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