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