBD><EFBFBD><EFBFBD>0MOn<h
}(uRR
		 * @param n
		 * 		<EFBFBD>0<EFBFBD>0<EFBFBD>0w<EFBFBD>
		 * @param last
		 * 		<EFBFBD>0<EFBFBD>0<EFBFBD>0MOn
		 * @return
		 * 		0: ck8^B}<EFBFBD>N
		 * 		< 0: <EFBFBD>0<EFBFBD>0<EFBFBD>0
		 */
		private unsafe bool setLastErrorPos(int* pos, int n, int last)
		{
			if (galois.toLog(last) >= n)
				return false;	// <EFBFBD>{<EFBFBD>VYj0n0g0<EFBFBD>0<EFBFBD>0<EFBFBD>0
			pos[0] = last;
			return true;
		}

		/**
		 * <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>c"}k0<6B>0<EFBFBD>0<EFBFBD><30><EFBFBD>0MOn<6E>0Bl<42>0<EFBFBD>0
		 *		<EFBFBD>(z) = 0n0㉒0<EFBFBD>c"}Y0<59>0
		 *		_0`0W0
0<EFBFBD>c"}o0<6F>0<EFBFBD>0<EFBFBD>0w<30><77>N<EFBFBD>Qn0<6E><30>n00g0
		 *		jisuPn0<EFBFBD><EFBFBD>L0<EFBFBD><EFBFBD>d0K0<EFBFBD>0j0Q0<EFBFBD>0p0
0<EFBFBD>0<EFBFBD>0<EFBFBD>0h0Y0<EFBFBD>0
		 * @param pos int[]
		 * 		<EFBFBD><EFBFBD><EFBFBD>0MOn<h
}(uM<EFBFBD>R
0jisuPn0<EFBFBD><EFBFBD>WL0<EFBFBD>_<EFBFBD><EFBFBD>
		 * @param n int
		 * 		<EFBFBD>0<EFBFBD>0<EFBFBD>0w<EFBFBD>
		 * @param jisu int
		 * 		<EFBFBD>n0!kpe
		 * @param sigma int[]
		 * 		<EFBFBD>0,<EFBFBD>1,<EFBFBD>2, ... <EFBFBD><jisu>
		 * @return int
		 *		0: ck8^B}<EFBFBD>N
		 *		< 0: <EFBFBD>0<EFBFBD>0<EFBFBD>0
		 */
		public unsafe bool chienSearch(int* pos, int n, int jisu, int* sigma)
		{
			/*
			 * <EFBFBD>(z) = (1-<EFBFBD>^i*z)(1-<EFBFBD>^j*z)(1-<EFBFBD>^k*z)
			 *       = 1 + <EFBFBD>1z + <EFBFBD>2z^2 +...
			 * <EFBFBD>1 = <EFBFBD>^i + <EFBFBD>^j + <EFBFBD>^k
			 * d0~0<EFBFBD>0<EFBFBD>1o0hQf0n0<EFBFBD><EFBFBD>n0T<EFBFBD>h0j0c0f0D0<EFBFBD>00
N<EFBFBD>n0'`ꌒ0)R(uW0f0
0<EFBFBD>0<EFBFBD>0gi<EFBFBD>S
			 * last = <EFBFBD>1K0<EFBFBD>0
0<EFBFBD><EFBFBD>d0Q0_0㉒0!k0h0_D0f0D0O0S0h0k0<EFBFBD>0<EFBFBD>0
0g<EFBFBD>_n0<EFBFBD><EFBFBD>o0lasth0j0<EFBFBD>0
			 */
			int last = sigma[1];
			if (jisu == 1)
			{
				// !kpeL01j0<EFBFBD>0p0lastL0]0n0<EFBFBD><EFBFBD>g0B0<EFBFBD>0
				return setLastErrorPos(pos, n, last);
			}
			int posIdx = jisu - 1;		// <EFBFBD><EFBFBD><EFBFBD>0MOn<h
}(u<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
			for (int i = 0; i < n; i++)
			{
				/*
				 * <EFBFBD>(z)n0<EFBFBD><EFBFBD>{
				 * w <EFBFBD>01(0WNn0<EFBFBD>)k0RgSW0_0<EFBFBD>_
0<EFBFBD>k<EFBFBD>0n0<EFBFBD><1..jisu><EFBFBD>0<EFBFBD>R<EFBFBD>{
				 * z = 1/<EFBFBD>^i = <EFBFBD>^Ih0Y0<EFBFBD>0h0
				 * <EFBFBD>(z) = 1 + <EFBFBD>1<EFBFBD>^I + <EFBFBD>2(<EFBFBD>^I)^2 + <EFBFBD>3(<EFBFBD>^I)^3 + ... + <EFBFBD><jisu>/(<EFBFBD>^I)^<jisu>
				 *      = 1 + <EFBFBD>1<EFBFBD>^I + <EFBFBD>2<EFBFBD>^(I*2) + <EFBFBD>3<EFBFBD>^(I*3) + ... + <EFBFBD><jisu><EFBFBD>^(I*<jisu>)
				 */
				int z = galois.Max - i;					// z = 1/<EFBFBD>^in0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
				int wk = 1;
				for (int j = 1; j <= jisu; j++)
				{
					wk ^= galois.mulExp(sigma[j], (z * j) % galois.Max);
				}
				if (wk == 0)
				{
					int pv = galois.toExp(i);		// <EFBFBD>(z) = 0n0<EFBFBD><EFBFBD>
					last ^= pv;					// lastK0<EFBFBD>0<EFBFBD>N<EFBFBD><EFBFBD>d0K0c0_0㉒0_O0
					pos[posIdx--] = pv;
					if (posIdx == 0)
					{
						// <EFBFBD>k<EFBFBD>0L0Nd0j0<EFBFBD>0p0
0lastL0]0n0<EFBFBD><EFBFBD>g0B0<EFBFBD>0
						return setLastErrorPos(pos, n, last);
					}
				}
			}
			// <EFBFBD>c"}k0<6B>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0w<30><77>N<EFBFBD>Qk0
0jisuPn0<6E><30>L0<4C><30>d0K0<4B>0j0K0c0_0
			return false;
		}

		public unsafe bool chienSearch(int[] pos, int n, int jisu, int[] sigma)
		{
			fixed (int* p = pos, s = sigma)
				return chienSearch(p, n, jisu, s);
		}

		public unsafe int doForney(int jisu, int ps, int* sigma, int* omega)
		{
			int zlog = galois.Max - galois.toLog(ps);					// zn0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0

			// <EFBFBD>(z)n0<EFBFBD><EFBFBD>{
			int ov = omega[0];
			for (int j = 1; j < jisu; j++)
			{
				ov ^= galois.mulExp(omega[j], (zlog * j) % galois.Max);		// ov += <EFBFBD>i * z^j
			}

			// <EFBFBD>'(z)n0$P<EFBFBD>0<EFBFBD><EFBFBD>{(<EFBFBD>(z)n0b__<EFBFBD>v<EFBFBD>_R)
			int dv = sigma[1];
			for (int j = 2; j < jisu; j += 2)
			{
				dv ^= galois.mulExp(sigma[j + 1], (zlog * j) % galois.Max);	// dv += <EFBFBD><j+1> * z^j
			}

			/*
			 * <EFBFBD><EFBFBD><EFBFBD>0<EFBFBD>ck E^i = <EFBFBD>^i * <EFBFBD>(z) / <EFBFBD>'(z)
			 * <EFBFBD><EFBFBD><EFBFBD>0MOnn0<EFBFBD>{<EFBFBD>Vo0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>c"}n0h0M0k0<6B>O<<3C>U0<55>0f0D0<44>0n0g0
0
			 * S0S0g0o0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0W0j0D0
			 */
			return galois.mul(ps, galois.div(ov, dv));
		}
	}

	public class RsDecode8: RsDecode
	{
		public RsDecode8(int npar)
			: base(npar, Galois81D.instance)
		{
		}

		/**
		 * Forney<EFBFBD>lg0<EFBFBD><EFBFBD><EFBFBD>0<EFBFBD>ck<EFBFBD>0L<EFBFBD>F0
		 *		<EFBFBD>(z) = (1-<EFBFBD>^i*z)(1-<EFBFBD>^j*z)(1-<EFBFBD>^k*z)
		 *		<EFBFBD>'(z) = <EFBFBD>^i * (1-<EFBFBD>^j*z)(1-<EFBFBD>^k*z)...
		 *			   + <EFBFBD>^j * (1-<EFBFBD>^i*z)(1-<EFBFBD>^k*z)...
		 *			   + <EFBFBD>^k * (1-<EFBFBD>^i*z)(1-<EFBFBD>^j*z)...
		 *		<EFBFBD>(z) = (E^i/(1-<EFBFBD>^i*z) + E^j/(1-<EFBFBD>^j*z) + ...) * <EFBFBD>(z)
		 *			  = E^i*(1-<EFBFBD>^j*z)(1-<EFBFBD>^k*z)...
		 *			  + E^j*(1-<EFBFBD>^i*z)(1-<EFBFBD>^k*z)...
		 *			  + E^k*(1-<EFBFBD>^i*z)(1-<EFBFBD>^j*z)...
		 *		4" E^i = <00>^i * <00>(z) / <00>'(z)
		 * @param data int[]
		 *		eQ<EFBFBD>R<EFBFBD>0<EFBFBD>0<EFBFBD>0M<EFBFBD>R
		 * @param length int
		 *		eQ<EFBFBD>R<EFBFBD>0<EFBFBD>0<EFBFBD>0w<EFBFBD>U0
		 * @param jisu int
		 *		<EFBFBD>n0!kpe
		 * @param pos int[]
		 *		<EFBFBD><EFBFBD><EFBFBD>0MOnM<EFBFBD>R
		 * @param sigma int[]
		 *		<EFBFBD>0,<EFBFBD>1,<EFBFBD>2, ... <EFBFBD><jisu>
		 * @param omega int[]
		 *		<EFBFBD>0,<EFBFBD>1,<EFBFBD>2, ... <EFBFBD><jisu-1>
		 */
		private unsafe void doForney(byte[] data, int length, int jisu, int[] pos, int[] sigma, int[] omega)
		{
			fixed (int* s = sigma, o = omega)
				for (int i = 0; i < jisu; i++)
				{
					int ps = pos[i];
					data[galois.toPos(length, ps)] ^= (byte)doForney(jisu, ps, s, o);
				}
		}

		/**
		 * RS<EFBFBD>0<EFBFBD>0<EFBFBD>0n0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
		 *
		 * @param data int[]
		 *		eQ<EFBFBD>R<EFBFBD>0<EFBFBD>0<EFBFBD>0M<EFBFBD>R
		 * @param length int
		 * 		<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0+T<EFBFBD>0_0<EFBFBD>0<EFBFBD>0<EFBFBD>0w<EFBFBD>
		 * @param noCorrect boolean
		 * 		<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0n00g0<EFBFBD>cko0L<EFBFBD><EFBFBD>0j0D0
		 * @return bool
		 * 		0: <EFBFBD>0<EFBFBD>0<EFBFBD>0j0W0
		 * 		> 0: ;b<EFBFBD>0$PPn0<EFBFBD><EFBFBD><EFBFBD>0<EFBFBD>0<EFBFBD>ckW0_0
		 * 		< 0: <EFBFBD>ck
N<EFBFBD><EFBFBD>
		 */
		public bool decode(byte[] data, int length, bool noCorrect, out int errors)
		{
			if (length < npar || length > galois.Max)
				throw new Exception("RsDecode: wrong length");

			errors = 0;

			// <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD><EFBFBD>{
			int[] syn = new int[npar];
			if (galois.calcSyndrome(data, length, syn))
				return true; // <EFBFBD>0<EFBFBD>0<EFBFBD>0!qW0

			// <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>h0<EFBFBD><EFBFBD>0Bl<EFBFBD>0<EFBFBD>0
			int[] sigma = new int[npar / 2 + 2];
			int[] omega = new int[npar / 2 + 1];
			int jisu = calcSigmaMBM(sigma, omega, syn);
			if (jisu <= 0)
				return false;
			
			// <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>c"}k0<6B>0<EFBFBD>0<EFBFBD><30><EFBFBD>0MOn<6E>0Bl<42>0<EFBFBD>0
			int[] pos = new int[jisu];
			if (!chienSearch(pos, length, jisu, sigma))
				return false;
			if (!noCorrect) // <EFBFBD><EFBFBD><EFBFBD>0<EFBFBD>ck
				doForney(data, length, jisu, pos, sigma, omega);
			errors = jisu;
			return true;
		}
	}

	public class RsDecode16 : RsDecode
	{
		public RsDecode16(int npar, Galois galois)
			: base(npar, galois)
		{
		}

		public RsDecode16(int npar)
			: this(npar, Galois16.instance)
		{
		}

		/**
		 * Forney<EFBFBD>lg0<EFBFBD><EFBFBD><EFBFBD>0<EFBFBD>ck<EFBFBD>0L<EFBFBD>F0
		 *		<EFBFBD>(z) = (1-<EFBFBD>^i*z)(1-<EFBFBD>^j*z)(1-<EFBFBD>^k*z)
		 *		<EFBFBD>'(z) = <EFBFBD>^i * (1-<EFBFBD>^j*z)(1-<EFBFBD>^k*z)...
		 *			   + <EFBFBD>^j * (1-<EFBFBD>^i*z)(1-<EFBFBD>^k*z)...
		 *			   + <EFBFBD>^k * (1-<EFBFBD>^i*z)(1-<EFBFBD>^j*z)...
		 *		<EFBFBD>(z) = (E^i/(1-<EFBFBD>^i*z) + E^j/(1-<EFBFBD>^j*z) + ...) * <EFBFBD>(z)
		 *			  = E^i*(1-<EFBFBD>^j*z)(1-<EFBFBD>^k*z)...
		 *			  + E^j*(1-<EFBFBD>^i*z)(1-<EFBFBD>^k*z)...
		 *			  + E^k*(1-<EFBFBD>^i*z)(1-<EFBFBD>^j*z)...
		 *		4" E^i = <00>^i * <00>(z) / <00>'(z)
		 * @param data int[]
		 *		eQ<EFBFBD>R<EFBFBD>0<EFBFBD>0<EFBFBD>0M<EFBFBD>R
		 * @param length int
		 *		eQ<EFBFBD>R<EFBFBD>0<EFBFBD>0<EFBFBD>0w<EFBFBD>U0
		 * @param jisu int
		 *		<EFBFBD>n0!kpe
		 * @param pos int[]
		 *		<EFBFBD><EFBFBD><EFBFBD>0MOnM<EFBFBD>R
		 * @param sigma int[]
		 *		<EFBFBD>0,<EFBFBD>1,<EFBFBD>2, ... <EFBFBD><jisu>
		 * @param omega int[]
		 *		<EFBFBD>0,<EFBFBD>1,<EFBFBD>2, ... <EFBFBD><jisu-1>
		 */
		private unsafe void doForney(ushort* data, int length, int jisu, int[] pos, int[] sigma, int[] omega)
		{
			fixed (int* s = sigma, o = omega)
				for (int i = 0; i < jisu; i++)
				{
					int ps = pos[i];
					data[galois.toPos(length, ps)] ^= (ushort)doForney(jisu, ps, s, o);
				}
		}

		/**
		 * RS<EFBFBD>0<EFBFBD>0<EFBFBD>0n0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
		 *
		 * @param data int[]
		 *		eQ<EFBFBD>R<EFBFBD>0<EFBFBD>0<EFBFBD>0M<EFBFBD>R
		 * @param length int
		 * 		<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0+T<EFBFBD>0_0<EFBFBD>0<EFBFBD>0<EFBFBD>0w<EFBFBD>
		 * @param noCorrect boolean
		 * 		<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0n00g0<EFBFBD>cko0L<EFBFBD><EFBFBD>0j0D0
		 * @return bool
		 * 		0: <EFBFBD>0<EFBFBD>0<EFBFBD>0j0W0
		 * 		> 0: ;b<EFBFBD>0$PPn0<EFBFBD><EFBFBD><EFBFBD>0<EFBFBD>0<EFBFBD>ckW0_0
		 * 		< 0: <EFBFBD>ck
N<EFBFBD><EFBFBD>
		 */
		public unsafe bool decode(ushort* data, int length, bool noCorrect, out int errors)
		{
			if (length < npar || length > galois.Max)
				throw new Exception("RsDecode: wrong length");

			errors = 0;

			// <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD><EFBFBD>{
			int[] syn = new int[npar];
			if (galois.calcSyndrome(data, length, syn))
				return true; // <EFBFBD>0<EFBFBD>0<EFBFBD>0!qW0

			// <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>h0<EFBFBD><EFBFBD>0Bl<EFBFBD>0<EFBFBD>0
			int[] sigma = new int[npar / 2 + 2];
			int[] omega = new int[npar / 2 + 1];
			int jisu = calcSigmaMBM(sigma, omega, syn);
			if (jisu <= 0)
				return false;

			// <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>c"}k0<6B>0<EFBFBD>0<EFBFBD><30><EFBFBD>0MOn<6E>0Bl<42>0<EFBFBD>0
			int[] pos = new int[jisu];
			if (!chienSearch(pos, length, jisu, sigma))
				return false;
			if (!noCorrect) // <EFBFBD><EFBFBD><EFBFBD>0<EFBFBD>ck
				doForney(data, length, jisu, pos, sigma, omega);
			errors = jisu;
			return true;
		}

		public unsafe bool decode(byte[] data, int datapos, int length, bool noCorrect, out int errors)
		{
			if ((length & 1) != 0)
				throw new Exception("RsDecode: wrong length");
			fixed (byte* bytes = &data[datapos])
				return decode((ushort*)bytes, length >> 1, noCorrect, out errors);
		}
	}
}