File: /usr/src/linux/drivers/mtd/devices/docecc.c
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 1.1 2000/11/03 12:43:43 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/mtd.h>
40 #include <linux/mtd/doc2000.h>
41
42 /* need to undef it (from asm/termbits.h) */
43 #undef B0
44
45 #define MM 10 /* Symbol size in bits */
46 #define KK (1023-4) /* Number of data symbols per block */
47 #define B0 510 /* First root of generator polynomial, alpha form */
48 #define PRIM 1 /* power of alpha used to generate roots of generator poly */
49 #define NN ((1 << MM) - 1)
50
51 typedef unsigned short dtype;
52
53 /* 1+x^3+x^10 */
54 static const int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
55
56 /* This defines the type used to store an element of the Galois Field
57 * used by the code. Make sure this is something larger than a char if
58 * if anything larger than GF(256) is used.
59 *
60 * Note: unsigned char will work up to GF(256) but int seems to run
61 * faster on the Pentium.
62 */
63 typedef int gf;
64
65 /* No legal value in index form represents zero, so
66 * we need a special value for this purpose
67 */
68 #define A0 (NN)
69
70 /* Compute x % NN, where NN is 2**MM - 1,
71 * without a slow divide
72 */
73 static inline gf
74 modnn(int x)
75 {
76 while (x >= NN) {
77 x -= NN;
78 x = (x >> MM) + (x & NN);
79 }
80 return x;
81 }
82
83 #define CLEAR(a,n) {\
84 int ci;\
85 for(ci=(n)-1;ci >=0;ci--)\
86 (a)[ci] = 0;\
87 }
88
89 #define COPY(a,b,n) {\
90 int ci;\
91 for(ci=(n)-1;ci >=0;ci--)\
92 (a)[ci] = (b)[ci];\
93 }
94
95 #define COPYDOWN(a,b,n) {\
96 int ci;\
97 for(ci=(n)-1;ci >=0;ci--)\
98 (a)[ci] = (b)[ci];\
99 }
100
101 #define Ldec 1
102
103 /* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m]
104 lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
105 polynomial form -> index form index_of[j=alpha**i] = i
106 alpha=2 is the primitive element of GF(2**m)
107 HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
108 Let @ represent the primitive element commonly called "alpha" that
109 is the root of the primitive polynomial p(x). Then in GF(2^m), for any
110 0 <= i <= 2^m-2,
111 @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
112 where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
113 of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
114 example the polynomial representation of @^5 would be given by the binary
115 representation of the integer "alpha_to[5]".
116 Similarily, index_of[] can be used as follows:
117 As above, let @ represent the primitive element of GF(2^m) that is
118 the root of the primitive polynomial p(x). In order to find the power
119 of @ (alpha) that has the polynomial representation
120 a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
121 we consider the integer "i" whose binary representation with a(0) being LSB
122 and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
123 "index_of[i]". Now, @^index_of[i] is that element whose polynomial
124 representation is (a(0),a(1),a(2),...,a(m-1)).
125 NOTE:
126 The element alpha_to[2^m-1] = 0 always signifying that the
127 representation of "@^infinity" = 0 is (0,0,0,...,0).
128 Similarily, the element index_of[0] = A0 always signifying
129 that the power of alpha which has the polynomial representation
130 (0,0,...,0) is "infinity".
131
132 */
133
134 static void
135 generate_gf(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1])
136 {
137 register int i, mask;
138
139 mask = 1;
140 Alpha_to[MM] = 0;
141 for (i = 0; i < MM; i++) {
142 Alpha_to[i] = mask;
143 Index_of[Alpha_to[i]] = i;
144 /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
145 if (Pp[i] != 0)
146 Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
147 mask <<= 1; /* single left-shift */
148 }
149 Index_of[Alpha_to[MM]] = MM;
150 /*
151 * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
152 * poly-repr of @^i shifted left one-bit and accounting for any @^MM
153 * term that may occur when poly-repr of @^i is shifted.
154 */
155 mask >>= 1;
156 for (i = MM + 1; i < NN; i++) {
157 if (Alpha_to[i - 1] >= mask)
158 Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
159 else
160 Alpha_to[i] = Alpha_to[i - 1] << 1;
161 Index_of[Alpha_to[i]] = i;
162 }
163 Index_of[0] = A0;
164 Alpha_to[NN] = 0;
165 }
166
167 /*
168 * Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content
169 * of the feedback shift register after having processed the data and
170 * the ECC.
171 *
172 * Return number of symbols corrected, or -1 if codeword is illegal
173 * or uncorrectable. If eras_pos is non-null, the detected error locations
174 * are written back. NOTE! This array must be at least NN-KK elements long.
175 * The corrected data are written in eras_val[]. They must be xor with the data
176 * to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] .
177 *
178 * First "no_eras" erasures are declared by the calling program. Then, the
179 * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
180 * If the number of channel errors is not greater than "t_after_eras" the
181 * transmitted codeword will be recovered. Details of algorithm can be found
182 * in R. Blahut's "Theory ... of Error-Correcting Codes".
183
184 * Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
185 * will result. The decoder *could* check for this condition, but it would involve
186 * extra time on every decoding operation.
187 * */
188 static int
189 eras_dec_rs(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1],
190 gf bb[NN - KK + 1], gf eras_val[NN-KK], int eras_pos[NN-KK],
191 int no_eras)
192 {
193 int deg_lambda, el, deg_omega;
194 int i, j, r,k;
195 gf u,q,tmp,num1,num2,den,discr_r;
196 gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
197 * and syndrome poly */
198 gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
199 gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
200 int syn_error, count;
201
202 syn_error = 0;
203 for(i=0;i<NN-KK;i++)
204 syn_error |= bb[i];
205
206 if (!syn_error) {
207 /* if remainder is zero, data[] is a codeword and there are no
208 * errors to correct. So return data[] unmodified
209 */
210 count = 0;
211 goto finish;
212 }
213
214 for(i=1;i<=NN-KK;i++){
215 s[i] = bb[0];
216 }
217 for(j=1;j<NN-KK;j++){
218 if(bb[j] == 0)
219 continue;
220 tmp = Index_of[bb[j]];
221
222 for(i=1;i<=NN-KK;i++)
223 s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)];
224 }
225
226 /* undo the feedback register implicit multiplication and convert
227 syndromes to index form */
228
229 for(i=1;i<=NN-KK;i++) {
230 tmp = Index_of[s[i]];
231 if (tmp != A0)
232 tmp = modnn(tmp + 2 * KK * (B0+i-1)*PRIM);
233 s[i] = tmp;
234 }
235
236 CLEAR(&lambda[1],NN-KK);
237 lambda[0] = 1;
238
239 if (no_eras > 0) {
240 /* Init lambda to be the erasure locator polynomial */
241 lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])];
242 for (i = 1; i < no_eras; i++) {
243 u = modnn(PRIM*eras_pos[i]);
244 for (j = i+1; j > 0; j--) {
245 tmp = Index_of[lambda[j - 1]];
246 if(tmp != A0)
247 lambda[j] ^= Alpha_to[modnn(u + tmp)];
248 }
249 }
250 #if DEBUG >= 1
251 /* Test code that verifies the erasure locator polynomial just constructed
252 Needed only for decoder debugging. */
253
254 /* find roots of the erasure location polynomial */
255 for(i=1;i<=no_eras;i++)
256 reg[i] = Index_of[lambda[i]];
257 count = 0;
258 for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
259 q = 1;
260 for (j = 1; j <= no_eras; j++)
261 if (reg[j] != A0) {
262 reg[j] = modnn(reg[j] + j);
263 q ^= Alpha_to[reg[j]];
264 }
265 if (q != 0)
266 continue;
267 /* store root and error location number indices */
268 root[count] = i;
269 loc[count] = k;
270 count++;
271 }
272 if (count != no_eras) {
273 printf("\n lambda(x) is WRONG\n");
274 count = -1;
275 goto finish;
276 }
277 #if DEBUG >= 2
278 printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
279 for (i = 0; i < count; i++)
280 printf("%d ", loc[i]);
281 printf("\n");
282 #endif
283 #endif
284 }
285 for(i=0;i<NN-KK+1;i++)
286 b[i] = Index_of[lambda[i]];
287
288 /*
289 * Begin Berlekamp-Massey algorithm to determine error+erasure
290 * locator polynomial
291 */
292 r = no_eras;
293 el = no_eras;
294 while (++r <= NN-KK) { /* r is the step number */
295 /* Compute discrepancy at the r-th step in poly-form */
296 discr_r = 0;
297 for (i = 0; i < r; i++){
298 if ((lambda[i] != 0) && (s[r - i] != A0)) {
299 discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
300 }
301 }
302 discr_r = Index_of[discr_r]; /* Index form */
303 if (discr_r == A0) {
304 /* 2 lines below: B(x) <-- x*B(x) */
305 COPYDOWN(&b[1],b,NN-KK);
306 b[0] = A0;
307 } else {
308 /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
309 t[0] = lambda[0];
310 for (i = 0 ; i < NN-KK; i++) {
311 if(b[i] != A0)
312 t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
313 else
314 t[i+1] = lambda[i+1];
315 }
316 if (2 * el <= r + no_eras - 1) {
317 el = r + no_eras - el;
318 /*
319 * 2 lines below: B(x) <-- inv(discr_r) *
320 * lambda(x)
321 */
322 for (i = 0; i <= NN-KK; i++)
323 b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
324 } else {
325 /* 2 lines below: B(x) <-- x*B(x) */
326 COPYDOWN(&b[1],b,NN-KK);
327 b[0] = A0;
328 }
329 COPY(lambda,t,NN-KK+1);
330 }
331 }
332
333 /* Convert lambda to index form and compute deg(lambda(x)) */
334 deg_lambda = 0;
335 for(i=0;i<NN-KK+1;i++){
336 lambda[i] = Index_of[lambda[i]];
337 if(lambda[i] != A0)
338 deg_lambda = i;
339 }
340 /*
341 * Find roots of the error+erasure locator polynomial by Chien
342 * Search
343 */
344 COPY(®[1],&lambda[1],NN-KK);
345 count = 0; /* Number of roots of lambda(x) */
346 for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
347 q = 1;
348 for (j = deg_lambda; j > 0; j--){
349 if (reg[j] != A0) {
350 reg[j] = modnn(reg[j] + j);
351 q ^= Alpha_to[reg[j]];
352 }
353 }
354 if (q != 0)
355 continue;
356 /* store root (index-form) and error location number */
357 root[count] = i;
358 loc[count] = k;
359 /* If we've already found max possible roots,
360 * abort the search to save time
361 */
362 if(++count == deg_lambda)
363 break;
364 }
365 if (deg_lambda != count) {
366 /*
367 * deg(lambda) unequal to number of roots => uncorrectable
368 * error detected
369 */
370 count = -1;
371 goto finish;
372 }
373 /*
374 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
375 * x**(NN-KK)). in index form. Also find deg(omega).
376 */
377 deg_omega = 0;
378 for (i = 0; i < NN-KK;i++){
379 tmp = 0;
380 j = (deg_lambda < i) ? deg_lambda : i;
381 for(;j >= 0; j--){
382 if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
383 tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
384 }
385 if(tmp != 0)
386 deg_omega = i;
387 omega[i] = Index_of[tmp];
388 }
389 omega[NN-KK] = A0;
390
391 /*
392 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
393 * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
394 */
395 for (j = count-1; j >=0; j--) {
396 num1 = 0;
397 for (i = deg_omega; i >= 0; i--) {
398 if (omega[i] != A0)
399 num1 ^= Alpha_to[modnn(omega[i] + i * root[j])];
400 }
401 num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
402 den = 0;
403
404 /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
405 for (i = min_t(int, deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
406 if(lambda[i+1] != A0)
407 den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
408 }
409 if (den == 0) {
410 #if DEBUG >= 1
411 printf("\n ERROR: denominator = 0\n");
412 #endif
413 /* Convert to dual- basis */
414 count = -1;
415 goto finish;
416 }
417 /* Apply error to data */
418 if (num1 != 0) {
419 eras_val[j] = Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
420 } else {
421 eras_val[j] = 0;
422 }
423 }
424 finish:
425 for(i=0;i<count;i++)
426 eras_pos[i] = loc[i];
427 return count;
428 }
429
430 /***************************************************************************/
431 /* The DOC specific code begins here */
432
433 #define SECTOR_SIZE 512
434 /* The sector bytes are packed into NB_DATA MM bits words */
435 #define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM)
436
437 /*
438 * Correct the errors in 'sector[]' by using 'ecc1[]' which is the
439 * content of the feedback shift register applyied to the sector and
440 * the ECC. Return the number of errors corrected (and correct them in
441 * sector), or -1 if error
442 */
443 int doc_decode_ecc(unsigned char sector[SECTOR_SIZE], unsigned char ecc1[6])
444 {
445 int parity, i, nb_errors;
446 gf bb[NN - KK + 1];
447 gf error_val[NN-KK];
448 int error_pos[NN-KK], pos, bitpos, index, val;
449 dtype *Alpha_to, *Index_of;
450
451 /* init log and exp tables here to save memory. However, it is slower */
452 Alpha_to = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
453 if (!Alpha_to)
454 return -1;
455
456 Index_of = kmalloc((NN + 1) * sizeof(dtype), GFP_KERNEL);
457 if (!Index_of) {
458 kfree(Alpha_to);
459 return -1;
460 }
461
462 generate_gf(Alpha_to, Index_of);
463
464 parity = ecc1[1];
465
466 bb[0] = (ecc1[4] & 0xff) | ((ecc1[5] & 0x03) << 8);
467 bb[1] = ((ecc1[5] & 0xfc) >> 2) | ((ecc1[2] & 0x0f) << 6);
468 bb[2] = ((ecc1[2] & 0xf0) >> 4) | ((ecc1[3] & 0x3f) << 4);
469 bb[3] = ((ecc1[3] & 0xc0) >> 6) | ((ecc1[0] & 0xff) << 2);
470
471 nb_errors = eras_dec_rs(Alpha_to, Index_of, bb,
472 error_val, error_pos, 0);
473 if (nb_errors <= 0)
474 goto the_end;
475
476 /* correct the errors */
477 for(i=0;i<nb_errors;i++) {
478 pos = error_pos[i];
479 if (pos >= NB_DATA && pos < KK) {
480 nb_errors = -1;
481 goto the_end;
482 }
483 if (pos < NB_DATA) {
484 /* extract bit position (MSB first) */
485 pos = 10 * (NB_DATA - 1 - pos) - 6;
486 /* now correct the following 10 bits. At most two bytes
487 can be modified since pos is even */
488 index = (pos >> 3) ^ 1;
489 bitpos = pos & 7;
490 if ((index >= 0 && index < SECTOR_SIZE) ||
491 index == (SECTOR_SIZE + 1)) {
492 val = error_val[i] >> (2 + bitpos);
493 parity ^= val;
494 if (index < SECTOR_SIZE)
495 sector[index] ^= val;
496 }
497 index = ((pos >> 3) + 1) ^ 1;
498 bitpos = (bitpos + 10) & 7;
499 if (bitpos == 0)
500 bitpos = 8;
501 if ((index >= 0 && index < SECTOR_SIZE) ||
502 index == (SECTOR_SIZE + 1)) {
503 val = error_val[i] << (8 - bitpos);
504 parity ^= val;
505 if (index < SECTOR_SIZE)
506 sector[index] ^= val;
507 }
508 }
509 }
510
511 /* use parity to test extra errors */
512 if ((parity & 0xff) != 0)
513 nb_errors = -1;
514
515 the_end:
516 kfree(Alpha_to);
517 kfree(Index_of);
518 return nb_errors;
519 }
520
521