1 /* 2 * Generic binary BCH encoding/decoding library 3 * 4 * SPDX-License-Identifier: GPL-2.0 5 * 6 * Copyright © 2011 Parrot S.A. 7 * 8 * Author: Ivan Djelic <ivan.djelic@parrot.com> 9 * 10 * Description: 11 * 12 * This library provides runtime configurable encoding/decoding of binary 13 * Bose-Chaudhuri-Hocquenghem (BCH) codes. 14 * 15 * Call init_bch to get a pointer to a newly allocated bch_control structure for 16 * the given m (Galois field order), t (error correction capability) and 17 * (optional) primitive polynomial parameters. 18 * 19 * Call encode_bch to compute and store ecc parity bytes to a given buffer. 20 * Call decode_bch to detect and locate errors in received data. 21 * 22 * On systems supporting hw BCH features, intermediate results may be provided 23 * to decode_bch in order to skip certain steps. See decode_bch() documentation 24 * for details. 25 * 26 * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of 27 * parameters m and t; thus allowing extra compiler optimizations and providing 28 * better (up to 2x) encoding performance. Using this option makes sense when 29 * (m,t) are fixed and known in advance, e.g. when using BCH error correction 30 * on a particular NAND flash device. 31 * 32 * Algorithmic details: 33 * 34 * Encoding is performed by processing 32 input bits in parallel, using 4 35 * remainder lookup tables. 36 * 37 * The final stage of decoding involves the following internal steps: 38 * a. Syndrome computation 39 * b. Error locator polynomial computation using Berlekamp-Massey algorithm 40 * c. Error locator root finding (by far the most expensive step) 41 * 42 * In this implementation, step c is not performed using the usual Chien search. 43 * Instead, an alternative approach described in [1] is used. It consists in 44 * factoring the error locator polynomial using the Berlekamp Trace algorithm 45 * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial 46 * solving techniques [2] are used. The resulting algorithm, called BTZ, yields 47 * much better performance than Chien search for usual (m,t) values (typically 48 * m >= 13, t < 32, see [1]). 49 * 50 * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields 51 * of characteristic 2, in: Western European Workshop on Research in Cryptology 52 * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear. 53 * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over 54 * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996. 55 */ 56 57 #ifndef USE_HOSTCC 58 #include <common.h> 59 #include <ubi_uboot.h> 60 61 #include <linux/bitops.h> 62 #else 63 #include <errno.h> 64 #if defined(__FreeBSD__) 65 #include <sys/endian.h> 66 #else 67 #include <endian.h> 68 #endif 69 #include <stdint.h> 70 #include <stdlib.h> 71 #include <string.h> 72 73 #undef cpu_to_be32 74 #define cpu_to_be32 htobe32 75 #define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d)) 76 #define kmalloc(size, flags) malloc(size) 77 #define kzalloc(size, flags) calloc(1, size) 78 #define kfree free 79 #define ARRAY_SIZE(arr) (sizeof(arr) / sizeof((arr)[0])) 80 #endif 81 82 #include <asm/byteorder.h> 83 #include <linux/bch.h> 84 85 #if defined(CONFIG_BCH_CONST_PARAMS) 86 #define GF_M(_p) (CONFIG_BCH_CONST_M) 87 #define GF_T(_p) (CONFIG_BCH_CONST_T) 88 #define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1) 89 #else 90 #define GF_M(_p) ((_p)->m) 91 #define GF_T(_p) ((_p)->t) 92 #define GF_N(_p) ((_p)->n) 93 #endif 94 95 #define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32) 96 #define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8) 97 98 #ifndef dbg 99 #define dbg(_fmt, args...) do {} while (0) 100 #endif 101 102 /* 103 * represent a polynomial over GF(2^m) 104 */ 105 struct gf_poly { 106 unsigned int deg; /* polynomial degree */ 107 unsigned int c[0]; /* polynomial terms */ 108 }; 109 110 /* given its degree, compute a polynomial size in bytes */ 111 #define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int)) 112 113 /* polynomial of degree 1 */ 114 struct gf_poly_deg1 { 115 struct gf_poly poly; 116 unsigned int c[2]; 117 }; 118 119 #ifdef USE_HOSTCC 120 #if !defined(__DragonFly__) && !defined(__FreeBSD__) 121 static int fls(int x) 122 { 123 int r = 32; 124 125 if (!x) 126 return 0; 127 if (!(x & 0xffff0000u)) { 128 x <<= 16; 129 r -= 16; 130 } 131 if (!(x & 0xff000000u)) { 132 x <<= 8; 133 r -= 8; 134 } 135 if (!(x & 0xf0000000u)) { 136 x <<= 4; 137 r -= 4; 138 } 139 if (!(x & 0xc0000000u)) { 140 x <<= 2; 141 r -= 2; 142 } 143 if (!(x & 0x80000000u)) { 144 x <<= 1; 145 r -= 1; 146 } 147 return r; 148 } 149 #endif 150 #endif 151 152 /* 153 * same as encode_bch(), but process input data one byte at a time 154 */ 155 static void encode_bch_unaligned(struct bch_control *bch, 156 const unsigned char *data, unsigned int len, 157 uint32_t *ecc) 158 { 159 int i; 160 const uint32_t *p; 161 const int l = BCH_ECC_WORDS(bch)-1; 162 163 while (len--) { 164 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff); 165 166 for (i = 0; i < l; i++) 167 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++); 168 169 ecc[l] = (ecc[l] << 8)^(*p); 170 } 171 } 172 173 /* 174 * convert ecc bytes to aligned, zero-padded 32-bit ecc words 175 */ 176 static void load_ecc8(struct bch_control *bch, uint32_t *dst, 177 const uint8_t *src) 178 { 179 uint8_t pad[4] = {0, 0, 0, 0}; 180 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; 181 182 for (i = 0; i < nwords; i++, src += 4) 183 dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3]; 184 185 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords); 186 dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3]; 187 } 188 189 /* 190 * convert 32-bit ecc words to ecc bytes 191 */ 192 static void store_ecc8(struct bch_control *bch, uint8_t *dst, 193 const uint32_t *src) 194 { 195 uint8_t pad[4]; 196 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; 197 198 for (i = 0; i < nwords; i++) { 199 *dst++ = (src[i] >> 24); 200 *dst++ = (src[i] >> 16) & 0xff; 201 *dst++ = (src[i] >> 8) & 0xff; 202 *dst++ = (src[i] >> 0) & 0xff; 203 } 204 pad[0] = (src[nwords] >> 24); 205 pad[1] = (src[nwords] >> 16) & 0xff; 206 pad[2] = (src[nwords] >> 8) & 0xff; 207 pad[3] = (src[nwords] >> 0) & 0xff; 208 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords); 209 } 210 211 /** 212 * encode_bch - calculate BCH ecc parity of data 213 * @bch: BCH control structure 214 * @data: data to encode 215 * @len: data length in bytes 216 * @ecc: ecc parity data, must be initialized by caller 217 * 218 * The @ecc parity array is used both as input and output parameter, in order to 219 * allow incremental computations. It should be of the size indicated by member 220 * @ecc_bytes of @bch, and should be initialized to 0 before the first call. 221 * 222 * The exact number of computed ecc parity bits is given by member @ecc_bits of 223 * @bch; it may be less than m*t for large values of t. 224 */ 225 void encode_bch(struct bch_control *bch, const uint8_t *data, 226 unsigned int len, uint8_t *ecc) 227 { 228 const unsigned int l = BCH_ECC_WORDS(bch)-1; 229 unsigned int i, mlen; 230 unsigned long m; 231 uint32_t w, r[l+1]; 232 const uint32_t * const tab0 = bch->mod8_tab; 233 const uint32_t * const tab1 = tab0 + 256*(l+1); 234 const uint32_t * const tab2 = tab1 + 256*(l+1); 235 const uint32_t * const tab3 = tab2 + 256*(l+1); 236 const uint32_t *pdata, *p0, *p1, *p2, *p3; 237 238 if (ecc) { 239 /* load ecc parity bytes into internal 32-bit buffer */ 240 load_ecc8(bch, bch->ecc_buf, ecc); 241 } else { 242 memset(bch->ecc_buf, 0, sizeof(r)); 243 } 244 245 /* process first unaligned data bytes */ 246 m = ((unsigned long)data) & 3; 247 if (m) { 248 mlen = (len < (4-m)) ? len : 4-m; 249 encode_bch_unaligned(bch, data, mlen, bch->ecc_buf); 250 data += mlen; 251 len -= mlen; 252 } 253 254 /* process 32-bit aligned data words */ 255 pdata = (uint32_t *)data; 256 mlen = len/4; 257 data += 4*mlen; 258 len -= 4*mlen; 259 memcpy(r, bch->ecc_buf, sizeof(r)); 260 261 /* 262 * split each 32-bit word into 4 polynomials of weight 8 as follows: 263 * 264 * 31 ...24 23 ...16 15 ... 8 7 ... 0 265 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt 266 * tttttttt mod g = r0 (precomputed) 267 * zzzzzzzz 00000000 mod g = r1 (precomputed) 268 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed) 269 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed) 270 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3 271 */ 272 while (mlen--) { 273 /* input data is read in big-endian format */ 274 w = r[0]^cpu_to_be32(*pdata++); 275 p0 = tab0 + (l+1)*((w >> 0) & 0xff); 276 p1 = tab1 + (l+1)*((w >> 8) & 0xff); 277 p2 = tab2 + (l+1)*((w >> 16) & 0xff); 278 p3 = tab3 + (l+1)*((w >> 24) & 0xff); 279 280 for (i = 0; i < l; i++) 281 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i]; 282 283 r[l] = p0[l]^p1[l]^p2[l]^p3[l]; 284 } 285 memcpy(bch->ecc_buf, r, sizeof(r)); 286 287 /* process last unaligned bytes */ 288 if (len) 289 encode_bch_unaligned(bch, data, len, bch->ecc_buf); 290 291 /* store ecc parity bytes into original parity buffer */ 292 if (ecc) 293 store_ecc8(bch, ecc, bch->ecc_buf); 294 } 295 296 static inline int modulo(struct bch_control *bch, unsigned int v) 297 { 298 const unsigned int n = GF_N(bch); 299 while (v >= n) { 300 v -= n; 301 v = (v & n) + (v >> GF_M(bch)); 302 } 303 return v; 304 } 305 306 /* 307 * shorter and faster modulo function, only works when v < 2N. 308 */ 309 static inline int mod_s(struct bch_control *bch, unsigned int v) 310 { 311 const unsigned int n = GF_N(bch); 312 return (v < n) ? v : v-n; 313 } 314 315 static inline int deg(unsigned int poly) 316 { 317 /* polynomial degree is the most-significant bit index */ 318 return fls(poly)-1; 319 } 320 321 static inline int parity(unsigned int x) 322 { 323 /* 324 * public domain code snippet, lifted from 325 * http://www-graphics.stanford.edu/~seander/bithacks.html 326 */ 327 x ^= x >> 1; 328 x ^= x >> 2; 329 x = (x & 0x11111111U) * 0x11111111U; 330 return (x >> 28) & 1; 331 } 332 333 /* Galois field basic operations: multiply, divide, inverse, etc. */ 334 335 static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a, 336 unsigned int b) 337 { 338 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ 339 bch->a_log_tab[b])] : 0; 340 } 341 342 static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a) 343 { 344 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0; 345 } 346 347 static inline unsigned int gf_div(struct bch_control *bch, unsigned int a, 348 unsigned int b) 349 { 350 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ 351 GF_N(bch)-bch->a_log_tab[b])] : 0; 352 } 353 354 static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a) 355 { 356 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]]; 357 } 358 359 static inline unsigned int a_pow(struct bch_control *bch, int i) 360 { 361 return bch->a_pow_tab[modulo(bch, i)]; 362 } 363 364 static inline int a_log(struct bch_control *bch, unsigned int x) 365 { 366 return bch->a_log_tab[x]; 367 } 368 369 static inline int a_ilog(struct bch_control *bch, unsigned int x) 370 { 371 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]); 372 } 373 374 /* 375 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t 376 */ 377 static void compute_syndromes(struct bch_control *bch, uint32_t *ecc, 378 unsigned int *syn) 379 { 380 int i, j, s; 381 unsigned int m; 382 uint32_t poly; 383 const int t = GF_T(bch); 384 385 s = bch->ecc_bits; 386 387 /* make sure extra bits in last ecc word are cleared */ 388 m = ((unsigned int)s) & 31; 389 if (m) 390 ecc[s/32] &= ~((1u << (32-m))-1); 391 memset(syn, 0, 2*t*sizeof(*syn)); 392 393 /* compute v(a^j) for j=1 .. 2t-1 */ 394 do { 395 poly = *ecc++; 396 s -= 32; 397 while (poly) { 398 i = deg(poly); 399 for (j = 0; j < 2*t; j += 2) 400 syn[j] ^= a_pow(bch, (j+1)*(i+s)); 401 402 poly ^= (1 << i); 403 } 404 } while (s > 0); 405 406 /* v(a^(2j)) = v(a^j)^2 */ 407 for (j = 0; j < t; j++) 408 syn[2*j+1] = gf_sqr(bch, syn[j]); 409 } 410 411 static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src) 412 { 413 memcpy(dst, src, GF_POLY_SZ(src->deg)); 414 } 415 416 static int compute_error_locator_polynomial(struct bch_control *bch, 417 const unsigned int *syn) 418 { 419 const unsigned int t = GF_T(bch); 420 const unsigned int n = GF_N(bch); 421 unsigned int i, j, tmp, l, pd = 1, d = syn[0]; 422 struct gf_poly *elp = bch->elp; 423 struct gf_poly *pelp = bch->poly_2t[0]; 424 struct gf_poly *elp_copy = bch->poly_2t[1]; 425 int k, pp = -1; 426 427 memset(pelp, 0, GF_POLY_SZ(2*t)); 428 memset(elp, 0, GF_POLY_SZ(2*t)); 429 430 pelp->deg = 0; 431 pelp->c[0] = 1; 432 elp->deg = 0; 433 elp->c[0] = 1; 434 435 /* use simplified binary Berlekamp-Massey algorithm */ 436 for (i = 0; (i < t) && (elp->deg <= t); i++) { 437 if (d) { 438 k = 2*i-pp; 439 gf_poly_copy(elp_copy, elp); 440 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */ 441 tmp = a_log(bch, d)+n-a_log(bch, pd); 442 for (j = 0; j <= pelp->deg; j++) { 443 if (pelp->c[j]) { 444 l = a_log(bch, pelp->c[j]); 445 elp->c[j+k] ^= a_pow(bch, tmp+l); 446 } 447 } 448 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */ 449 tmp = pelp->deg+k; 450 if (tmp > elp->deg) { 451 elp->deg = tmp; 452 gf_poly_copy(pelp, elp_copy); 453 pd = d; 454 pp = 2*i; 455 } 456 } 457 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */ 458 if (i < t-1) { 459 d = syn[2*i+2]; 460 for (j = 1; j <= elp->deg; j++) 461 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]); 462 } 463 } 464 dbg("elp=%s\n", gf_poly_str(elp)); 465 return (elp->deg > t) ? -1 : (int)elp->deg; 466 } 467 468 /* 469 * solve a m x m linear system in GF(2) with an expected number of solutions, 470 * and return the number of found solutions 471 */ 472 static int solve_linear_system(struct bch_control *bch, unsigned int *rows, 473 unsigned int *sol, int nsol) 474 { 475 const int m = GF_M(bch); 476 unsigned int tmp, mask; 477 int rem, c, r, p, k, param[m]; 478 479 k = 0; 480 mask = 1 << m; 481 482 /* Gaussian elimination */ 483 for (c = 0; c < m; c++) { 484 rem = 0; 485 p = c-k; 486 /* find suitable row for elimination */ 487 for (r = p; r < m; r++) { 488 if (rows[r] & mask) { 489 if (r != p) { 490 tmp = rows[r]; 491 rows[r] = rows[p]; 492 rows[p] = tmp; 493 } 494 rem = r+1; 495 break; 496 } 497 } 498 if (rem) { 499 /* perform elimination on remaining rows */ 500 tmp = rows[p]; 501 for (r = rem; r < m; r++) { 502 if (rows[r] & mask) 503 rows[r] ^= tmp; 504 } 505 } else { 506 /* elimination not needed, store defective row index */ 507 param[k++] = c; 508 } 509 mask >>= 1; 510 } 511 /* rewrite system, inserting fake parameter rows */ 512 if (k > 0) { 513 p = k; 514 for (r = m-1; r >= 0; r--) { 515 if ((r > m-1-k) && rows[r]) 516 /* system has no solution */ 517 return 0; 518 519 rows[r] = (p && (r == param[p-1])) ? 520 p--, 1u << (m-r) : rows[r-p]; 521 } 522 } 523 524 if (nsol != (1 << k)) 525 /* unexpected number of solutions */ 526 return 0; 527 528 for (p = 0; p < nsol; p++) { 529 /* set parameters for p-th solution */ 530 for (c = 0; c < k; c++) 531 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1); 532 533 /* compute unique solution */ 534 tmp = 0; 535 for (r = m-1; r >= 0; r--) { 536 mask = rows[r] & (tmp|1); 537 tmp |= parity(mask) << (m-r); 538 } 539 sol[p] = tmp >> 1; 540 } 541 return nsol; 542 } 543 544 /* 545 * this function builds and solves a linear system for finding roots of a degree 546 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m). 547 */ 548 static int find_affine4_roots(struct bch_control *bch, unsigned int a, 549 unsigned int b, unsigned int c, 550 unsigned int *roots) 551 { 552 int i, j, k; 553 const int m = GF_M(bch); 554 unsigned int mask = 0xff, t, rows[16] = {0,}; 555 556 j = a_log(bch, b); 557 k = a_log(bch, a); 558 rows[0] = c; 559 560 /* buid linear system to solve X^4+aX^2+bX+c = 0 */ 561 for (i = 0; i < m; i++) { 562 rows[i+1] = bch->a_pow_tab[4*i]^ 563 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^ 564 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0); 565 j++; 566 k += 2; 567 } 568 /* 569 * transpose 16x16 matrix before passing it to linear solver 570 * warning: this code assumes m < 16 571 */ 572 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) { 573 for (k = 0; k < 16; k = (k+j+1) & ~j) { 574 t = ((rows[k] >> j)^rows[k+j]) & mask; 575 rows[k] ^= (t << j); 576 rows[k+j] ^= t; 577 } 578 } 579 return solve_linear_system(bch, rows, roots, 4); 580 } 581 582 /* 583 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r)) 584 */ 585 static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly, 586 unsigned int *roots) 587 { 588 int n = 0; 589 590 if (poly->c[0]) 591 /* poly[X] = bX+c with c!=0, root=c/b */ 592 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+ 593 bch->a_log_tab[poly->c[1]]); 594 return n; 595 } 596 597 /* 598 * compute roots of a degree 2 polynomial over GF(2^m) 599 */ 600 static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly, 601 unsigned int *roots) 602 { 603 int n = 0, i, l0, l1, l2; 604 unsigned int u, v, r; 605 606 if (poly->c[0] && poly->c[1]) { 607 608 l0 = bch->a_log_tab[poly->c[0]]; 609 l1 = bch->a_log_tab[poly->c[1]]; 610 l2 = bch->a_log_tab[poly->c[2]]; 611 612 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */ 613 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1)); 614 /* 615 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi): 616 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) = 617 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u) 618 * i.e. r and r+1 are roots iff Tr(u)=0 619 */ 620 r = 0; 621 v = u; 622 while (v) { 623 i = deg(v); 624 r ^= bch->xi_tab[i]; 625 v ^= (1 << i); 626 } 627 /* verify root */ 628 if ((gf_sqr(bch, r)^r) == u) { 629 /* reverse z=a/bX transformation and compute log(1/r) */ 630 roots[n++] = modulo(bch, 2*GF_N(bch)-l1- 631 bch->a_log_tab[r]+l2); 632 roots[n++] = modulo(bch, 2*GF_N(bch)-l1- 633 bch->a_log_tab[r^1]+l2); 634 } 635 } 636 return n; 637 } 638 639 /* 640 * compute roots of a degree 3 polynomial over GF(2^m) 641 */ 642 static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly, 643 unsigned int *roots) 644 { 645 int i, n = 0; 646 unsigned int a, b, c, a2, b2, c2, e3, tmp[4]; 647 648 if (poly->c[0]) { 649 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */ 650 e3 = poly->c[3]; 651 c2 = gf_div(bch, poly->c[0], e3); 652 b2 = gf_div(bch, poly->c[1], e3); 653 a2 = gf_div(bch, poly->c[2], e3); 654 655 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */ 656 c = gf_mul(bch, a2, c2); /* c = a2c2 */ 657 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */ 658 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */ 659 660 /* find the 4 roots of this affine polynomial */ 661 if (find_affine4_roots(bch, a, b, c, tmp) == 4) { 662 /* remove a2 from final list of roots */ 663 for (i = 0; i < 4; i++) { 664 if (tmp[i] != a2) 665 roots[n++] = a_ilog(bch, tmp[i]); 666 } 667 } 668 } 669 return n; 670 } 671 672 /* 673 * compute roots of a degree 4 polynomial over GF(2^m) 674 */ 675 static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly, 676 unsigned int *roots) 677 { 678 int i, l, n = 0; 679 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4; 680 681 if (poly->c[0] == 0) 682 return 0; 683 684 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */ 685 e4 = poly->c[4]; 686 d = gf_div(bch, poly->c[0], e4); 687 c = gf_div(bch, poly->c[1], e4); 688 b = gf_div(bch, poly->c[2], e4); 689 a = gf_div(bch, poly->c[3], e4); 690 691 /* use Y=1/X transformation to get an affine polynomial */ 692 if (a) { 693 /* first, eliminate cX by using z=X+e with ae^2+c=0 */ 694 if (c) { 695 /* compute e such that e^2 = c/a */ 696 f = gf_div(bch, c, a); 697 l = a_log(bch, f); 698 l += (l & 1) ? GF_N(bch) : 0; 699 e = a_pow(bch, l/2); 700 /* 701 * use transformation z=X+e: 702 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d 703 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d 704 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d 705 * z^4 + az^3 + b'z^2 + d' 706 */ 707 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d; 708 b = gf_mul(bch, a, e)^b; 709 } 710 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */ 711 if (d == 0) 712 /* assume all roots have multiplicity 1 */ 713 return 0; 714 715 c2 = gf_inv(bch, d); 716 b2 = gf_div(bch, a, d); 717 a2 = gf_div(bch, b, d); 718 } else { 719 /* polynomial is already affine */ 720 c2 = d; 721 b2 = c; 722 a2 = b; 723 } 724 /* find the 4 roots of this affine polynomial */ 725 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) { 726 for (i = 0; i < 4; i++) { 727 /* post-process roots (reverse transformations) */ 728 f = a ? gf_inv(bch, roots[i]) : roots[i]; 729 roots[i] = a_ilog(bch, f^e); 730 } 731 n = 4; 732 } 733 return n; 734 } 735 736 /* 737 * build monic, log-based representation of a polynomial 738 */ 739 static void gf_poly_logrep(struct bch_control *bch, 740 const struct gf_poly *a, int *rep) 741 { 742 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]); 743 744 /* represent 0 values with -1; warning, rep[d] is not set to 1 */ 745 for (i = 0; i < d; i++) 746 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1; 747 } 748 749 /* 750 * compute polynomial Euclidean division remainder in GF(2^m)[X] 751 */ 752 static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a, 753 const struct gf_poly *b, int *rep) 754 { 755 int la, p, m; 756 unsigned int i, j, *c = a->c; 757 const unsigned int d = b->deg; 758 759 if (a->deg < d) 760 return; 761 762 /* reuse or compute log representation of denominator */ 763 if (!rep) { 764 rep = bch->cache; 765 gf_poly_logrep(bch, b, rep); 766 } 767 768 for (j = a->deg; j >= d; j--) { 769 if (c[j]) { 770 la = a_log(bch, c[j]); 771 p = j-d; 772 for (i = 0; i < d; i++, p++) { 773 m = rep[i]; 774 if (m >= 0) 775 c[p] ^= bch->a_pow_tab[mod_s(bch, 776 m+la)]; 777 } 778 } 779 } 780 a->deg = d-1; 781 while (!c[a->deg] && a->deg) 782 a->deg--; 783 } 784 785 /* 786 * compute polynomial Euclidean division quotient in GF(2^m)[X] 787 */ 788 static void gf_poly_div(struct bch_control *bch, struct gf_poly *a, 789 const struct gf_poly *b, struct gf_poly *q) 790 { 791 if (a->deg >= b->deg) { 792 q->deg = a->deg-b->deg; 793 /* compute a mod b (modifies a) */ 794 gf_poly_mod(bch, a, b, NULL); 795 /* quotient is stored in upper part of polynomial a */ 796 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int)); 797 } else { 798 q->deg = 0; 799 q->c[0] = 0; 800 } 801 } 802 803 /* 804 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X] 805 */ 806 static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a, 807 struct gf_poly *b) 808 { 809 struct gf_poly *tmp; 810 811 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b)); 812 813 if (a->deg < b->deg) { 814 tmp = b; 815 b = a; 816 a = tmp; 817 } 818 819 while (b->deg > 0) { 820 gf_poly_mod(bch, a, b, NULL); 821 tmp = b; 822 b = a; 823 a = tmp; 824 } 825 826 dbg("%s\n", gf_poly_str(a)); 827 828 return a; 829 } 830 831 /* 832 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f 833 * This is used in Berlekamp Trace algorithm for splitting polynomials 834 */ 835 static void compute_trace_bk_mod(struct bch_control *bch, int k, 836 const struct gf_poly *f, struct gf_poly *z, 837 struct gf_poly *out) 838 { 839 const int m = GF_M(bch); 840 int i, j; 841 842 /* z contains z^2j mod f */ 843 z->deg = 1; 844 z->c[0] = 0; 845 z->c[1] = bch->a_pow_tab[k]; 846 847 out->deg = 0; 848 memset(out, 0, GF_POLY_SZ(f->deg)); 849 850 /* compute f log representation only once */ 851 gf_poly_logrep(bch, f, bch->cache); 852 853 for (i = 0; i < m; i++) { 854 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */ 855 for (j = z->deg; j >= 0; j--) { 856 out->c[j] ^= z->c[j]; 857 z->c[2*j] = gf_sqr(bch, z->c[j]); 858 z->c[2*j+1] = 0; 859 } 860 if (z->deg > out->deg) 861 out->deg = z->deg; 862 863 if (i < m-1) { 864 z->deg *= 2; 865 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */ 866 gf_poly_mod(bch, z, f, bch->cache); 867 } 868 } 869 while (!out->c[out->deg] && out->deg) 870 out->deg--; 871 872 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out)); 873 } 874 875 /* 876 * factor a polynomial using Berlekamp Trace algorithm (BTA) 877 */ 878 static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f, 879 struct gf_poly **g, struct gf_poly **h) 880 { 881 struct gf_poly *f2 = bch->poly_2t[0]; 882 struct gf_poly *q = bch->poly_2t[1]; 883 struct gf_poly *tk = bch->poly_2t[2]; 884 struct gf_poly *z = bch->poly_2t[3]; 885 struct gf_poly *gcd; 886 887 dbg("factoring %s...\n", gf_poly_str(f)); 888 889 *g = f; 890 *h = NULL; 891 892 /* tk = Tr(a^k.X) mod f */ 893 compute_trace_bk_mod(bch, k, f, z, tk); 894 895 if (tk->deg > 0) { 896 /* compute g = gcd(f, tk) (destructive operation) */ 897 gf_poly_copy(f2, f); 898 gcd = gf_poly_gcd(bch, f2, tk); 899 if (gcd->deg < f->deg) { 900 /* compute h=f/gcd(f,tk); this will modify f and q */ 901 gf_poly_div(bch, f, gcd, q); 902 /* store g and h in-place (clobbering f) */ 903 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly; 904 gf_poly_copy(*g, gcd); 905 gf_poly_copy(*h, q); 906 } 907 } 908 } 909 910 /* 911 * find roots of a polynomial, using BTZ algorithm; see the beginning of this 912 * file for details 913 */ 914 static int find_poly_roots(struct bch_control *bch, unsigned int k, 915 struct gf_poly *poly, unsigned int *roots) 916 { 917 int cnt; 918 struct gf_poly *f1, *f2; 919 920 switch (poly->deg) { 921 /* handle low degree polynomials with ad hoc techniques */ 922 case 1: 923 cnt = find_poly_deg1_roots(bch, poly, roots); 924 break; 925 case 2: 926 cnt = find_poly_deg2_roots(bch, poly, roots); 927 break; 928 case 3: 929 cnt = find_poly_deg3_roots(bch, poly, roots); 930 break; 931 case 4: 932 cnt = find_poly_deg4_roots(bch, poly, roots); 933 break; 934 default: 935 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */ 936 cnt = 0; 937 if (poly->deg && (k <= GF_M(bch))) { 938 factor_polynomial(bch, k, poly, &f1, &f2); 939 if (f1) 940 cnt += find_poly_roots(bch, k+1, f1, roots); 941 if (f2) 942 cnt += find_poly_roots(bch, k+1, f2, roots+cnt); 943 } 944 break; 945 } 946 return cnt; 947 } 948 949 #if defined(USE_CHIEN_SEARCH) 950 /* 951 * exhaustive root search (Chien) implementation - not used, included only for 952 * reference/comparison tests 953 */ 954 static int chien_search(struct bch_control *bch, unsigned int len, 955 struct gf_poly *p, unsigned int *roots) 956 { 957 int m; 958 unsigned int i, j, syn, syn0, count = 0; 959 const unsigned int k = 8*len+bch->ecc_bits; 960 961 /* use a log-based representation of polynomial */ 962 gf_poly_logrep(bch, p, bch->cache); 963 bch->cache[p->deg] = 0; 964 syn0 = gf_div(bch, p->c[0], p->c[p->deg]); 965 966 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) { 967 /* compute elp(a^i) */ 968 for (j = 1, syn = syn0; j <= p->deg; j++) { 969 m = bch->cache[j]; 970 if (m >= 0) 971 syn ^= a_pow(bch, m+j*i); 972 } 973 if (syn == 0) { 974 roots[count++] = GF_N(bch)-i; 975 if (count == p->deg) 976 break; 977 } 978 } 979 return (count == p->deg) ? count : 0; 980 } 981 #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc) 982 #endif /* USE_CHIEN_SEARCH */ 983 984 /** 985 * decode_bch - decode received codeword and find bit error locations 986 * @bch: BCH control structure 987 * @data: received data, ignored if @calc_ecc is provided 988 * @len: data length in bytes, must always be provided 989 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc 990 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data 991 * @syn: hw computed syndrome data (if NULL, syndrome is calculated) 992 * @errloc: output array of error locations 993 * 994 * Returns: 995 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if 996 * invalid parameters were provided 997 * 998 * Depending on the available hw BCH support and the need to compute @calc_ecc 999 * separately (using encode_bch()), this function should be called with one of 1000 * the following parameter configurations - 1001 * 1002 * by providing @data and @recv_ecc only: 1003 * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc) 1004 * 1005 * by providing @recv_ecc and @calc_ecc: 1006 * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc) 1007 * 1008 * by providing ecc = recv_ecc XOR calc_ecc: 1009 * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc) 1010 * 1011 * by providing syndrome results @syn: 1012 * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc) 1013 * 1014 * Once decode_bch() has successfully returned with a positive value, error 1015 * locations returned in array @errloc should be interpreted as follows - 1016 * 1017 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for 1018 * data correction) 1019 * 1020 * if (errloc[n] < 8*len), then n-th error is located in data and can be 1021 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8); 1022 * 1023 * Note that this function does not perform any data correction by itself, it 1024 * merely indicates error locations. 1025 */ 1026 int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len, 1027 const uint8_t *recv_ecc, const uint8_t *calc_ecc, 1028 const unsigned int *syn, unsigned int *errloc) 1029 { 1030 const unsigned int ecc_words = BCH_ECC_WORDS(bch); 1031 unsigned int nbits; 1032 int i, err, nroots; 1033 uint32_t sum; 1034 1035 /* sanity check: make sure data length can be handled */ 1036 if (8*len > (bch->n-bch->ecc_bits)) 1037 return -EINVAL; 1038 1039 /* if caller does not provide syndromes, compute them */ 1040 if (!syn) { 1041 if (!calc_ecc) { 1042 /* compute received data ecc into an internal buffer */ 1043 if (!data || !recv_ecc) 1044 return -EINVAL; 1045 encode_bch(bch, data, len, NULL); 1046 } else { 1047 /* load provided calculated ecc */ 1048 load_ecc8(bch, bch->ecc_buf, calc_ecc); 1049 } 1050 /* load received ecc or assume it was XORed in calc_ecc */ 1051 if (recv_ecc) { 1052 load_ecc8(bch, bch->ecc_buf2, recv_ecc); 1053 /* XOR received and calculated ecc */ 1054 for (i = 0, sum = 0; i < (int)ecc_words; i++) { 1055 bch->ecc_buf[i] ^= bch->ecc_buf2[i]; 1056 sum |= bch->ecc_buf[i]; 1057 } 1058 if (!sum) 1059 /* no error found */ 1060 return 0; 1061 } 1062 compute_syndromes(bch, bch->ecc_buf, bch->syn); 1063 syn = bch->syn; 1064 } 1065 1066 err = compute_error_locator_polynomial(bch, syn); 1067 if (err > 0) { 1068 nroots = find_poly_roots(bch, 1, bch->elp, errloc); 1069 if (err != nroots) 1070 err = -1; 1071 } 1072 if (err > 0) { 1073 /* post-process raw error locations for easier correction */ 1074 nbits = (len*8)+bch->ecc_bits; 1075 for (i = 0; i < err; i++) { 1076 if (errloc[i] >= nbits) { 1077 err = -1; 1078 break; 1079 } 1080 errloc[i] = nbits-1-errloc[i]; 1081 errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7)); 1082 } 1083 } 1084 return (err >= 0) ? err : -EBADMSG; 1085 } 1086 1087 /* 1088 * generate Galois field lookup tables 1089 */ 1090 static int build_gf_tables(struct bch_control *bch, unsigned int poly) 1091 { 1092 unsigned int i, x = 1; 1093 const unsigned int k = 1 << deg(poly); 1094 1095 /* primitive polynomial must be of degree m */ 1096 if (k != (1u << GF_M(bch))) 1097 return -1; 1098 1099 for (i = 0; i < GF_N(bch); i++) { 1100 bch->a_pow_tab[i] = x; 1101 bch->a_log_tab[x] = i; 1102 if (i && (x == 1)) 1103 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */ 1104 return -1; 1105 x <<= 1; 1106 if (x & k) 1107 x ^= poly; 1108 } 1109 bch->a_pow_tab[GF_N(bch)] = 1; 1110 bch->a_log_tab[0] = 0; 1111 1112 return 0; 1113 } 1114 1115 /* 1116 * compute generator polynomial remainder tables for fast encoding 1117 */ 1118 static void build_mod8_tables(struct bch_control *bch, const uint32_t *g) 1119 { 1120 int i, j, b, d; 1121 uint32_t data, hi, lo, *tab; 1122 const int l = BCH_ECC_WORDS(bch); 1123 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32); 1124 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32); 1125 1126 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab)); 1127 1128 for (i = 0; i < 256; i++) { 1129 /* p(X)=i is a small polynomial of weight <= 8 */ 1130 for (b = 0; b < 4; b++) { 1131 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */ 1132 tab = bch->mod8_tab + (b*256+i)*l; 1133 data = i << (8*b); 1134 while (data) { 1135 d = deg(data); 1136 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */ 1137 data ^= g[0] >> (31-d); 1138 for (j = 0; j < ecclen; j++) { 1139 hi = (d < 31) ? g[j] << (d+1) : 0; 1140 lo = (j+1 < plen) ? 1141 g[j+1] >> (31-d) : 0; 1142 tab[j] ^= hi|lo; 1143 } 1144 } 1145 } 1146 } 1147 } 1148 1149 /* 1150 * build a base for factoring degree 2 polynomials 1151 */ 1152 static int build_deg2_base(struct bch_control *bch) 1153 { 1154 const int m = GF_M(bch); 1155 int i, j, r; 1156 unsigned int sum, x, y, remaining, ak = 0, xi[m]; 1157 1158 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */ 1159 for (i = 0; i < m; i++) { 1160 for (j = 0, sum = 0; j < m; j++) 1161 sum ^= a_pow(bch, i*(1 << j)); 1162 1163 if (sum) { 1164 ak = bch->a_pow_tab[i]; 1165 break; 1166 } 1167 } 1168 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */ 1169 remaining = m; 1170 memset(xi, 0, sizeof(xi)); 1171 1172 for (x = 0; (x <= GF_N(bch)) && remaining; x++) { 1173 y = gf_sqr(bch, x)^x; 1174 for (i = 0; i < 2; i++) { 1175 r = a_log(bch, y); 1176 if (y && (r < m) && !xi[r]) { 1177 bch->xi_tab[r] = x; 1178 xi[r] = 1; 1179 remaining--; 1180 dbg("x%d = %x\n", r, x); 1181 break; 1182 } 1183 y ^= ak; 1184 } 1185 } 1186 /* should not happen but check anyway */ 1187 return remaining ? -1 : 0; 1188 } 1189 1190 static void *bch_alloc(size_t size, int *err) 1191 { 1192 void *ptr; 1193 1194 ptr = kmalloc(size, GFP_KERNEL); 1195 if (ptr == NULL) 1196 *err = 1; 1197 return ptr; 1198 } 1199 1200 /* 1201 * compute generator polynomial for given (m,t) parameters. 1202 */ 1203 static uint32_t *compute_generator_polynomial(struct bch_control *bch) 1204 { 1205 const unsigned int m = GF_M(bch); 1206 const unsigned int t = GF_T(bch); 1207 int n, err = 0; 1208 unsigned int i, j, nbits, r, word, *roots; 1209 struct gf_poly *g; 1210 uint32_t *genpoly; 1211 1212 g = bch_alloc(GF_POLY_SZ(m*t), &err); 1213 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err); 1214 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err); 1215 1216 if (err) { 1217 kfree(genpoly); 1218 genpoly = NULL; 1219 goto finish; 1220 } 1221 1222 /* enumerate all roots of g(X) */ 1223 memset(roots , 0, (bch->n+1)*sizeof(*roots)); 1224 for (i = 0; i < t; i++) { 1225 for (j = 0, r = 2*i+1; j < m; j++) { 1226 roots[r] = 1; 1227 r = mod_s(bch, 2*r); 1228 } 1229 } 1230 /* build generator polynomial g(X) */ 1231 g->deg = 0; 1232 g->c[0] = 1; 1233 for (i = 0; i < GF_N(bch); i++) { 1234 if (roots[i]) { 1235 /* multiply g(X) by (X+root) */ 1236 r = bch->a_pow_tab[i]; 1237 g->c[g->deg+1] = 1; 1238 for (j = g->deg; j > 0; j--) 1239 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1]; 1240 1241 g->c[0] = gf_mul(bch, g->c[0], r); 1242 g->deg++; 1243 } 1244 } 1245 /* store left-justified binary representation of g(X) */ 1246 n = g->deg+1; 1247 i = 0; 1248 1249 while (n > 0) { 1250 nbits = (n > 32) ? 32 : n; 1251 for (j = 0, word = 0; j < nbits; j++) { 1252 if (g->c[n-1-j]) 1253 word |= 1u << (31-j); 1254 } 1255 genpoly[i++] = word; 1256 n -= nbits; 1257 } 1258 bch->ecc_bits = g->deg; 1259 1260 finish: 1261 kfree(g); 1262 kfree(roots); 1263 1264 return genpoly; 1265 } 1266 1267 /** 1268 * init_bch - initialize a BCH encoder/decoder 1269 * @m: Galois field order, should be in the range 5-15 1270 * @t: maximum error correction capability, in bits 1271 * @prim_poly: user-provided primitive polynomial (or 0 to use default) 1272 * 1273 * Returns: 1274 * a newly allocated BCH control structure if successful, NULL otherwise 1275 * 1276 * This initialization can take some time, as lookup tables are built for fast 1277 * encoding/decoding; make sure not to call this function from a time critical 1278 * path. Usually, init_bch() should be called on module/driver init and 1279 * free_bch() should be called to release memory on exit. 1280 * 1281 * You may provide your own primitive polynomial of degree @m in argument 1282 * @prim_poly, or let init_bch() use its default polynomial. 1283 * 1284 * Once init_bch() has successfully returned a pointer to a newly allocated 1285 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of 1286 * the structure. 1287 */ 1288 struct bch_control *init_bch(int m, int t, unsigned int prim_poly) 1289 { 1290 int err = 0; 1291 unsigned int i, words; 1292 uint32_t *genpoly; 1293 struct bch_control *bch = NULL; 1294 1295 const int min_m = 5; 1296 const int max_m = 15; 1297 1298 /* default primitive polynomials */ 1299 static const unsigned int prim_poly_tab[] = { 1300 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b, 1301 0x402b, 0x8003, 1302 }; 1303 1304 #if defined(CONFIG_BCH_CONST_PARAMS) 1305 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) { 1306 printk(KERN_ERR "bch encoder/decoder was configured to support " 1307 "parameters m=%d, t=%d only!\n", 1308 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T); 1309 goto fail; 1310 } 1311 #endif 1312 if ((m < min_m) || (m > max_m)) 1313 /* 1314 * values of m greater than 15 are not currently supported; 1315 * supporting m > 15 would require changing table base type 1316 * (uint16_t) and a small patch in matrix transposition 1317 */ 1318 goto fail; 1319 1320 /* sanity checks */ 1321 if ((t < 1) || (m*t >= ((1 << m)-1))) 1322 /* invalid t value */ 1323 goto fail; 1324 1325 /* select a primitive polynomial for generating GF(2^m) */ 1326 if (prim_poly == 0) 1327 prim_poly = prim_poly_tab[m-min_m]; 1328 1329 bch = kzalloc(sizeof(*bch), GFP_KERNEL); 1330 if (bch == NULL) 1331 goto fail; 1332 1333 bch->m = m; 1334 bch->t = t; 1335 bch->n = (1 << m)-1; 1336 words = DIV_ROUND_UP(m*t, 32); 1337 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8); 1338 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err); 1339 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err); 1340 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err); 1341 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err); 1342 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err); 1343 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err); 1344 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err); 1345 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err); 1346 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err); 1347 1348 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) 1349 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err); 1350 1351 if (err) 1352 goto fail; 1353 1354 err = build_gf_tables(bch, prim_poly); 1355 if (err) 1356 goto fail; 1357 1358 /* use generator polynomial for computing encoding tables */ 1359 genpoly = compute_generator_polynomial(bch); 1360 if (genpoly == NULL) 1361 goto fail; 1362 1363 build_mod8_tables(bch, genpoly); 1364 kfree(genpoly); 1365 1366 err = build_deg2_base(bch); 1367 if (err) 1368 goto fail; 1369 1370 return bch; 1371 1372 fail: 1373 free_bch(bch); 1374 return NULL; 1375 } 1376 1377 /** 1378 * free_bch - free the BCH control structure 1379 * @bch: BCH control structure to release 1380 */ 1381 void free_bch(struct bch_control *bch) 1382 { 1383 unsigned int i; 1384 1385 if (bch) { 1386 kfree(bch->a_pow_tab); 1387 kfree(bch->a_log_tab); 1388 kfree(bch->mod8_tab); 1389 kfree(bch->ecc_buf); 1390 kfree(bch->ecc_buf2); 1391 kfree(bch->xi_tab); 1392 kfree(bch->syn); 1393 kfree(bch->cache); 1394 kfree(bch->elp); 1395 1396 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) 1397 kfree(bch->poly_2t[i]); 1398 1399 kfree(bch); 1400 } 1401 } 1402