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Diffstat (limited to 'common/docecc.c')
| -rw-r--r-- | common/docecc.c | 519 |
1 files changed, 519 insertions, 0 deletions
diff --git a/common/docecc.c b/common/docecc.c new file mode 100644 index 0000000..09e8233 --- /dev/null +++ b/common/docecc.c @@ -0,0 +1,519 @@ +/* + * 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> + +#include <linux/mtd/doc2000.h> + +#undef ECC_DEBUG +#undef PSYCHO_DEBUG + +#if (CONFIG_COMMANDS & CFG_CMD_DOC) + +#define min(x,y) ((x)<(y)?(x):(y)) + +/* 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; +} + +#endif /* (CONFIG_COMMANDS & CFG_CMD_DOC) */ |