aboutsummaryrefslogtreecommitdiffstats
path: root/drivers/mtd/devices/docecc.c
blob: 874e51b110a2d4cfbdadef073e146aab68040bdc (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
/*
 * 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.
 *
 * 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/delay.h>
#include <linux/slab.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>

#define DEBUG_ECC 0
/* 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_ECC >= 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_ECC >= 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(&reg[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_ECC >= 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");