diff options
Diffstat (limited to 'common/docecc.c')
| -rw-r--r-- | common/docecc.c | 513 |
1 files changed, 0 insertions, 513 deletions
diff --git a/common/docecc.c b/common/docecc.c deleted file mode 100644 index 3412aff..0000000 --- a/common/docecc.c +++ /dev/null @@ -1,513 +0,0 @@ -/* - * 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 1.4 2001/10/02 15:05:13 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 <config.h> -#include <common.h> -#include <malloc.h> - -#undef ECC_DEBUG -#undef PSYCHO_DEBUG - -#include <linux/mtd/doc2000.h> - -/* 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)]; - } - } -#ifdef ECC_DEBUG - /* 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; - } -#ifdef PSYCHO_DEBUG - 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) { -#ifdef ECC_DEBUG - 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 = malloc((NN + 1) * sizeof(dtype)); - if (!Alpha_to) - return -1; - - Index_of = malloc((NN + 1) * sizeof(dtype)); - if (!Index_of) { - free(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: - free(Alpha_to); - free(Index_of); - return nb_errors; -} |