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wdenkaffae2b2002-08-17 09:36:01 +00001/*
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
27#include <config.h>
28#include <common.h>
29#include <malloc.h>
30
wdenkaffae2b2002-08-17 09:36:01 +000031#undef ECC_DEBUG
32#undef PSYCHO_DEBUG
33
Jon Loeligerb4539602007-06-11 19:02:05 -050034#if (CONFIG_COMMANDS & CFG_CMD_DOC) || defined(CONFIG_CMD_DOC)
wdenkaffae2b2002-08-17 09:36:01 +000035
wdenk81050922004-07-11 20:04:51 +000036#include <linux/mtd/doc2000.h>
37
wdenkaffae2b2002-08-17 09:36:01 +000038/* need to undef it (from asm/termbits.h) */
39#undef B0
40
41#define MM 10 /* Symbol size in bits */
42#define KK (1023-4) /* Number of data symbols per block */
43#define B0 510 /* First root of generator polynomial, alpha form */
44#define PRIM 1 /* power of alpha used to generate roots of generator poly */
45#define NN ((1 << MM) - 1)
46
47typedef unsigned short dtype;
48
49/* 1+x^3+x^10 */
50static const int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
51
52/* This defines the type used to store an element of the Galois Field
53 * used by the code. Make sure this is something larger than a char if
54 * if anything larger than GF(256) is used.
55 *
56 * Note: unsigned char will work up to GF(256) but int seems to run
57 * faster on the Pentium.
58 */
59typedef int gf;
60
61/* No legal value in index form represents zero, so
62 * we need a special value for this purpose
63 */
64#define A0 (NN)
65
66/* Compute x % NN, where NN is 2**MM - 1,
67 * without a slow divide
68 */
69static inline gf
70modnn(int x)
71{
72 while (x >= NN) {
73 x -= NN;
74 x = (x >> MM) + (x & NN);
75 }
76 return x;
77}
78
79#define CLEAR(a,n) {\
80int ci;\
81for(ci=(n)-1;ci >=0;ci--)\
82(a)[ci] = 0;\
83}
84
85#define COPY(a,b,n) {\
86int ci;\
87for(ci=(n)-1;ci >=0;ci--)\
88(a)[ci] = (b)[ci];\
89}
90
91#define COPYDOWN(a,b,n) {\
92int ci;\
93for(ci=(n)-1;ci >=0;ci--)\
94(a)[ci] = (b)[ci];\
95}
96
97#define Ldec 1
98
99/* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m]
100 lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
wdenk8bde7f72003-06-27 21:31:46 +0000101 polynomial form -> index form index_of[j=alpha**i] = i
wdenkaffae2b2002-08-17 09:36:01 +0000102 alpha=2 is the primitive element of GF(2**m)
103 HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
wdenk8bde7f72003-06-27 21:31:46 +0000104 Let @ represent the primitive element commonly called "alpha" that
wdenkaffae2b2002-08-17 09:36:01 +0000105 is the root of the primitive polynomial p(x). Then in GF(2^m), for any
106 0 <= i <= 2^m-2,
wdenk8bde7f72003-06-27 21:31:46 +0000107 @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
wdenkaffae2b2002-08-17 09:36:01 +0000108 where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
109 of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
110 example the polynomial representation of @^5 would be given by the binary
111 representation of the integer "alpha_to[5]".
wdenk8bde7f72003-06-27 21:31:46 +0000112 Similarily, index_of[] can be used as follows:
113 As above, let @ represent the primitive element of GF(2^m) that is
wdenkaffae2b2002-08-17 09:36:01 +0000114 the root of the primitive polynomial p(x). In order to find the power
115 of @ (alpha) that has the polynomial representation
wdenk8bde7f72003-06-27 21:31:46 +0000116 a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
wdenkaffae2b2002-08-17 09:36:01 +0000117 we consider the integer "i" whose binary representation with a(0) being LSB
118 and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
119 "index_of[i]". Now, @^index_of[i] is that element whose polynomial
120 representation is (a(0),a(1),a(2),...,a(m-1)).
121 NOTE:
wdenk8bde7f72003-06-27 21:31:46 +0000122 The element alpha_to[2^m-1] = 0 always signifying that the
wdenkaffae2b2002-08-17 09:36:01 +0000123 representation of "@^infinity" = 0 is (0,0,0,...,0).
wdenk8bde7f72003-06-27 21:31:46 +0000124 Similarily, the element index_of[0] = A0 always signifying
wdenkaffae2b2002-08-17 09:36:01 +0000125 that the power of alpha which has the polynomial representation
126 (0,0,...,0) is "infinity".
127
128*/
129
130static void
131generate_gf(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1])
132{
133 register int i, mask;
134
135 mask = 1;
136 Alpha_to[MM] = 0;
137 for (i = 0; i < MM; i++) {
138 Alpha_to[i] = mask;
139 Index_of[Alpha_to[i]] = i;
140 /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
141 if (Pp[i] != 0)
142 Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
143 mask <<= 1; /* single left-shift */
144 }
145 Index_of[Alpha_to[MM]] = MM;
146 /*
147 * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
148 * poly-repr of @^i shifted left one-bit and accounting for any @^MM
149 * term that may occur when poly-repr of @^i is shifted.
150 */
151 mask >>= 1;
152 for (i = MM + 1; i < NN; i++) {
153 if (Alpha_to[i - 1] >= mask)
154 Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
155 else
156 Alpha_to[i] = Alpha_to[i - 1] << 1;
157 Index_of[Alpha_to[i]] = i;
158 }
159 Index_of[0] = A0;
160 Alpha_to[NN] = 0;
161}
162
163/*
164 * Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content
165 * of the feedback shift register after having processed the data and
166 * the ECC.
167 *
168 * Return number of symbols corrected, or -1 if codeword is illegal
169 * or uncorrectable. If eras_pos is non-null, the detected error locations
170 * are written back. NOTE! This array must be at least NN-KK elements long.
171 * The corrected data are written in eras_val[]. They must be xor with the data
172 * to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] .
173 *
174 * First "no_eras" erasures are declared by the calling program. Then, the
175 * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
176 * If the number of channel errors is not greater than "t_after_eras" the
177 * transmitted codeword will be recovered. Details of algorithm can be found
178 * in R. Blahut's "Theory ... of Error-Correcting Codes".
179
180 * Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
181 * will result. The decoder *could* check for this condition, but it would involve
182 * extra time on every decoding operation.
183 * */
184static int
185eras_dec_rs(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1],
wdenk8bde7f72003-06-27 21:31:46 +0000186 gf bb[NN - KK + 1], gf eras_val[NN-KK], int eras_pos[NN-KK],
187 int no_eras)
wdenkaffae2b2002-08-17 09:36:01 +0000188{
189 int deg_lambda, el, deg_omega;
190 int i, j, r,k;
191 gf u,q,tmp,num1,num2,den,discr_r;
192 gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
193 * and syndrome poly */
194 gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
195 gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
196 int syn_error, count;
197
198 syn_error = 0;
199 for(i=0;i<NN-KK;i++)
200 syn_error |= bb[i];
201
202 if (!syn_error) {
203 /* if remainder is zero, data[] is a codeword and there are no
204 * errors to correct. So return data[] unmodified
205 */
206 count = 0;
207 goto finish;
208 }
209
210 for(i=1;i<=NN-KK;i++){
211 s[i] = bb[0];
212 }
213 for(j=1;j<NN-KK;j++){
214 if(bb[j] == 0)
215 continue;
216 tmp = Index_of[bb[j]];
217
218 for(i=1;i<=NN-KK;i++)
219 s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)];
220 }
221
222 /* undo the feedback register implicit multiplication and convert
223 syndromes to index form */
224
225 for(i=1;i<=NN-KK;i++) {
226 tmp = Index_of[s[i]];
227 if (tmp != A0)
wdenk8bde7f72003-06-27 21:31:46 +0000228 tmp = modnn(tmp + 2 * KK * (B0+i-1)*PRIM);
wdenkaffae2b2002-08-17 09:36:01 +0000229 s[i] = tmp;
230 }
231
232 CLEAR(&lambda[1],NN-KK);
233 lambda[0] = 1;
234
235 if (no_eras > 0) {
236 /* Init lambda to be the erasure locator polynomial */
237 lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])];
238 for (i = 1; i < no_eras; i++) {
239 u = modnn(PRIM*eras_pos[i]);
240 for (j = i+1; j > 0; j--) {
241 tmp = Index_of[lambda[j - 1]];
242 if(tmp != A0)
243 lambda[j] ^= Alpha_to[modnn(u + tmp)];
244 }
245 }
246#ifdef ECC_DEBUG
247 /* Test code that verifies the erasure locator polynomial just constructed
248 Needed only for decoder debugging. */
249
250 /* find roots of the erasure location polynomial */
251 for(i=1;i<=no_eras;i++)
252 reg[i] = Index_of[lambda[i]];
253 count = 0;
254 for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
255 q = 1;
256 for (j = 1; j <= no_eras; j++)
257 if (reg[j] != A0) {
258 reg[j] = modnn(reg[j] + j);
259 q ^= Alpha_to[reg[j]];
260 }
261 if (q != 0)
262 continue;
263 /* store root and error location number indices */
264 root[count] = i;
265 loc[count] = k;
266 count++;
267 }
268 if (count != no_eras) {
269 printf("\n lambda(x) is WRONG\n");
270 count = -1;
271 goto finish;
272 }
273#ifdef PSYCHO_DEBUG
274 printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
275 for (i = 0; i < count; i++)
276 printf("%d ", loc[i]);
277 printf("\n");
278#endif
279#endif
280 }
281 for(i=0;i<NN-KK+1;i++)
282 b[i] = Index_of[lambda[i]];
283
284 /*
285 * Begin Berlekamp-Massey algorithm to determine error+erasure
286 * locator polynomial
287 */
288 r = no_eras;
289 el = no_eras;
290 while (++r <= NN-KK) { /* r is the step number */
291 /* Compute discrepancy at the r-th step in poly-form */
292 discr_r = 0;
293 for (i = 0; i < r; i++){
294 if ((lambda[i] != 0) && (s[r - i] != A0)) {
295 discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
296 }
297 }
298 discr_r = Index_of[discr_r]; /* Index form */
299 if (discr_r == A0) {
300 /* 2 lines below: B(x) <-- x*B(x) */
301 COPYDOWN(&b[1],b,NN-KK);
302 b[0] = A0;
303 } else {
304 /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
305 t[0] = lambda[0];
306 for (i = 0 ; i < NN-KK; i++) {
307 if(b[i] != A0)
308 t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
309 else
310 t[i+1] = lambda[i+1];
311 }
312 if (2 * el <= r + no_eras - 1) {
313 el = r + no_eras - el;
314 /*
315 * 2 lines below: B(x) <-- inv(discr_r) *
316 * lambda(x)
317 */
318 for (i = 0; i <= NN-KK; i++)
319 b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
320 } else {
321 /* 2 lines below: B(x) <-- x*B(x) */
322 COPYDOWN(&b[1],b,NN-KK);
323 b[0] = A0;
324 }
325 COPY(lambda,t,NN-KK+1);
326 }
327 }
328
329 /* Convert lambda to index form and compute deg(lambda(x)) */
330 deg_lambda = 0;
331 for(i=0;i<NN-KK+1;i++){
332 lambda[i] = Index_of[lambda[i]];
333 if(lambda[i] != A0)
334 deg_lambda = i;
335 }
336 /*
337 * Find roots of the error+erasure locator polynomial by Chien
338 * Search
339 */
340 COPY(&reg[1],&lambda[1],NN-KK);
341 count = 0; /* Number of roots of lambda(x) */
342 for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
343 q = 1;
344 for (j = deg_lambda; j > 0; j--){
345 if (reg[j] != A0) {
346 reg[j] = modnn(reg[j] + j);
347 q ^= Alpha_to[reg[j]];
348 }
349 }
350 if (q != 0)
351 continue;
352 /* store root (index-form) and error location number */
353 root[count] = i;
354 loc[count] = k;
355 /* If we've already found max possible roots,
356 * abort the search to save time
357 */
358 if(++count == deg_lambda)
359 break;
360 }
361 if (deg_lambda != count) {
362 /*
363 * deg(lambda) unequal to number of roots => uncorrectable
364 * error detected
365 */
366 count = -1;
367 goto finish;
368 }
369 /*
370 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
371 * x**(NN-KK)). in index form. Also find deg(omega).
372 */
373 deg_omega = 0;
374 for (i = 0; i < NN-KK;i++){
375 tmp = 0;
376 j = (deg_lambda < i) ? deg_lambda : i;
377 for(;j >= 0; j--){
378 if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
379 tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
380 }
381 if(tmp != 0)
382 deg_omega = i;
383 omega[i] = Index_of[tmp];
384 }
385 omega[NN-KK] = A0;
386
387 /*
388 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
389 * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
390 */
391 for (j = count-1; j >=0; j--) {
392 num1 = 0;
393 for (i = deg_omega; i >= 0; i--) {
394 if (omega[i] != A0)
395 num1 ^= Alpha_to[modnn(omega[i] + i * root[j])];
396 }
397 num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
398 den = 0;
399
400 /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
401 for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
402 if(lambda[i+1] != A0)
403 den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
404 }
405 if (den == 0) {
406#ifdef ECC_DEBUG
407 printf("\n ERROR: denominator = 0\n");
408#endif
409 /* Convert to dual- basis */
410 count = -1;
411 goto finish;
412 }
413 /* Apply error to data */
414 if (num1 != 0) {
wdenk8bde7f72003-06-27 21:31:46 +0000415 eras_val[j] = Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
wdenkaffae2b2002-08-17 09:36:01 +0000416 } else {
wdenk8bde7f72003-06-27 21:31:46 +0000417 eras_val[j] = 0;
wdenkaffae2b2002-08-17 09:36:01 +0000418 }
419 }
420 finish:
421 for(i=0;i<count;i++)
422 eras_pos[i] = loc[i];
423 return count;
424}
425
426/***************************************************************************/
427/* The DOC specific code begins here */
428
429#define SECTOR_SIZE 512
430/* The sector bytes are packed into NB_DATA MM bits words */
431#define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM)
432
433/*
434 * Correct the errors in 'sector[]' by using 'ecc1[]' which is the
435 * content of the feedback shift register applyied to the sector and
436 * the ECC. Return the number of errors corrected (and correct them in
437 * sector), or -1 if error
438 */
439int doc_decode_ecc(unsigned char sector[SECTOR_SIZE], unsigned char ecc1[6])
440{
441 int parity, i, nb_errors;
442 gf bb[NN - KK + 1];
443 gf error_val[NN-KK];
444 int error_pos[NN-KK], pos, bitpos, index, val;
445 dtype *Alpha_to, *Index_of;
446
447 /* init log and exp tables here to save memory. However, it is slower */
448 Alpha_to = malloc((NN + 1) * sizeof(dtype));
449 if (!Alpha_to)
wdenk8bde7f72003-06-27 21:31:46 +0000450 return -1;
wdenkaffae2b2002-08-17 09:36:01 +0000451
452 Index_of = malloc((NN + 1) * sizeof(dtype));
453 if (!Index_of) {
wdenk8bde7f72003-06-27 21:31:46 +0000454 free(Alpha_to);
455 return -1;
wdenkaffae2b2002-08-17 09:36:01 +0000456 }
457
458 generate_gf(Alpha_to, Index_of);
459
460 parity = ecc1[1];
461
462 bb[0] = (ecc1[4] & 0xff) | ((ecc1[5] & 0x03) << 8);
463 bb[1] = ((ecc1[5] & 0xfc) >> 2) | ((ecc1[2] & 0x0f) << 6);
464 bb[2] = ((ecc1[2] & 0xf0) >> 4) | ((ecc1[3] & 0x3f) << 4);
465 bb[3] = ((ecc1[3] & 0xc0) >> 6) | ((ecc1[0] & 0xff) << 2);
466
467 nb_errors = eras_dec_rs(Alpha_to, Index_of, bb,
wdenk8bde7f72003-06-27 21:31:46 +0000468 error_val, error_pos, 0);
wdenkaffae2b2002-08-17 09:36:01 +0000469 if (nb_errors <= 0)
wdenk8bde7f72003-06-27 21:31:46 +0000470 goto the_end;
wdenkaffae2b2002-08-17 09:36:01 +0000471
472 /* correct the errors */
473 for(i=0;i<nb_errors;i++) {
wdenk8bde7f72003-06-27 21:31:46 +0000474 pos = error_pos[i];
475 if (pos >= NB_DATA && pos < KK) {
476 nb_errors = -1;
477 goto the_end;
478 }
479 if (pos < NB_DATA) {
480 /* extract bit position (MSB first) */
481 pos = 10 * (NB_DATA - 1 - pos) - 6;
482 /* now correct the following 10 bits. At most two bytes
483 can be modified since pos is even */
484 index = (pos >> 3) ^ 1;
485 bitpos = pos & 7;
486 if ((index >= 0 && index < SECTOR_SIZE) ||
487 index == (SECTOR_SIZE + 1)) {
488 val = error_val[i] >> (2 + bitpos);
489 parity ^= val;
490 if (index < SECTOR_SIZE)
491 sector[index] ^= val;
492 }
493 index = ((pos >> 3) + 1) ^ 1;
494 bitpos = (bitpos + 10) & 7;
495 if (bitpos == 0)
496 bitpos = 8;
497 if ((index >= 0 && index < SECTOR_SIZE) ||
498 index == (SECTOR_SIZE + 1)) {
499 val = error_val[i] << (8 - bitpos);
500 parity ^= val;
501 if (index < SECTOR_SIZE)
502 sector[index] ^= val;
503 }
504 }
wdenkaffae2b2002-08-17 09:36:01 +0000505 }
506
507 /* use parity to test extra errors */
508 if ((parity & 0xff) != 0)
wdenk8bde7f72003-06-27 21:31:46 +0000509 nb_errors = -1;
wdenkaffae2b2002-08-17 09:36:01 +0000510
511 the_end:
512 free(Alpha_to);
513 free(Index_of);
514 return nb_errors;
515}
516
517#endif /* (CONFIG_COMMANDS & CFG_CMD_DOC) */