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beetle-pce-fast-libretro/mednafen/cdrom/l-ec.cpp
Themaister e942ae84aa Initial commit.
2012-06-03 17:48:14 +02:00

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/* dvdisaster: Additional error correction for optical media.
* Copyright (C) 2004-2007 Carsten Gnoerlich.
* Project home page: http://www.dvdisaster.com
* Email: carsten@dvdisaster.com -or- cgnoerlich@fsfe.org
*
* The Reed-Solomon error correction draws a lot of inspiration - and even code -
* from Phil Karn's excellent Reed-Solomon library: http://www.ka9q.net/code/fec/
*
* 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 2 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, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA,
* or direct your browser at http://www.gnu.org.
*/
#include "dvdisaster.h"
#include "galois-inlines.h"
#define MIN(a, b) (((a) < (b)) ? (a) : (b))
/***
*** Mapping between cd frame and parity vectors
***/
/*
* Mapping of frame bytes to P/Q Vectors
*/
int PToByteIndex(int p, int i)
{ return 12 + p + i*86;
}
void ByteIndexToP(int b, int *p, int *i)
{ *p = (b-12)%86;
*i = (b-12)/86;
}
int QToByteIndex(int q, int i)
{ int offset = 12 + (q & 1);
if(i == 43) return 2248+q;
if(i == 44) return 2300+q;
q&=~1;
return offset + (q*43 + i*88) % 2236;
}
void ByteIndexToQ(int b, int *q, int *i)
{ int x,y,offset;
if(b >= 2300)
{ *i = 44;
*q = (b-2300);
return;
}
if(b >= 2248)
{ *i = 43;
*q = (b-2248);
return;
}
offset = b&1;
b = (b-12)/2;
x = b/43;
y = (b-(x*43))%26;
*i = b-(x*43);
*q = 2*((x+26-y)%26)+offset;
}
/*
* There are 86 vectors of P-parity, yielding a RS(26,24) code.
*/
void GetPVector(unsigned char *frame, unsigned char *data, int n)
{ int i;
int w_idx = n+12;
for(i=0; i<26; i++, w_idx+=86)
data[i] = frame[w_idx];
}
void SetPVector(unsigned char *frame, unsigned char *data, int n)
{ int i;
int w_idx = n+12;
for(i=0; i<26; i++, w_idx+=86)
frame[w_idx] = data[i];
}
void FillPVector(unsigned char *frame, unsigned char data, int n)
{ int i;
int w_idx = n+12;
for(i=0; i<26; i++, w_idx+=86)
frame[w_idx] = data;
}
void OrPVector(unsigned char *frame, unsigned char value, int n)
{ int i;
int w_idx = n+12;
for(i=0; i<26; i++, w_idx+=86)
frame[w_idx] |= value;
}
void AndPVector(unsigned char *frame, unsigned char value, int n)
{ int i;
int w_idx = n+12;
for(i=0; i<26; i++, w_idx+=86)
frame[w_idx] &= value;
}
/*
* There are 52 vectors of Q-parity, yielding a RS(45,43) code.
*/
void GetQVector(unsigned char *frame, unsigned char *data, int n)
{ int offset = 12 + (n & 1);
int w_idx = (n&~1) * 43;
int i;
for(i=0; i<43; i++, w_idx+=88)
data[i] = frame[(w_idx % 2236) + offset];
data[43] = frame[2248 + n];
data[44] = frame[2300 + n];
}
void SetQVector(unsigned char *frame, unsigned char *data, int n)
{ int offset = 12 + (n & 1);
int w_idx = (n&~1) * 43;
int i;
for(i=0; i<43; i++, w_idx+=88)
frame[(w_idx % 2236) + offset] = data[i];
frame[2248 + n] = data[43];
frame[2300 + n] = data[44];
}
void FillQVector(unsigned char *frame, unsigned char data, int n)
{ int offset = 12 + (n & 1);
int w_idx = (n&~1) * 43;
int i;
for(i=0; i<43; i++, w_idx+=88)
frame[(w_idx % 2236) + offset] = data;
frame[2248 + n] = data;
frame[2300 + n] = data;
}
void OrQVector(unsigned char *frame, unsigned char data, int n)
{ int offset = 12 + (n & 1);
int w_idx = (n&~1) * 43;
int i;
for(i=0; i<43; i++, w_idx+=88)
frame[(w_idx % 2236) + offset] |= data;
frame[2248 + n] |= data;
frame[2300 + n] |= data;
}
void AndQVector(unsigned char *frame, unsigned char data, int n)
{ int offset = 12 + (n & 1);
int w_idx = (n&~1) * 43;
int i;
for(i=0; i<43; i++, w_idx+=88)
frame[(w_idx % 2236) + offset] &= data;
frame[2248 + n] &= data;
frame[2300 + n] &= data;
}
/***
*** C2 error counting
***/
int CountC2Errors(unsigned char *frame)
{ int i,count = 0;
frame += 2352;
for(i=0; i<294; i++, frame++)
{ if(*frame & 0x01) count++;
if(*frame & 0x02) count++;
if(*frame & 0x04) count++;
if(*frame & 0x08) count++;
if(*frame & 0x10) count++;
if(*frame & 0x20) count++;
if(*frame & 0x40) count++;
if(*frame & 0x80) count++;
}
return count;
}
/***
*** L-EC error correction for CD raw data sectors
***/
/*
* These could be used from ReedSolomonTables,
* but hardcoding them is faster.
*/
#define NROOTS 2
#define LEC_FIRST_ROOT 0 //GF_ALPHA0
#define LEC_PRIM_ELEM 1
#define LEC_PRIMTH_ROOT 1
/*
* Calculate the error syndrome
*/
int DecodePQ(ReedSolomonTables *rt, unsigned char *data, int padding,
int *erasure_list, int erasure_count)
{ GaloisTables *gt = rt->gfTables;
int syndrome[NROOTS];
int lambda[NROOTS+1];
int omega[NROOTS+1];
int b[NROOTS+1];
int reg[NROOTS+1];
int root[NROOTS];
int loc[NROOTS];
int syn_error;
int deg_lambda,lambda_roots;
int deg_omega;
int shortened_size = GF_FIELDMAX - padding;
int corrected = 0;
int i,j,k;
int r,el;
/*** Form the syndromes: Evaluate data(x) at roots of g(x) */
for(i=0; i<NROOTS; i++)
syndrome[i] = data[0];
for(j=1; j<shortened_size; j++)
for(i=0; i<NROOTS; i++)
if(syndrome[i] == 0)
syndrome[i] = data[j];
else syndrome[i] = data[j] ^ gt->alphaTo[mod_fieldmax(gt->indexOf[syndrome[i]]
+ (LEC_FIRST_ROOT+i)*LEC_PRIM_ELEM)];
/*** Convert syndrome to index form, check for nonzero condition. */
syn_error = 0;
for(i=0; i<NROOTS; i++)
{ syn_error |= syndrome[i];
syndrome[i] = gt->indexOf[syndrome[i]];
}
/*** If the syndrome is zero, everything is fine. */
if(!syn_error)
return 0;
/*** Initialize lambda to be the erasure locator polynomial */
lambda[0] = 1;
lambda[1] = lambda[2] = 0;
erasure_list[0] += padding;
erasure_list[1] += padding;
if(erasure_count > 2) /* sanity check */
erasure_count = 0;
if(erasure_count > 0)
{ lambda[1] = gt->alphaTo[mod_fieldmax(LEC_PRIM_ELEM*(GF_FIELDMAX-1-erasure_list[0]))];
for(i=1; i<erasure_count; i++)
{ int u = mod_fieldmax(LEC_PRIM_ELEM*(GF_FIELDMAX-1-erasure_list[i]));
for(j=i+1; j>0; j--)
{ int tmp = gt->indexOf[lambda[j-1]];
if(tmp != GF_ALPHA0)
lambda[j] ^= gt->alphaTo[mod_fieldmax(u + tmp)];
}
}
}
for(i=0; i<NROOTS+1; i++)
b[i] = gt->indexOf[lambda[i]];
/*** Berlekamp-Massey algorithm to determine error+erasure locator polynomial */
r = erasure_count; /* r is the step number */
el = erasure_count;
/* Compute discrepancy at the r-th step in poly-form */
while(++r <= NROOTS)
{ int discr_r = 0;
for(i=0; i<r; i++)
if((lambda[i] != 0) && (syndrome[r-i-1] != GF_ALPHA0))
discr_r ^= gt->alphaTo[mod_fieldmax(gt->indexOf[lambda[i]] + syndrome[r-i-1])];
discr_r = gt->indexOf[discr_r];
if(discr_r == GF_ALPHA0)
{ /* B(x) = x*B(x) */
memmove(b+1, b, NROOTS*sizeof(b[0]));
b[0] = GF_ALPHA0;
}
else
{ int t[NROOTS+1];
/* T(x) = lambda(x) - discr_r*x*b(x) */
t[0] = lambda[0];
for(i=0; i<NROOTS; i++)
{ if(b[i] != GF_ALPHA0)
t[i+1] = lambda[i+1] ^ gt->alphaTo[mod_fieldmax(discr_r + b[i])];
else t[i+1] = lambda[i+1];
}
if(2*el <= r+erasure_count-1)
{ el = r + erasure_count - el;
/* B(x) <-- inv(discr_r) * lambda(x) */
for(i=0; i<=NROOTS; i++)
b[i] = (lambda[i] == 0) ? GF_ALPHA0
: mod_fieldmax(gt->indexOf[lambda[i]] - discr_r + GF_FIELDMAX);
}
else
{ /* 2 lines below: B(x) <-- x*B(x) */
memmove(b+1, b, NROOTS*sizeof(b[0]));
b[0] = GF_ALPHA0;
}
memcpy(lambda, t, (NROOTS+1)*sizeof(t[0]));
}
}
/*** Convert lambda to index form and compute deg(lambda(x)) */
deg_lambda = 0;
for(i=0; i<NROOTS+1; i++)
{ lambda[i] = gt->indexOf[lambda[i]];
if(lambda[i] != GF_ALPHA0)
deg_lambda = i;
}
/*** Find roots of the error+erasure locator polynomial by Chien search */
memcpy(reg+1, lambda+1, NROOTS*sizeof(reg[0]));
lambda_roots = 0; /* Number of roots of lambda(x) */
for(i=1, k=LEC_PRIMTH_ROOT-1; i<=GF_FIELDMAX; i++, k=mod_fieldmax(k+LEC_PRIMTH_ROOT))
{ int q=1; /* lambda[0] is always 0 */
for(j=deg_lambda; j>0; j--)
{ if(reg[j] != GF_ALPHA0)
{ reg[j] = mod_fieldmax(reg[j] + j);
q ^= gt->alphaTo[reg[j]];
}
}
if(q != 0) continue; /* Not a root */
/* store root in index-form and the error location number */
root[lambda_roots] = i;
loc[lambda_roots] = k;
/* If we've already found max possible roots, abort the search to save time */
if(++lambda_roots == deg_lambda) break;
}
/* deg(lambda) unequal to number of roots => uncorrectable error detected
This is not reliable for very small numbers of roots, e.g. nroots = 2 */
if(deg_lambda != lambda_roots)
{ return -1;
}
/* Compute err+eras evaluator poly omega(x) = syn(x)*lambda(x)
(modulo x**nroots). in index form. Also find deg(omega). */
deg_omega = deg_lambda-1;
for(i=0; i<=deg_omega; i++)
{ int tmp = 0;
for(j=i; j>=0; j--)
{ if((syndrome[i - j] != GF_ALPHA0) && (lambda[j] != GF_ALPHA0))
tmp ^= gt->alphaTo[mod_fieldmax(syndrome[i - j] + lambda[j])];
}
omega[i] = gt->indexOf[tmp];
}
/* Compute error values in poly-form.
num1 = omega(inv(X(l))),
num2 = inv(X(l))**(FIRST_ROOT-1) and
den = lambda_pr(inv(X(l))) all in poly-form. */
for(j=lambda_roots-1; j>=0; j--)
{ int num1 = 0;
int num2;
int den;
int location = loc[j];
for(i=deg_omega; i>=0; i--)
{ if(omega[i] != GF_ALPHA0)
num1 ^= gt->alphaTo[mod_fieldmax(omega[i] + i * root[j])];
}
num2 = gt->alphaTo[mod_fieldmax(root[j] * (LEC_FIRST_ROOT - 1) + GF_FIELDMAX)];
den = 0;
/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
for(i=MIN(deg_lambda, NROOTS-1) & ~1; i>=0; i-=2)
{ if(lambda[i+1] != GF_ALPHA0)
den ^= gt->alphaTo[mod_fieldmax(lambda[i+1] + i * root[j])];
}
/* Apply error to data */
if(num1 != 0 && location >= padding)
{
corrected++;
data[location-padding] ^= gt->alphaTo[mod_fieldmax(gt->indexOf[num1] + gt->indexOf[num2]
+ GF_FIELDMAX - gt->indexOf[den])];
/* If no erasures were given, at most one error was corrected.
Return its position in erasure_list[0]. */
if(!erasure_count)
erasure_list[0] = location-padding;
}
#if 1
else return -3;
#endif
}
/*** Form the syndromes: Evaluate data(x) at roots of g(x) */
for(i=0; i<NROOTS; i++)
syndrome[i] = data[0];
for(j=1; j<shortened_size; j++)
for(i=0; i<NROOTS; i++)
{ if(syndrome[i] == 0)
syndrome[i] = data[j];
else syndrome[i] = data[j] ^ gt->alphaTo[mod_fieldmax(gt->indexOf[syndrome[i]]
+ (LEC_FIRST_ROOT+i)*LEC_PRIM_ELEM)];
}
/*** Convert syndrome to index form, check for nonzero condition. */
#if 1
for(i=0; i<NROOTS; i++)
if(syndrome[i])
return -2;
#endif
return corrected;
}
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