1 /* 2 * Generic binary BCH encoding/decoding library 3 * 4 * This program is free software; you can redistribute it and/or modify it 5 * under the terms of the GNU General Public License version 2 as published by 6 * the Free Software Foundation. 7 * 8 * This program is distributed in the hope that it will be useful, but WITHOUT 9 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 10 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for 11 * more details. 12 * 13 * You should have received a copy of the GNU General Public License along with 14 * this program; if not, write to the Free Software Foundation, Inc., 51 15 * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 16 * 17 * Copyright © 2011 Parrot S.A. 18 * 19 * Author: Ivan Djelic <ivan.djelic@parrot.com> 20 * 21 * Description: 22 * 23 * This library provides runtime configurable encoding/decoding of binary 24 * Bose-Chaudhuri-Hocquenghem (BCH) codes. 25 * 26 * Call init_bch to get a pointer to a newly allocated bch_control structure for 27 * the given m (Galois field order), t (error correction capability) and 28 * (optional) primitive polynomial parameters. 29 * 30 * Call encode_bch to compute and store ecc parity bytes to a given buffer. 31 * Call decode_bch to detect and locate errors in received data. 32 * 33 * On systems supporting hw BCH features, intermediate results may be provided 34 * to decode_bch in order to skip certain steps. See decode_bch() documentation 35 * for details. 36 * 37 * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of 38 * parameters m and t; thus allowing extra compiler optimizations and providing 39 * better (up to 2x) encoding performance. Using this option makes sense when 40 * (m,t) are fixed and known in advance, e.g. when using BCH error correction 41 * on a particular NAND flash device. 42 * 43 * Algorithmic details: 44 * 45 * Encoding is performed by processing 32 input bits in parallel, using 4 46 * remainder lookup tables. 47 * 48 * The final stage of decoding involves the following internal steps: 49 * a. Syndrome computation 50 * b. Error locator polynomial computation using Berlekamp-Massey algorithm 51 * c. Error locator root finding (by far the most expensive step) 52 * 53 * In this implementation, step c is not performed using the usual Chien search. 54 * Instead, an alternative approach described in [1] is used. It consists in 55 * factoring the error locator polynomial using the Berlekamp Trace algorithm 56 * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial 57 * solving techniques [2] are used. The resulting algorithm, called BTZ, yields 58 * much better performance than Chien search for usual (m,t) values (typically 59 * m >= 13, t < 32, see [1]). 60 * 61 * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields 62 * of characteristic 2, in: Western European Workshop on Research in Cryptology 63 * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear. 64 * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over 65 * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996. 66 */ 67 68 #include <linux/kernel.h> 69 #include <linux/errno.h> 70 #include <linux/init.h> 71 #include <linux/module.h> 72 #include <linux/slab.h> 73 #include <linux/bitops.h> 74 #include <asm/byteorder.h> 75 #include <linux/bch.h> 76 77 #if defined(CONFIG_BCH_CONST_PARAMS) 78 #define GF_M(_p) (CONFIG_BCH_CONST_M) 79 #define GF_T(_p) (CONFIG_BCH_CONST_T) 80 #define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1) 81 #else 82 #define GF_M(_p) ((_p)->m) 83 #define GF_T(_p) ((_p)->t) 84 #define GF_N(_p) ((_p)->n) 85 #endif 86 87 #define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32) 88 #define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8) 89 90 #ifndef dbg 91 #define dbg(_fmt, args...) do {} while (0) 92 #endif 93 94 /* 95 * represent a polynomial over GF(2^m) 96 */ 97 struct gf_poly { 98 unsigned int deg; /* polynomial degree */ 99 unsigned int c[0]; /* polynomial terms */ 100 }; 101 102 /* given its degree, compute a polynomial size in bytes */ 103 #define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int)) 104 105 /* polynomial of degree 1 */ 106 struct gf_poly_deg1 { 107 struct gf_poly poly; 108 unsigned int c[2]; 109 }; 110 111 /* 112 * same as encode_bch(), but process input data one byte at a time 113 */ 114 static void encode_bch_unaligned(struct bch_control *bch, 115 const unsigned char *data, unsigned int len, 116 uint32_t *ecc) 117 { 118 int i; 119 const uint32_t *p; 120 const int l = BCH_ECC_WORDS(bch)-1; 121 122 while (len--) { 123 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff); 124 125 for (i = 0; i < l; i++) 126 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++); 127 128 ecc[l] = (ecc[l] << 8)^(*p); 129 } 130 } 131 132 /* 133 * convert ecc bytes to aligned, zero-padded 32-bit ecc words 134 */ 135 static void load_ecc8(struct bch_control *bch, uint32_t *dst, 136 const uint8_t *src) 137 { 138 uint8_t pad[4] = {0, 0, 0, 0}; 139 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; 140 141 for (i = 0; i < nwords; i++, src += 4) 142 dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3]; 143 144 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords); 145 dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3]; 146 } 147 148 /* 149 * convert 32-bit ecc words to ecc bytes 150 */ 151 static void store_ecc8(struct bch_control *bch, uint8_t *dst, 152 const uint32_t *src) 153 { 154 uint8_t pad[4]; 155 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; 156 157 for (i = 0; i < nwords; i++) { 158 *dst++ = (src[i] >> 24); 159 *dst++ = (src[i] >> 16) & 0xff; 160 *dst++ = (src[i] >> 8) & 0xff; 161 *dst++ = (src[i] >> 0) & 0xff; 162 } 163 pad[0] = (src[nwords] >> 24); 164 pad[1] = (src[nwords] >> 16) & 0xff; 165 pad[2] = (src[nwords] >> 8) & 0xff; 166 pad[3] = (src[nwords] >> 0) & 0xff; 167 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords); 168 } 169 170 /** 171 * encode_bch - calculate BCH ecc parity of data 172 * @bch: BCH control structure 173 * @data: data to encode 174 * @len: data length in bytes 175 * @ecc: ecc parity data, must be initialized by caller 176 * 177 * The @ecc parity array is used both as input and output parameter, in order to 178 * allow incremental computations. It should be of the size indicated by member 179 * @ecc_bytes of @bch, and should be initialized to 0 before the first call. 180 * 181 * The exact number of computed ecc parity bits is given by member @ecc_bits of 182 * @bch; it may be less than m*t for large values of t. 183 */ 184 void encode_bch(struct bch_control *bch, const uint8_t *data, 185 unsigned int len, uint8_t *ecc) 186 { 187 const unsigned int l = BCH_ECC_WORDS(bch)-1; 188 unsigned int i, mlen; 189 unsigned long m; 190 uint32_t w, r[l+1]; 191 const uint32_t * const tab0 = bch->mod8_tab; 192 const uint32_t * const tab1 = tab0 + 256*(l+1); 193 const uint32_t * const tab2 = tab1 + 256*(l+1); 194 const uint32_t * const tab3 = tab2 + 256*(l+1); 195 const uint32_t *pdata, *p0, *p1, *p2, *p3; 196 197 if (ecc) { 198 /* load ecc parity bytes into internal 32-bit buffer */ 199 load_ecc8(bch, bch->ecc_buf, ecc); 200 } else { 201 memset(bch->ecc_buf, 0, sizeof(r)); 202 } 203 204 /* process first unaligned data bytes */ 205 m = ((unsigned long)data) & 3; 206 if (m) { 207 mlen = (len < (4-m)) ? len : 4-m; 208 encode_bch_unaligned(bch, data, mlen, bch->ecc_buf); 209 data += mlen; 210 len -= mlen; 211 } 212 213 /* process 32-bit aligned data words */ 214 pdata = (uint32_t *)data; 215 mlen = len/4; 216 data += 4*mlen; 217 len -= 4*mlen; 218 memcpy(r, bch->ecc_buf, sizeof(r)); 219 220 /* 221 * split each 32-bit word into 4 polynomials of weight 8 as follows: 222 * 223 * 31 ...24 23 ...16 15 ... 8 7 ... 0 224 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt 225 * tttttttt mod g = r0 (precomputed) 226 * zzzzzzzz 00000000 mod g = r1 (precomputed) 227 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed) 228 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed) 229 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3 230 */ 231 while (mlen--) { 232 /* input data is read in big-endian format */ 233 w = r[0]^cpu_to_be32(*pdata++); 234 p0 = tab0 + (l+1)*((w >> 0) & 0xff); 235 p1 = tab1 + (l+1)*((w >> 8) & 0xff); 236 p2 = tab2 + (l+1)*((w >> 16) & 0xff); 237 p3 = tab3 + (l+1)*((w >> 24) & 0xff); 238 239 for (i = 0; i < l; i++) 240 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i]; 241 242 r[l] = p0[l]^p1[l]^p2[l]^p3[l]; 243 } 244 memcpy(bch->ecc_buf, r, sizeof(r)); 245 246 /* process last unaligned bytes */ 247 if (len) 248 encode_bch_unaligned(bch, data, len, bch->ecc_buf); 249 250 /* store ecc parity bytes into original parity buffer */ 251 if (ecc) 252 store_ecc8(bch, ecc, bch->ecc_buf); 253 } 254 EXPORT_SYMBOL_GPL(encode_bch); 255 256 static inline int modulo(struct bch_control *bch, unsigned int v) 257 { 258 const unsigned int n = GF_N(bch); 259 while (v >= n) { 260 v -= n; 261 v = (v & n) + (v >> GF_M(bch)); 262 } 263 return v; 264 } 265 266 /* 267 * shorter and faster modulo function, only works when v < 2N. 268 */ 269 static inline int mod_s(struct bch_control *bch, unsigned int v) 270 { 271 const unsigned int n = GF_N(bch); 272 return (v < n) ? v : v-n; 273 } 274 275 static inline int deg(unsigned int poly) 276 { 277 /* polynomial degree is the most-significant bit index */ 278 return fls(poly)-1; 279 } 280 281 static inline int parity(unsigned int x) 282 { 283 /* 284 * public domain code snippet, lifted from 285 * http://www-graphics.stanford.edu/~seander/bithacks.html 286 */ 287 x ^= x >> 1; 288 x ^= x >> 2; 289 x = (x & 0x11111111U) * 0x11111111U; 290 return (x >> 28) & 1; 291 } 292 293 /* Galois field basic operations: multiply, divide, inverse, etc. */ 294 295 static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a, 296 unsigned int b) 297 { 298 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ 299 bch->a_log_tab[b])] : 0; 300 } 301 302 static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a) 303 { 304 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0; 305 } 306 307 static inline unsigned int gf_div(struct bch_control *bch, unsigned int a, 308 unsigned int b) 309 { 310 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ 311 GF_N(bch)-bch->a_log_tab[b])] : 0; 312 } 313 314 static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a) 315 { 316 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]]; 317 } 318 319 static inline unsigned int a_pow(struct bch_control *bch, int i) 320 { 321 return bch->a_pow_tab[modulo(bch, i)]; 322 } 323 324 static inline int a_log(struct bch_control *bch, unsigned int x) 325 { 326 return bch->a_log_tab[x]; 327 } 328 329 static inline int a_ilog(struct bch_control *bch, unsigned int x) 330 { 331 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]); 332 } 333 334 /* 335 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t 336 */ 337 static void compute_syndromes(struct bch_control *bch, uint32_t *ecc, 338 unsigned int *syn) 339 { 340 int i, j, s; 341 unsigned int m; 342 uint32_t poly; 343 const int t = GF_T(bch); 344 345 s = bch->ecc_bits; 346 347 /* make sure extra bits in last ecc word are cleared */ 348 m = ((unsigned int)s) & 31; 349 if (m) 350 ecc[s/32] &= ~((1u << (32-m))-1); 351 memset(syn, 0, 2*t*sizeof(*syn)); 352 353 /* compute v(a^j) for j=1 .. 2t-1 */ 354 do { 355 poly = *ecc++; 356 s -= 32; 357 while (poly) { 358 i = deg(poly); 359 for (j = 0; j < 2*t; j += 2) 360 syn[j] ^= a_pow(bch, (j+1)*(i+s)); 361 362 poly ^= (1 << i); 363 } 364 } while (s > 0); 365 366 /* v(a^(2j)) = v(a^j)^2 */ 367 for (j = 0; j < t; j++) 368 syn[2*j+1] = gf_sqr(bch, syn[j]); 369 } 370 371 static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src) 372 { 373 memcpy(dst, src, GF_POLY_SZ(src->deg)); 374 } 375 376 static int compute_error_locator_polynomial(struct bch_control *bch, 377 const unsigned int *syn) 378 { 379 const unsigned int t = GF_T(bch); 380 const unsigned int n = GF_N(bch); 381 unsigned int i, j, tmp, l, pd = 1, d = syn[0]; 382 struct gf_poly *elp = bch->elp; 383 struct gf_poly *pelp = bch->poly_2t[0]; 384 struct gf_poly *elp_copy = bch->poly_2t[1]; 385 int k, pp = -1; 386 387 memset(pelp, 0, GF_POLY_SZ(2*t)); 388 memset(elp, 0, GF_POLY_SZ(2*t)); 389 390 pelp->deg = 0; 391 pelp->c[0] = 1; 392 elp->deg = 0; 393 elp->c[0] = 1; 394 395 /* use simplified binary Berlekamp-Massey algorithm */ 396 for (i = 0; (i < t) && (elp->deg <= t); i++) { 397 if (d) { 398 k = 2*i-pp; 399 gf_poly_copy(elp_copy, elp); 400 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */ 401 tmp = a_log(bch, d)+n-a_log(bch, pd); 402 for (j = 0; j <= pelp->deg; j++) { 403 if (pelp->c[j]) { 404 l = a_log(bch, pelp->c[j]); 405 elp->c[j+k] ^= a_pow(bch, tmp+l); 406 } 407 } 408 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */ 409 tmp = pelp->deg+k; 410 if (tmp > elp->deg) { 411 elp->deg = tmp; 412 gf_poly_copy(pelp, elp_copy); 413 pd = d; 414 pp = 2*i; 415 } 416 } 417 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */ 418 if (i < t-1) { 419 d = syn[2*i+2]; 420 for (j = 1; j <= elp->deg; j++) 421 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]); 422 } 423 } 424 dbg("elp=%s\n", gf_poly_str(elp)); 425 return (elp->deg > t) ? -1 : (int)elp->deg; 426 } 427 428 /* 429 * solve a m x m linear system in GF(2) with an expected number of solutions, 430 * and return the number of found solutions 431 */ 432 static int solve_linear_system(struct bch_control *bch, unsigned int *rows, 433 unsigned int *sol, int nsol) 434 { 435 const int m = GF_M(bch); 436 unsigned int tmp, mask; 437 int rem, c, r, p, k, param[m]; 438 439 k = 0; 440 mask = 1 << m; 441 442 /* Gaussian elimination */ 443 for (c = 0; c < m; c++) { 444 rem = 0; 445 p = c-k; 446 /* find suitable row for elimination */ 447 for (r = p; r < m; r++) { 448 if (rows[r] & mask) { 449 if (r != p) { 450 tmp = rows[r]; 451 rows[r] = rows[p]; 452 rows[p] = tmp; 453 } 454 rem = r+1; 455 break; 456 } 457 } 458 if (rem) { 459 /* perform elimination on remaining rows */ 460 tmp = rows[p]; 461 for (r = rem; r < m; r++) { 462 if (rows[r] & mask) 463 rows[r] ^= tmp; 464 } 465 } else { 466 /* elimination not needed, store defective row index */ 467 param[k++] = c; 468 } 469 mask >>= 1; 470 } 471 /* rewrite system, inserting fake parameter rows */ 472 if (k > 0) { 473 p = k; 474 for (r = m-1; r >= 0; r--) { 475 if ((r > m-1-k) && rows[r]) 476 /* system has no solution */ 477 return 0; 478 479 rows[r] = (p && (r == param[p-1])) ? 480 p--, 1u << (m-r) : rows[r-p]; 481 } 482 } 483 484 if (nsol != (1 << k)) 485 /* unexpected number of solutions */ 486 return 0; 487 488 for (p = 0; p < nsol; p++) { 489 /* set parameters for p-th solution */ 490 for (c = 0; c < k; c++) 491 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1); 492 493 /* compute unique solution */ 494 tmp = 0; 495 for (r = m-1; r >= 0; r--) { 496 mask = rows[r] & (tmp|1); 497 tmp |= parity(mask) << (m-r); 498 } 499 sol[p] = tmp >> 1; 500 } 501 return nsol; 502 } 503 504 /* 505 * this function builds and solves a linear system for finding roots of a degree 506 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m). 507 */ 508 static int find_affine4_roots(struct bch_control *bch, unsigned int a, 509 unsigned int b, unsigned int c, 510 unsigned int *roots) 511 { 512 int i, j, k; 513 const int m = GF_M(bch); 514 unsigned int mask = 0xff, t, rows[16] = {0,}; 515 516 j = a_log(bch, b); 517 k = a_log(bch, a); 518 rows[0] = c; 519 520 /* buid linear system to solve X^4+aX^2+bX+c = 0 */ 521 for (i = 0; i < m; i++) { 522 rows[i+1] = bch->a_pow_tab[4*i]^ 523 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^ 524 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0); 525 j++; 526 k += 2; 527 } 528 /* 529 * transpose 16x16 matrix before passing it to linear solver 530 * warning: this code assumes m < 16 531 */ 532 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) { 533 for (k = 0; k < 16; k = (k+j+1) & ~j) { 534 t = ((rows[k] >> j)^rows[k+j]) & mask; 535 rows[k] ^= (t << j); 536 rows[k+j] ^= t; 537 } 538 } 539 return solve_linear_system(bch, rows, roots, 4); 540 } 541 542 /* 543 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r)) 544 */ 545 static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly, 546 unsigned int *roots) 547 { 548 int n = 0; 549 550 if (poly->c[0]) 551 /* poly[X] = bX+c with c!=0, root=c/b */ 552 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+ 553 bch->a_log_tab[poly->c[1]]); 554 return n; 555 } 556 557 /* 558 * compute roots of a degree 2 polynomial over GF(2^m) 559 */ 560 static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly, 561 unsigned int *roots) 562 { 563 int n = 0, i, l0, l1, l2; 564 unsigned int u, v, r; 565 566 if (poly->c[0] && poly->c[1]) { 567 568 l0 = bch->a_log_tab[poly->c[0]]; 569 l1 = bch->a_log_tab[poly->c[1]]; 570 l2 = bch->a_log_tab[poly->c[2]]; 571 572 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */ 573 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1)); 574 /* 575 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi): 576 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) = 577 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u) 578 * i.e. r and r+1 are roots iff Tr(u)=0 579 */ 580 r = 0; 581 v = u; 582 while (v) { 583 i = deg(v); 584 r ^= bch->xi_tab[i]; 585 v ^= (1 << i); 586 } 587 /* verify root */ 588 if ((gf_sqr(bch, r)^r) == u) { 589 /* reverse z=a/bX transformation and compute log(1/r) */ 590 roots[n++] = modulo(bch, 2*GF_N(bch)-l1- 591 bch->a_log_tab[r]+l2); 592 roots[n++] = modulo(bch, 2*GF_N(bch)-l1- 593 bch->a_log_tab[r^1]+l2); 594 } 595 } 596 return n; 597 } 598 599 /* 600 * compute roots of a degree 3 polynomial over GF(2^m) 601 */ 602 static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly, 603 unsigned int *roots) 604 { 605 int i, n = 0; 606 unsigned int a, b, c, a2, b2, c2, e3, tmp[4]; 607 608 if (poly->c[0]) { 609 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */ 610 e3 = poly->c[3]; 611 c2 = gf_div(bch, poly->c[0], e3); 612 b2 = gf_div(bch, poly->c[1], e3); 613 a2 = gf_div(bch, poly->c[2], e3); 614 615 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */ 616 c = gf_mul(bch, a2, c2); /* c = a2c2 */ 617 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */ 618 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */ 619 620 /* find the 4 roots of this affine polynomial */ 621 if (find_affine4_roots(bch, a, b, c, tmp) == 4) { 622 /* remove a2 from final list of roots */ 623 for (i = 0; i < 4; i++) { 624 if (tmp[i] != a2) 625 roots[n++] = a_ilog(bch, tmp[i]); 626 } 627 } 628 } 629 return n; 630 } 631 632 /* 633 * compute roots of a degree 4 polynomial over GF(2^m) 634 */ 635 static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly, 636 unsigned int *roots) 637 { 638 int i, l, n = 0; 639 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4; 640 641 if (poly->c[0] == 0) 642 return 0; 643 644 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */ 645 e4 = poly->c[4]; 646 d = gf_div(bch, poly->c[0], e4); 647 c = gf_div(bch, poly->c[1], e4); 648 b = gf_div(bch, poly->c[2], e4); 649 a = gf_div(bch, poly->c[3], e4); 650 651 /* use Y=1/X transformation to get an affine polynomial */ 652 if (a) { 653 /* first, eliminate cX by using z=X+e with ae^2+c=0 */ 654 if (c) { 655 /* compute e such that e^2 = c/a */ 656 f = gf_div(bch, c, a); 657 l = a_log(bch, f); 658 l += (l & 1) ? GF_N(bch) : 0; 659 e = a_pow(bch, l/2); 660 /* 661 * use transformation z=X+e: 662 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d 663 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d 664 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d 665 * z^4 + az^3 + b'z^2 + d' 666 */ 667 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d; 668 b = gf_mul(bch, a, e)^b; 669 } 670 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */ 671 if (d == 0) 672 /* assume all roots have multiplicity 1 */ 673 return 0; 674 675 c2 = gf_inv(bch, d); 676 b2 = gf_div(bch, a, d); 677 a2 = gf_div(bch, b, d); 678 } else { 679 /* polynomial is already affine */ 680 c2 = d; 681 b2 = c; 682 a2 = b; 683 } 684 /* find the 4 roots of this affine polynomial */ 685 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) { 686 for (i = 0; i < 4; i++) { 687 /* post-process roots (reverse transformations) */ 688 f = a ? gf_inv(bch, roots[i]) : roots[i]; 689 roots[i] = a_ilog(bch, f^e); 690 } 691 n = 4; 692 } 693 return n; 694 } 695 696 /* 697 * build monic, log-based representation of a polynomial 698 */ 699 static void gf_poly_logrep(struct bch_control *bch, 700 const struct gf_poly *a, int *rep) 701 { 702 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]); 703 704 /* represent 0 values with -1; warning, rep[d] is not set to 1 */ 705 for (i = 0; i < d; i++) 706 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1; 707 } 708 709 /* 710 * compute polynomial Euclidean division remainder in GF(2^m)[X] 711 */ 712 static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a, 713 const struct gf_poly *b, int *rep) 714 { 715 int la, p, m; 716 unsigned int i, j, *c = a->c; 717 const unsigned int d = b->deg; 718 719 if (a->deg < d) 720 return; 721 722 /* reuse or compute log representation of denominator */ 723 if (!rep) { 724 rep = bch->cache; 725 gf_poly_logrep(bch, b, rep); 726 } 727 728 for (j = a->deg; j >= d; j--) { 729 if (c[j]) { 730 la = a_log(bch, c[j]); 731 p = j-d; 732 for (i = 0; i < d; i++, p++) { 733 m = rep[i]; 734 if (m >= 0) 735 c[p] ^= bch->a_pow_tab[mod_s(bch, 736 m+la)]; 737 } 738 } 739 } 740 a->deg = d-1; 741 while (!c[a->deg] && a->deg) 742 a->deg--; 743 } 744 745 /* 746 * compute polynomial Euclidean division quotient in GF(2^m)[X] 747 */ 748 static void gf_poly_div(struct bch_control *bch, struct gf_poly *a, 749 const struct gf_poly *b, struct gf_poly *q) 750 { 751 if (a->deg >= b->deg) { 752 q->deg = a->deg-b->deg; 753 /* compute a mod b (modifies a) */ 754 gf_poly_mod(bch, a, b, NULL); 755 /* quotient is stored in upper part of polynomial a */ 756 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int)); 757 } else { 758 q->deg = 0; 759 q->c[0] = 0; 760 } 761 } 762 763 /* 764 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X] 765 */ 766 static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a, 767 struct gf_poly *b) 768 { 769 struct gf_poly *tmp; 770 771 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b)); 772 773 if (a->deg < b->deg) { 774 tmp = b; 775 b = a; 776 a = tmp; 777 } 778 779 while (b->deg > 0) { 780 gf_poly_mod(bch, a, b, NULL); 781 tmp = b; 782 b = a; 783 a = tmp; 784 } 785 786 dbg("%s\n", gf_poly_str(a)); 787 788 return a; 789 } 790 791 /* 792 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f 793 * This is used in Berlekamp Trace algorithm for splitting polynomials 794 */ 795 static void compute_trace_bk_mod(struct bch_control *bch, int k, 796 const struct gf_poly *f, struct gf_poly *z, 797 struct gf_poly *out) 798 { 799 const int m = GF_M(bch); 800 int i, j; 801 802 /* z contains z^2j mod f */ 803 z->deg = 1; 804 z->c[0] = 0; 805 z->c[1] = bch->a_pow_tab[k]; 806 807 out->deg = 0; 808 memset(out, 0, GF_POLY_SZ(f->deg)); 809 810 /* compute f log representation only once */ 811 gf_poly_logrep(bch, f, bch->cache); 812 813 for (i = 0; i < m; i++) { 814 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */ 815 for (j = z->deg; j >= 0; j--) { 816 out->c[j] ^= z->c[j]; 817 z->c[2*j] = gf_sqr(bch, z->c[j]); 818 z->c[2*j+1] = 0; 819 } 820 if (z->deg > out->deg) 821 out->deg = z->deg; 822 823 if (i < m-1) { 824 z->deg *= 2; 825 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */ 826 gf_poly_mod(bch, z, f, bch->cache); 827 } 828 } 829 while (!out->c[out->deg] && out->deg) 830 out->deg--; 831 832 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out)); 833 } 834 835 /* 836 * factor a polynomial using Berlekamp Trace algorithm (BTA) 837 */ 838 static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f, 839 struct gf_poly **g, struct gf_poly **h) 840 { 841 struct gf_poly *f2 = bch->poly_2t[0]; 842 struct gf_poly *q = bch->poly_2t[1]; 843 struct gf_poly *tk = bch->poly_2t[2]; 844 struct gf_poly *z = bch->poly_2t[3]; 845 struct gf_poly *gcd; 846 847 dbg("factoring %s...\n", gf_poly_str(f)); 848 849 *g = f; 850 *h = NULL; 851 852 /* tk = Tr(a^k.X) mod f */ 853 compute_trace_bk_mod(bch, k, f, z, tk); 854 855 if (tk->deg > 0) { 856 /* compute g = gcd(f, tk) (destructive operation) */ 857 gf_poly_copy(f2, f); 858 gcd = gf_poly_gcd(bch, f2, tk); 859 if (gcd->deg < f->deg) { 860 /* compute h=f/gcd(f,tk); this will modify f and q */ 861 gf_poly_div(bch, f, gcd, q); 862 /* store g and h in-place (clobbering f) */ 863 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly; 864 gf_poly_copy(*g, gcd); 865 gf_poly_copy(*h, q); 866 } 867 } 868 } 869 870 /* 871 * find roots of a polynomial, using BTZ algorithm; see the beginning of this 872 * file for details 873 */ 874 static int find_poly_roots(struct bch_control *bch, unsigned int k, 875 struct gf_poly *poly, unsigned int *roots) 876 { 877 int cnt; 878 struct gf_poly *f1, *f2; 879 880 switch (poly->deg) { 881 /* handle low degree polynomials with ad hoc techniques */ 882 case 1: 883 cnt = find_poly_deg1_roots(bch, poly, roots); 884 break; 885 case 2: 886 cnt = find_poly_deg2_roots(bch, poly, roots); 887 break; 888 case 3: 889 cnt = find_poly_deg3_roots(bch, poly, roots); 890 break; 891 case 4: 892 cnt = find_poly_deg4_roots(bch, poly, roots); 893 break; 894 default: 895 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */ 896 cnt = 0; 897 if (poly->deg && (k <= GF_M(bch))) { 898 factor_polynomial(bch, k, poly, &f1, &f2); 899 if (f1) 900 cnt += find_poly_roots(bch, k+1, f1, roots); 901 if (f2) 902 cnt += find_poly_roots(bch, k+1, f2, roots+cnt); 903 } 904 break; 905 } 906 return cnt; 907 } 908 909 #if defined(USE_CHIEN_SEARCH) 910 /* 911 * exhaustive root search (Chien) implementation - not used, included only for 912 * reference/comparison tests 913 */ 914 static int chien_search(struct bch_control *bch, unsigned int len, 915 struct gf_poly *p, unsigned int *roots) 916 { 917 int m; 918 unsigned int i, j, syn, syn0, count = 0; 919 const unsigned int k = 8*len+bch->ecc_bits; 920 921 /* use a log-based representation of polynomial */ 922 gf_poly_logrep(bch, p, bch->cache); 923 bch->cache[p->deg] = 0; 924 syn0 = gf_div(bch, p->c[0], p->c[p->deg]); 925 926 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) { 927 /* compute elp(a^i) */ 928 for (j = 1, syn = syn0; j <= p->deg; j++) { 929 m = bch->cache[j]; 930 if (m >= 0) 931 syn ^= a_pow(bch, m+j*i); 932 } 933 if (syn == 0) { 934 roots[count++] = GF_N(bch)-i; 935 if (count == p->deg) 936 break; 937 } 938 } 939 return (count == p->deg) ? count : 0; 940 } 941 #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc) 942 #endif /* USE_CHIEN_SEARCH */ 943 944 /** 945 * decode_bch - decode received codeword and find bit error locations 946 * @bch: BCH control structure 947 * @data: received data, ignored if @calc_ecc is provided 948 * @len: data length in bytes, must always be provided 949 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc 950 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data 951 * @syn: hw computed syndrome data (if NULL, syndrome is calculated) 952 * @errloc: output array of error locations 953 * 954 * Returns: 955 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if 956 * invalid parameters were provided 957 * 958 * Depending on the available hw BCH support and the need to compute @calc_ecc 959 * separately (using encode_bch()), this function should be called with one of 960 * the following parameter configurations - 961 * 962 * by providing @data and @recv_ecc only: 963 * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc) 964 * 965 * by providing @recv_ecc and @calc_ecc: 966 * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc) 967 * 968 * by providing ecc = recv_ecc XOR calc_ecc: 969 * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc) 970 * 971 * by providing syndrome results @syn: 972 * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc) 973 * 974 * Once decode_bch() has successfully returned with a positive value, error 975 * locations returned in array @errloc should be interpreted as follows - 976 * 977 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for 978 * data correction) 979 * 980 * if (errloc[n] < 8*len), then n-th error is located in data and can be 981 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8); 982 * 983 * Note that this function does not perform any data correction by itself, it 984 * merely indicates error locations. 985 */ 986 int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len, 987 const uint8_t *recv_ecc, const uint8_t *calc_ecc, 988 const unsigned int *syn, unsigned int *errloc) 989 { 990 const unsigned int ecc_words = BCH_ECC_WORDS(bch); 991 unsigned int nbits; 992 int i, err, nroots; 993 uint32_t sum; 994 995 /* sanity check: make sure data length can be handled */ 996 if (8*len > (bch->n-bch->ecc_bits)) 997 return -EINVAL; 998 999 /* if caller does not provide syndromes, compute them */ 1000 if (!syn) { 1001 if (!calc_ecc) { 1002 /* compute received data ecc into an internal buffer */ 1003 if (!data || !recv_ecc) 1004 return -EINVAL; 1005 encode_bch(bch, data, len, NULL); 1006 } else { 1007 /* load provided calculated ecc */ 1008 load_ecc8(bch, bch->ecc_buf, calc_ecc); 1009 } 1010 /* load received ecc or assume it was XORed in calc_ecc */ 1011 if (recv_ecc) { 1012 load_ecc8(bch, bch->ecc_buf2, recv_ecc); 1013 /* XOR received and calculated ecc */ 1014 for (i = 0, sum = 0; i < (int)ecc_words; i++) { 1015 bch->ecc_buf[i] ^= bch->ecc_buf2[i]; 1016 sum |= bch->ecc_buf[i]; 1017 } 1018 if (!sum) 1019 /* no error found */ 1020 return 0; 1021 } 1022 compute_syndromes(bch, bch->ecc_buf, bch->syn); 1023 syn = bch->syn; 1024 } 1025 1026 err = compute_error_locator_polynomial(bch, syn); 1027 if (err > 0) { 1028 nroots = find_poly_roots(bch, 1, bch->elp, errloc); 1029 if (err != nroots) 1030 err = -1; 1031 } 1032 if (err > 0) { 1033 /* post-process raw error locations for easier correction */ 1034 nbits = (len*8)+bch->ecc_bits; 1035 for (i = 0; i < err; i++) { 1036 if (errloc[i] >= nbits) { 1037 err = -1; 1038 break; 1039 } 1040 errloc[i] = nbits-1-errloc[i]; 1041 errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7)); 1042 } 1043 } 1044 return (err >= 0) ? err : -EBADMSG; 1045 } 1046 EXPORT_SYMBOL_GPL(decode_bch); 1047 1048 /* 1049 * generate Galois field lookup tables 1050 */ 1051 static int build_gf_tables(struct bch_control *bch, unsigned int poly) 1052 { 1053 unsigned int i, x = 1; 1054 const unsigned int k = 1 << deg(poly); 1055 1056 /* primitive polynomial must be of degree m */ 1057 if (k != (1u << GF_M(bch))) 1058 return -1; 1059 1060 for (i = 0; i < GF_N(bch); i++) { 1061 bch->a_pow_tab[i] = x; 1062 bch->a_log_tab[x] = i; 1063 if (i && (x == 1)) 1064 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */ 1065 return -1; 1066 x <<= 1; 1067 if (x & k) 1068 x ^= poly; 1069 } 1070 bch->a_pow_tab[GF_N(bch)] = 1; 1071 bch->a_log_tab[0] = 0; 1072 1073 return 0; 1074 } 1075 1076 /* 1077 * compute generator polynomial remainder tables for fast encoding 1078 */ 1079 static void build_mod8_tables(struct bch_control *bch, const uint32_t *g) 1080 { 1081 int i, j, b, d; 1082 uint32_t data, hi, lo, *tab; 1083 const int l = BCH_ECC_WORDS(bch); 1084 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32); 1085 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32); 1086 1087 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab)); 1088 1089 for (i = 0; i < 256; i++) { 1090 /* p(X)=i is a small polynomial of weight <= 8 */ 1091 for (b = 0; b < 4; b++) { 1092 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */ 1093 tab = bch->mod8_tab + (b*256+i)*l; 1094 data = i << (8*b); 1095 while (data) { 1096 d = deg(data); 1097 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */ 1098 data ^= g[0] >> (31-d); 1099 for (j = 0; j < ecclen; j++) { 1100 hi = (d < 31) ? g[j] << (d+1) : 0; 1101 lo = (j+1 < plen) ? 1102 g[j+1] >> (31-d) : 0; 1103 tab[j] ^= hi|lo; 1104 } 1105 } 1106 } 1107 } 1108 } 1109 1110 /* 1111 * build a base for factoring degree 2 polynomials 1112 */ 1113 static int build_deg2_base(struct bch_control *bch) 1114 { 1115 const int m = GF_M(bch); 1116 int i, j, r; 1117 unsigned int sum, x, y, remaining, ak = 0, xi[m]; 1118 1119 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */ 1120 for (i = 0; i < m; i++) { 1121 for (j = 0, sum = 0; j < m; j++) 1122 sum ^= a_pow(bch, i*(1 << j)); 1123 1124 if (sum) { 1125 ak = bch->a_pow_tab[i]; 1126 break; 1127 } 1128 } 1129 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */ 1130 remaining = m; 1131 memset(xi, 0, sizeof(xi)); 1132 1133 for (x = 0; (x <= GF_N(bch)) && remaining; x++) { 1134 y = gf_sqr(bch, x)^x; 1135 for (i = 0; i < 2; i++) { 1136 r = a_log(bch, y); 1137 if (y && (r < m) && !xi[r]) { 1138 bch->xi_tab[r] = x; 1139 xi[r] = 1; 1140 remaining--; 1141 dbg("x%d = %x\n", r, x); 1142 break; 1143 } 1144 y ^= ak; 1145 } 1146 } 1147 /* should not happen but check anyway */ 1148 return remaining ? -1 : 0; 1149 } 1150 1151 static void *bch_alloc(size_t size, int *err) 1152 { 1153 void *ptr; 1154 1155 ptr = kmalloc(size, GFP_KERNEL); 1156 if (ptr == NULL) 1157 *err = 1; 1158 return ptr; 1159 } 1160 1161 /* 1162 * compute generator polynomial for given (m,t) parameters. 1163 */ 1164 static uint32_t *compute_generator_polynomial(struct bch_control *bch) 1165 { 1166 const unsigned int m = GF_M(bch); 1167 const unsigned int t = GF_T(bch); 1168 int n, err = 0; 1169 unsigned int i, j, nbits, r, word, *roots; 1170 struct gf_poly *g; 1171 uint32_t *genpoly; 1172 1173 g = bch_alloc(GF_POLY_SZ(m*t), &err); 1174 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err); 1175 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err); 1176 1177 if (err) { 1178 kfree(genpoly); 1179 genpoly = NULL; 1180 goto finish; 1181 } 1182 1183 /* enumerate all roots of g(X) */ 1184 memset(roots , 0, (bch->n+1)*sizeof(*roots)); 1185 for (i = 0; i < t; i++) { 1186 for (j = 0, r = 2*i+1; j < m; j++) { 1187 roots[r] = 1; 1188 r = mod_s(bch, 2*r); 1189 } 1190 } 1191 /* build generator polynomial g(X) */ 1192 g->deg = 0; 1193 g->c[0] = 1; 1194 for (i = 0; i < GF_N(bch); i++) { 1195 if (roots[i]) { 1196 /* multiply g(X) by (X+root) */ 1197 r = bch->a_pow_tab[i]; 1198 g->c[g->deg+1] = 1; 1199 for (j = g->deg; j > 0; j--) 1200 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1]; 1201 1202 g->c[0] = gf_mul(bch, g->c[0], r); 1203 g->deg++; 1204 } 1205 } 1206 /* store left-justified binary representation of g(X) */ 1207 n = g->deg+1; 1208 i = 0; 1209 1210 while (n > 0) { 1211 nbits = (n > 32) ? 32 : n; 1212 for (j = 0, word = 0; j < nbits; j++) { 1213 if (g->c[n-1-j]) 1214 word |= 1u << (31-j); 1215 } 1216 genpoly[i++] = word; 1217 n -= nbits; 1218 } 1219 bch->ecc_bits = g->deg; 1220 1221 finish: 1222 kfree(g); 1223 kfree(roots); 1224 1225 return genpoly; 1226 } 1227 1228 /** 1229 * init_bch - initialize a BCH encoder/decoder 1230 * @m: Galois field order, should be in the range 5-15 1231 * @t: maximum error correction capability, in bits 1232 * @prim_poly: user-provided primitive polynomial (or 0 to use default) 1233 * 1234 * Returns: 1235 * a newly allocated BCH control structure if successful, NULL otherwise 1236 * 1237 * This initialization can take some time, as lookup tables are built for fast 1238 * encoding/decoding; make sure not to call this function from a time critical 1239 * path. Usually, init_bch() should be called on module/driver init and 1240 * free_bch() should be called to release memory on exit. 1241 * 1242 * You may provide your own primitive polynomial of degree @m in argument 1243 * @prim_poly, or let init_bch() use its default polynomial. 1244 * 1245 * Once init_bch() has successfully returned a pointer to a newly allocated 1246 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of 1247 * the structure. 1248 */ 1249 struct bch_control *init_bch(int m, int t, unsigned int prim_poly) 1250 { 1251 int err = 0; 1252 unsigned int i, words; 1253 uint32_t *genpoly; 1254 struct bch_control *bch = NULL; 1255 1256 const int min_m = 5; 1257 const int max_m = 15; 1258 1259 /* default primitive polynomials */ 1260 static const unsigned int prim_poly_tab[] = { 1261 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b, 1262 0x402b, 0x8003, 1263 }; 1264 1265 #if defined(CONFIG_BCH_CONST_PARAMS) 1266 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) { 1267 printk(KERN_ERR "bch encoder/decoder was configured to support " 1268 "parameters m=%d, t=%d only!\n", 1269 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T); 1270 goto fail; 1271 } 1272 #endif 1273 if ((m < min_m) || (m > max_m)) 1274 /* 1275 * values of m greater than 15 are not currently supported; 1276 * supporting m > 15 would require changing table base type 1277 * (uint16_t) and a small patch in matrix transposition 1278 */ 1279 goto fail; 1280 1281 /* sanity checks */ 1282 if ((t < 1) || (m*t >= ((1 << m)-1))) 1283 /* invalid t value */ 1284 goto fail; 1285 1286 /* select a primitive polynomial for generating GF(2^m) */ 1287 if (prim_poly == 0) 1288 prim_poly = prim_poly_tab[m-min_m]; 1289 1290 bch = kzalloc(sizeof(*bch), GFP_KERNEL); 1291 if (bch == NULL) 1292 goto fail; 1293 1294 bch->m = m; 1295 bch->t = t; 1296 bch->n = (1 << m)-1; 1297 words = DIV_ROUND_UP(m*t, 32); 1298 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8); 1299 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err); 1300 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err); 1301 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err); 1302 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err); 1303 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err); 1304 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err); 1305 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err); 1306 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err); 1307 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err); 1308 1309 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) 1310 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err); 1311 1312 if (err) 1313 goto fail; 1314 1315 err = build_gf_tables(bch, prim_poly); 1316 if (err) 1317 goto fail; 1318 1319 /* use generator polynomial for computing encoding tables */ 1320 genpoly = compute_generator_polynomial(bch); 1321 if (genpoly == NULL) 1322 goto fail; 1323 1324 build_mod8_tables(bch, genpoly); 1325 kfree(genpoly); 1326 1327 err = build_deg2_base(bch); 1328 if (err) 1329 goto fail; 1330 1331 return bch; 1332 1333 fail: 1334 free_bch(bch); 1335 return NULL; 1336 } 1337 EXPORT_SYMBOL_GPL(init_bch); 1338 1339 /** 1340 * free_bch - free the BCH control structure 1341 * @bch: BCH control structure to release 1342 */ 1343 void free_bch(struct bch_control *bch) 1344 { 1345 unsigned int i; 1346 1347 if (bch) { 1348 kfree(bch->a_pow_tab); 1349 kfree(bch->a_log_tab); 1350 kfree(bch->mod8_tab); 1351 kfree(bch->ecc_buf); 1352 kfree(bch->ecc_buf2); 1353 kfree(bch->xi_tab); 1354 kfree(bch->syn); 1355 kfree(bch->cache); 1356 kfree(bch->elp); 1357 1358 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) 1359 kfree(bch->poly_2t[i]); 1360 1361 kfree(bch); 1362 } 1363 } 1364 EXPORT_SYMBOL_GPL(free_bch); 1365 1366 MODULE_LICENSE("GPL"); 1367 MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>"); 1368 MODULE_DESCRIPTION("Binary BCH encoder/decoder"); 1369