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 1.1.1.1 2007/08/03 18:52:43 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/delay.h> 33#include <linux/slab.h> 34#include <linux/init.h> 35#include <linux/types.h> 36 37#include <linux/mtd/compatmac.h> /* for min() in older kernels */ 38#include <linux/mtd/mtd.h> 39#include <linux/mtd/doc2000.h> 40 41#define DEBUG_ECC 0 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 51typedef unsigned short dtype; 52 53/* 1+x^3+x^10 */ 54static 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 */ 63typedef 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 */ 73static inline gf 74modnn(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) {\ 84int ci;\ 85for(ci=(n)-1;ci >=0;ci--)\ 86(a)[ci] = 0;\ 87} 88 89#define COPY(a,b,n) {\ 90int ci;\ 91for(ci=(n)-1;ci >=0;ci--)\ 92(a)[ci] = (b)[ci];\ 93} 94 95#define COPYDOWN(a,b,n) {\ 96int ci;\ 97for(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 134static void 135generate_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 * */ 188static int 189eras_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_ECC >= 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_ECC >= 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(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_ECC >= 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 */ 443int 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 521EXPORT_SYMBOL_GPL(doc_decode_ecc); 522 523MODULE_LICENSE("GPL"); 524MODULE_AUTHOR("Fabrice Bellard <fabrice.bellard@netgem.com>"); 525MODULE_DESCRIPTION("ECC code for correcting errors detected by DiskOnChip 2000 and Millennium ECC hardware"); 526