518 lines
15 KiB
C
518 lines
15 KiB
C
/*
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* ECC algorithm for M-systems disk on chip. We use the excellent Reed
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* Solmon code of Phil Karn (karn@ka9q.ampr.org) available under the
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* GNU GPL License. The rest is simply to convert the disk on chip
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* syndrom into a standard syndom.
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*
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* Author: Fabrice Bellard (fabrice.bellard@netgem.com)
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* Copyright (C) 2000 Netgem S.A.
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*
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* $Id: docecc.c,v 1.1.1.1 2008/12/15 11:39:21 wokes Exp $
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*/
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#include <config.h>
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#include <common.h>
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#include <malloc.h>
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#undef ECC_DEBUG
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#undef PSYCHO_DEBUG
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#if (CONFIG_COMMANDS & CFG_CMD_DOC)
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#include <linux/mtd/doc2000.h>
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/* need to undef it (from asm/termbits.h) */
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#undef B0
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#define MM 10 /* Symbol size in bits */
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#define KK (1023-4) /* Number of data symbols per block */
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#define B0 510 /* First root of generator polynomial, alpha form */
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#define PRIM 1 /* power of alpha used to generate roots of generator poly */
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#define NN ((1 << MM) - 1)
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typedef unsigned short dtype;
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/* 1+x^3+x^10 */
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static const int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
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/* This defines the type used to store an element of the Galois Field
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* used by the code. Make sure this is something larger than a char if
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* if anything larger than GF(256) is used.
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*
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* Note: unsigned char will work up to GF(256) but int seems to run
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* faster on the Pentium.
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*/
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typedef int gf;
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/* No legal value in index form represents zero, so
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* we need a special value for this purpose
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*/
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#define A0 (NN)
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/* Compute x % NN, where NN is 2**MM - 1,
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* without a slow divide
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*/
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static inline gf
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modnn(int x)
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{
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while (x >= NN) {
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x -= NN;
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x = (x >> MM) + (x & NN);
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}
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return x;
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}
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#define CLEAR(a,n) {\
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int ci;\
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for(ci=(n)-1;ci >=0;ci--)\
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(a)[ci] = 0;\
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}
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#define COPY(a,b,n) {\
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int ci;\
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for(ci=(n)-1;ci >=0;ci--)\
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(a)[ci] = (b)[ci];\
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}
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#define COPYDOWN(a,b,n) {\
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int ci;\
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for(ci=(n)-1;ci >=0;ci--)\
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(a)[ci] = (b)[ci];\
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}
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#define Ldec 1
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/* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m]
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lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
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polynomial form -> index form index_of[j=alpha**i] = i
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alpha=2 is the primitive element of GF(2**m)
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HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
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Let @ represent the primitive element commonly called "alpha" that
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is the root of the primitive polynomial p(x). Then in GF(2^m), for any
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0 <= i <= 2^m-2,
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@^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
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where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
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of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
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example the polynomial representation of @^5 would be given by the binary
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representation of the integer "alpha_to[5]".
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Similarily, index_of[] can be used as follows:
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As above, let @ represent the primitive element of GF(2^m) that is
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the root of the primitive polynomial p(x). In order to find the power
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of @ (alpha) that has the polynomial representation
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a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
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we consider the integer "i" whose binary representation with a(0) being LSB
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and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
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"index_of[i]". Now, @^index_of[i] is that element whose polynomial
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representation is (a(0),a(1),a(2),...,a(m-1)).
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NOTE:
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The element alpha_to[2^m-1] = 0 always signifying that the
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representation of "@^infinity" = 0 is (0,0,0,...,0).
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Similarily, the element index_of[0] = A0 always signifying
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that the power of alpha which has the polynomial representation
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(0,0,...,0) is "infinity".
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*/
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static void
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generate_gf(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1])
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{
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register int i, mask;
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mask = 1;
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Alpha_to[MM] = 0;
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for (i = 0; i < MM; i++) {
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Alpha_to[i] = mask;
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Index_of[Alpha_to[i]] = i;
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/* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
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if (Pp[i] != 0)
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Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
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mask <<= 1; /* single left-shift */
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}
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Index_of[Alpha_to[MM]] = MM;
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/*
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* Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
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* poly-repr of @^i shifted left one-bit and accounting for any @^MM
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* term that may occur when poly-repr of @^i is shifted.
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*/
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mask >>= 1;
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for (i = MM + 1; i < NN; i++) {
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if (Alpha_to[i - 1] >= mask)
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Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
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else
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Alpha_to[i] = Alpha_to[i - 1] << 1;
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Index_of[Alpha_to[i]] = i;
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}
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Index_of[0] = A0;
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Alpha_to[NN] = 0;
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}
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/*
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* Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content
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* of the feedback shift register after having processed the data and
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* the ECC.
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*
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* Return number of symbols corrected, or -1 if codeword is illegal
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* or uncorrectable. If eras_pos is non-null, the detected error locations
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* are written back. NOTE! This array must be at least NN-KK elements long.
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* The corrected data are written in eras_val[]. They must be xor with the data
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* to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] .
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*
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* First "no_eras" erasures are declared by the calling program. Then, the
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* maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
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* If the number of channel errors is not greater than "t_after_eras" the
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* transmitted codeword will be recovered. Details of algorithm can be found
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* in R. Blahut's "Theory ... of Error-Correcting Codes".
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* Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
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* will result. The decoder *could* check for this condition, but it would involve
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* extra time on every decoding operation.
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* */
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static int
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eras_dec_rs(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1],
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gf bb[NN - KK + 1], gf eras_val[NN-KK], int eras_pos[NN-KK],
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int no_eras)
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{
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int deg_lambda, el, deg_omega;
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int i, j, r,k;
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gf u,q,tmp,num1,num2,den,discr_r;
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gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
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* and syndrome poly */
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gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
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gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
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int syn_error, count;
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syn_error = 0;
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for(i=0;i<NN-KK;i++)
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syn_error |= bb[i];
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if (!syn_error) {
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/* if remainder is zero, data[] is a codeword and there are no
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* errors to correct. So return data[] unmodified
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*/
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count = 0;
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goto finish;
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}
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for(i=1;i<=NN-KK;i++){
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s[i] = bb[0];
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}
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for(j=1;j<NN-KK;j++){
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if(bb[j] == 0)
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continue;
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tmp = Index_of[bb[j]];
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for(i=1;i<=NN-KK;i++)
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s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)];
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}
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/* undo the feedback register implicit multiplication and convert
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syndromes to index form */
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for(i=1;i<=NN-KK;i++) {
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tmp = Index_of[s[i]];
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if (tmp != A0)
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tmp = modnn(tmp + 2 * KK * (B0+i-1)*PRIM);
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s[i] = tmp;
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}
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CLEAR(&lambda[1],NN-KK);
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lambda[0] = 1;
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if (no_eras > 0) {
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/* Init lambda to be the erasure locator polynomial */
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lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])];
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for (i = 1; i < no_eras; i++) {
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u = modnn(PRIM*eras_pos[i]);
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for (j = i+1; j > 0; j--) {
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tmp = Index_of[lambda[j - 1]];
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if(tmp != A0)
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lambda[j] ^= Alpha_to[modnn(u + tmp)];
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}
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}
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#ifdef ECC_DEBUG
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/* Test code that verifies the erasure locator polynomial just constructed
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Needed only for decoder debugging. */
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/* find roots of the erasure location polynomial */
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for(i=1;i<=no_eras;i++)
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reg[i] = Index_of[lambda[i]];
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count = 0;
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for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
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q = 1;
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for (j = 1; j <= no_eras; j++)
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if (reg[j] != A0) {
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reg[j] = modnn(reg[j] + j);
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q ^= Alpha_to[reg[j]];
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}
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if (q != 0)
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continue;
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/* store root and error location number indices */
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root[count] = i;
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loc[count] = k;
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count++;
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}
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if (count != no_eras) {
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printf("\n lambda(x) is WRONG\n");
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count = -1;
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goto finish;
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}
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#ifdef PSYCHO_DEBUG
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printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
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for (i = 0; i < count; i++)
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printf("%d ", loc[i]);
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printf("\n");
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#endif
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#endif
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}
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for(i=0;i<NN-KK+1;i++)
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b[i] = Index_of[lambda[i]];
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/*
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* Begin Berlekamp-Massey algorithm to determine error+erasure
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* locator polynomial
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*/
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r = no_eras;
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el = no_eras;
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while (++r <= NN-KK) { /* r is the step number */
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/* Compute discrepancy at the r-th step in poly-form */
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discr_r = 0;
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for (i = 0; i < r; i++){
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if ((lambda[i] != 0) && (s[r - i] != A0)) {
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discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
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}
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}
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discr_r = Index_of[discr_r]; /* Index form */
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if (discr_r == A0) {
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/* 2 lines below: B(x) <-- x*B(x) */
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COPYDOWN(&b[1],b,NN-KK);
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b[0] = A0;
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} else {
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/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
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t[0] = lambda[0];
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for (i = 0 ; i < NN-KK; i++) {
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if(b[i] != A0)
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t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
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else
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t[i+1] = lambda[i+1];
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}
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if (2 * el <= r + no_eras - 1) {
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el = r + no_eras - el;
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/*
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* 2 lines below: B(x) <-- inv(discr_r) *
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* lambda(x)
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*/
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for (i = 0; i <= NN-KK; i++)
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b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
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} else {
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/* 2 lines below: B(x) <-- x*B(x) */
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COPYDOWN(&b[1],b,NN-KK);
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b[0] = A0;
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}
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COPY(lambda,t,NN-KK+1);
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}
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}
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/* Convert lambda to index form and compute deg(lambda(x)) */
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deg_lambda = 0;
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for(i=0;i<NN-KK+1;i++){
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lambda[i] = Index_of[lambda[i]];
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if(lambda[i] != A0)
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deg_lambda = i;
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}
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/*
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* Find roots of the error+erasure locator polynomial by Chien
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* Search
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*/
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COPY(®[1],&lambda[1],NN-KK);
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count = 0; /* Number of roots of lambda(x) */
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for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
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q = 1;
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for (j = deg_lambda; j > 0; j--){
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if (reg[j] != A0) {
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reg[j] = modnn(reg[j] + j);
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q ^= Alpha_to[reg[j]];
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}
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}
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if (q != 0)
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continue;
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/* store root (index-form) and error location number */
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root[count] = i;
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loc[count] = k;
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/* If we've already found max possible roots,
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* abort the search to save time
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*/
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if(++count == deg_lambda)
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break;
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}
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if (deg_lambda != count) {
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/*
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* deg(lambda) unequal to number of roots => uncorrectable
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* error detected
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*/
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count = -1;
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goto finish;
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}
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/*
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* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
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* x**(NN-KK)). in index form. Also find deg(omega).
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*/
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deg_omega = 0;
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for (i = 0; i < NN-KK;i++){
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tmp = 0;
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j = (deg_lambda < i) ? deg_lambda : i;
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for(;j >= 0; j--){
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if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
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tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
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}
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if(tmp != 0)
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deg_omega = i;
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omega[i] = Index_of[tmp];
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}
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omega[NN-KK] = A0;
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/*
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* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
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* inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
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*/
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for (j = count-1; j >=0; j--) {
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num1 = 0;
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for (i = deg_omega; i >= 0; i--) {
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if (omega[i] != A0)
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num1 ^= Alpha_to[modnn(omega[i] + i * root[j])];
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}
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num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
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den = 0;
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/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
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for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
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if(lambda[i+1] != A0)
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den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
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}
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if (den == 0) {
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#ifdef ECC_DEBUG
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printf("\n ERROR: denominator = 0\n");
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#endif
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/* Convert to dual- basis */
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count = -1;
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goto finish;
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}
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/* Apply error to data */
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if (num1 != 0) {
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eras_val[j] = Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
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} else {
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eras_val[j] = 0;
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}
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}
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finish:
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for(i=0;i<count;i++)
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eras_pos[i] = loc[i];
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return count;
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}
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/***************************************************************************/
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/* The DOC specific code begins here */
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#define SECTOR_SIZE 512
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/* The sector bytes are packed into NB_DATA MM bits words */
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#define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM)
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/*
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* Correct the errors in 'sector[]' by using 'ecc1[]' which is the
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* content of the feedback shift register applyied to the sector and
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* the ECC. Return the number of errors corrected (and correct them in
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* sector), or -1 if error
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*/
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int doc_decode_ecc(unsigned char sector[SECTOR_SIZE], unsigned char ecc1[6])
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{
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int parity, i, nb_errors;
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gf bb[NN - KK + 1];
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gf error_val[NN-KK];
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int error_pos[NN-KK], pos, bitpos, index, val;
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dtype *Alpha_to, *Index_of;
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/* init log and exp tables here to save memory. However, it is slower */
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Alpha_to = malloc((NN + 1) * sizeof(dtype));
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if (!Alpha_to)
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return -1;
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Index_of = malloc((NN + 1) * sizeof(dtype));
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if (!Index_of) {
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free(Alpha_to);
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return -1;
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}
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generate_gf(Alpha_to, Index_of);
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parity = ecc1[1];
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bb[0] = (ecc1[4] & 0xff) | ((ecc1[5] & 0x03) << 8);
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bb[1] = ((ecc1[5] & 0xfc) >> 2) | ((ecc1[2] & 0x0f) << 6);
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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:
|
|
free(Alpha_to);
|
|
free(Index_of);
|
|
return nb_errors;
|
|
}
|
|
|
|
#endif /* (CONFIG_COMMANDS & CFG_CMD_DOC) */
|