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 bch_init 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 bch_encode to compute and store ecc parity bytes to a given buffer. 31 * Call bch_decode to detect and locate errors in received data. 32 * 33 * On systems supporting hw BCH features, intermediate results may be provided 34 * to bch_decode in order to skip certain steps. See bch_decode() 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 <linux/bitrev.h> 75 #include <asm/byteorder.h> 76 #include <linux/bch.h> 77 78 #if defined(CONFIG_BCH_CONST_PARAMS) 79 #define GF_M(_p) (CONFIG_BCH_CONST_M) 80 #define GF_T(_p) (CONFIG_BCH_CONST_T) 81 #define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1) 82 #define BCH_MAX_M (CONFIG_BCH_CONST_M) 83 #define BCH_MAX_T (CONFIG_BCH_CONST_T) 84 #else 85 #define GF_M(_p) ((_p)->m) 86 #define GF_T(_p) ((_p)->t) 87 #define GF_N(_p) ((_p)->n) 88 #define BCH_MAX_M 15 /* 2KB */ 89 #define BCH_MAX_T 64 /* 64 bit correction */ 90 #endif 91 92 #define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32) 93 #define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8) 94 95 #define BCH_ECC_MAX_WORDS DIV_ROUND_UP(BCH_MAX_M * BCH_MAX_T, 32) 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[]; /* 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 static u8 swap_bits(struct bch_control *bch, u8 in) 119 { 120 if (!bch->swap_bits) 121 return in; 122 123 return bitrev8(in); 124 } 125 126 /* 127 * same as bch_encode(), but process input data one byte at a time 128 */ 129 static void bch_encode_unaligned(struct bch_control *bch, 130 const unsigned char *data, unsigned int len, 131 uint32_t *ecc) 132 { 133 int i; 134 const uint32_t *p; 135 const int l = BCH_ECC_WORDS(bch)-1; 136 137 while (len--) { 138 u8 tmp = swap_bits(bch, *data++); 139 140 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(tmp)) & 0xff); 141 142 for (i = 0; i < l; i++) 143 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++); 144 145 ecc[l] = (ecc[l] << 8)^(*p); 146 } 147 } 148 149 /* 150 * convert ecc bytes to aligned, zero-padded 32-bit ecc words 151 */ 152 static void load_ecc8(struct bch_control *bch, uint32_t *dst, 153 const uint8_t *src) 154 { 155 uint8_t pad[4] = {0, 0, 0, 0}; 156 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; 157 158 for (i = 0; i < nwords; i++, src += 4) 159 dst[i] = ((u32)swap_bits(bch, src[0]) << 24) | 160 ((u32)swap_bits(bch, src[1]) << 16) | 161 ((u32)swap_bits(bch, src[2]) << 8) | 162 swap_bits(bch, src[3]); 163 164 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords); 165 dst[nwords] = ((u32)swap_bits(bch, pad[0]) << 24) | 166 ((u32)swap_bits(bch, pad[1]) << 16) | 167 ((u32)swap_bits(bch, pad[2]) << 8) | 168 swap_bits(bch, pad[3]); 169 } 170 171 /* 172 * convert 32-bit ecc words to ecc bytes 173 */ 174 static void store_ecc8(struct bch_control *bch, uint8_t *dst, 175 const uint32_t *src) 176 { 177 uint8_t pad[4]; 178 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; 179 180 for (i = 0; i < nwords; i++) { 181 *dst++ = swap_bits(bch, src[i] >> 24); 182 *dst++ = swap_bits(bch, src[i] >> 16); 183 *dst++ = swap_bits(bch, src[i] >> 8); 184 *dst++ = swap_bits(bch, src[i]); 185 } 186 pad[0] = swap_bits(bch, src[nwords] >> 24); 187 pad[1] = swap_bits(bch, src[nwords] >> 16); 188 pad[2] = swap_bits(bch, src[nwords] >> 8); 189 pad[3] = swap_bits(bch, src[nwords]); 190 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords); 191 } 192 193 /** 194 * bch_encode - calculate BCH ecc parity of data 195 * @bch: BCH control structure 196 * @data: data to encode 197 * @len: data length in bytes 198 * @ecc: ecc parity data, must be initialized by caller 199 * 200 * The @ecc parity array is used both as input and output parameter, in order to 201 * allow incremental computations. It should be of the size indicated by member 202 * @ecc_bytes of @bch, and should be initialized to 0 before the first call. 203 * 204 * The exact number of computed ecc parity bits is given by member @ecc_bits of 205 * @bch; it may be less than m*t for large values of t. 206 */ 207 void bch_encode(struct bch_control *bch, const uint8_t *data, 208 unsigned int len, uint8_t *ecc) 209 { 210 const unsigned int l = BCH_ECC_WORDS(bch)-1; 211 unsigned int i, mlen; 212 unsigned long m; 213 uint32_t w, r[BCH_ECC_MAX_WORDS]; 214 const size_t r_bytes = BCH_ECC_WORDS(bch) * sizeof(*r); 215 const uint32_t * const tab0 = bch->mod8_tab; 216 const uint32_t * const tab1 = tab0 + 256*(l+1); 217 const uint32_t * const tab2 = tab1 + 256*(l+1); 218 const uint32_t * const tab3 = tab2 + 256*(l+1); 219 const uint32_t *pdata, *p0, *p1, *p2, *p3; 220 221 if (WARN_ON(r_bytes > sizeof(r))) 222 return; 223 224 if (ecc) { 225 /* load ecc parity bytes into internal 32-bit buffer */ 226 load_ecc8(bch, bch->ecc_buf, ecc); 227 } else { 228 memset(bch->ecc_buf, 0, r_bytes); 229 } 230 231 /* process first unaligned data bytes */ 232 m = ((unsigned long)data) & 3; 233 if (m) { 234 mlen = (len < (4-m)) ? len : 4-m; 235 bch_encode_unaligned(bch, data, mlen, bch->ecc_buf); 236 data += mlen; 237 len -= mlen; 238 } 239 240 /* process 32-bit aligned data words */ 241 pdata = (uint32_t *)data; 242 mlen = len/4; 243 data += 4*mlen; 244 len -= 4*mlen; 245 memcpy(r, bch->ecc_buf, r_bytes); 246 247 /* 248 * split each 32-bit word into 4 polynomials of weight 8 as follows: 249 * 250 * 31 ...24 23 ...16 15 ... 8 7 ... 0 251 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt 252 * tttttttt mod g = r0 (precomputed) 253 * zzzzzzzz 00000000 mod g = r1 (precomputed) 254 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed) 255 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed) 256 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3 257 */ 258 while (mlen--) { 259 /* input data is read in big-endian format */ 260 w = cpu_to_be32(*pdata++); 261 if (bch->swap_bits) 262 w = (u32)swap_bits(bch, w) | 263 ((u32)swap_bits(bch, w >> 8) << 8) | 264 ((u32)swap_bits(bch, w >> 16) << 16) | 265 ((u32)swap_bits(bch, w >> 24) << 24); 266 w ^= r[0]; 267 p0 = tab0 + (l+1)*((w >> 0) & 0xff); 268 p1 = tab1 + (l+1)*((w >> 8) & 0xff); 269 p2 = tab2 + (l+1)*((w >> 16) & 0xff); 270 p3 = tab3 + (l+1)*((w >> 24) & 0xff); 271 272 for (i = 0; i < l; i++) 273 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i]; 274 275 r[l] = p0[l]^p1[l]^p2[l]^p3[l]; 276 } 277 memcpy(bch->ecc_buf, r, r_bytes); 278 279 /* process last unaligned bytes */ 280 if (len) 281 bch_encode_unaligned(bch, data, len, bch->ecc_buf); 282 283 /* store ecc parity bytes into original parity buffer */ 284 if (ecc) 285 store_ecc8(bch, ecc, bch->ecc_buf); 286 } 287 EXPORT_SYMBOL_GPL(bch_encode); 288 289 static inline int modulo(struct bch_control *bch, unsigned int v) 290 { 291 const unsigned int n = GF_N(bch); 292 while (v >= n) { 293 v -= n; 294 v = (v & n) + (v >> GF_M(bch)); 295 } 296 return v; 297 } 298 299 /* 300 * shorter and faster modulo function, only works when v < 2N. 301 */ 302 static inline int mod_s(struct bch_control *bch, unsigned int v) 303 { 304 const unsigned int n = GF_N(bch); 305 return (v < n) ? v : v-n; 306 } 307 308 static inline int deg(unsigned int poly) 309 { 310 /* polynomial degree is the most-significant bit index */ 311 return fls(poly)-1; 312 } 313 314 static inline int parity(unsigned int x) 315 { 316 /* 317 * public domain code snippet, lifted from 318 * http://www-graphics.stanford.edu/~seander/bithacks.html 319 */ 320 x ^= x >> 1; 321 x ^= x >> 2; 322 x = (x & 0x11111111U) * 0x11111111U; 323 return (x >> 28) & 1; 324 } 325 326 /* Galois field basic operations: multiply, divide, inverse, etc. */ 327 328 static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a, 329 unsigned int b) 330 { 331 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ 332 bch->a_log_tab[b])] : 0; 333 } 334 335 static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a) 336 { 337 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0; 338 } 339 340 static inline unsigned int gf_div(struct bch_control *bch, unsigned int a, 341 unsigned int b) 342 { 343 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ 344 GF_N(bch)-bch->a_log_tab[b])] : 0; 345 } 346 347 static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a) 348 { 349 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]]; 350 } 351 352 static inline unsigned int a_pow(struct bch_control *bch, int i) 353 { 354 return bch->a_pow_tab[modulo(bch, i)]; 355 } 356 357 static inline int a_log(struct bch_control *bch, unsigned int x) 358 { 359 return bch->a_log_tab[x]; 360 } 361 362 static inline int a_ilog(struct bch_control *bch, unsigned int x) 363 { 364 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]); 365 } 366 367 /* 368 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t 369 */ 370 static void compute_syndromes(struct bch_control *bch, uint32_t *ecc, 371 unsigned int *syn) 372 { 373 int i, j, s; 374 unsigned int m; 375 uint32_t poly; 376 const int t = GF_T(bch); 377 378 s = bch->ecc_bits; 379 380 /* make sure extra bits in last ecc word are cleared */ 381 m = ((unsigned int)s) & 31; 382 if (m) 383 ecc[s/32] &= ~((1u << (32-m))-1); 384 memset(syn, 0, 2*t*sizeof(*syn)); 385 386 /* compute v(a^j) for j=1 .. 2t-1 */ 387 do { 388 poly = *ecc++; 389 s -= 32; 390 while (poly) { 391 i = deg(poly); 392 for (j = 0; j < 2*t; j += 2) 393 syn[j] ^= a_pow(bch, (j+1)*(i+s)); 394 395 poly ^= (1 << i); 396 } 397 } while (s > 0); 398 399 /* v(a^(2j)) = v(a^j)^2 */ 400 for (j = 0; j < t; j++) 401 syn[2*j+1] = gf_sqr(bch, syn[j]); 402 } 403 404 static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src) 405 { 406 memcpy(dst, src, GF_POLY_SZ(src->deg)); 407 } 408 409 static int compute_error_locator_polynomial(struct bch_control *bch, 410 const unsigned int *syn) 411 { 412 const unsigned int t = GF_T(bch); 413 const unsigned int n = GF_N(bch); 414 unsigned int i, j, tmp, l, pd = 1, d = syn[0]; 415 struct gf_poly *elp = bch->elp; 416 struct gf_poly *pelp = bch->poly_2t[0]; 417 struct gf_poly *elp_copy = bch->poly_2t[1]; 418 int k, pp = -1; 419 420 memset(pelp, 0, GF_POLY_SZ(2*t)); 421 memset(elp, 0, GF_POLY_SZ(2*t)); 422 423 pelp->deg = 0; 424 pelp->c[0] = 1; 425 elp->deg = 0; 426 elp->c[0] = 1; 427 428 /* use simplified binary Berlekamp-Massey algorithm */ 429 for (i = 0; (i < t) && (elp->deg <= t); i++) { 430 if (d) { 431 k = 2*i-pp; 432 gf_poly_copy(elp_copy, elp); 433 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */ 434 tmp = a_log(bch, d)+n-a_log(bch, pd); 435 for (j = 0; j <= pelp->deg; j++) { 436 if (pelp->c[j]) { 437 l = a_log(bch, pelp->c[j]); 438 elp->c[j+k] ^= a_pow(bch, tmp+l); 439 } 440 } 441 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */ 442 tmp = pelp->deg+k; 443 if (tmp > elp->deg) { 444 elp->deg = tmp; 445 gf_poly_copy(pelp, elp_copy); 446 pd = d; 447 pp = 2*i; 448 } 449 } 450 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */ 451 if (i < t-1) { 452 d = syn[2*i+2]; 453 for (j = 1; j <= elp->deg; j++) 454 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]); 455 } 456 } 457 dbg("elp=%s\n", gf_poly_str(elp)); 458 return (elp->deg > t) ? -1 : (int)elp->deg; 459 } 460 461 /* 462 * solve a m x m linear system in GF(2) with an expected number of solutions, 463 * and return the number of found solutions 464 */ 465 static int solve_linear_system(struct bch_control *bch, unsigned int *rows, 466 unsigned int *sol, int nsol) 467 { 468 const int m = GF_M(bch); 469 unsigned int tmp, mask; 470 int rem, c, r, p, k, param[BCH_MAX_M]; 471 472 k = 0; 473 mask = 1 << m; 474 475 /* Gaussian elimination */ 476 for (c = 0; c < m; c++) { 477 rem = 0; 478 p = c-k; 479 /* find suitable row for elimination */ 480 for (r = p; r < m; r++) { 481 if (rows[r] & mask) { 482 if (r != p) { 483 tmp = rows[r]; 484 rows[r] = rows[p]; 485 rows[p] = tmp; 486 } 487 rem = r+1; 488 break; 489 } 490 } 491 if (rem) { 492 /* perform elimination on remaining rows */ 493 tmp = rows[p]; 494 for (r = rem; r < m; r++) { 495 if (rows[r] & mask) 496 rows[r] ^= tmp; 497 } 498 } else { 499 /* elimination not needed, store defective row index */ 500 param[k++] = c; 501 } 502 mask >>= 1; 503 } 504 /* rewrite system, inserting fake parameter rows */ 505 if (k > 0) { 506 p = k; 507 for (r = m-1; r >= 0; r--) { 508 if ((r > m-1-k) && rows[r]) 509 /* system has no solution */ 510 return 0; 511 512 rows[r] = (p && (r == param[p-1])) ? 513 p--, 1u << (m-r) : rows[r-p]; 514 } 515 } 516 517 if (nsol != (1 << k)) 518 /* unexpected number of solutions */ 519 return 0; 520 521 for (p = 0; p < nsol; p++) { 522 /* set parameters for p-th solution */ 523 for (c = 0; c < k; c++) 524 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1); 525 526 /* compute unique solution */ 527 tmp = 0; 528 for (r = m-1; r >= 0; r--) { 529 mask = rows[r] & (tmp|1); 530 tmp |= parity(mask) << (m-r); 531 } 532 sol[p] = tmp >> 1; 533 } 534 return nsol; 535 } 536 537 /* 538 * this function builds and solves a linear system for finding roots of a degree 539 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m). 540 */ 541 static int find_affine4_roots(struct bch_control *bch, unsigned int a, 542 unsigned int b, unsigned int c, 543 unsigned int *roots) 544 { 545 int i, j, k; 546 const int m = GF_M(bch); 547 unsigned int mask = 0xff, t, rows[16] = {0,}; 548 549 j = a_log(bch, b); 550 k = a_log(bch, a); 551 rows[0] = c; 552 553 /* build linear system to solve X^4+aX^2+bX+c = 0 */ 554 for (i = 0; i < m; i++) { 555 rows[i+1] = bch->a_pow_tab[4*i]^ 556 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^ 557 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0); 558 j++; 559 k += 2; 560 } 561 /* 562 * transpose 16x16 matrix before passing it to linear solver 563 * warning: this code assumes m < 16 564 */ 565 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) { 566 for (k = 0; k < 16; k = (k+j+1) & ~j) { 567 t = ((rows[k] >> j)^rows[k+j]) & mask; 568 rows[k] ^= (t << j); 569 rows[k+j] ^= t; 570 } 571 } 572 return solve_linear_system(bch, rows, roots, 4); 573 } 574 575 /* 576 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r)) 577 */ 578 static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly, 579 unsigned int *roots) 580 { 581 int n = 0; 582 583 if (poly->c[0]) 584 /* poly[X] = bX+c with c!=0, root=c/b */ 585 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+ 586 bch->a_log_tab[poly->c[1]]); 587 return n; 588 } 589 590 /* 591 * compute roots of a degree 2 polynomial over GF(2^m) 592 */ 593 static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly, 594 unsigned int *roots) 595 { 596 int n = 0, i, l0, l1, l2; 597 unsigned int u, v, r; 598 599 if (poly->c[0] && poly->c[1]) { 600 601 l0 = bch->a_log_tab[poly->c[0]]; 602 l1 = bch->a_log_tab[poly->c[1]]; 603 l2 = bch->a_log_tab[poly->c[2]]; 604 605 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */ 606 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1)); 607 /* 608 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi): 609 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) = 610 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u) 611 * i.e. r and r+1 are roots iff Tr(u)=0 612 */ 613 r = 0; 614 v = u; 615 while (v) { 616 i = deg(v); 617 r ^= bch->xi_tab[i]; 618 v ^= (1 << i); 619 } 620 /* verify root */ 621 if ((gf_sqr(bch, r)^r) == u) { 622 /* reverse z=a/bX transformation and compute log(1/r) */ 623 roots[n++] = modulo(bch, 2*GF_N(bch)-l1- 624 bch->a_log_tab[r]+l2); 625 roots[n++] = modulo(bch, 2*GF_N(bch)-l1- 626 bch->a_log_tab[r^1]+l2); 627 } 628 } 629 return n; 630 } 631 632 /* 633 * compute roots of a degree 3 polynomial over GF(2^m) 634 */ 635 static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly, 636 unsigned int *roots) 637 { 638 int i, n = 0; 639 unsigned int a, b, c, a2, b2, c2, e3, tmp[4]; 640 641 if (poly->c[0]) { 642 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */ 643 e3 = poly->c[3]; 644 c2 = gf_div(bch, poly->c[0], e3); 645 b2 = gf_div(bch, poly->c[1], e3); 646 a2 = gf_div(bch, poly->c[2], e3); 647 648 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */ 649 c = gf_mul(bch, a2, c2); /* c = a2c2 */ 650 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */ 651 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */ 652 653 /* find the 4 roots of this affine polynomial */ 654 if (find_affine4_roots(bch, a, b, c, tmp) == 4) { 655 /* remove a2 from final list of roots */ 656 for (i = 0; i < 4; i++) { 657 if (tmp[i] != a2) 658 roots[n++] = a_ilog(bch, tmp[i]); 659 } 660 } 661 } 662 return n; 663 } 664 665 /* 666 * compute roots of a degree 4 polynomial over GF(2^m) 667 */ 668 static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly, 669 unsigned int *roots) 670 { 671 int i, l, n = 0; 672 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4; 673 674 if (poly->c[0] == 0) 675 return 0; 676 677 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */ 678 e4 = poly->c[4]; 679 d = gf_div(bch, poly->c[0], e4); 680 c = gf_div(bch, poly->c[1], e4); 681 b = gf_div(bch, poly->c[2], e4); 682 a = gf_div(bch, poly->c[3], e4); 683 684 /* use Y=1/X transformation to get an affine polynomial */ 685 if (a) { 686 /* first, eliminate cX by using z=X+e with ae^2+c=0 */ 687 if (c) { 688 /* compute e such that e^2 = c/a */ 689 f = gf_div(bch, c, a); 690 l = a_log(bch, f); 691 l += (l & 1) ? GF_N(bch) : 0; 692 e = a_pow(bch, l/2); 693 /* 694 * use transformation z=X+e: 695 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d 696 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d 697 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d 698 * z^4 + az^3 + b'z^2 + d' 699 */ 700 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d; 701 b = gf_mul(bch, a, e)^b; 702 } 703 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */ 704 if (d == 0) 705 /* assume all roots have multiplicity 1 */ 706 return 0; 707 708 c2 = gf_inv(bch, d); 709 b2 = gf_div(bch, a, d); 710 a2 = gf_div(bch, b, d); 711 } else { 712 /* polynomial is already affine */ 713 c2 = d; 714 b2 = c; 715 a2 = b; 716 } 717 /* find the 4 roots of this affine polynomial */ 718 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) { 719 for (i = 0; i < 4; i++) { 720 /* post-process roots (reverse transformations) */ 721 f = a ? gf_inv(bch, roots[i]) : roots[i]; 722 roots[i] = a_ilog(bch, f^e); 723 } 724 n = 4; 725 } 726 return n; 727 } 728 729 /* 730 * build monic, log-based representation of a polynomial 731 */ 732 static void gf_poly_logrep(struct bch_control *bch, 733 const struct gf_poly *a, int *rep) 734 { 735 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]); 736 737 /* represent 0 values with -1; warning, rep[d] is not set to 1 */ 738 for (i = 0; i < d; i++) 739 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1; 740 } 741 742 /* 743 * compute polynomial Euclidean division remainder in GF(2^m)[X] 744 */ 745 static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a, 746 const struct gf_poly *b, int *rep) 747 { 748 int la, p, m; 749 unsigned int i, j, *c = a->c; 750 const unsigned int d = b->deg; 751 752 if (a->deg < d) 753 return; 754 755 /* reuse or compute log representation of denominator */ 756 if (!rep) { 757 rep = bch->cache; 758 gf_poly_logrep(bch, b, rep); 759 } 760 761 for (j = a->deg; j >= d; j--) { 762 if (c[j]) { 763 la = a_log(bch, c[j]); 764 p = j-d; 765 for (i = 0; i < d; i++, p++) { 766 m = rep[i]; 767 if (m >= 0) 768 c[p] ^= bch->a_pow_tab[mod_s(bch, 769 m+la)]; 770 } 771 } 772 } 773 a->deg = d-1; 774 while (!c[a->deg] && a->deg) 775 a->deg--; 776 } 777 778 /* 779 * compute polynomial Euclidean division quotient in GF(2^m)[X] 780 */ 781 static void gf_poly_div(struct bch_control *bch, struct gf_poly *a, 782 const struct gf_poly *b, struct gf_poly *q) 783 { 784 if (a->deg >= b->deg) { 785 q->deg = a->deg-b->deg; 786 /* compute a mod b (modifies a) */ 787 gf_poly_mod(bch, a, b, NULL); 788 /* quotient is stored in upper part of polynomial a */ 789 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int)); 790 } else { 791 q->deg = 0; 792 q->c[0] = 0; 793 } 794 } 795 796 /* 797 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X] 798 */ 799 static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a, 800 struct gf_poly *b) 801 { 802 struct gf_poly *tmp; 803 804 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b)); 805 806 if (a->deg < b->deg) { 807 tmp = b; 808 b = a; 809 a = tmp; 810 } 811 812 while (b->deg > 0) { 813 gf_poly_mod(bch, a, b, NULL); 814 tmp = b; 815 b = a; 816 a = tmp; 817 } 818 819 dbg("%s\n", gf_poly_str(a)); 820 821 return a; 822 } 823 824 /* 825 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f 826 * This is used in Berlekamp Trace algorithm for splitting polynomials 827 */ 828 static void compute_trace_bk_mod(struct bch_control *bch, int k, 829 const struct gf_poly *f, struct gf_poly *z, 830 struct gf_poly *out) 831 { 832 const int m = GF_M(bch); 833 int i, j; 834 835 /* z contains z^2j mod f */ 836 z->deg = 1; 837 z->c[0] = 0; 838 z->c[1] = bch->a_pow_tab[k]; 839 840 out->deg = 0; 841 memset(out, 0, GF_POLY_SZ(f->deg)); 842 843 /* compute f log representation only once */ 844 gf_poly_logrep(bch, f, bch->cache); 845 846 for (i = 0; i < m; i++) { 847 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */ 848 for (j = z->deg; j >= 0; j--) { 849 out->c[j] ^= z->c[j]; 850 z->c[2*j] = gf_sqr(bch, z->c[j]); 851 z->c[2*j+1] = 0; 852 } 853 if (z->deg > out->deg) 854 out->deg = z->deg; 855 856 if (i < m-1) { 857 z->deg *= 2; 858 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */ 859 gf_poly_mod(bch, z, f, bch->cache); 860 } 861 } 862 while (!out->c[out->deg] && out->deg) 863 out->deg--; 864 865 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out)); 866 } 867 868 /* 869 * factor a polynomial using Berlekamp Trace algorithm (BTA) 870 */ 871 static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f, 872 struct gf_poly **g, struct gf_poly **h) 873 { 874 struct gf_poly *f2 = bch->poly_2t[0]; 875 struct gf_poly *q = bch->poly_2t[1]; 876 struct gf_poly *tk = bch->poly_2t[2]; 877 struct gf_poly *z = bch->poly_2t[3]; 878 struct gf_poly *gcd; 879 880 dbg("factoring %s...\n", gf_poly_str(f)); 881 882 *g = f; 883 *h = NULL; 884 885 /* tk = Tr(a^k.X) mod f */ 886 compute_trace_bk_mod(bch, k, f, z, tk); 887 888 if (tk->deg > 0) { 889 /* compute g = gcd(f, tk) (destructive operation) */ 890 gf_poly_copy(f2, f); 891 gcd = gf_poly_gcd(bch, f2, tk); 892 if (gcd->deg < f->deg) { 893 /* compute h=f/gcd(f,tk); this will modify f and q */ 894 gf_poly_div(bch, f, gcd, q); 895 /* store g and h in-place (clobbering f) */ 896 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly; 897 gf_poly_copy(*g, gcd); 898 gf_poly_copy(*h, q); 899 } 900 } 901 } 902 903 /* 904 * find roots of a polynomial, using BTZ algorithm; see the beginning of this 905 * file for details 906 */ 907 static int find_poly_roots(struct bch_control *bch, unsigned int k, 908 struct gf_poly *poly, unsigned int *roots) 909 { 910 int cnt; 911 struct gf_poly *f1, *f2; 912 913 switch (poly->deg) { 914 /* handle low degree polynomials with ad hoc techniques */ 915 case 1: 916 cnt = find_poly_deg1_roots(bch, poly, roots); 917 break; 918 case 2: 919 cnt = find_poly_deg2_roots(bch, poly, roots); 920 break; 921 case 3: 922 cnt = find_poly_deg3_roots(bch, poly, roots); 923 break; 924 case 4: 925 cnt = find_poly_deg4_roots(bch, poly, roots); 926 break; 927 default: 928 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */ 929 cnt = 0; 930 if (poly->deg && (k <= GF_M(bch))) { 931 factor_polynomial(bch, k, poly, &f1, &f2); 932 if (f1) 933 cnt += find_poly_roots(bch, k+1, f1, roots); 934 if (f2) 935 cnt += find_poly_roots(bch, k+1, f2, roots+cnt); 936 } 937 break; 938 } 939 return cnt; 940 } 941 942 #if defined(USE_CHIEN_SEARCH) 943 /* 944 * exhaustive root search (Chien) implementation - not used, included only for 945 * reference/comparison tests 946 */ 947 static int chien_search(struct bch_control *bch, unsigned int len, 948 struct gf_poly *p, unsigned int *roots) 949 { 950 int m; 951 unsigned int i, j, syn, syn0, count = 0; 952 const unsigned int k = 8*len+bch->ecc_bits; 953 954 /* use a log-based representation of polynomial */ 955 gf_poly_logrep(bch, p, bch->cache); 956 bch->cache[p->deg] = 0; 957 syn0 = gf_div(bch, p->c[0], p->c[p->deg]); 958 959 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) { 960 /* compute elp(a^i) */ 961 for (j = 1, syn = syn0; j <= p->deg; j++) { 962 m = bch->cache[j]; 963 if (m >= 0) 964 syn ^= a_pow(bch, m+j*i); 965 } 966 if (syn == 0) { 967 roots[count++] = GF_N(bch)-i; 968 if (count == p->deg) 969 break; 970 } 971 } 972 return (count == p->deg) ? count : 0; 973 } 974 #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc) 975 #endif /* USE_CHIEN_SEARCH */ 976 977 /** 978 * bch_decode - decode received codeword and find bit error locations 979 * @bch: BCH control structure 980 * @data: received data, ignored if @calc_ecc is provided 981 * @len: data length in bytes, must always be provided 982 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc 983 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data 984 * @syn: hw computed syndrome data (if NULL, syndrome is calculated) 985 * @errloc: output array of error locations 986 * 987 * Returns: 988 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if 989 * invalid parameters were provided 990 * 991 * Depending on the available hw BCH support and the need to compute @calc_ecc 992 * separately (using bch_encode()), this function should be called with one of 993 * the following parameter configurations - 994 * 995 * by providing @data and @recv_ecc only: 996 * bch_decode(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc) 997 * 998 * by providing @recv_ecc and @calc_ecc: 999 * bch_decode(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc) 1000 * 1001 * by providing ecc = recv_ecc XOR calc_ecc: 1002 * bch_decode(@bch, NULL, @len, NULL, ecc, NULL, @errloc) 1003 * 1004 * by providing syndrome results @syn: 1005 * bch_decode(@bch, NULL, @len, NULL, NULL, @syn, @errloc) 1006 * 1007 * Once bch_decode() has successfully returned with a positive value, error 1008 * locations returned in array @errloc should be interpreted as follows - 1009 * 1010 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for 1011 * data correction) 1012 * 1013 * if (errloc[n] < 8*len), then n-th error is located in data and can be 1014 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8); 1015 * 1016 * Note that this function does not perform any data correction by itself, it 1017 * merely indicates error locations. 1018 */ 1019 int bch_decode(struct bch_control *bch, const uint8_t *data, unsigned int len, 1020 const uint8_t *recv_ecc, const uint8_t *calc_ecc, 1021 const unsigned int *syn, unsigned int *errloc) 1022 { 1023 const unsigned int ecc_words = BCH_ECC_WORDS(bch); 1024 unsigned int nbits; 1025 int i, err, nroots; 1026 uint32_t sum; 1027 1028 /* sanity check: make sure data length can be handled */ 1029 if (8*len > (bch->n-bch->ecc_bits)) 1030 return -EINVAL; 1031 1032 /* if caller does not provide syndromes, compute them */ 1033 if (!syn) { 1034 if (!calc_ecc) { 1035 /* compute received data ecc into an internal buffer */ 1036 if (!data || !recv_ecc) 1037 return -EINVAL; 1038 bch_encode(bch, data, len, NULL); 1039 } else { 1040 /* load provided calculated ecc */ 1041 load_ecc8(bch, bch->ecc_buf, calc_ecc); 1042 } 1043 /* load received ecc or assume it was XORed in calc_ecc */ 1044 if (recv_ecc) { 1045 load_ecc8(bch, bch->ecc_buf2, recv_ecc); 1046 /* XOR received and calculated ecc */ 1047 for (i = 0, sum = 0; i < (int)ecc_words; i++) { 1048 bch->ecc_buf[i] ^= bch->ecc_buf2[i]; 1049 sum |= bch->ecc_buf[i]; 1050 } 1051 if (!sum) 1052 /* no error found */ 1053 return 0; 1054 } 1055 compute_syndromes(bch, bch->ecc_buf, bch->syn); 1056 syn = bch->syn; 1057 } 1058 1059 err = compute_error_locator_polynomial(bch, syn); 1060 if (err > 0) { 1061 nroots = find_poly_roots(bch, 1, bch->elp, errloc); 1062 if (err != nroots) 1063 err = -1; 1064 } 1065 if (err > 0) { 1066 /* post-process raw error locations for easier correction */ 1067 nbits = (len*8)+bch->ecc_bits; 1068 for (i = 0; i < err; i++) { 1069 if (errloc[i] >= nbits) { 1070 err = -1; 1071 break; 1072 } 1073 errloc[i] = nbits-1-errloc[i]; 1074 if (!bch->swap_bits) 1075 errloc[i] = (errloc[i] & ~7) | 1076 (7-(errloc[i] & 7)); 1077 } 1078 } 1079 return (err >= 0) ? err : -EBADMSG; 1080 } 1081 EXPORT_SYMBOL_GPL(bch_decode); 1082 1083 /* 1084 * generate Galois field lookup tables 1085 */ 1086 static int build_gf_tables(struct bch_control *bch, unsigned int poly) 1087 { 1088 unsigned int i, x = 1; 1089 const unsigned int k = 1 << deg(poly); 1090 1091 /* primitive polynomial must be of degree m */ 1092 if (k != (1u << GF_M(bch))) 1093 return -1; 1094 1095 for (i = 0; i < GF_N(bch); i++) { 1096 bch->a_pow_tab[i] = x; 1097 bch->a_log_tab[x] = i; 1098 if (i && (x == 1)) 1099 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */ 1100 return -1; 1101 x <<= 1; 1102 if (x & k) 1103 x ^= poly; 1104 } 1105 bch->a_pow_tab[GF_N(bch)] = 1; 1106 bch->a_log_tab[0] = 0; 1107 1108 return 0; 1109 } 1110 1111 /* 1112 * compute generator polynomial remainder tables for fast encoding 1113 */ 1114 static void build_mod8_tables(struct bch_control *bch, const uint32_t *g) 1115 { 1116 int i, j, b, d; 1117 uint32_t data, hi, lo, *tab; 1118 const int l = BCH_ECC_WORDS(bch); 1119 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32); 1120 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32); 1121 1122 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab)); 1123 1124 for (i = 0; i < 256; i++) { 1125 /* p(X)=i is a small polynomial of weight <= 8 */ 1126 for (b = 0; b < 4; b++) { 1127 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */ 1128 tab = bch->mod8_tab + (b*256+i)*l; 1129 data = i << (8*b); 1130 while (data) { 1131 d = deg(data); 1132 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */ 1133 data ^= g[0] >> (31-d); 1134 for (j = 0; j < ecclen; j++) { 1135 hi = (d < 31) ? g[j] << (d+1) : 0; 1136 lo = (j+1 < plen) ? 1137 g[j+1] >> (31-d) : 0; 1138 tab[j] ^= hi|lo; 1139 } 1140 } 1141 } 1142 } 1143 } 1144 1145 /* 1146 * build a base for factoring degree 2 polynomials 1147 */ 1148 static int build_deg2_base(struct bch_control *bch) 1149 { 1150 const int m = GF_M(bch); 1151 int i, j, r; 1152 unsigned int sum, x, y, remaining, ak = 0, xi[BCH_MAX_M]; 1153 1154 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */ 1155 for (i = 0; i < m; i++) { 1156 for (j = 0, sum = 0; j < m; j++) 1157 sum ^= a_pow(bch, i*(1 << j)); 1158 1159 if (sum) { 1160 ak = bch->a_pow_tab[i]; 1161 break; 1162 } 1163 } 1164 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */ 1165 remaining = m; 1166 memset(xi, 0, sizeof(xi)); 1167 1168 for (x = 0; (x <= GF_N(bch)) && remaining; x++) { 1169 y = gf_sqr(bch, x)^x; 1170 for (i = 0; i < 2; i++) { 1171 r = a_log(bch, y); 1172 if (y && (r < m) && !xi[r]) { 1173 bch->xi_tab[r] = x; 1174 xi[r] = 1; 1175 remaining--; 1176 dbg("x%d = %x\n", r, x); 1177 break; 1178 } 1179 y ^= ak; 1180 } 1181 } 1182 /* should not happen but check anyway */ 1183 return remaining ? -1 : 0; 1184 } 1185 1186 static void *bch_alloc(size_t size, int *err) 1187 { 1188 void *ptr; 1189 1190 ptr = kmalloc(size, GFP_KERNEL); 1191 if (ptr == NULL) 1192 *err = 1; 1193 return ptr; 1194 } 1195 1196 /* 1197 * compute generator polynomial for given (m,t) parameters. 1198 */ 1199 static uint32_t *compute_generator_polynomial(struct bch_control *bch) 1200 { 1201 const unsigned int m = GF_M(bch); 1202 const unsigned int t = GF_T(bch); 1203 int n, err = 0; 1204 unsigned int i, j, nbits, r, word, *roots; 1205 struct gf_poly *g; 1206 uint32_t *genpoly; 1207 1208 g = bch_alloc(GF_POLY_SZ(m*t), &err); 1209 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err); 1210 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err); 1211 1212 if (err) { 1213 kfree(genpoly); 1214 genpoly = NULL; 1215 goto finish; 1216 } 1217 1218 /* enumerate all roots of g(X) */ 1219 memset(roots , 0, (bch->n+1)*sizeof(*roots)); 1220 for (i = 0; i < t; i++) { 1221 for (j = 0, r = 2*i+1; j < m; j++) { 1222 roots[r] = 1; 1223 r = mod_s(bch, 2*r); 1224 } 1225 } 1226 /* build generator polynomial g(X) */ 1227 g->deg = 0; 1228 g->c[0] = 1; 1229 for (i = 0; i < GF_N(bch); i++) { 1230 if (roots[i]) { 1231 /* multiply g(X) by (X+root) */ 1232 r = bch->a_pow_tab[i]; 1233 g->c[g->deg+1] = 1; 1234 for (j = g->deg; j > 0; j--) 1235 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1]; 1236 1237 g->c[0] = gf_mul(bch, g->c[0], r); 1238 g->deg++; 1239 } 1240 } 1241 /* store left-justified binary representation of g(X) */ 1242 n = g->deg+1; 1243 i = 0; 1244 1245 while (n > 0) { 1246 nbits = (n > 32) ? 32 : n; 1247 for (j = 0, word = 0; j < nbits; j++) { 1248 if (g->c[n-1-j]) 1249 word |= 1u << (31-j); 1250 } 1251 genpoly[i++] = word; 1252 n -= nbits; 1253 } 1254 bch->ecc_bits = g->deg; 1255 1256 finish: 1257 kfree(g); 1258 kfree(roots); 1259 1260 return genpoly; 1261 } 1262 1263 /** 1264 * bch_init - initialize a BCH encoder/decoder 1265 * @m: Galois field order, should be in the range 5-15 1266 * @t: maximum error correction capability, in bits 1267 * @prim_poly: user-provided primitive polynomial (or 0 to use default) 1268 * @swap_bits: swap bits within data and syndrome bytes 1269 * 1270 * Returns: 1271 * a newly allocated BCH control structure if successful, NULL otherwise 1272 * 1273 * This initialization can take some time, as lookup tables are built for fast 1274 * encoding/decoding; make sure not to call this function from a time critical 1275 * path. Usually, bch_init() should be called on module/driver init and 1276 * bch_free() should be called to release memory on exit. 1277 * 1278 * You may provide your own primitive polynomial of degree @m in argument 1279 * @prim_poly, or let bch_init() use its default polynomial. 1280 * 1281 * Once bch_init() has successfully returned a pointer to a newly allocated 1282 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of 1283 * the structure. 1284 */ 1285 struct bch_control *bch_init(int m, int t, unsigned int prim_poly, 1286 bool swap_bits) 1287 { 1288 int err = 0; 1289 unsigned int i, words; 1290 uint32_t *genpoly; 1291 struct bch_control *bch = NULL; 1292 1293 const int min_m = 5; 1294 1295 /* default primitive polynomials */ 1296 static const unsigned int prim_poly_tab[] = { 1297 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b, 1298 0x402b, 0x8003, 1299 }; 1300 1301 #if defined(CONFIG_BCH_CONST_PARAMS) 1302 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) { 1303 printk(KERN_ERR "bch encoder/decoder was configured to support " 1304 "parameters m=%d, t=%d only!\n", 1305 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T); 1306 goto fail; 1307 } 1308 #endif 1309 if ((m < min_m) || (m > BCH_MAX_M)) 1310 /* 1311 * values of m greater than 15 are not currently supported; 1312 * supporting m > 15 would require changing table base type 1313 * (uint16_t) and a small patch in matrix transposition 1314 */ 1315 goto fail; 1316 1317 if (t > BCH_MAX_T) 1318 /* 1319 * we can support larger than 64 bits if necessary, at the 1320 * cost of higher stack usage. 1321 */ 1322 goto fail; 1323 1324 /* sanity checks */ 1325 if ((t < 1) || (m*t >= ((1 << m)-1))) 1326 /* invalid t value */ 1327 goto fail; 1328 1329 /* select a primitive polynomial for generating GF(2^m) */ 1330 if (prim_poly == 0) 1331 prim_poly = prim_poly_tab[m-min_m]; 1332 1333 bch = kzalloc(sizeof(*bch), GFP_KERNEL); 1334 if (bch == NULL) 1335 goto fail; 1336 1337 bch->m = m; 1338 bch->t = t; 1339 bch->n = (1 << m)-1; 1340 words = DIV_ROUND_UP(m*t, 32); 1341 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8); 1342 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err); 1343 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err); 1344 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err); 1345 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err); 1346 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err); 1347 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err); 1348 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err); 1349 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err); 1350 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err); 1351 bch->swap_bits = swap_bits; 1352 1353 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) 1354 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err); 1355 1356 if (err) 1357 goto fail; 1358 1359 err = build_gf_tables(bch, prim_poly); 1360 if (err) 1361 goto fail; 1362 1363 /* use generator polynomial for computing encoding tables */ 1364 genpoly = compute_generator_polynomial(bch); 1365 if (genpoly == NULL) 1366 goto fail; 1367 1368 build_mod8_tables(bch, genpoly); 1369 kfree(genpoly); 1370 1371 err = build_deg2_base(bch); 1372 if (err) 1373 goto fail; 1374 1375 return bch; 1376 1377 fail: 1378 bch_free(bch); 1379 return NULL; 1380 } 1381 EXPORT_SYMBOL_GPL(bch_init); 1382 1383 /** 1384 * bch_free - free the BCH control structure 1385 * @bch: BCH control structure to release 1386 */ 1387 void bch_free(struct bch_control *bch) 1388 { 1389 unsigned int i; 1390 1391 if (bch) { 1392 kfree(bch->a_pow_tab); 1393 kfree(bch->a_log_tab); 1394 kfree(bch->mod8_tab); 1395 kfree(bch->ecc_buf); 1396 kfree(bch->ecc_buf2); 1397 kfree(bch->xi_tab); 1398 kfree(bch->syn); 1399 kfree(bch->cache); 1400 kfree(bch->elp); 1401 1402 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) 1403 kfree(bch->poly_2t[i]); 1404 1405 kfree(bch); 1406 } 1407 } 1408 EXPORT_SYMBOL_GPL(bch_free); 1409 1410 MODULE_LICENSE("GPL"); 1411 MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>"); 1412 MODULE_DESCRIPTION("Binary BCH encoder/decoder"); 1413