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/*
* 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.
*
* $Id: docecc.c,v 1.5 2003/05/21 15:15:06 dwmw2 Exp $
*
* 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/miscdevice.h>
#include <linux/pci.h>
#include <linux/delay.h>
#include <linux/slab.h>
#include <linux/sched.h>
#include <linux/init.h>
#include <linux/types.h>
#include <linux/mtd/compatmac.h> /* for min() in older kernels */
#include <linux/mtd/mtd.h>
#include <linux/mtd/doc2000.h>
#define DEBUG 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 >= 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)) {
|