/*
* ECC algorithm for M-systems disk on chip. We use the excellent Reed
* Solmon code of Phil Karn (karn@ka9q.ampr.org) available under the
* GNU GPL License. The rest is simply to convert the disk on chip
* syndrom into a standard syndom.
*
* Author: Fabrice Bellard (fabrice.bellard@netgem.com)
* Copyright (C) 2000 Netgem S.A.
*
* 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
*/
#include <linux/kernel.h>
#include <linux/module.h>
#include <asm/errno.h>
#include <asm/io.h>
#include <asm/uaccess.h>
#include <linux/delay.h>
#include <linux/slab.h>
#include <linux/init.h>
#include <linux/types.h>
#include <linux/mtd/mtd.h>
#include <linux/mtd/doc2000.h>
#define DEBUG_ECC 0
/* need to undef it (from asm/termbits.h) */
#undef B0
#define MM 10 /* Symbol size in bits */
#define KK (1023-4) /* Number of data symbols per block */
#define B0 510 /* First root of generator polynomial, alpha form */
#define PRIM 1 /* power of alpha used to generate roots of generator poly */
#define NN ((1 << MM) - 1)
typedef unsigned short dtype;
/* 1+x^3+x^10 */
static const int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
/* This defines the type used to store an element of the Galois Field
* used by the code. Make sure this is something larger than a char if
* if anything larger than GF(256) is used.
*
* Note: unsigned char will work up to GF(256) but int seems to run
* faster on the Pentium.
*/
typedef int gf;
/* No legal value in index form represents zero, so
* we need a special value for this purpose
*/
#define A0 (NN)
/* Compute x % NN, where NN is 2**MM - 1,
* without a slow divide
*/
static inline gf
modnn(int x)
{
while (x >= NN) {
x -= NN;
x = (x >> MM) + (x & NN);
}
return x;
}
#define CLEAR(a,n) {\
int ci;\
for(ci=(n)-1;ci >=0;ci--)\
(a)[ci] = 0;\
}
#define COPY(a,b,n) {\
int ci;\
for(ci=(n)-1;ci >=0;ci--)\
(a)[ci] = (b)[ci];\
}
#define COPYDOWN(a,b,n) {\
int ci;\
for(ci=(n)-1;ci >=0;ci--)\
(a)[ci] = (b)[ci];\
}
#define Ldec 1
/* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[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".
*/
static void
generate_gf(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1])
{
register 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;
}
/*
* Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content
* of the feedback shift register after having processed the data and
* the ECC.
*
* Return number of symbols corrected, or -1 if codeword is illegal
* or uncorrectable. If eras_pos is non-null, the detected error locations
* are written back. NOTE! This array must be at least NN-KK elements long.
* The corrected data are written in eras_val[]. They must be xor with the data
* to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] .
*
* 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".
* Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
* will result. The decoder *could* check for this condition, but it would involve
* extra time on every decoding operation.
* */
static int
eras_dec_rs(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1],
gf bb[NN - KK + 1], gf eras_val[NN-KK], int eras_pos[NN-KK],
int no_eras)
{
int deg_lambda, el, deg_omega;
int i, j, r,k;
gf u,q,tmp,num1,num2,den,discr_r;
gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
* and syndrome poly */
gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
int syn_error, count;
syn_error = 0;
for(i=0;i<NN-KK;i++)
syn_error |= bb[i];
if (!syn_error) {
/* if remainder is zero, data[] is a codeword and there are no
* errors to correct. So return data[] unmodified
*/
count = 0;
goto finish;
}
for(i=1;i<=NN-KK;i++){
s[i] = bb[0];
}
for(j=1;j<NN-KK;j++){
if(bb[j] == 0)
continue;
tmp = Index_of[bb[j]];
for(i=1;i<=NN-KK;i++)
s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)];
}
/* undo the feedback register implicit multiplication and convert
syndromes to index form */
for(i=1;i<=NN-KK;i++) {
tmp = Index_of[s[i]];
if (tmp != A0)
tmp = modnn(tmp + 2 * KK * (B0+i-1)*PRIM);
s[i] = tmp;
}
CLEAR(&lambda[1],NN-KK);
lambda[0] = 1;
if (no_eras > 0) {
/* Init lambda to be the erasure locator polynomial */
lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])];
for (i = 1; i < no_eras; i++) {
u = modnn(PRIM*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 DEBUG_ECC >= 1
/* Test code that verifies the erasure locator polynomial just constructed
Needed only for decoder debugging. */
/* 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,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
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)
continue;
/* store root and error location number indices */
root[count] = i;
loc[count] = k;
count++;
}
if (count != no_eras) {
printf("\n lambda(x) is WRONG\n");
count = -1;
goto finish;
}
#if DEBUG_ECC >= 2
printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
for (i = 0; i < count; i++)
printf("%d ", loc[i]);
printf("\n");
#endif
#endif
}
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(&b[1],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(&b[1],b,NN-KK);
b[0] = A0;
}
COPY(lambda,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
*/
COPY(®[1],&lambda[1],NN-KK);
count = 0; /* Number of roots of lambda(x) */
for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
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)
continue;
/* store root (index-form) and error location number */
root[count] = i;
loc[count] = k;
/* If we've already found max possible roots,
* abort the search to save time
*/
if(++count == deg_lambda)
break;
}
if (deg_lambda != count) {
/*
* deg(lambda) unequal to number of roots => uncorrectable
* error detected
*/
count = -1;
goto finish;
}
/*
* 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 DEBUG_ECC >= 1
printf("\n ERROR: denominator = 0\n");
#endif
/* Convert to dual- basis */
count = -1;
goto finish;
}
/* Apply error to data */
if (num1 != 0) {
eras_val[j] = Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
} else {
eras_val[j] = 0;
}
}
finish:
for(i=0;i<count;i++)
eras_pos[i] = loc[i];
return count;
}
/***************************************************************************/
/* The DOC specific code begins here */
#define SECTOR_SIZE 512
/* The sector bytes are packed into NB_DATA MM bits words */
#define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM)
/*
* Correct the errors in 'sector[]' by using 'ecc1[]' which is the
* content of the feedback shift register applyied to the sector and
* the ECC. Return the number of errors corrected (and correct them in
* sector), or -1 if error
*/
int doc_decode_ecc(unsigned char sector[SECTOR_SIZE], unsigned char ecc1[6])
{
int parity, i, nb_errors;
gf bb[NN - KK + 1];
gf error_val[NN-KK];
int error_pos[NN-KK], pos, bitpos, index, val;
dtype *Alpha_to, *Index_of;
/* init log and exp tables here to save memory. However, it is slower */
Alpha_to = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
if (!Alpha_to)
return -1;
Index_of = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
if (!Index_of) {
kfree(Alpha_to);
return -1;
}
generate_gf(Alpha_to, Index_of);
parity = ecc1[1];
bb[0] = (ecc1[4] & 0xff) | ((ecc1[5] & 0x03) << 8);
bb[1] = ((ecc1[5] & 0xfc) >> 2) | ((ecc1[2] & 0x0f) << 6);
bb[2] = ((ecc1[2] & 0xf0) >> 4) | ((ecc1[3] & 0x3f) << 4);
bb[3] = ((ecc1[3] & 0xc0) >> 6) | ((ecc1[0] & 0xff) << 2);
nb_errors = eras_dec_rs(Alpha_to, Index_of, bb,
error_val, error_pos, 0);
if (nb_errors <= 0)
goto the_end;
/* correct the errors */
for(i=0;i<nb_errors;i++) {
pos = error_pos[i];
if (pos >= NB_DATA && pos < KK) {
nb_errors = -1;
goto the_end;
}
if (pos < NB_DATA) {
/* extract bit position (MSB first) */
pos = 10 * (NB_DATA - 1 - pos) - 6;
/* now correct the following 10 bits. At most two bytes
can be modified since pos is even */
index = (pos >> 3) ^ 1;
bitpos = pos & 7;
if ((index >= 0 && index < SECTOR_SIZE) ||
index == (SECTOR_SIZE + 1)) {
val = error_val[i] >> (2 + bitpos);
parity ^= val;
if (index < SECTOR_SIZE)
sector[index] ^= val;
}
index = ((pos >> 3) + 1) ^ 1;
bitpos = (bitpos + 10) & 7;
if (bitpos == 0)
bitpos = 8;
if ((index >= 0 && index < SECTOR_SIZE) ||
index == (SECTOR_SIZE + 1)) {
val = error_val[i] << (8 - bitpos);
parity ^= val;
if (index < SECTOR_SIZE)
sector[index] ^= val;
}
}
}
/* use parity to test extra errors */
if ((parity & 0xff) != 0)
nb_errors = -1;
the_end:
kfree(Alpha_to);
kfree(Index_of);
return nb_errors;
}
EXPORT_SYMBOL_GPL(doc_decode_ecc);
MODULE_LICENSE("GPL");
MODULE_AUTHOR("Fabrice Bellard <fabrice.bellard@netgem.com>");
MODULE_DESCRIPTION("ECC code for correcting errors detected by DiskOnChip 2000 and Millennium ECC hardware");
