| /* |
| * 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> |
| |
| /* 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)) { |
| 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 >= 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 >= 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"); |