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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
wdenk81050922004-07-11 20:04:51 +000034#include <linux/mtd/doc2000.h>
35
wdenkaffae2b2002-08-17 09:36:01 +000036/* need to undef it (from asm/termbits.h) */
37#undef B0
38
39#define MM 10 /* Symbol size in bits */
40#define KK (1023-4) /* Number of data symbols per block */
41#define B0 510 /* First root of generator polynomial, alpha form */
42#define PRIM 1 /* power of alpha used to generate roots of generator poly */
43#define NN ((1 << MM) - 1)
44
45typedef unsigned short dtype;
46
47/* 1+x^3+x^10 */
48static const int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
49
50/* This defines the type used to store an element of the Galois Field
51 * used by the code. Make sure this is something larger than a char if
52 * if anything larger than GF(256) is used.
53 *
54 * Note: unsigned char will work up to GF(256) but int seems to run
55 * faster on the Pentium.
56 */
57typedef int gf;
58
59/* No legal value in index form represents zero, so
60 * we need a special value for this purpose
61 */
62#define A0 (NN)
63
64/* Compute x % NN, where NN is 2**MM - 1,
65 * without a slow divide
66 */
67static inline gf
68modnn(int x)
69{
70 while (x >= NN) {
71 x -= NN;
72 x = (x >> MM) + (x & NN);
73 }
74 return x;
75}
76
77#define CLEAR(a,n) {\
78int ci;\
79for(ci=(n)-1;ci >=0;ci--)\
80(a)[ci] = 0;\
81}
82
83#define COPY(a,b,n) {\
84int ci;\
85for(ci=(n)-1;ci >=0;ci--)\
86(a)[ci] = (b)[ci];\
87}
88
89#define COPYDOWN(a,b,n) {\
90int ci;\
91for(ci=(n)-1;ci >=0;ci--)\
92(a)[ci] = (b)[ci];\
93}
94
95#define Ldec 1
96
97/* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m]
98 lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
wdenk8bde7f72003-06-27 21:31:46 +000099 polynomial form -> index form index_of[j=alpha**i] = i
wdenkaffae2b2002-08-17 09:36:01 +0000100 alpha=2 is the primitive element of GF(2**m)
101 HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
wdenk8bde7f72003-06-27 21:31:46 +0000102 Let @ represent the primitive element commonly called "alpha" that
wdenkaffae2b2002-08-17 09:36:01 +0000103 is the root of the primitive polynomial p(x). Then in GF(2^m), for any
104 0 <= i <= 2^m-2,
wdenk8bde7f72003-06-27 21:31:46 +0000105 @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
wdenkaffae2b2002-08-17 09:36:01 +0000106 where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
107 of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
108 example the polynomial representation of @^5 would be given by the binary
109 representation of the integer "alpha_to[5]".
wdenk8bde7f72003-06-27 21:31:46 +0000110 Similarily, index_of[] can be used as follows:
111 As above, let @ represent the primitive element of GF(2^m) that is
wdenkaffae2b2002-08-17 09:36:01 +0000112 the root of the primitive polynomial p(x). In order to find the power
113 of @ (alpha) that has the polynomial representation
wdenk8bde7f72003-06-27 21:31:46 +0000114 a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
wdenkaffae2b2002-08-17 09:36:01 +0000115 we consider the integer "i" whose binary representation with a(0) being LSB
116 and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
117 "index_of[i]". Now, @^index_of[i] is that element whose polynomial
118 representation is (a(0),a(1),a(2),...,a(m-1)).
119 NOTE:
wdenk8bde7f72003-06-27 21:31:46 +0000120 The element alpha_to[2^m-1] = 0 always signifying that the
wdenkaffae2b2002-08-17 09:36:01 +0000121 representation of "@^infinity" = 0 is (0,0,0,...,0).
wdenk8bde7f72003-06-27 21:31:46 +0000122 Similarily, the element index_of[0] = A0 always signifying
wdenkaffae2b2002-08-17 09:36:01 +0000123 that the power of alpha which has the polynomial representation
124 (0,0,...,0) is "infinity".
125
126*/
127
128static void
129generate_gf(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1])
130{
131 register int i, mask;
132
133 mask = 1;
134 Alpha_to[MM] = 0;
135 for (i = 0; i < MM; i++) {
136 Alpha_to[i] = mask;
137 Index_of[Alpha_to[i]] = i;
138 /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
139 if (Pp[i] != 0)
140 Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
141 mask <<= 1; /* single left-shift */
142 }
143 Index_of[Alpha_to[MM]] = MM;
144 /*
145 * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
146 * poly-repr of @^i shifted left one-bit and accounting for any @^MM
147 * term that may occur when poly-repr of @^i is shifted.
148 */
149 mask >>= 1;
150 for (i = MM + 1; i < NN; i++) {
151 if (Alpha_to[i - 1] >= mask)
152 Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
153 else
154 Alpha_to[i] = Alpha_to[i - 1] << 1;
155 Index_of[Alpha_to[i]] = i;
156 }
157 Index_of[0] = A0;
158 Alpha_to[NN] = 0;
159}
160
161/*
162 * Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content
163 * of the feedback shift register after having processed the data and
164 * the ECC.
165 *
166 * Return number of symbols corrected, or -1 if codeword is illegal
167 * or uncorrectable. If eras_pos is non-null, the detected error locations
168 * are written back. NOTE! This array must be at least NN-KK elements long.
169 * The corrected data are written in eras_val[]. They must be xor with the data
170 * to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] .
171 *
172 * First "no_eras" erasures are declared by the calling program. Then, the
173 * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
174 * If the number of channel errors is not greater than "t_after_eras" the
175 * transmitted codeword will be recovered. Details of algorithm can be found
176 * in R. Blahut's "Theory ... of Error-Correcting Codes".
177
178 * Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
179 * will result. The decoder *could* check for this condition, but it would involve
180 * extra time on every decoding operation.
181 * */
182static int
183eras_dec_rs(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1],
wdenk8bde7f72003-06-27 21:31:46 +0000184 gf bb[NN - KK + 1], gf eras_val[NN-KK], int eras_pos[NN-KK],
185 int no_eras)
wdenkaffae2b2002-08-17 09:36:01 +0000186{
187 int deg_lambda, el, deg_omega;
188 int i, j, r,k;
189 gf u,q,tmp,num1,num2,den,discr_r;
190 gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
191 * and syndrome poly */
192 gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
193 gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
194 int syn_error, count;
195
196 syn_error = 0;
197 for(i=0;i<NN-KK;i++)
198 syn_error |= bb[i];
199
200 if (!syn_error) {
201 /* if remainder is zero, data[] is a codeword and there are no
202 * errors to correct. So return data[] unmodified
203 */
204 count = 0;
205 goto finish;
206 }
207
208 for(i=1;i<=NN-KK;i++){
209 s[i] = bb[0];
210 }
211 for(j=1;j<NN-KK;j++){
212 if(bb[j] == 0)
213 continue;
214 tmp = Index_of[bb[j]];
215
216 for(i=1;i<=NN-KK;i++)
217 s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)];
218 }
219
220 /* undo the feedback register implicit multiplication and convert
221 syndromes to index form */
222
223 for(i=1;i<=NN-KK;i++) {
224 tmp = Index_of[s[i]];
225 if (tmp != A0)
wdenk8bde7f72003-06-27 21:31:46 +0000226 tmp = modnn(tmp + 2 * KK * (B0+i-1)*PRIM);
wdenkaffae2b2002-08-17 09:36:01 +0000227 s[i] = tmp;
228 }
229
230 CLEAR(&lambda[1],NN-KK);
231 lambda[0] = 1;
232
233 if (no_eras > 0) {
234 /* Init lambda to be the erasure locator polynomial */
235 lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])];
236 for (i = 1; i < no_eras; i++) {
237 u = modnn(PRIM*eras_pos[i]);
238 for (j = i+1; j > 0; j--) {
239 tmp = Index_of[lambda[j - 1]];
240 if(tmp != A0)
241 lambda[j] ^= Alpha_to[modnn(u + tmp)];
242 }
243 }
244#ifdef ECC_DEBUG
245 /* Test code that verifies the erasure locator polynomial just constructed
246 Needed only for decoder debugging. */
247
248 /* find roots of the erasure location polynomial */
249 for(i=1;i<=no_eras;i++)
250 reg[i] = Index_of[lambda[i]];
251 count = 0;
252 for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
253 q = 1;
254 for (j = 1; j <= no_eras; j++)
255 if (reg[j] != A0) {
256 reg[j] = modnn(reg[j] + j);
257 q ^= Alpha_to[reg[j]];
258 }
259 if (q != 0)
260 continue;
261 /* store root and error location number indices */
262 root[count] = i;
263 loc[count] = k;
264 count++;
265 }
266 if (count != no_eras) {
267 printf("\n lambda(x) is WRONG\n");
268 count = -1;
269 goto finish;
270 }
271#ifdef PSYCHO_DEBUG
272 printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
273 for (i = 0; i < count; i++)
274 printf("%d ", loc[i]);
275 printf("\n");
276#endif
277#endif
278 }
279 for(i=0;i<NN-KK+1;i++)
280 b[i] = Index_of[lambda[i]];
281
282 /*
283 * Begin Berlekamp-Massey algorithm to determine error+erasure
284 * locator polynomial
285 */
286 r = no_eras;
287 el = no_eras;
288 while (++r <= NN-KK) { /* r is the step number */
289 /* Compute discrepancy at the r-th step in poly-form */
290 discr_r = 0;
291 for (i = 0; i < r; i++){
292 if ((lambda[i] != 0) && (s[r - i] != A0)) {
293 discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
294 }
295 }
296 discr_r = Index_of[discr_r]; /* Index form */
297 if (discr_r == A0) {
298 /* 2 lines below: B(x) <-- x*B(x) */
299 COPYDOWN(&b[1],b,NN-KK);
300 b[0] = A0;
301 } else {
302 /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
303 t[0] = lambda[0];
304 for (i = 0 ; i < NN-KK; i++) {
305 if(b[i] != A0)
306 t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
307 else
308 t[i+1] = lambda[i+1];
309 }
310 if (2 * el <= r + no_eras - 1) {
311 el = r + no_eras - el;
312 /*
313 * 2 lines below: B(x) <-- inv(discr_r) *
314 * lambda(x)
315 */
316 for (i = 0; i <= NN-KK; i++)
317 b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
318 } else {
319 /* 2 lines below: B(x) <-- x*B(x) */
320 COPYDOWN(&b[1],b,NN-KK);
321 b[0] = A0;
322 }
323 COPY(lambda,t,NN-KK+1);
324 }
325 }
326
327 /* Convert lambda to index form and compute deg(lambda(x)) */
328 deg_lambda = 0;
329 for(i=0;i<NN-KK+1;i++){
330 lambda[i] = Index_of[lambda[i]];
331 if(lambda[i] != A0)
332 deg_lambda = i;
333 }
334 /*
335 * Find roots of the error+erasure locator polynomial by Chien
336 * Search
337 */
338 COPY(&reg[1],&lambda[1],NN-KK);
339 count = 0; /* Number of roots of lambda(x) */
340 for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
341 q = 1;
342 for (j = deg_lambda; j > 0; j--){
343 if (reg[j] != A0) {
344 reg[j] = modnn(reg[j] + j);
345 q ^= Alpha_to[reg[j]];
346 }
347 }
348 if (q != 0)
349 continue;
350 /* store root (index-form) and error location number */
351 root[count] = i;
352 loc[count] = k;
353 /* If we've already found max possible roots,
354 * abort the search to save time
355 */
356 if(++count == deg_lambda)
357 break;
358 }
359 if (deg_lambda != count) {
360 /*
361 * deg(lambda) unequal to number of roots => uncorrectable
362 * error detected
363 */
364 count = -1;
365 goto finish;
366 }
367 /*
368 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
369 * x**(NN-KK)). in index form. Also find deg(omega).
370 */
371 deg_omega = 0;
372 for (i = 0; i < NN-KK;i++){
373 tmp = 0;
374 j = (deg_lambda < i) ? deg_lambda : i;
375 for(;j >= 0; j--){
376 if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
377 tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
378 }
379 if(tmp != 0)
380 deg_omega = i;
381 omega[i] = Index_of[tmp];
382 }
383 omega[NN-KK] = A0;
384
385 /*
386 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
387 * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
388 */
389 for (j = count-1; j >=0; j--) {
390 num1 = 0;
391 for (i = deg_omega; i >= 0; i--) {
392 if (omega[i] != A0)
393 num1 ^= Alpha_to[modnn(omega[i] + i * root[j])];
394 }
395 num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
396 den = 0;
397
398 /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
399 for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
400 if(lambda[i+1] != A0)
401 den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
402 }
403 if (den == 0) {
404#ifdef ECC_DEBUG
405 printf("\n ERROR: denominator = 0\n");
406#endif
407 /* Convert to dual- basis */
408 count = -1;
409 goto finish;
410 }
411 /* Apply error to data */
412 if (num1 != 0) {
wdenk8bde7f72003-06-27 21:31:46 +0000413 eras_val[j] = Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
wdenkaffae2b2002-08-17 09:36:01 +0000414 } else {
wdenk8bde7f72003-06-27 21:31:46 +0000415 eras_val[j] = 0;
wdenkaffae2b2002-08-17 09:36:01 +0000416 }
417 }
418 finish:
419 for(i=0;i<count;i++)
420 eras_pos[i] = loc[i];
421 return count;
422}
423
424/***************************************************************************/
425/* The DOC specific code begins here */
426
427#define SECTOR_SIZE 512
428/* The sector bytes are packed into NB_DATA MM bits words */
429#define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM)
430
431/*
432 * Correct the errors in 'sector[]' by using 'ecc1[]' which is the
433 * content of the feedback shift register applyied to the sector and
434 * the ECC. Return the number of errors corrected (and correct them in
435 * sector), or -1 if error
436 */
437int doc_decode_ecc(unsigned char sector[SECTOR_SIZE], unsigned char ecc1[6])
438{
439 int parity, i, nb_errors;
440 gf bb[NN - KK + 1];
441 gf error_val[NN-KK];
442 int error_pos[NN-KK], pos, bitpos, index, val;
443 dtype *Alpha_to, *Index_of;
444
445 /* init log and exp tables here to save memory. However, it is slower */
446 Alpha_to = malloc((NN + 1) * sizeof(dtype));
447 if (!Alpha_to)
wdenk8bde7f72003-06-27 21:31:46 +0000448 return -1;
wdenkaffae2b2002-08-17 09:36:01 +0000449
450 Index_of = malloc((NN + 1) * sizeof(dtype));
451 if (!Index_of) {
wdenk8bde7f72003-06-27 21:31:46 +0000452 free(Alpha_to);
453 return -1;
wdenkaffae2b2002-08-17 09:36:01 +0000454 }
455
456 generate_gf(Alpha_to, Index_of);
457
458 parity = ecc1[1];
459
460 bb[0] = (ecc1[4] & 0xff) | ((ecc1[5] & 0x03) << 8);
461 bb[1] = ((ecc1[5] & 0xfc) >> 2) | ((ecc1[2] & 0x0f) << 6);
462 bb[2] = ((ecc1[2] & 0xf0) >> 4) | ((ecc1[3] & 0x3f) << 4);
463 bb[3] = ((ecc1[3] & 0xc0) >> 6) | ((ecc1[0] & 0xff) << 2);
464
465 nb_errors = eras_dec_rs(Alpha_to, Index_of, bb,
wdenk8bde7f72003-06-27 21:31:46 +0000466 error_val, error_pos, 0);
wdenkaffae2b2002-08-17 09:36:01 +0000467 if (nb_errors <= 0)
wdenk8bde7f72003-06-27 21:31:46 +0000468 goto the_end;
wdenkaffae2b2002-08-17 09:36:01 +0000469
470 /* correct the errors */
471 for(i=0;i<nb_errors;i++) {
wdenk8bde7f72003-06-27 21:31:46 +0000472 pos = error_pos[i];
473 if (pos >= NB_DATA && pos < KK) {
474 nb_errors = -1;
475 goto the_end;
476 }
477 if (pos < NB_DATA) {
478 /* extract bit position (MSB first) */
479 pos = 10 * (NB_DATA - 1 - pos) - 6;
480 /* now correct the following 10 bits. At most two bytes
481 can be modified since pos is even */
482 index = (pos >> 3) ^ 1;
483 bitpos = pos & 7;
484 if ((index >= 0 && index < SECTOR_SIZE) ||
485 index == (SECTOR_SIZE + 1)) {
486 val = error_val[i] >> (2 + bitpos);
487 parity ^= val;
488 if (index < SECTOR_SIZE)
489 sector[index] ^= val;
490 }
491 index = ((pos >> 3) + 1) ^ 1;
492 bitpos = (bitpos + 10) & 7;
493 if (bitpos == 0)
494 bitpos = 8;
495 if ((index >= 0 && index < SECTOR_SIZE) ||
496 index == (SECTOR_SIZE + 1)) {
497 val = error_val[i] << (8 - bitpos);
498 parity ^= val;
499 if (index < SECTOR_SIZE)
500 sector[index] ^= val;
501 }
502 }
wdenkaffae2b2002-08-17 09:36:01 +0000503 }
504
505 /* use parity to test extra errors */
506 if ((parity & 0xff) != 0)
wdenk8bde7f72003-06-27 21:31:46 +0000507 nb_errors = -1;
wdenkaffae2b2002-08-17 09:36:01 +0000508
509 the_end:
510 free(Alpha_to);
511 free(Index_of);
512 return nb_errors;
513}