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1/*2 * Generic binary BCH encoding/decoding library3 *4 * This program is free software; you can redistribute it and/or modify it5 * under the terms of the GNU General Public License version 2 as published by6 * the Free Software Foundation.7 *8 * This program is distributed in the hope that it will be useful, but WITHOUT9 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or10 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for11 * more details.12 *13 * You should have received a copy of the GNU General Public License along with14 * this program; if not, write to the Free Software Foundation, Inc., 5115 * 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 binary24 * Bose-Chaudhuri-Hocquenghem (BCH) codes.25 *26 * Call bch_init to get a pointer to a newly allocated bch_control structure for27 * the given m (Galois field order), t (error correction capability) and28 * (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 provided34 * to bch_decode in order to skip certain steps. See bch_decode() documentation35 * for details.36 *37 * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of38 * parameters m and t; thus allowing extra compiler optimizations and providing39 * better (up to 2x) encoding performance. Using this option makes sense when40 * (m,t) are fixed and known in advance, e.g. when using BCH error correction41 * on a particular NAND flash device.42 *43 * Algorithmic details:44 *45 * Encoding is performed by processing 32 input bits in parallel, using 446 * remainder lookup tables.47 *48 * The final stage of decoding involves the following internal steps:49 * a. Syndrome computation50 * b. Error locator polynomial computation using Berlekamp-Massey algorithm51 * 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 in55 * factoring the error locator polynomial using the Berlekamp Trace algorithm56 * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial57 * solving techniques [2] are used. The resulting algorithm, called BTZ, yields58 * much better performance than Chien search for usual (m,t) values (typically59 * m >= 13, t < 32, see [1]).60 *61 * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields62 * of characteristic 2, in: Western European Workshop on Research in Cryptology63 * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.64 * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over65 * 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#else85#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#endif91 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 dbg98#define dbg(_fmt, args...) do {} while (0)99#endif100 101/*102 * represent a polynomial over GF(2^m)103 */104struct 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 */113struct gf_poly_deg1 {114 struct gf_poly poly;115 unsigned int c[2];116};117 118static 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 time128 */129static 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 words151 */152static 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 bytes173 */174static 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 data195 * @bch: BCH control structure196 * @data: data to encode197 * @len: data length in bytes198 * @ecc: ecc parity data, must be initialized by caller199 *200 * The @ecc parity array is used both as input and output parameter, in order to201 * allow incremental computations. It should be of the size indicated by member202 * @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 of205 * @bch; it may be less than m*t for large values of t.206 */207void 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 ... 0251 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt252 * 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^r3257 */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}287EXPORT_SYMBOL_GPL(bch_encode);288 289static 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 */302static 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 308static inline int deg(unsigned int poly)309{310 /* polynomial degree is the most-significant bit index */311 return fls(poly)-1;312}313 314static inline int parity(unsigned int x)315{316 /*317 * public domain code snippet, lifted from318 * http://www-graphics.stanford.edu/~seander/bithacks.html319 */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 328static 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 335static 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 340static 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 347static 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 352static inline unsigned int a_pow(struct bch_control *bch, int i)353{354 return bch->a_pow_tab[modulo(bch, i)];355}356 357static inline int a_log(struct bch_control *bch, unsigned int x)358{359 return bch->a_log_tab[x];360}361 362static 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..2t369 */370static 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 404static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)405{406 memcpy(dst, src, GF_POLY_SZ(src->deg));407}408 409static 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 solutions464 */465static 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 swap(rows[r], rows[p]);484 rem = r+1;485 break;486 }487 }488 if (rem) {489 /* perform elimination on remaining rows */490 tmp = rows[p];491 for (r = rem; r < m; r++) {492 if (rows[r] & mask)493 rows[r] ^= tmp;494 }495 } else {496 /* elimination not needed, store defective row index */497 param[k++] = c;498 }499 mask >>= 1;500 }501 /* rewrite system, inserting fake parameter rows */502 if (k > 0) {503 p = k;504 for (r = m-1; r >= 0; r--) {505 if ((r > m-1-k) && rows[r])506 /* system has no solution */507 return 0;508 509 rows[r] = (p && (r == param[p-1])) ?510 p--, 1u << (m-r) : rows[r-p];511 }512 }513 514 if (nsol != (1 << k))515 /* unexpected number of solutions */516 return 0;517 518 for (p = 0; p < nsol; p++) {519 /* set parameters for p-th solution */520 for (c = 0; c < k; c++)521 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);522 523 /* compute unique solution */524 tmp = 0;525 for (r = m-1; r >= 0; r--) {526 mask = rows[r] & (tmp|1);527 tmp |= parity(mask) << (m-r);528 }529 sol[p] = tmp >> 1;530 }531 return nsol;532}533 534/*535 * this function builds and solves a linear system for finding roots of a degree536 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).537 */538static int find_affine4_roots(struct bch_control *bch, unsigned int a,539 unsigned int b, unsigned int c,540 unsigned int *roots)541{542 int i, j, k;543 const int m = GF_M(bch);544 unsigned int mask = 0xff, t, rows[16] = {0,};545 546 j = a_log(bch, b);547 k = a_log(bch, a);548 rows[0] = c;549 550 /* build linear system to solve X^4+aX^2+bX+c = 0 */551 for (i = 0; i < m; i++) {552 rows[i+1] = bch->a_pow_tab[4*i]^553 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^554 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);555 j++;556 k += 2;557 }558 /*559 * transpose 16x16 matrix before passing it to linear solver560 * warning: this code assumes m < 16561 */562 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {563 for (k = 0; k < 16; k = (k+j+1) & ~j) {564 t = ((rows[k] >> j)^rows[k+j]) & mask;565 rows[k] ^= (t << j);566 rows[k+j] ^= t;567 }568 }569 return solve_linear_system(bch, rows, roots, 4);570}571 572/*573 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))574 */575static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,576 unsigned int *roots)577{578 int n = 0;579 580 if (poly->c[0])581 /* poly[X] = bX+c with c!=0, root=c/b */582 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+583 bch->a_log_tab[poly->c[1]]);584 return n;585}586 587/*588 * compute roots of a degree 2 polynomial over GF(2^m)589 */590static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,591 unsigned int *roots)592{593 int n = 0, i, l0, l1, l2;594 unsigned int u, v, r;595 596 if (poly->c[0] && poly->c[1]) {597 598 l0 = bch->a_log_tab[poly->c[0]];599 l1 = bch->a_log_tab[poly->c[1]];600 l2 = bch->a_log_tab[poly->c[2]];601 602 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */603 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));604 /*605 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):606 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =607 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)608 * i.e. r and r+1 are roots iff Tr(u)=0609 */610 r = 0;611 v = u;612 while (v) {613 i = deg(v);614 r ^= bch->xi_tab[i];615 v ^= (1 << i);616 }617 /* verify root */618 if ((gf_sqr(bch, r)^r) == u) {619 /* reverse z=a/bX transformation and compute log(1/r) */620 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-621 bch->a_log_tab[r]+l2);622 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-623 bch->a_log_tab[r^1]+l2);624 }625 }626 return n;627}628 629/*630 * compute roots of a degree 3 polynomial over GF(2^m)631 */632static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,633 unsigned int *roots)634{635 int i, n = 0;636 unsigned int a, b, c, a2, b2, c2, e3, tmp[4];637 638 if (poly->c[0]) {639 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */640 e3 = poly->c[3];641 c2 = gf_div(bch, poly->c[0], e3);642 b2 = gf_div(bch, poly->c[1], e3);643 a2 = gf_div(bch, poly->c[2], e3);644 645 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */646 c = gf_mul(bch, a2, c2); /* c = a2c2 */647 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */648 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */649 650 /* find the 4 roots of this affine polynomial */651 if (find_affine4_roots(bch, a, b, c, tmp) == 4) {652 /* remove a2 from final list of roots */653 for (i = 0; i < 4; i++) {654 if (tmp[i] != a2)655 roots[n++] = a_ilog(bch, tmp[i]);656 }657 }658 }659 return n;660}661 662/*663 * compute roots of a degree 4 polynomial over GF(2^m)664 */665static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,666 unsigned int *roots)667{668 int i, l, n = 0;669 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;670 671 if (poly->c[0] == 0)672 return 0;673 674 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */675 e4 = poly->c[4];676 d = gf_div(bch, poly->c[0], e4);677 c = gf_div(bch, poly->c[1], e4);678 b = gf_div(bch, poly->c[2], e4);679 a = gf_div(bch, poly->c[3], e4);680 681 /* use Y=1/X transformation to get an affine polynomial */682 if (a) {683 /* first, eliminate cX by using z=X+e with ae^2+c=0 */684 if (c) {685 /* compute e such that e^2 = c/a */686 f = gf_div(bch, c, a);687 l = a_log(bch, f);688 l += (l & 1) ? GF_N(bch) : 0;689 e = a_pow(bch, l/2);690 /*691 * use transformation z=X+e:692 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d693 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d694 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d695 * z^4 + az^3 + b'z^2 + d'696 */697 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;698 b = gf_mul(bch, a, e)^b;699 }700 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */701 if (d == 0)702 /* assume all roots have multiplicity 1 */703 return 0;704 705 c2 = gf_inv(bch, d);706 b2 = gf_div(bch, a, d);707 a2 = gf_div(bch, b, d);708 } else {709 /* polynomial is already affine */710 c2 = d;711 b2 = c;712 a2 = b;713 }714 /* find the 4 roots of this affine polynomial */715 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {716 for (i = 0; i < 4; i++) {717 /* post-process roots (reverse transformations) */718 f = a ? gf_inv(bch, roots[i]) : roots[i];719 roots[i] = a_ilog(bch, f^e);720 }721 n = 4;722 }723 return n;724}725 726/*727 * build monic, log-based representation of a polynomial728 */729static void gf_poly_logrep(struct bch_control *bch,730 const struct gf_poly *a, int *rep)731{732 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);733 734 /* represent 0 values with -1; warning, rep[d] is not set to 1 */735 for (i = 0; i < d; i++)736 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;737}738 739/*740 * compute polynomial Euclidean division remainder in GF(2^m)[X]741 */742static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,743 const struct gf_poly *b, int *rep)744{745 int la, p, m;746 unsigned int i, j, *c = a->c;747 const unsigned int d = b->deg;748 749 if (a->deg < d)750 return;751 752 /* reuse or compute log representation of denominator */753 if (!rep) {754 rep = bch->cache;755 gf_poly_logrep(bch, b, rep);756 }757 758 for (j = a->deg; j >= d; j--) {759 if (c[j]) {760 la = a_log(bch, c[j]);761 p = j-d;762 for (i = 0; i < d; i++, p++) {763 m = rep[i];764 if (m >= 0)765 c[p] ^= bch->a_pow_tab[mod_s(bch,766 m+la)];767 }768 }769 }770 a->deg = d-1;771 while (!c[a->deg] && a->deg)772 a->deg--;773}774 775/*776 * compute polynomial Euclidean division quotient in GF(2^m)[X]777 */778static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,779 const struct gf_poly *b, struct gf_poly *q)780{781 if (a->deg >= b->deg) {782 q->deg = a->deg-b->deg;783 /* compute a mod b (modifies a) */784 gf_poly_mod(bch, a, b, NULL);785 /* quotient is stored in upper part of polynomial a */786 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));787 } else {788 q->deg = 0;789 q->c[0] = 0;790 }791}792 793/*794 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]795 */796static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,797 struct gf_poly *b)798{799 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));800 801 if (a->deg < b->deg)802 swap(a, b);803 804 while (b->deg > 0) {805 gf_poly_mod(bch, a, b, NULL);806 swap(a, b);807 }808 809 dbg("%s\n", gf_poly_str(a));810 811 return a;812}813 814/*815 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f816 * This is used in Berlekamp Trace algorithm for splitting polynomials817 */818static void compute_trace_bk_mod(struct bch_control *bch, int k,819 const struct gf_poly *f, struct gf_poly *z,820 struct gf_poly *out)821{822 const int m = GF_M(bch);823 int i, j;824 825 /* z contains z^2j mod f */826 z->deg = 1;827 z->c[0] = 0;828 z->c[1] = bch->a_pow_tab[k];829 830 out->deg = 0;831 memset(out, 0, GF_POLY_SZ(f->deg));832 833 /* compute f log representation only once */834 gf_poly_logrep(bch, f, bch->cache);835 836 for (i = 0; i < m; i++) {837 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */838 for (j = z->deg; j >= 0; j--) {839 out->c[j] ^= z->c[j];840 z->c[2*j] = gf_sqr(bch, z->c[j]);841 z->c[2*j+1] = 0;842 }843 if (z->deg > out->deg)844 out->deg = z->deg;845 846 if (i < m-1) {847 z->deg *= 2;848 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */849 gf_poly_mod(bch, z, f, bch->cache);850 }851 }852 while (!out->c[out->deg] && out->deg)853 out->deg--;854 855 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));856}857 858/*859 * factor a polynomial using Berlekamp Trace algorithm (BTA)860 */861static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,862 struct gf_poly **g, struct gf_poly **h)863{864 struct gf_poly *f2 = bch->poly_2t[0];865 struct gf_poly *q = bch->poly_2t[1];866 struct gf_poly *tk = bch->poly_2t[2];867 struct gf_poly *z = bch->poly_2t[3];868 struct gf_poly *gcd;869 870 dbg("factoring %s...\n", gf_poly_str(f));871 872 *g = f;873 *h = NULL;874 875 /* tk = Tr(a^k.X) mod f */876 compute_trace_bk_mod(bch, k, f, z, tk);877 878 if (tk->deg > 0) {879 /* compute g = gcd(f, tk) (destructive operation) */880 gf_poly_copy(f2, f);881 gcd = gf_poly_gcd(bch, f2, tk);882 if (gcd->deg < f->deg) {883 /* compute h=f/gcd(f,tk); this will modify f and q */884 gf_poly_div(bch, f, gcd, q);885 /* store g and h in-place (clobbering f) */886 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;887 gf_poly_copy(*g, gcd);888 gf_poly_copy(*h, q);889 }890 }891}892 893/*894 * find roots of a polynomial, using BTZ algorithm; see the beginning of this895 * file for details896 */897static int find_poly_roots(struct bch_control *bch, unsigned int k,898 struct gf_poly *poly, unsigned int *roots)899{900 int cnt;901 struct gf_poly *f1, *f2;902 903 switch (poly->deg) {904 /* handle low degree polynomials with ad hoc techniques */905 case 1:906 cnt = find_poly_deg1_roots(bch, poly, roots);907 break;908 case 2:909 cnt = find_poly_deg2_roots(bch, poly, roots);910 break;911 case 3:912 cnt = find_poly_deg3_roots(bch, poly, roots);913 break;914 case 4:915 cnt = find_poly_deg4_roots(bch, poly, roots);916 break;917 default:918 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */919 cnt = 0;920 if (poly->deg && (k <= GF_M(bch))) {921 factor_polynomial(bch, k, poly, &f1, &f2);922 if (f1)923 cnt += find_poly_roots(bch, k+1, f1, roots);924 if (f2)925 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);926 }927 break;928 }929 return cnt;930}931 932#if defined(USE_CHIEN_SEARCH)933/*934 * exhaustive root search (Chien) implementation - not used, included only for935 * reference/comparison tests936 */937static int chien_search(struct bch_control *bch, unsigned int len,938 struct gf_poly *p, unsigned int *roots)939{940 int m;941 unsigned int i, j, syn, syn0, count = 0;942 const unsigned int k = 8*len+bch->ecc_bits;943 944 /* use a log-based representation of polynomial */945 gf_poly_logrep(bch, p, bch->cache);946 bch->cache[p->deg] = 0;947 syn0 = gf_div(bch, p->c[0], p->c[p->deg]);948 949 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {950 /* compute elp(a^i) */951 for (j = 1, syn = syn0; j <= p->deg; j++) {952 m = bch->cache[j];953 if (m >= 0)954 syn ^= a_pow(bch, m+j*i);955 }956 if (syn == 0) {957 roots[count++] = GF_N(bch)-i;958 if (count == p->deg)959 break;960 }961 }962 return (count == p->deg) ? count : 0;963}964#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)965#endif /* USE_CHIEN_SEARCH */966 967/**968 * bch_decode - decode received codeword and find bit error locations969 * @bch: BCH control structure970 * @data: received data, ignored if @calc_ecc is provided971 * @len: data length in bytes, must always be provided972 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc973 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data974 * @syn: hw computed syndrome data (if NULL, syndrome is calculated)975 * @errloc: output array of error locations976 *977 * Returns:978 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if979 * invalid parameters were provided980 *981 * Depending on the available hw BCH support and the need to compute @calc_ecc982 * separately (using bch_encode()), this function should be called with one of983 * the following parameter configurations -984 *985 * by providing @data and @recv_ecc only:986 * bch_decode(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)987 *988 * by providing @recv_ecc and @calc_ecc:989 * bch_decode(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)990 *991 * by providing ecc = recv_ecc XOR calc_ecc:992 * bch_decode(@bch, NULL, @len, NULL, ecc, NULL, @errloc)993 *994 * by providing syndrome results @syn:995 * bch_decode(@bch, NULL, @len, NULL, NULL, @syn, @errloc)996 *997 * Once bch_decode() has successfully returned with a positive value, error998 * locations returned in array @errloc should be interpreted as follows -999 *1000 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for1001 * data correction)1002 *1003 * if (errloc[n] < 8*len), then n-th error is located in data and can be1004 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);1005 *1006 * Note that this function does not perform any data correction by itself, it1007 * merely indicates error locations.1008 */1009int bch_decode(struct bch_control *bch, const uint8_t *data, unsigned int len,1010 const uint8_t *recv_ecc, const uint8_t *calc_ecc,1011 const unsigned int *syn, unsigned int *errloc)1012{1013 const unsigned int ecc_words = BCH_ECC_WORDS(bch);1014 unsigned int nbits;1015 int i, err, nroots;1016 uint32_t sum;1017 1018 /* sanity check: make sure data length can be handled */1019 if (8*len > (bch->n-bch->ecc_bits))1020 return -EINVAL;1021 1022 /* if caller does not provide syndromes, compute them */1023 if (!syn) {1024 if (!calc_ecc) {1025 /* compute received data ecc into an internal buffer */1026 if (!data || !recv_ecc)1027 return -EINVAL;1028 bch_encode(bch, data, len, NULL);1029 } else {1030 /* load provided calculated ecc */1031 load_ecc8(bch, bch->ecc_buf, calc_ecc);1032 }1033 /* load received ecc or assume it was XORed in calc_ecc */1034 if (recv_ecc) {1035 load_ecc8(bch, bch->ecc_buf2, recv_ecc);1036 /* XOR received and calculated ecc */1037 for (i = 0, sum = 0; i < (int)ecc_words; i++) {1038 bch->ecc_buf[i] ^= bch->ecc_buf2[i];1039 sum |= bch->ecc_buf[i];1040 }1041 if (!sum)1042 /* no error found */1043 return 0;1044 }1045 compute_syndromes(bch, bch->ecc_buf, bch->syn);1046 syn = bch->syn;1047 }1048 1049 err = compute_error_locator_polynomial(bch, syn);1050 if (err > 0) {1051 nroots = find_poly_roots(bch, 1, bch->elp, errloc);1052 if (err != nroots)1053 err = -1;1054 }1055 if (err > 0) {1056 /* post-process raw error locations for easier correction */1057 nbits = (len*8)+bch->ecc_bits;1058 for (i = 0; i < err; i++) {1059 if (errloc[i] >= nbits) {1060 err = -1;1061 break;1062 }1063 errloc[i] = nbits-1-errloc[i];1064 if (!bch->swap_bits)1065 errloc[i] = (errloc[i] & ~7) |1066 (7-(errloc[i] & 7));1067 }1068 }1069 return (err >= 0) ? err : -EBADMSG;1070}1071EXPORT_SYMBOL_GPL(bch_decode);1072 1073/*1074 * generate Galois field lookup tables1075 */1076static int build_gf_tables(struct bch_control *bch, unsigned int poly)1077{1078 unsigned int i, x = 1;1079 const unsigned int k = 1 << deg(poly);1080 1081 /* primitive polynomial must be of degree m */1082 if (k != (1u << GF_M(bch)))1083 return -1;1084 1085 for (i = 0; i < GF_N(bch); i++) {1086 bch->a_pow_tab[i] = x;1087 bch->a_log_tab[x] = i;1088 if (i && (x == 1))1089 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */1090 return -1;1091 x <<= 1;1092 if (x & k)1093 x ^= poly;1094 }1095 bch->a_pow_tab[GF_N(bch)] = 1;1096 bch->a_log_tab[0] = 0;1097 1098 return 0;1099}1100 1101/*1102 * compute generator polynomial remainder tables for fast encoding1103 */1104static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)1105{1106 int i, j, b, d;1107 uint32_t data, hi, lo, *tab;1108 const int l = BCH_ECC_WORDS(bch);1109 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);1110 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);1111 1112 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));1113 1114 for (i = 0; i < 256; i++) {1115 /* p(X)=i is a small polynomial of weight <= 8 */1116 for (b = 0; b < 4; b++) {1117 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */1118 tab = bch->mod8_tab + (b*256+i)*l;1119 data = i << (8*b);1120 while (data) {1121 d = deg(data);1122 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */1123 data ^= g[0] >> (31-d);1124 for (j = 0; j < ecclen; j++) {1125 hi = (d < 31) ? g[j] << (d+1) : 0;1126 lo = (j+1 < plen) ?1127 g[j+1] >> (31-d) : 0;1128 tab[j] ^= hi|lo;1129 }1130 }1131 }1132 }1133}1134 1135/*1136 * build a base for factoring degree 2 polynomials1137 */1138static int build_deg2_base(struct bch_control *bch)1139{1140 const int m = GF_M(bch);1141 int i, j, r;1142 unsigned int sum, x, y, remaining, ak = 0, xi[BCH_MAX_M];1143 1144 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */1145 for (i = 0; i < m; i++) {1146 for (j = 0, sum = 0; j < m; j++)1147 sum ^= a_pow(bch, i*(1 << j));1148 1149 if (sum) {1150 ak = bch->a_pow_tab[i];1151 break;1152 }1153 }1154 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */1155 remaining = m;1156 memset(xi, 0, sizeof(xi));1157 1158 for (x = 0; (x <= GF_N(bch)) && remaining; x++) {1159 y = gf_sqr(bch, x)^x;1160 for (i = 0; i < 2; i++) {1161 r = a_log(bch, y);1162 if (y && (r < m) && !xi[r]) {1163 bch->xi_tab[r] = x;1164 xi[r] = 1;1165 remaining--;1166 dbg("x%d = %x\n", r, x);1167 break;1168 }1169 y ^= ak;1170 }1171 }1172 /* should not happen but check anyway */1173 return remaining ? -1 : 0;1174}1175 1176static void *bch_alloc(size_t size, int *err)1177{1178 void *ptr;1179 1180 ptr = kmalloc(size, GFP_KERNEL);1181 if (ptr == NULL)1182 *err = 1;1183 return ptr;1184}1185 1186/*1187 * compute generator polynomial for given (m,t) parameters.1188 */1189static uint32_t *compute_generator_polynomial(struct bch_control *bch)1190{1191 const unsigned int m = GF_M(bch);1192 const unsigned int t = GF_T(bch);1193 int n, err = 0;1194 unsigned int i, j, nbits, r, word, *roots;1195 struct gf_poly *g;1196 uint32_t *genpoly;1197 1198 g = bch_alloc(GF_POLY_SZ(m*t), &err);1199 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);1200 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);1201 1202 if (err) {1203 kfree(genpoly);1204 genpoly = NULL;1205 goto finish;1206 }1207 1208 /* enumerate all roots of g(X) */1209 memset(roots , 0, (bch->n+1)*sizeof(*roots));1210 for (i = 0; i < t; i++) {1211 for (j = 0, r = 2*i+1; j < m; j++) {1212 roots[r] = 1;1213 r = mod_s(bch, 2*r);1214 }1215 }1216 /* build generator polynomial g(X) */1217 g->deg = 0;1218 g->c[0] = 1;1219 for (i = 0; i < GF_N(bch); i++) {1220 if (roots[i]) {1221 /* multiply g(X) by (X+root) */1222 r = bch->a_pow_tab[i];1223 g->c[g->deg+1] = 1;1224 for (j = g->deg; j > 0; j--)1225 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];1226 1227 g->c[0] = gf_mul(bch, g->c[0], r);1228 g->deg++;1229 }1230 }1231 /* store left-justified binary representation of g(X) */1232 n = g->deg+1;1233 i = 0;1234 1235 while (n > 0) {1236 nbits = (n > 32) ? 32 : n;1237 for (j = 0, word = 0; j < nbits; j++) {1238 if (g->c[n-1-j])1239 word |= 1u << (31-j);1240 }1241 genpoly[i++] = word;1242 n -= nbits;1243 }1244 bch->ecc_bits = g->deg;1245 1246finish:1247 kfree(g);1248 kfree(roots);1249 1250 return genpoly;1251}1252 1253/**1254 * bch_init - initialize a BCH encoder/decoder1255 * @m: Galois field order, should be in the range 5-151256 * @t: maximum error correction capability, in bits1257 * @prim_poly: user-provided primitive polynomial (or 0 to use default)1258 * @swap_bits: swap bits within data and syndrome bytes1259 *1260 * Returns:1261 * a newly allocated BCH control structure if successful, NULL otherwise1262 *1263 * This initialization can take some time, as lookup tables are built for fast1264 * encoding/decoding; make sure not to call this function from a time critical1265 * path. Usually, bch_init() should be called on module/driver init and1266 * bch_free() should be called to release memory on exit.1267 *1268 * You may provide your own primitive polynomial of degree @m in argument1269 * @prim_poly, or let bch_init() use its default polynomial.1270 *1271 * Once bch_init() has successfully returned a pointer to a newly allocated1272 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of1273 * the structure.1274 */1275struct bch_control *bch_init(int m, int t, unsigned int prim_poly,1276 bool swap_bits)1277{1278 int err = 0;1279 unsigned int i, words;1280 uint32_t *genpoly;1281 struct bch_control *bch = NULL;1282 1283 const int min_m = 5;1284 1285 /* default primitive polynomials */1286 static const unsigned int prim_poly_tab[] = {1287 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,1288 0x402b, 0x8003,1289 };1290 1291#if defined(CONFIG_BCH_CONST_PARAMS)1292 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {1293 printk(KERN_ERR "bch encoder/decoder was configured to support "1294 "parameters m=%d, t=%d only!\n",1295 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);1296 goto fail;1297 }1298#endif1299 if ((m < min_m) || (m > BCH_MAX_M))1300 /*1301 * values of m greater than 15 are not currently supported;1302 * supporting m > 15 would require changing table base type1303 * (uint16_t) and a small patch in matrix transposition1304 */1305 goto fail;1306 1307 if (t > BCH_MAX_T)1308 /*1309 * we can support larger than 64 bits if necessary, at the1310 * cost of higher stack usage.1311 */1312 goto fail;1313 1314 /* sanity checks */1315 if ((t < 1) || (m*t >= ((1 << m)-1)))1316 /* invalid t value */1317 goto fail;1318 1319 /* select a primitive polynomial for generating GF(2^m) */1320 if (prim_poly == 0)1321 prim_poly = prim_poly_tab[m-min_m];1322 1323 bch = kzalloc(sizeof(*bch), GFP_KERNEL);1324 if (bch == NULL)1325 goto fail;1326 1327 bch->m = m;1328 bch->t = t;1329 bch->n = (1 << m)-1;1330 words = DIV_ROUND_UP(m*t, 32);1331 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);1332 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);1333 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);1334 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);1335 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err);1336 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);1337 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err);1338 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err);1339 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err);1340 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);1341 bch->swap_bits = swap_bits;1342 1343 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)1344 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);1345 1346 if (err)1347 goto fail;1348 1349 err = build_gf_tables(bch, prim_poly);1350 if (err)1351 goto fail;1352 1353 /* use generator polynomial for computing encoding tables */1354 genpoly = compute_generator_polynomial(bch);1355 if (genpoly == NULL)1356 goto fail;1357 1358 build_mod8_tables(bch, genpoly);1359 kfree(genpoly);1360 1361 err = build_deg2_base(bch);1362 if (err)1363 goto fail;1364 1365 return bch;1366 1367fail:1368 bch_free(bch);1369 return NULL;1370}1371EXPORT_SYMBOL_GPL(bch_init);1372 1373/**1374 * bch_free - free the BCH control structure1375 * @bch: BCH control structure to release1376 */1377void bch_free(struct bch_control *bch)1378{1379 unsigned int i;1380 1381 if (bch) {1382 kfree(bch->a_pow_tab);1383 kfree(bch->a_log_tab);1384 kfree(bch->mod8_tab);1385 kfree(bch->ecc_buf);1386 kfree(bch->ecc_buf2);1387 kfree(bch->xi_tab);1388 kfree(bch->syn);1389 kfree(bch->cache);1390 kfree(bch->elp);1391 1392 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)1393 kfree(bch->poly_2t[i]);1394 1395 kfree(bch);1396 }1397}1398EXPORT_SYMBOL_GPL(bch_free);1399 1400MODULE_LICENSE("GPL");1401MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");1402MODULE_DESCRIPTION("Binary BCH encoder/decoder");1403