linux-old/drivers/mtd/devices/docecc.c
<<
>>
Prefs
   1/*
   2 * ECC algorithm for M-systems disk on chip. We use the excellent Reed
   3 * Solmon code of Phil Karn (karn@ka9q.ampr.org) available under the
   4 * GNU GPL License. The rest is simply to convert the disk on chip
   5 * syndrom into a standard syndom.
   6 *
   7 * Author: Fabrice Bellard (fabrice.bellard@netgem.com) 
   8 * Copyright (C) 2000 Netgem S.A.
   9 *
  10 * $Id: docecc.c,v 1.4 2001/10/02 15:05:13 dwmw2 Exp $
  11 *
  12 * This program is free software; you can redistribute it and/or modify
  13 * it under the terms of the GNU General Public License as published by
  14 * the Free Software Foundation; either version 2 of the License, or
  15 * (at your option) any later version.
  16 *
  17 * This program is distributed in the hope that it will be useful,
  18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20 * GNU General Public License for more details.
  21 *
  22 * You should have received a copy of the GNU General Public License
  23 * along with this program; if not, write to the Free Software
  24 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  25 */
  26#include <linux/kernel.h>
  27#include <linux/module.h>
  28#include <asm/errno.h>
  29#include <asm/io.h>
  30#include <asm/uaccess.h>
  31#include <linux/miscdevice.h>
  32#include <linux/pci.h>
  33#include <linux/delay.h>
  34#include <linux/slab.h>
  35#include <linux/sched.h>
  36#include <linux/init.h>
  37#include <linux/types.h>
  38
  39#include <linux/mtd/compatmac.h> /* for min() in older kernels */
  40#include <linux/mtd/mtd.h>
  41#include <linux/mtd/doc2000.h>
  42
  43/* need to undef it (from asm/termbits.h) */
  44#undef B0
  45
  46#define MM 10 /* Symbol size in bits */
  47#define KK (1023-4) /* Number of data symbols per block */
  48#define B0 510 /* First root of generator polynomial, alpha form */
  49#define PRIM 1 /* power of alpha used to generate roots of generator poly */
  50#define NN ((1 << MM) - 1)
  51
  52typedef unsigned short dtype;
  53
  54/* 1+x^3+x^10 */
  55static const int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
  56
  57/* This defines the type used to store an element of the Galois Field
  58 * used by the code. Make sure this is something larger than a char if
  59 * if anything larger than GF(256) is used.
  60 *
  61 * Note: unsigned char will work up to GF(256) but int seems to run
  62 * faster on the Pentium.
  63 */
  64typedef int gf;
  65
  66/* No legal value in index form represents zero, so
  67 * we need a special value for this purpose
  68 */
  69#define A0      (NN)
  70
  71/* Compute x % NN, where NN is 2**MM - 1,
  72 * without a slow divide
  73 */
  74static inline gf
  75modnn(int x)
  76{
  77  while (x >= NN) {
  78    x -= NN;
  79    x = (x >> MM) + (x & NN);
  80  }
  81  return x;
  82}
  83
  84#define CLEAR(a,n) {\
  85int ci;\
  86for(ci=(n)-1;ci >=0;ci--)\
  87(a)[ci] = 0;\
  88}
  89
  90#define COPY(a,b,n) {\
  91int ci;\
  92for(ci=(n)-1;ci >=0;ci--)\
  93(a)[ci] = (b)[ci];\
  94}
  95
  96#define COPYDOWN(a,b,n) {\
  97int ci;\
  98for(ci=(n)-1;ci >=0;ci--)\
  99(a)[ci] = (b)[ci];\
 100}
 101
 102#define Ldec 1
 103
 104/* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m]
 105   lookup tables:  index->polynomial form   alpha_to[] contains j=alpha**i;
 106                   polynomial form -> index form  index_of[j=alpha**i] = i
 107   alpha=2 is the primitive element of GF(2**m)
 108   HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
 109        Let @ represent the primitive element commonly called "alpha" that
 110   is the root of the primitive polynomial p(x). Then in GF(2^m), for any
 111   0 <= i <= 2^m-2,
 112        @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
 113   where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
 114   of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
 115   example the polynomial representation of @^5 would be given by the binary
 116   representation of the integer "alpha_to[5]".
 117                   Similarily, index_of[] can be used as follows:
 118        As above, let @ represent the primitive element of GF(2^m) that is
 119   the root of the primitive polynomial p(x). In order to find the power
 120   of @ (alpha) that has the polynomial representation
 121        a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
 122   we consider the integer "i" whose binary representation with a(0) being LSB
 123   and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
 124   "index_of[i]". Now, @^index_of[i] is that element whose polynomial 
 125    representation is (a(0),a(1),a(2),...,a(m-1)).
 126   NOTE:
 127        The element alpha_to[2^m-1] = 0 always signifying that the
 128   representation of "@^infinity" = 0 is (0,0,0,...,0).
 129        Similarily, the element index_of[0] = A0 always signifying
 130   that the power of alpha which has the polynomial representation
 131   (0,0,...,0) is "infinity".
 132 
 133*/
 134
 135static void
 136generate_gf(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1])
 137{
 138  register int i, mask;
 139
 140  mask = 1;
 141  Alpha_to[MM] = 0;
 142  for (i = 0; i < MM; i++) {
 143    Alpha_to[i] = mask;
 144    Index_of[Alpha_to[i]] = i;
 145    /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
 146    if (Pp[i] != 0)
 147      Alpha_to[MM] ^= mask;     /* Bit-wise EXOR operation */
 148    mask <<= 1; /* single left-shift */
 149  }
 150  Index_of[Alpha_to[MM]] = MM;
 151  /*
 152   * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
 153   * poly-repr of @^i shifted left one-bit and accounting for any @^MM
 154   * term that may occur when poly-repr of @^i is shifted.
 155   */
 156  mask >>= 1;
 157  for (i = MM + 1; i < NN; i++) {
 158    if (Alpha_to[i - 1] >= mask)
 159      Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
 160    else
 161      Alpha_to[i] = Alpha_to[i - 1] << 1;
 162    Index_of[Alpha_to[i]] = i;
 163  }
 164  Index_of[0] = A0;
 165  Alpha_to[NN] = 0;
 166}
 167
 168/*
 169 * Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content
 170 * of the feedback shift register after having processed the data and
 171 * the ECC.
 172 *
 173 * Return number of symbols corrected, or -1 if codeword is illegal
 174 * or uncorrectable. If eras_pos is non-null, the detected error locations
 175 * are written back. NOTE! This array must be at least NN-KK elements long.
 176 * The corrected data are written in eras_val[]. They must be xor with the data
 177 * to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] .
 178 * 
 179 * First "no_eras" erasures are declared by the calling program. Then, the
 180 * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
 181 * If the number of channel errors is not greater than "t_after_eras" the
 182 * transmitted codeword will be recovered. Details of algorithm can be found
 183 * in R. Blahut's "Theory ... of Error-Correcting Codes".
 184
 185 * Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
 186 * will result. The decoder *could* check for this condition, but it would involve
 187 * extra time on every decoding operation.
 188 * */
 189static int
 190eras_dec_rs(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1],
 191            gf bb[NN - KK + 1], gf eras_val[NN-KK], int eras_pos[NN-KK], 
 192            int no_eras)
 193{
 194  int deg_lambda, el, deg_omega;
 195  int i, j, r,k;
 196  gf u,q,tmp,num1,num2,den,discr_r;
 197  gf lambda[NN-KK + 1], s[NN-KK + 1];   /* Err+Eras Locator poly
 198                                         * and syndrome poly */
 199  gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
 200  gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
 201  int syn_error, count;
 202
 203  syn_error = 0;
 204  for(i=0;i<NN-KK;i++)
 205      syn_error |= bb[i];
 206
 207  if (!syn_error) {
 208    /* if remainder is zero, data[] is a codeword and there are no
 209     * errors to correct. So return data[] unmodified
 210     */
 211    count = 0;
 212    goto finish;
 213  }
 214  
 215  for(i=1;i<=NN-KK;i++){
 216    s[i] = bb[0];
 217  }
 218  for(j=1;j<NN-KK;j++){
 219    if(bb[j] == 0)
 220      continue;
 221    tmp = Index_of[bb[j]];
 222    
 223    for(i=1;i<=NN-KK;i++)
 224      s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)];
 225  }
 226
 227  /* undo the feedback register implicit multiplication and convert
 228     syndromes to index form */
 229
 230  for(i=1;i<=NN-KK;i++) {
 231      tmp = Index_of[s[i]];
 232      if (tmp != A0)
 233          tmp = modnn(tmp + 2 * KK * (B0+i-1)*PRIM);
 234      s[i] = tmp;
 235  }
 236  
 237  CLEAR(&lambda[1],NN-KK);
 238  lambda[0] = 1;
 239
 240  if (no_eras > 0) {
 241    /* Init lambda to be the erasure locator polynomial */
 242    lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])];
 243    for (i = 1; i < no_eras; i++) {
 244      u = modnn(PRIM*eras_pos[i]);
 245      for (j = i+1; j > 0; j--) {
 246        tmp = Index_of[lambda[j - 1]];
 247        if(tmp != A0)
 248          lambda[j] ^= Alpha_to[modnn(u + tmp)];
 249      }
 250    }
 251#if DEBUG >= 1
 252    /* Test code that verifies the erasure locator polynomial just constructed
 253       Needed only for decoder debugging. */
 254    
 255    /* find roots of the erasure location polynomial */
 256    for(i=1;i<=no_eras;i++)
 257      reg[i] = Index_of[lambda[i]];
 258    count = 0;
 259    for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
 260      q = 1;
 261      for (j = 1; j <= no_eras; j++)
 262        if (reg[j] != A0) {
 263          reg[j] = modnn(reg[j] + j);
 264          q ^= Alpha_to[reg[j]];
 265        }
 266      if (q != 0)
 267        continue;
 268      /* store root and error location number indices */
 269      root[count] = i;
 270      loc[count] = k;
 271      count++;
 272    }
 273    if (count != no_eras) {
 274      printf("\n lambda(x) is WRONG\n");
 275      count = -1;
 276      goto finish;
 277    }
 278#if DEBUG >= 2
 279    printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
 280    for (i = 0; i < count; i++)
 281      printf("%d ", loc[i]);
 282    printf("\n");
 283#endif
 284#endif
 285  }
 286  for(i=0;i<NN-KK+1;i++)
 287    b[i] = Index_of[lambda[i]];
 288  
 289  /*
 290   * Begin Berlekamp-Massey algorithm to determine error+erasure
 291   * locator polynomial
 292   */
 293  r = no_eras;
 294  el = no_eras;
 295  while (++r <= NN-KK) {        /* r is the step number */
 296    /* Compute discrepancy at the r-th step in poly-form */
 297    discr_r = 0;
 298    for (i = 0; i < r; i++){
 299      if ((lambda[i] != 0) && (s[r - i] != A0)) {
 300        discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
 301      }
 302    }
 303    discr_r = Index_of[discr_r];        /* Index form */
 304    if (discr_r == A0) {
 305      /* 2 lines below: B(x) <-- x*B(x) */
 306      COPYDOWN(&b[1],b,NN-KK);
 307      b[0] = A0;
 308    } else {
 309      /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
 310      t[0] = lambda[0];
 311      for (i = 0 ; i < NN-KK; i++) {
 312        if(b[i] != A0)
 313          t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
 314        else
 315          t[i+1] = lambda[i+1];
 316      }
 317      if (2 * el <= r + no_eras - 1) {
 318        el = r + no_eras - el;
 319        /*
 320         * 2 lines below: B(x) <-- inv(discr_r) *
 321         * lambda(x)
 322         */
 323        for (i = 0; i <= NN-KK; i++)
 324          b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
 325      } else {
 326        /* 2 lines below: B(x) <-- x*B(x) */
 327        COPYDOWN(&b[1],b,NN-KK);
 328        b[0] = A0;
 329      }
 330      COPY(lambda,t,NN-KK+1);
 331    }
 332  }
 333
 334  /* Convert lambda to index form and compute deg(lambda(x)) */
 335  deg_lambda = 0;
 336  for(i=0;i<NN-KK+1;i++){
 337    lambda[i] = Index_of[lambda[i]];
 338    if(lambda[i] != A0)
 339      deg_lambda = i;
 340  }
 341  /*
 342   * Find roots of the error+erasure locator polynomial by Chien
 343   * Search
 344   */
 345  COPY(&reg[1],&lambda[1],NN-KK);
 346  count = 0;            /* Number of roots of lambda(x) */
 347  for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
 348    q = 1;
 349    for (j = deg_lambda; j > 0; j--){
 350      if (reg[j] != A0) {
 351        reg[j] = modnn(reg[j] + j);
 352        q ^= Alpha_to[reg[j]];
 353      }
 354    }
 355    if (q != 0)
 356      continue;
 357    /* store root (index-form) and error location number */
 358    root[count] = i;
 359    loc[count] = k;
 360    /* If we've already found max possible roots,
 361     * abort the search to save time
 362     */
 363    if(++count == deg_lambda)
 364      break;
 365  }
 366  if (deg_lambda != count) {
 367    /*
 368     * deg(lambda) unequal to number of roots => uncorrectable
 369     * error detected
 370     */
 371    count = -1;
 372    goto finish;
 373  }
 374  /*
 375   * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
 376   * x**(NN-KK)). in index form. Also find deg(omega).
 377   */
 378  deg_omega = 0;
 379  for (i = 0; i < NN-KK;i++){
 380    tmp = 0;
 381    j = (deg_lambda < i) ? deg_lambda : i;
 382    for(;j >= 0; j--){
 383      if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
 384        tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
 385    }
 386    if(tmp != 0)
 387      deg_omega = i;
 388    omega[i] = Index_of[tmp];
 389  }
 390  omega[NN-KK] = A0;
 391  
 392  /*
 393   * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
 394   * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
 395   */
 396  for (j = count-1; j >=0; j--) {
 397    num1 = 0;
 398    for (i = deg_omega; i >= 0; i--) {
 399      if (omega[i] != A0)
 400        num1  ^= Alpha_to[modnn(omega[i] + i * root[j])];
 401    }
 402    num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
 403    den = 0;
 404    
 405    /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
 406    for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
 407      if(lambda[i+1] != A0)
 408        den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
 409    }
 410    if (den == 0) {
 411#if DEBUG >= 1
 412      printf("\n ERROR: denominator = 0\n");
 413#endif
 414      /* Convert to dual- basis */
 415      count = -1;
 416      goto finish;
 417    }
 418    /* Apply error to data */
 419    if (num1 != 0) {
 420        eras_val[j] = Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
 421    } else {
 422        eras_val[j] = 0;
 423    }
 424  }
 425 finish:
 426  for(i=0;i<count;i++)
 427      eras_pos[i] = loc[i];
 428  return count;
 429}
 430
 431/***************************************************************************/
 432/* The DOC specific code begins here */
 433
 434#define SECTOR_SIZE 512
 435/* The sector bytes are packed into NB_DATA MM bits words */
 436#define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM)
 437
 438/* 
 439 * Correct the errors in 'sector[]' by using 'ecc1[]' which is the
 440 * content of the feedback shift register applyied to the sector and
 441 * the ECC. Return the number of errors corrected (and correct them in
 442 * sector), or -1 if error 
 443 */
 444int doc_decode_ecc(unsigned char sector[SECTOR_SIZE], unsigned char ecc1[6])
 445{
 446    int parity, i, nb_errors;
 447    gf bb[NN - KK + 1];
 448    gf error_val[NN-KK];
 449    int error_pos[NN-KK], pos, bitpos, index, val;
 450    dtype *Alpha_to, *Index_of;
 451
 452    /* init log and exp tables here to save memory. However, it is slower */
 453    Alpha_to = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
 454    if (!Alpha_to)
 455        return -1;
 456    
 457    Index_of = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
 458    if (!Index_of) {
 459        kfree(Alpha_to);
 460        return -1;
 461    }
 462
 463    generate_gf(Alpha_to, Index_of);
 464
 465    parity = ecc1[1];
 466
 467    bb[0] =  (ecc1[4] & 0xff) | ((ecc1[5] & 0x03) << 8);
 468    bb[1] = ((ecc1[5] & 0xfc) >> 2) | ((ecc1[2] & 0x0f) << 6);
 469    bb[2] = ((ecc1[2] & 0xf0) >> 4) | ((ecc1[3] & 0x3f) << 4);
 470    bb[3] = ((ecc1[3] & 0xc0) >> 6) | ((ecc1[0] & 0xff) << 2);
 471
 472    nb_errors = eras_dec_rs(Alpha_to, Index_of, bb, 
 473                            error_val, error_pos, 0);
 474    if (nb_errors <= 0)
 475        goto the_end;
 476
 477    /* correct the errors */
 478    for(i=0;i<nb_errors;i++) {
 479        pos = error_pos[i];
 480        if (pos >= NB_DATA && pos < KK) {
 481            nb_errors = -1;
 482            goto the_end;
 483        }
 484        if (pos < NB_DATA) {
 485            /* extract bit position (MSB first) */
 486            pos = 10 * (NB_DATA - 1 - pos) - 6;
 487            /* now correct the following 10 bits. At most two bytes
 488               can be modified since pos is even */
 489            index = (pos >> 3) ^ 1;
 490            bitpos = pos & 7;
 491            if ((index >= 0 && index < SECTOR_SIZE) || 
 492                index == (SECTOR_SIZE + 1)) {
 493                val = error_val[i] >> (2 + bitpos);
 494                parity ^= val;
 495                if (index < SECTOR_SIZE)
 496                    sector[index] ^= val;
 497            }
 498            index = ((pos >> 3) + 1) ^ 1;
 499            bitpos = (bitpos + 10) & 7;
 500            if (bitpos == 0)
 501                bitpos = 8;
 502            if ((index >= 0 && index < SECTOR_SIZE) || 
 503                index == (SECTOR_SIZE + 1)) {
 504                val = error_val[i] << (8 - bitpos);
 505                parity ^= val;
 506                if (index < SECTOR_SIZE)
 507                    sector[index] ^= val;
 508            }
 509        }
 510    }
 511    
 512    /* use parity to test extra errors */
 513    if ((parity & 0xff) != 0)
 514        nb_errors = -1;
 515
 516 the_end:
 517    kfree(Alpha_to);
 518    kfree(Index_of);
 519    return nb_errors;
 520}
 521
 522MODULE_LICENSE("GPL");
 523MODULE_AUTHOR("Fabrice Bellard <fabrice.bellard@netgem.com>");
 524MODULE_DESCRIPTION("ECC code for correcting errors detected by DiskOnChip 2000 and Millennium ECC hardware");
 525