diff --git a/DiscImageChef/Checksums/CDChecksums.cs b/DiscImageChef/Checksums/CDChecksums.cs index 44980736..26ad7b08 100644 --- a/DiscImageChef/Checksums/CDChecksums.cs +++ b/DiscImageChef/Checksums/CDChecksums.cs @@ -455,6 +455,37 @@ namespace DiscImageChef.Checksums CDSubRWPack4[j] = (byte)(subchannel[i++] & 0x3F); } + if(MainClass.isDebug) + { + switch(CDSubRWPack1[0]) + { + case 0x00: + Console.WriteLine("Detected Zero Pack in subchannel"); + break; + case 0x08: + Console.WriteLine("Detected Line Graphics Pack in subchannel"); + break; + case 0x09: + Console.WriteLine("Detected CD+G Pack in subchannel"); + break; + case 0x0A: + Console.WriteLine("Detected CD+EG Pack in subchannel"); + break; + case 0x14: + Console.WriteLine("Detected CD-TEXT Pack in subchannel"); + break; + case 0x18: + Console.WriteLine("Detected CD+MIDI Pack in subchannel"); + break; + case 0x38: + Console.WriteLine("Detected User Pack in subchannel"); + break; + default: + Console.WriteLine("Detected unknown Pack type in subchannel: mode {0}, item {1}", Convert.ToString(CDSubRWPack1[0] & 0x38, 2), Convert.ToString(CDSubRWPack1[0] & 0x07, 2)); + break; + } + } + BigEndianBitConverter.IsLittleEndian = true; UInt16 QSubChannelCRC = BigEndianBitConverter.ToUInt16(QSubChannel, 10); diff --git a/DiscImageChef/Checksums/ReedSolomon.cs b/DiscImageChef/Checksums/ReedSolomon.cs new file mode 100644 index 00000000..0f9166b6 --- /dev/null +++ b/DiscImageChef/Checksums/ReedSolomon.cs @@ -0,0 +1,650 @@ +/*************************************************************************** +The Disc Image Chef +---------------------------------------------------------------------------- + +Filename : ReedSolomon.cs +Version : 1.0 +Author(s) : Natalia Portillo + +Component : Checksums. + +Revision : $Revision$ +Last change by : $Author$ +Date : $Date$ + +--[ Description ] ---------------------------------------------------------- + +Calculates a Reed-Solomon + +--[ License ] -------------------------------------------------------------- + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as + published by the Free Software Foundation, either version 3 of the + License, or (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . + +---------------------------------------------------------------------------- +Copyright (C) 2011-2014 Claunia.com +Copyright (C) 1996 Phil Karn +Copyright (C) 1995 Robert Morelos-Zaragoza +Copyright (C) 1995 Hari Thirumoorthy +****************************************************************************/ +//$Id$ + +/* + * Reed-Solomon coding and decoding + * Phil Karn (karn at ka9q.ampr.org) September 1996 + * + * This file is derived from the program "new_rs_erasures.c" by Robert + * Morelos-Zaragoza (robert at spectra.eng.hawaii.edu) and Hari Thirumoorthy + * (harit at spectra.eng.hawaii.edu), Aug 1995 + * + * I've made changes to improve performance, clean up the code and make it + * easier to follow. Data is now passed to the encoding and decoding functions + * through arguments rather than in global arrays. The decode function returns + * the number of corrected symbols, or -1 if the word is uncorrectable. + * + * This code supports a symbol size from 2 bits up to 16 bits, + * implying a block size of 3 2-bit symbols (6 bits) up to 65535 + * 16-bit symbols (1,048,560 bits). The code parameters are set in rs.h. + * + * Note that if symbols larger than 8 bits are used, the type of each + * data array element switches from unsigned char to unsigned int. The + * caller must ensure that elements larger than the symbol range are + * not passed to the encoder or decoder. + * + */ + +using System; + +namespace DiscImageChef.Checksums +{ + public class ReedSolomon + { + /* Primitive polynomials - see Lin & Costello, Error Control Coding Appendix A, + * and Lee & Messerschmitt, Digital Communication p. 453. + */ + int[] Pp; + /* index->polynomial form conversion table */ + int[] Alpha_to; + /* Polynomial->index form conversion table */ + int[] Index_of; + /* Generator polynomial g(x) + * Degree of g(x) = 2*TT + * has roots @**B0, @**(B0+1), ... ,@^(B0+2*TT-1) + */ + int[] Gg; + int MM, KK, NN; + /* No legal value in index form represents zero, so + * we need a special value for this purpose + */ + int A0; + bool initialized; + /* Alpha exponent for the first root of the generator polynomial */ + const int B0 = 1; + + /// + /// Initializes the Reed-Solomon with RS(n,k) with GF(2^m) + /// + public void InitRS(int n, int k, int m) + { + switch (m) + { + case 2: + Pp = new []{ 1, 1, 1 }; + break; + case 3: + Pp = new []{ 1, 1, 0, 1 }; + break; + case 4: + Pp = new []{ 1, 1, 0, 0, 1 }; + break; + case 5: + Pp = new []{ 1, 0, 1, 0, 0, 1 }; + break; + case 6: + Pp = new []{ 1, 1, 0, 0, 0, 0, 1 }; + break; + case 7: + Pp = new []{ 1, 0, 0, 1, 0, 0, 0, 1 }; + break; + case 8: + Pp = new []{ 1, 0, 1, 1, 1, 0, 0, 0, 1 }; + break; + case 9: + Pp = new []{ 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 }; + break; + case 10: + Pp = new []{ 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 }; + break; + case 11: + Pp = new []{ 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 }; + break; + case 12: + Pp = new []{ 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1 }; + break; + case 13: + Pp = new []{ 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 }; + break; + case 14: + Pp = new []{ 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 }; + break; + case 15: + Pp = new []{ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 }; + break; + case 16: + Pp = new []{ 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 }; + break; + default: + throw new ArgumentOutOfRangeException("m", "m must be between 2 and 16 inclusive"); + } + + MM = m; + KK = k; + NN = n; + A0 = n; + Alpha_to = new int[n + 1]; + Index_of = new int[n + 1]; + + + Gg = new int[NN - KK + 1]; + + generate_gf(); + gen_poly(); + + initialized = true; + } + + int modnn(int x) + { + while (x >= NN) + { + x -= NN; + x = (x >> MM) + (x & NN); + } + return x; + } + + static int min(int a, int b) + { + return ((a) < (b) ? (a) : (b)); + } + + static void CLEAR(ref int[] a, int n) + { + int ci; + for (ci = (n) - 1; ci >= 0; ci--) + (a)[ci] = 0; + } + + static void COPY(ref int[] a, ref int[] b, int n) + { + int ci; + for (ci = (n) - 1; ci >= 0; ci--) + (a)[ci] = (b)[ci]; + } + + static void COPYDOWN(ref int[] a, ref int[] b, int n) + { + int ci; + for (ci = (n) - 1; ci >= 0; ci--) + (a)[ci] = (b)[ci]; + } + + /* generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m] + lookup tables: index->polynomial form alpha_to[] contains j=alpha**i; + polynomial form -> index form index_of[j=alpha**i] = i + alpha=2 is the primitive element of GF(2**m) + HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows: + Let @ represent the primitive element commonly called "alpha" that + is the root of the primitive polynomial p(x). Then in GF(2^m), for any + 0 <= i <= 2^m-2, + @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1) + where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation + of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for + example the polynomial representation of @^5 would be given by the binary + representation of the integer "alpha_to[5]". + Similarily, index_of[] can be used as follows: + As above, let @ represent the primitive element of GF(2^m) that is + the root of the primitive polynomial p(x). In order to find the power + of @ (alpha) that has the polynomial representation + a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1) + we consider the integer "i" whose binary representation with a(0) being LSB + and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry + "index_of[i]". Now, @^index_of[i] is that element whose polynomial + representation is (a(0),a(1),a(2),...,a(m-1)). + NOTE: + The element alpha_to[2^m-1] = 0 always signifying that the + representation of "@^infinity" = 0 is (0,0,0,...,0). + Similarily, the element index_of[0] = A0 always signifying + that the power of alpha which has the polynomial representation + (0,0,...,0) is "infinity". + + */ + void generate_gf() + { + int i, mask; + + mask = 1; + Alpha_to[MM] = 0; + for (i = 0; i < MM; i++) + { + Alpha_to[i] = mask; + Index_of[Alpha_to[i]] = i; + /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */ + if (Pp[i] != 0) + Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */ + mask <<= 1; /* single left-shift */ + } + Index_of[Alpha_to[MM]] = MM; + /* + * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by + * poly-repr of @^i shifted left one-bit and accounting for any @^MM + * term that may occur when poly-repr of @^i is shifted. + */ + mask >>= 1; + for (i = MM + 1; i < NN; i++) + { + if (Alpha_to[i - 1] >= mask) + Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1); + else + Alpha_to[i] = Alpha_to[i - 1] << 1; + Index_of[Alpha_to[i]] = i; + } + Index_of[0] = A0; + Alpha_to[NN] = 0; + } + + /* + * Obtain the generator polynomial of the TT-error correcting, length + * NN=(2**MM -1) Reed Solomon code from the product of (X+@**(B0+i)), i = 0, + * ... ,(2*TT-1) + * + * Examples: + * + * If B0 = 1, TT = 1. deg(g(x)) = 2*TT = 2. + * g(x) = (x+@) (x+@**2) + * + * If B0 = 0, TT = 2. deg(g(x)) = 2*TT = 4. + * g(x) = (x+1) (x+@) (x+@**2) (x+@**3) + */ + void gen_poly() + { + int i, j; + + Gg[0] = Alpha_to[B0]; + Gg[1] = 1; /* g(x) = (X+@**B0) initially */ + for (i = 2; i <= NN - KK; i++) + { + Gg[i] = 1; + /* + * Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by + * (@**(B0+i-1) + x) + */ + for (j = i - 1; j > 0; j--) + if (Gg[j] != 0) + Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + B0 + i - 1)]; + else + Gg[j] = Gg[j - 1]; + /* Gg[0] can never be zero */ + Gg[0] = Alpha_to[modnn((Index_of[Gg[0]]) + B0 + i - 1)]; + } + /* convert Gg[] to index form for quicker encoding */ + for (i = 0; i <= NN - KK; i++) + Gg[i] = Index_of[Gg[i]]; + } + + /* + * take the string of symbols in data[i], i=0..(k-1) and encode + * systematically to produce NN-KK parity symbols in bb[0]..bb[NN-KK-1] data[] + * is input and bb[] is output in polynomial form. Encoding is done by using + * a feedback shift register with appropriate connections specified by the + * elements of Gg[], which was generated above. Codeword is c(X) = + * data(X)*X**(NN-KK)+ b(X) + */ + /// + /// Takes the symbols in data to output parity in bb. + /// + /// Returns -1 if an illegal symbol is found. + /// Data symbols. + /// Outs parity symbols. + public int encode_rs(int[] data, out int[] bb) + { + if (initialized) + { + int i, j; + int feedback; + bb = new int[NN - KK]; + + CLEAR(ref bb, NN - KK); + for (i = KK - 1; i >= 0; i--) + { + if (MM != 8) + { + if (data[i] > NN) + return -1; /* Illegal symbol */ + } + feedback = Index_of[data[i] ^ bb[NN - KK - 1]]; + if (feedback != A0) + { /* feedback term is non-zero */ + for (j = NN - KK - 1; j > 0; j--) + if (Gg[j] != A0) + bb[j] = bb[j - 1] ^ Alpha_to[modnn(Gg[j] + feedback)]; + else + bb[j] = bb[j - 1]; + bb[0] = Alpha_to[modnn(Gg[0] + feedback)]; + } + else + { /* feedback term is zero. encoder becomes a + * single-byte shifter */ + for (j = NN - KK - 1; j > 0; j--) + bb[j] = bb[j - 1]; + bb[0] = 0; + } + } + return 0; + } + throw new UnauthorizedAccessException("Trying to calculate RS without initializing!"); + } + + /* + * Performs ERRORS+ERASURES decoding of RS codes. If decoding is successful, + * writes the codeword into data[] itself. Otherwise data[] is unaltered. + * + * Return number of symbols corrected, or -1 if codeword is illegal + * or uncorrectable. + * + * First "no_eras" erasures are declared by the calling program. Then, the + * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2). + * If the number of channel errors is not greater than "t_after_eras" the + * transmitted codeword will be recovered. Details of algorithm can be found + * in R. Blahut's "Theory ... of Error-Correcting Codes". + */ + /// + /// Decodes the RS. If decoding is successful outputs corrected data symbols. + /// + /// Returns corrected symbols, -1 if illegal or uncorrectable + /// Data symbols. + /// Position of erasures. + /// Number of erasures. + public int eras_dec_rs(ref int[] data, out int[] eras_pos, int no_eras) + { + if (initialized) + { + eras_pos = new int[NN - KK]; + int deg_lambda, el, deg_omega; + int i, j, r; + int u, q, tmp, num1, num2, den, discr_r; + int[] recd = new int[NN]; + int[] lambda = new int[NN - KK + 1]; /* Err+Eras Locator poly */ + int[] s = new int[NN - KK + 1]; /* syndrome poly */ + int[] b = new int[NN - KK + 1]; + int[] t = new int[NN - KK + 1]; + int[] omega = new int[NN - KK + 1]; + int[] root = new int[NN - KK]; + int[] reg = new int[NN - KK + 1]; + int[] loc = new int[NN - KK]; + int syn_error, count; + + /* data[] is in polynomial form, copy and convert to index form */ + for (i = NN - 1; i >= 0; i--) + { + if (MM != 8) + { + if (data[i] > NN) + return -1; /* Illegal symbol */ + } + recd[i] = Index_of[data[i]]; + } + /* first form the syndromes; i.e., evaluate recd(x) at roots of g(x) + * namely @**(B0+i), i = 0, ... ,(NN-KK-1) + */ + syn_error = 0; + for (i = 1; i <= NN - KK; i++) + { + tmp = 0; + for (j = 0; j < NN; j++) + if (recd[j] != A0) /* recd[j] in index form */ + tmp ^= Alpha_to[modnn(recd[j] + (B0 + i - 1) * j)]; + syn_error |= tmp; /* set flag if non-zero syndrome => + * error */ + /* store syndrome in index form */ + s[i] = Index_of[tmp]; + } + if (syn_error == 0) + { + /* + * if syndrome is zero, data[] is a codeword and there are no + * errors to correct. So return data[] unmodified + */ + return 0; + } + CLEAR(ref lambda, NN - KK); + lambda[0] = 1; + if (no_eras > 0) + { + /* Init lambda to be the erasure locator polynomial */ + lambda[1] = Alpha_to[eras_pos[0]]; + for (i = 1; i < no_eras; i++) + { + u = eras_pos[i]; + for (j = i + 1; j > 0; j--) + { + tmp = Index_of[lambda[j - 1]]; + if (tmp != A0) + lambda[j] ^= Alpha_to[modnn(u + tmp)]; + } + } + if (MainClass.isDebug) + { + /* find roots of the erasure location polynomial */ + for (i = 1; i <= no_eras; i++) + reg[i] = Index_of[lambda[i]]; + count = 0; + for (i = 1; i <= NN; i++) + { + q = 1; + for (j = 1; j <= no_eras; j++) + if (reg[j] != A0) + { + reg[j] = modnn(reg[j] + j); + q ^= Alpha_to[reg[j]]; + } + if (q == 0) + { + /* store root and error location + * number indices + */ + root[count] = i; + loc[count] = NN - i; + count++; + } + } + if (count != no_eras) + { + Console.WriteLine("\n lambda(x) is WRONG\n"); + return -1; + } + + Console.WriteLine("\n Erasure positions as determined by roots of Eras Loc Poly:\n"); + for (i = 0; i < count; i++) + Console.WriteLine("{0} ", loc[i]); + Console.WriteLine("\n"); + } + } + for (i = 0; i < NN - KK + 1; i++) + b[i] = Index_of[lambda[i]]; + + /* + * Begin Berlekamp-Massey algorithm to determine error+erasure + * locator polynomial + */ + r = no_eras; + el = no_eras; + while (++r <= NN - KK) + { /* r is the step number */ + /* Compute discrepancy at the r-th step in poly-form */ + discr_r = 0; + for (i = 0; i < r; i++) + { + if ((lambda[i] != 0) && (s[r - i] != A0)) + { + discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])]; + } + } + discr_r = Index_of[discr_r]; /* Index form */ + if (discr_r == A0) + { + /* 2 lines below: B(x) <-- x*B(x) */ + COPYDOWN(ref b, ref b, NN - KK); + b[0] = A0; + } + else + { + /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */ + t[0] = lambda[0]; + for (i = 0; i < NN - KK; i++) + { + if (b[i] != A0) + t[i + 1] = lambda[i + 1] ^ Alpha_to[modnn(discr_r + b[i])]; + else + t[i + 1] = lambda[i + 1]; + } + if (2 * el <= r + no_eras - 1) + { + el = r + no_eras - el; + /* + * 2 lines below: B(x) <-- inv(discr_r) * + * lambda(x) + */ + for (i = 0; i <= NN - KK; i++) + b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN); + } + else + { + /* 2 lines below: B(x) <-- x*B(x) */ + COPYDOWN(ref b, ref b, NN - KK); + b[0] = A0; + } + COPY(ref lambda, ref t, NN - KK + 1); + } + } + + /* Convert lambda to index form and compute deg(lambda(x)) */ + deg_lambda = 0; + for (i = 0; i < NN - KK + 1; i++) + { + lambda[i] = Index_of[lambda[i]]; + if (lambda[i] != A0) + deg_lambda = i; + } + /* + * Find roots of the error+erasure locator polynomial. By Chien + * Search + */ + int temp = reg[0]; + COPY(ref reg, ref lambda, NN - KK); + reg[0] = temp; + count = 0; /* Number of roots of lambda(x) */ + for (i = 1; i <= NN; i++) + { + q = 1; + for (j = deg_lambda; j > 0; j--) + if (reg[j] != A0) + { + reg[j] = modnn(reg[j] + j); + q ^= Alpha_to[reg[j]]; + } + if (q == 0) + { + /* store root (index-form) and error location number */ + root[count] = i; + loc[count] = NN - i; + count++; + } + } + + if (MainClass.isDebug) + { + Console.WriteLine("\n Final error positions:\t"); + for (i = 0; i < count; i++) + Console.WriteLine("{0} ", loc[i]); + Console.WriteLine("\n"); + } + if (deg_lambda != count) + { + /* + * deg(lambda) unequal to number of roots => uncorrectable + * error detected + */ + return -1; + } + /* + * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo + * x**(NN-KK)). in index form. Also find deg(omega). + */ + deg_omega = 0; + for (i = 0; i < NN - KK; i++) + { + tmp = 0; + j = (deg_lambda < i) ? deg_lambda : i; + for (; j >= 0; j--) + { + if ((s[i + 1 - j] != A0) && (lambda[j] != A0)) + tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])]; + } + if (tmp != 0) + deg_omega = i; + omega[i] = Index_of[tmp]; + } + omega[NN - KK] = A0; + + /* + * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 = + * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form + */ + for (j = count - 1; j >= 0; j--) + { + num1 = 0; + for (i = deg_omega; i >= 0; i--) + { + if (omega[i] != A0) + num1 ^= Alpha_to[modnn(omega[i] + i * root[j])]; + } + num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)]; + den = 0; + + /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */ + for (i = min(deg_lambda, NN - KK - 1) & ~1; i >= 0; i -= 2) + { + if (lambda[i + 1] != A0) + den ^= Alpha_to[modnn(lambda[i + 1] + i * root[j])]; + } + if (den == 0) + { + if (MainClass.isDebug) + { + Console.WriteLine("\n ERROR: denominator = 0\n"); + } + return -1; + } + /* Apply error to data */ + if (num1 != 0) + { + data[loc[j]] ^= Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])]; + } + } + return count; + } + throw new UnauthorizedAccessException("Trying to calculate RS without initializing!"); + } + } +} diff --git a/DiscImageChef/DiscImageChef.csproj b/DiscImageChef/DiscImageChef.csproj index 1851282c..58148609 100644 --- a/DiscImageChef/DiscImageChef.csproj +++ b/DiscImageChef/DiscImageChef.csproj @@ -97,6 +97,7 @@ +