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Christian Hitz4c6de852011-10-12 09:31:59 +02001/*
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 <common.h>
69#include <ubi_uboot.h>
70
71#include <linux/bitops.h>
72#include <asm/byteorder.h>
73#include <linux/bch.h>
74
75#if defined(CONFIG_BCH_CONST_PARAMS)
76#define GF_M(_p) (CONFIG_BCH_CONST_M)
77#define GF_T(_p) (CONFIG_BCH_CONST_T)
78#define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1)
79#else
80#define GF_M(_p) ((_p)->m)
81#define GF_T(_p) ((_p)->t)
82#define GF_N(_p) ((_p)->n)
83#endif
84
85#define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
86#define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
87
88#ifndef dbg
89#define dbg(_fmt, args...) do {} while (0)
90#endif
91
92/*
93 * represent a polynomial over GF(2^m)
94 */
95struct gf_poly {
96 unsigned int deg; /* polynomial degree */
97 unsigned int c[0]; /* polynomial terms */
98};
99
100/* given its degree, compute a polynomial size in bytes */
101#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
102
103/* polynomial of degree 1 */
104struct gf_poly_deg1 {
105 struct gf_poly poly;
106 unsigned int c[2];
107};
108
109/*
110 * same as encode_bch(), but process input data one byte at a time
111 */
112static void encode_bch_unaligned(struct bch_control *bch,
113 const unsigned char *data, unsigned int len,
114 uint32_t *ecc)
115{
116 int i;
117 const uint32_t *p;
118 const int l = BCH_ECC_WORDS(bch)-1;
119
120 while (len--) {
121 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
122
123 for (i = 0; i < l; i++)
124 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
125
126 ecc[l] = (ecc[l] << 8)^(*p);
127 }
128}
129
130/*
131 * convert ecc bytes to aligned, zero-padded 32-bit ecc words
132 */
133static void load_ecc8(struct bch_control *bch, uint32_t *dst,
134 const uint8_t *src)
135{
136 uint8_t pad[4] = {0, 0, 0, 0};
137 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
138
139 for (i = 0; i < nwords; i++, src += 4)
140 dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
141
142 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
143 dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
144}
145
146/*
147 * convert 32-bit ecc words to ecc bytes
148 */
149static void store_ecc8(struct bch_control *bch, uint8_t *dst,
150 const uint32_t *src)
151{
152 uint8_t pad[4];
153 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
154
155 for (i = 0; i < nwords; i++) {
156 *dst++ = (src[i] >> 24);
157 *dst++ = (src[i] >> 16) & 0xff;
158 *dst++ = (src[i] >> 8) & 0xff;
159 *dst++ = (src[i] >> 0) & 0xff;
160 }
161 pad[0] = (src[nwords] >> 24);
162 pad[1] = (src[nwords] >> 16) & 0xff;
163 pad[2] = (src[nwords] >> 8) & 0xff;
164 pad[3] = (src[nwords] >> 0) & 0xff;
165 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
166}
167
168/**
169 * encode_bch - calculate BCH ecc parity of data
170 * @bch: BCH control structure
171 * @data: data to encode
172 * @len: data length in bytes
173 * @ecc: ecc parity data, must be initialized by caller
174 *
175 * The @ecc parity array is used both as input and output parameter, in order to
176 * allow incremental computations. It should be of the size indicated by member
177 * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
178 *
179 * The exact number of computed ecc parity bits is given by member @ecc_bits of
180 * @bch; it may be less than m*t for large values of t.
181 */
182void encode_bch(struct bch_control *bch, const uint8_t *data,
183 unsigned int len, uint8_t *ecc)
184{
185 const unsigned int l = BCH_ECC_WORDS(bch)-1;
186 unsigned int i, mlen;
187 unsigned long m;
188 uint32_t w, r[l+1];
189 const uint32_t * const tab0 = bch->mod8_tab;
190 const uint32_t * const tab1 = tab0 + 256*(l+1);
191 const uint32_t * const tab2 = tab1 + 256*(l+1);
192 const uint32_t * const tab3 = tab2 + 256*(l+1);
193 const uint32_t *pdata, *p0, *p1, *p2, *p3;
194
195 if (ecc) {
196 /* load ecc parity bytes into internal 32-bit buffer */
197 load_ecc8(bch, bch->ecc_buf, ecc);
198 } else {
199 memset(bch->ecc_buf, 0, sizeof(r));
200 }
201
202 /* process first unaligned data bytes */
203 m = ((unsigned long)data) & 3;
204 if (m) {
205 mlen = (len < (4-m)) ? len : 4-m;
206 encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
207 data += mlen;
208 len -= mlen;
209 }
210
211 /* process 32-bit aligned data words */
212 pdata = (uint32_t *)data;
213 mlen = len/4;
214 data += 4*mlen;
215 len -= 4*mlen;
216 memcpy(r, bch->ecc_buf, sizeof(r));
217
218 /*
219 * split each 32-bit word into 4 polynomials of weight 8 as follows:
220 *
221 * 31 ...24 23 ...16 15 ... 8 7 ... 0
222 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt
223 * tttttttt mod g = r0 (precomputed)
224 * zzzzzzzz 00000000 mod g = r1 (precomputed)
225 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed)
226 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed)
227 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3
228 */
229 while (mlen--) {
230 /* input data is read in big-endian format */
231 w = r[0]^cpu_to_be32(*pdata++);
232 p0 = tab0 + (l+1)*((w >> 0) & 0xff);
233 p1 = tab1 + (l+1)*((w >> 8) & 0xff);
234 p2 = tab2 + (l+1)*((w >> 16) & 0xff);
235 p3 = tab3 + (l+1)*((w >> 24) & 0xff);
236
237 for (i = 0; i < l; i++)
238 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
239
240 r[l] = p0[l]^p1[l]^p2[l]^p3[l];
241 }
242 memcpy(bch->ecc_buf, r, sizeof(r));
243
244 /* process last unaligned bytes */
245 if (len)
246 encode_bch_unaligned(bch, data, len, bch->ecc_buf);
247
248 /* store ecc parity bytes into original parity buffer */
249 if (ecc)
250 store_ecc8(bch, ecc, bch->ecc_buf);
251}
252
253static inline int modulo(struct bch_control *bch, unsigned int v)
254{
255 const unsigned int n = GF_N(bch);
256 while (v >= n) {
257 v -= n;
258 v = (v & n) + (v >> GF_M(bch));
259 }
260 return v;
261}
262
263/*
264 * shorter and faster modulo function, only works when v < 2N.
265 */
266static inline int mod_s(struct bch_control *bch, unsigned int v)
267{
268 const unsigned int n = GF_N(bch);
269 return (v < n) ? v : v-n;
270}
271
272static inline int deg(unsigned int poly)
273{
274 /* polynomial degree is the most-significant bit index */
275 return fls(poly)-1;
276}
277
278static inline int parity(unsigned int x)
279{
280 /*
281 * public domain code snippet, lifted from
282 * http://www-graphics.stanford.edu/~seander/bithacks.html
283 */
284 x ^= x >> 1;
285 x ^= x >> 2;
286 x = (x & 0x11111111U) * 0x11111111U;
287 return (x >> 28) & 1;
288}
289
290/* Galois field basic operations: multiply, divide, inverse, etc. */
291
292static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
293 unsigned int b)
294{
295 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
296 bch->a_log_tab[b])] : 0;
297}
298
299static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
300{
301 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
302}
303
304static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
305 unsigned int b)
306{
307 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
308 GF_N(bch)-bch->a_log_tab[b])] : 0;
309}
310
311static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
312{
313 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
314}
315
316static inline unsigned int a_pow(struct bch_control *bch, int i)
317{
318 return bch->a_pow_tab[modulo(bch, i)];
319}
320
321static inline int a_log(struct bch_control *bch, unsigned int x)
322{
323 return bch->a_log_tab[x];
324}
325
326static inline int a_ilog(struct bch_control *bch, unsigned int x)
327{
328 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
329}
330
331/*
332 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
333 */
334static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
335 unsigned int *syn)
336{
337 int i, j, s;
338 unsigned int m;
339 uint32_t poly;
340 const int t = GF_T(bch);
341
342 s = bch->ecc_bits;
343
344 /* make sure extra bits in last ecc word are cleared */
345 m = ((unsigned int)s) & 31;
346 if (m)
347 ecc[s/32] &= ~((1u << (32-m))-1);
348 memset(syn, 0, 2*t*sizeof(*syn));
349
350 /* compute v(a^j) for j=1 .. 2t-1 */
351 do {
352 poly = *ecc++;
353 s -= 32;
354 while (poly) {
355 i = deg(poly);
356 for (j = 0; j < 2*t; j += 2)
357 syn[j] ^= a_pow(bch, (j+1)*(i+s));
358
359 poly ^= (1 << i);
360 }
361 } while (s > 0);
362
363 /* v(a^(2j)) = v(a^j)^2 */
364 for (j = 0; j < t; j++)
365 syn[2*j+1] = gf_sqr(bch, syn[j]);
366}
367
368static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
369{
370 memcpy(dst, src, GF_POLY_SZ(src->deg));
371}
372
373static int compute_error_locator_polynomial(struct bch_control *bch,
374 const unsigned int *syn)
375{
376 const unsigned int t = GF_T(bch);
377 const unsigned int n = GF_N(bch);
378 unsigned int i, j, tmp, l, pd = 1, d = syn[0];
379 struct gf_poly *elp = bch->elp;
380 struct gf_poly *pelp = bch->poly_2t[0];
381 struct gf_poly *elp_copy = bch->poly_2t[1];
382 int k, pp = -1;
383
384 memset(pelp, 0, GF_POLY_SZ(2*t));
385 memset(elp, 0, GF_POLY_SZ(2*t));
386
387 pelp->deg = 0;
388 pelp->c[0] = 1;
389 elp->deg = 0;
390 elp->c[0] = 1;
391
392 /* use simplified binary Berlekamp-Massey algorithm */
393 for (i = 0; (i < t) && (elp->deg <= t); i++) {
394 if (d) {
395 k = 2*i-pp;
396 gf_poly_copy(elp_copy, elp);
397 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
398 tmp = a_log(bch, d)+n-a_log(bch, pd);
399 for (j = 0; j <= pelp->deg; j++) {
400 if (pelp->c[j]) {
401 l = a_log(bch, pelp->c[j]);
402 elp->c[j+k] ^= a_pow(bch, tmp+l);
403 }
404 }
405 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
406 tmp = pelp->deg+k;
407 if (tmp > elp->deg) {
408 elp->deg = tmp;
409 gf_poly_copy(pelp, elp_copy);
410 pd = d;
411 pp = 2*i;
412 }
413 }
414 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
415 if (i < t-1) {
416 d = syn[2*i+2];
417 for (j = 1; j <= elp->deg; j++)
418 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
419 }
420 }
421 dbg("elp=%s\n", gf_poly_str(elp));
422 return (elp->deg > t) ? -1 : (int)elp->deg;
423}
424
425/*
426 * solve a m x m linear system in GF(2) with an expected number of solutions,
427 * and return the number of found solutions
428 */
429static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
430 unsigned int *sol, int nsol)
431{
432 const int m = GF_M(bch);
433 unsigned int tmp, mask;
434 int rem, c, r, p, k, param[m];
435
436 k = 0;
437 mask = 1 << m;
438
439 /* Gaussian elimination */
440 for (c = 0; c < m; c++) {
441 rem = 0;
442 p = c-k;
443 /* find suitable row for elimination */
444 for (r = p; r < m; r++) {
445 if (rows[r] & mask) {
446 if (r != p) {
447 tmp = rows[r];
448 rows[r] = rows[p];
449 rows[p] = tmp;
450 }
451 rem = r+1;
452 break;
453 }
454 }
455 if (rem) {
456 /* perform elimination on remaining rows */
457 tmp = rows[p];
458 for (r = rem; r < m; r++) {
459 if (rows[r] & mask)
460 rows[r] ^= tmp;
461 }
462 } else {
463 /* elimination not needed, store defective row index */
464 param[k++] = c;
465 }
466 mask >>= 1;
467 }
468 /* rewrite system, inserting fake parameter rows */
469 if (k > 0) {
470 p = k;
471 for (r = m-1; r >= 0; r--) {
472 if ((r > m-1-k) && rows[r])
473 /* system has no solution */
474 return 0;
475
476 rows[r] = (p && (r == param[p-1])) ?
477 p--, 1u << (m-r) : rows[r-p];
478 }
479 }
480
481 if (nsol != (1 << k))
482 /* unexpected number of solutions */
483 return 0;
484
485 for (p = 0; p < nsol; p++) {
486 /* set parameters for p-th solution */
487 for (c = 0; c < k; c++)
488 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
489
490 /* compute unique solution */
491 tmp = 0;
492 for (r = m-1; r >= 0; r--) {
493 mask = rows[r] & (tmp|1);
494 tmp |= parity(mask) << (m-r);
495 }
496 sol[p] = tmp >> 1;
497 }
498 return nsol;
499}
500
501/*
502 * this function builds and solves a linear system for finding roots of a degree
503 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
504 */
505static int find_affine4_roots(struct bch_control *bch, unsigned int a,
506 unsigned int b, unsigned int c,
507 unsigned int *roots)
508{
509 int i, j, k;
510 const int m = GF_M(bch);
511 unsigned int mask = 0xff, t, rows[16] = {0,};
512
513 j = a_log(bch, b);
514 k = a_log(bch, a);
515 rows[0] = c;
516
517 /* buid linear system to solve X^4+aX^2+bX+c = 0 */
518 for (i = 0; i < m; i++) {
519 rows[i+1] = bch->a_pow_tab[4*i]^
520 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
521 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
522 j++;
523 k += 2;
524 }
525 /*
526 * transpose 16x16 matrix before passing it to linear solver
527 * warning: this code assumes m < 16
528 */
529 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
530 for (k = 0; k < 16; k = (k+j+1) & ~j) {
531 t = ((rows[k] >> j)^rows[k+j]) & mask;
532 rows[k] ^= (t << j);
533 rows[k+j] ^= t;
534 }
535 }
536 return solve_linear_system(bch, rows, roots, 4);
537}
538
539/*
540 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
541 */
542static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
543 unsigned int *roots)
544{
545 int n = 0;
546
547 if (poly->c[0])
548 /* poly[X] = bX+c with c!=0, root=c/b */
549 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
550 bch->a_log_tab[poly->c[1]]);
551 return n;
552}
553
554/*
555 * compute roots of a degree 2 polynomial over GF(2^m)
556 */
557static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
558 unsigned int *roots)
559{
560 int n = 0, i, l0, l1, l2;
561 unsigned int u, v, r;
562
563 if (poly->c[0] && poly->c[1]) {
564
565 l0 = bch->a_log_tab[poly->c[0]];
566 l1 = bch->a_log_tab[poly->c[1]];
567 l2 = bch->a_log_tab[poly->c[2]];
568
569 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
570 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
571 /*
572 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
573 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
574 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
575 * i.e. r and r+1 are roots iff Tr(u)=0
576 */
577 r = 0;
578 v = u;
579 while (v) {
580 i = deg(v);
581 r ^= bch->xi_tab[i];
582 v ^= (1 << i);
583 }
584 /* verify root */
585 if ((gf_sqr(bch, r)^r) == u) {
586 /* reverse z=a/bX transformation and compute log(1/r) */
587 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
588 bch->a_log_tab[r]+l2);
589 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
590 bch->a_log_tab[r^1]+l2);
591 }
592 }
593 return n;
594}
595
596/*
597 * compute roots of a degree 3 polynomial over GF(2^m)
598 */
599static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
600 unsigned int *roots)
601{
602 int i, n = 0;
603 unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
604
605 if (poly->c[0]) {
606 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
607 e3 = poly->c[3];
608 c2 = gf_div(bch, poly->c[0], e3);
609 b2 = gf_div(bch, poly->c[1], e3);
610 a2 = gf_div(bch, poly->c[2], e3);
611
612 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
613 c = gf_mul(bch, a2, c2); /* c = a2c2 */
614 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */
615 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */
616
617 /* find the 4 roots of this affine polynomial */
618 if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
619 /* remove a2 from final list of roots */
620 for (i = 0; i < 4; i++) {
621 if (tmp[i] != a2)
622 roots[n++] = a_ilog(bch, tmp[i]);
623 }
624 }
625 }
626 return n;
627}
628
629/*
630 * compute roots of a degree 4 polynomial over GF(2^m)
631 */
632static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
633 unsigned int *roots)
634{
635 int i, l, n = 0;
636 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
637
638 if (poly->c[0] == 0)
639 return 0;
640
641 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
642 e4 = poly->c[4];
643 d = gf_div(bch, poly->c[0], e4);
644 c = gf_div(bch, poly->c[1], e4);
645 b = gf_div(bch, poly->c[2], e4);
646 a = gf_div(bch, poly->c[3], e4);
647
648 /* use Y=1/X transformation to get an affine polynomial */
649 if (a) {
650 /* first, eliminate cX by using z=X+e with ae^2+c=0 */
651 if (c) {
652 /* compute e such that e^2 = c/a */
653 f = gf_div(bch, c, a);
654 l = a_log(bch, f);
655 l += (l & 1) ? GF_N(bch) : 0;
656 e = a_pow(bch, l/2);
657 /*
658 * use transformation z=X+e:
659 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
660 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
661 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
662 * z^4 + az^3 + b'z^2 + d'
663 */
664 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
665 b = gf_mul(bch, a, e)^b;
666 }
667 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
668 if (d == 0)
669 /* assume all roots have multiplicity 1 */
670 return 0;
671
672 c2 = gf_inv(bch, d);
673 b2 = gf_div(bch, a, d);
674 a2 = gf_div(bch, b, d);
675 } else {
676 /* polynomial is already affine */
677 c2 = d;
678 b2 = c;
679 a2 = b;
680 }
681 /* find the 4 roots of this affine polynomial */
682 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
683 for (i = 0; i < 4; i++) {
684 /* post-process roots (reverse transformations) */
685 f = a ? gf_inv(bch, roots[i]) : roots[i];
686 roots[i] = a_ilog(bch, f^e);
687 }
688 n = 4;
689 }
690 return n;
691}
692
693/*
694 * build monic, log-based representation of a polynomial
695 */
696static void gf_poly_logrep(struct bch_control *bch,
697 const struct gf_poly *a, int *rep)
698{
699 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
700
701 /* represent 0 values with -1; warning, rep[d] is not set to 1 */
702 for (i = 0; i < d; i++)
703 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
704}
705
706/*
707 * compute polynomial Euclidean division remainder in GF(2^m)[X]
708 */
709static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
710 const struct gf_poly *b, int *rep)
711{
712 int la, p, m;
713 unsigned int i, j, *c = a->c;
714 const unsigned int d = b->deg;
715
716 if (a->deg < d)
717 return;
718
719 /* reuse or compute log representation of denominator */
720 if (!rep) {
721 rep = bch->cache;
722 gf_poly_logrep(bch, b, rep);
723 }
724
725 for (j = a->deg; j >= d; j--) {
726 if (c[j]) {
727 la = a_log(bch, c[j]);
728 p = j-d;
729 for (i = 0; i < d; i++, p++) {
730 m = rep[i];
731 if (m >= 0)
732 c[p] ^= bch->a_pow_tab[mod_s(bch,
733 m+la)];
734 }
735 }
736 }
737 a->deg = d-1;
738 while (!c[a->deg] && a->deg)
739 a->deg--;
740}
741
742/*
743 * compute polynomial Euclidean division quotient in GF(2^m)[X]
744 */
745static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
746 const struct gf_poly *b, struct gf_poly *q)
747{
748 if (a->deg >= b->deg) {
749 q->deg = a->deg-b->deg;
750 /* compute a mod b (modifies a) */
751 gf_poly_mod(bch, a, b, NULL);
752 /* quotient is stored in upper part of polynomial a */
753 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
754 } else {
755 q->deg = 0;
756 q->c[0] = 0;
757 }
758}
759
760/*
761 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
762 */
763static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
764 struct gf_poly *b)
765{
766 struct gf_poly *tmp;
767
768 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
769
770 if (a->deg < b->deg) {
771 tmp = b;
772 b = a;
773 a = tmp;
774 }
775
776 while (b->deg > 0) {
777 gf_poly_mod(bch, a, b, NULL);
778 tmp = b;
779 b = a;
780 a = tmp;
781 }
782
783 dbg("%s\n", gf_poly_str(a));
784
785 return a;
786}
787
788/*
789 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
790 * This is used in Berlekamp Trace algorithm for splitting polynomials
791 */
792static void compute_trace_bk_mod(struct bch_control *bch, int k,
793 const struct gf_poly *f, struct gf_poly *z,
794 struct gf_poly *out)
795{
796 const int m = GF_M(bch);
797 int i, j;
798
799 /* z contains z^2j mod f */
800 z->deg = 1;
801 z->c[0] = 0;
802 z->c[1] = bch->a_pow_tab[k];
803
804 out->deg = 0;
805 memset(out, 0, GF_POLY_SZ(f->deg));
806
807 /* compute f log representation only once */
808 gf_poly_logrep(bch, f, bch->cache);
809
810 for (i = 0; i < m; i++) {
811 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
812 for (j = z->deg; j >= 0; j--) {
813 out->c[j] ^= z->c[j];
814 z->c[2*j] = gf_sqr(bch, z->c[j]);
815 z->c[2*j+1] = 0;
816 }
817 if (z->deg > out->deg)
818 out->deg = z->deg;
819
820 if (i < m-1) {
821 z->deg *= 2;
822 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
823 gf_poly_mod(bch, z, f, bch->cache);
824 }
825 }
826 while (!out->c[out->deg] && out->deg)
827 out->deg--;
828
829 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
830}
831
832/*
833 * factor a polynomial using Berlekamp Trace algorithm (BTA)
834 */
835static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
836 struct gf_poly **g, struct gf_poly **h)
837{
838 struct gf_poly *f2 = bch->poly_2t[0];
839 struct gf_poly *q = bch->poly_2t[1];
840 struct gf_poly *tk = bch->poly_2t[2];
841 struct gf_poly *z = bch->poly_2t[3];
842 struct gf_poly *gcd;
843
844 dbg("factoring %s...\n", gf_poly_str(f));
845
846 *g = f;
847 *h = NULL;
848
849 /* tk = Tr(a^k.X) mod f */
850 compute_trace_bk_mod(bch, k, f, z, tk);
851
852 if (tk->deg > 0) {
853 /* compute g = gcd(f, tk) (destructive operation) */
854 gf_poly_copy(f2, f);
855 gcd = gf_poly_gcd(bch, f2, tk);
856 if (gcd->deg < f->deg) {
857 /* compute h=f/gcd(f,tk); this will modify f and q */
858 gf_poly_div(bch, f, gcd, q);
859 /* store g and h in-place (clobbering f) */
860 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
861 gf_poly_copy(*g, gcd);
862 gf_poly_copy(*h, q);
863 }
864 }
865}
866
867/*
868 * find roots of a polynomial, using BTZ algorithm; see the beginning of this
869 * file for details
870 */
871static int find_poly_roots(struct bch_control *bch, unsigned int k,
872 struct gf_poly *poly, unsigned int *roots)
873{
874 int cnt;
875 struct gf_poly *f1, *f2;
876
877 switch (poly->deg) {
878 /* handle low degree polynomials with ad hoc techniques */
879 case 1:
880 cnt = find_poly_deg1_roots(bch, poly, roots);
881 break;
882 case 2:
883 cnt = find_poly_deg2_roots(bch, poly, roots);
884 break;
885 case 3:
886 cnt = find_poly_deg3_roots(bch, poly, roots);
887 break;
888 case 4:
889 cnt = find_poly_deg4_roots(bch, poly, roots);
890 break;
891 default:
892 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */
893 cnt = 0;
894 if (poly->deg && (k <= GF_M(bch))) {
895 factor_polynomial(bch, k, poly, &f1, &f2);
896 if (f1)
897 cnt += find_poly_roots(bch, k+1, f1, roots);
898 if (f2)
899 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
900 }
901 break;
902 }
903 return cnt;
904}
905
906#if defined(USE_CHIEN_SEARCH)
907/*
908 * exhaustive root search (Chien) implementation - not used, included only for
909 * reference/comparison tests
910 */
911static int chien_search(struct bch_control *bch, unsigned int len,
912 struct gf_poly *p, unsigned int *roots)
913{
914 int m;
915 unsigned int i, j, syn, syn0, count = 0;
916 const unsigned int k = 8*len+bch->ecc_bits;
917
918 /* use a log-based representation of polynomial */
919 gf_poly_logrep(bch, p, bch->cache);
920 bch->cache[p->deg] = 0;
921 syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
922
923 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
924 /* compute elp(a^i) */
925 for (j = 1, syn = syn0; j <= p->deg; j++) {
926 m = bch->cache[j];
927 if (m >= 0)
928 syn ^= a_pow(bch, m+j*i);
929 }
930 if (syn == 0) {
931 roots[count++] = GF_N(bch)-i;
932 if (count == p->deg)
933 break;
934 }
935 }
936 return (count == p->deg) ? count : 0;
937}
938#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
939#endif /* USE_CHIEN_SEARCH */
940
941/**
942 * decode_bch - decode received codeword and find bit error locations
943 * @bch: BCH control structure
944 * @data: received data, ignored if @calc_ecc is provided
945 * @len: data length in bytes, must always be provided
946 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
947 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
948 * @syn: hw computed syndrome data (if NULL, syndrome is calculated)
949 * @errloc: output array of error locations
950 *
951 * Returns:
952 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
953 * invalid parameters were provided
954 *
955 * Depending on the available hw BCH support and the need to compute @calc_ecc
956 * separately (using encode_bch()), this function should be called with one of
957 * the following parameter configurations -
958 *
959 * by providing @data and @recv_ecc only:
960 * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
961 *
962 * by providing @recv_ecc and @calc_ecc:
963 * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
964 *
965 * by providing ecc = recv_ecc XOR calc_ecc:
966 * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
967 *
968 * by providing syndrome results @syn:
969 * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
970 *
971 * Once decode_bch() has successfully returned with a positive value, error
972 * locations returned in array @errloc should be interpreted as follows -
973 *
974 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
975 * data correction)
976 *
977 * if (errloc[n] < 8*len), then n-th error is located in data and can be
978 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
979 *
980 * Note that this function does not perform any data correction by itself, it
981 * merely indicates error locations.
982 */
983int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
984 const uint8_t *recv_ecc, const uint8_t *calc_ecc,
985 const unsigned int *syn, unsigned int *errloc)
986{
987 const unsigned int ecc_words = BCH_ECC_WORDS(bch);
988 unsigned int nbits;
989 int i, err, nroots;
990 uint32_t sum;
991
992 /* sanity check: make sure data length can be handled */
993 if (8*len > (bch->n-bch->ecc_bits))
994 return -EINVAL;
995
996 /* if caller does not provide syndromes, compute them */
997 if (!syn) {
998 if (!calc_ecc) {
999 /* compute received data ecc into an internal buffer */
1000 if (!data || !recv_ecc)
1001 return -EINVAL;
1002 encode_bch(bch, data, len, NULL);
1003 } else {
1004 /* load provided calculated ecc */
1005 load_ecc8(bch, bch->ecc_buf, calc_ecc);
1006 }
1007 /* load received ecc or assume it was XORed in calc_ecc */
1008 if (recv_ecc) {
1009 load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1010 /* XOR received and calculated ecc */
1011 for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1012 bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1013 sum |= bch->ecc_buf[i];
1014 }
1015 if (!sum)
1016 /* no error found */
1017 return 0;
1018 }
1019 compute_syndromes(bch, bch->ecc_buf, bch->syn);
1020 syn = bch->syn;
1021 }
1022
1023 err = compute_error_locator_polynomial(bch, syn);
1024 if (err > 0) {
1025 nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1026 if (err != nroots)
1027 err = -1;
1028 }
1029 if (err > 0) {
1030 /* post-process raw error locations for easier correction */
1031 nbits = (len*8)+bch->ecc_bits;
1032 for (i = 0; i < err; i++) {
1033 if (errloc[i] >= nbits) {
1034 err = -1;
1035 break;
1036 }
1037 errloc[i] = nbits-1-errloc[i];
1038 errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
1039 }
1040 }
1041 return (err >= 0) ? err : -EBADMSG;
1042}
1043
1044/*
1045 * generate Galois field lookup tables
1046 */
1047static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1048{
1049 unsigned int i, x = 1;
1050 const unsigned int k = 1 << deg(poly);
1051
1052 /* primitive polynomial must be of degree m */
1053 if (k != (1u << GF_M(bch)))
1054 return -1;
1055
1056 for (i = 0; i < GF_N(bch); i++) {
1057 bch->a_pow_tab[i] = x;
1058 bch->a_log_tab[x] = i;
1059 if (i && (x == 1))
1060 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1061 return -1;
1062 x <<= 1;
1063 if (x & k)
1064 x ^= poly;
1065 }
1066 bch->a_pow_tab[GF_N(bch)] = 1;
1067 bch->a_log_tab[0] = 0;
1068
1069 return 0;
1070}
1071
1072/*
1073 * compute generator polynomial remainder tables for fast encoding
1074 */
1075static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1076{
1077 int i, j, b, d;
1078 uint32_t data, hi, lo, *tab;
1079 const int l = BCH_ECC_WORDS(bch);
1080 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1081 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1082
1083 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1084
1085 for (i = 0; i < 256; i++) {
1086 /* p(X)=i is a small polynomial of weight <= 8 */
1087 for (b = 0; b < 4; b++) {
1088 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1089 tab = bch->mod8_tab + (b*256+i)*l;
1090 data = i << (8*b);
1091 while (data) {
1092 d = deg(data);
1093 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1094 data ^= g[0] >> (31-d);
1095 for (j = 0; j < ecclen; j++) {
1096 hi = (d < 31) ? g[j] << (d+1) : 0;
1097 lo = (j+1 < plen) ?
1098 g[j+1] >> (31-d) : 0;
1099 tab[j] ^= hi|lo;
1100 }
1101 }
1102 }
1103 }
1104}
1105
1106/*
1107 * build a base for factoring degree 2 polynomials
1108 */
1109static int build_deg2_base(struct bch_control *bch)
1110{
1111 const int m = GF_M(bch);
1112 int i, j, r;
1113 unsigned int sum, x, y, remaining, ak = 0, xi[m];
1114
1115 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1116 for (i = 0; i < m; i++) {
1117 for (j = 0, sum = 0; j < m; j++)
1118 sum ^= a_pow(bch, i*(1 << j));
1119
1120 if (sum) {
1121 ak = bch->a_pow_tab[i];
1122 break;
1123 }
1124 }
1125 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1126 remaining = m;
1127 memset(xi, 0, sizeof(xi));
1128
1129 for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1130 y = gf_sqr(bch, x)^x;
1131 for (i = 0; i < 2; i++) {
1132 r = a_log(bch, y);
1133 if (y && (r < m) && !xi[r]) {
1134 bch->xi_tab[r] = x;
1135 xi[r] = 1;
1136 remaining--;
1137 dbg("x%d = %x\n", r, x);
1138 break;
1139 }
1140 y ^= ak;
1141 }
1142 }
1143 /* should not happen but check anyway */
1144 return remaining ? -1 : 0;
1145}
1146
1147static void *bch_alloc(size_t size, int *err)
1148{
1149 void *ptr;
1150
1151 ptr = kmalloc(size, GFP_KERNEL);
1152 if (ptr == NULL)
1153 *err = 1;
1154 return ptr;
1155}
1156
1157/*
1158 * compute generator polynomial for given (m,t) parameters.
1159 */
1160static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1161{
1162 const unsigned int m = GF_M(bch);
1163 const unsigned int t = GF_T(bch);
1164 int n, err = 0;
1165 unsigned int i, j, nbits, r, word, *roots;
1166 struct gf_poly *g;
1167 uint32_t *genpoly;
1168
1169 g = bch_alloc(GF_POLY_SZ(m*t), &err);
1170 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1171 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1172
1173 if (err) {
1174 kfree(genpoly);
1175 genpoly = NULL;
1176 goto finish;
1177 }
1178
1179 /* enumerate all roots of g(X) */
1180 memset(roots , 0, (bch->n+1)*sizeof(*roots));
1181 for (i = 0; i < t; i++) {
1182 for (j = 0, r = 2*i+1; j < m; j++) {
1183 roots[r] = 1;
1184 r = mod_s(bch, 2*r);
1185 }
1186 }
1187 /* build generator polynomial g(X) */
1188 g->deg = 0;
1189 g->c[0] = 1;
1190 for (i = 0; i < GF_N(bch); i++) {
1191 if (roots[i]) {
1192 /* multiply g(X) by (X+root) */
1193 r = bch->a_pow_tab[i];
1194 g->c[g->deg+1] = 1;
1195 for (j = g->deg; j > 0; j--)
1196 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1197
1198 g->c[0] = gf_mul(bch, g->c[0], r);
1199 g->deg++;
1200 }
1201 }
1202 /* store left-justified binary representation of g(X) */
1203 n = g->deg+1;
1204 i = 0;
1205
1206 while (n > 0) {
1207 nbits = (n > 32) ? 32 : n;
1208 for (j = 0, word = 0; j < nbits; j++) {
1209 if (g->c[n-1-j])
1210 word |= 1u << (31-j);
1211 }
1212 genpoly[i++] = word;
1213 n -= nbits;
1214 }
1215 bch->ecc_bits = g->deg;
1216
1217finish:
1218 kfree(g);
1219 kfree(roots);
1220
1221 return genpoly;
1222}
1223
1224/**
1225 * init_bch - initialize a BCH encoder/decoder
1226 * @m: Galois field order, should be in the range 5-15
1227 * @t: maximum error correction capability, in bits
1228 * @prim_poly: user-provided primitive polynomial (or 0 to use default)
1229 *
1230 * Returns:
1231 * a newly allocated BCH control structure if successful, NULL otherwise
1232 *
1233 * This initialization can take some time, as lookup tables are built for fast
1234 * encoding/decoding; make sure not to call this function from a time critical
1235 * path. Usually, init_bch() should be called on module/driver init and
1236 * free_bch() should be called to release memory on exit.
1237 *
1238 * You may provide your own primitive polynomial of degree @m in argument
1239 * @prim_poly, or let init_bch() use its default polynomial.
1240 *
1241 * Once init_bch() has successfully returned a pointer to a newly allocated
1242 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1243 * the structure.
1244 */
1245struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
1246{
1247 int err = 0;
1248 unsigned int i, words;
1249 uint32_t *genpoly;
1250 struct bch_control *bch = NULL;
1251
1252 const int min_m = 5;
1253 const int max_m = 15;
1254
1255 /* default primitive polynomials */
1256 static const unsigned int prim_poly_tab[] = {
1257 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1258 0x402b, 0x8003,
1259 };
1260
1261#if defined(CONFIG_BCH_CONST_PARAMS)
1262 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1263 printk(KERN_ERR "bch encoder/decoder was configured to support "
1264 "parameters m=%d, t=%d only!\n",
1265 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1266 goto fail;
1267 }
1268#endif
1269 if ((m < min_m) || (m > max_m))
1270 /*
1271 * values of m greater than 15 are not currently supported;
1272 * supporting m > 15 would require changing table base type
1273 * (uint16_t) and a small patch in matrix transposition
1274 */
1275 goto fail;
1276
1277 /* sanity checks */
1278 if ((t < 1) || (m*t >= ((1 << m)-1)))
1279 /* invalid t value */
1280 goto fail;
1281
1282 /* select a primitive polynomial for generating GF(2^m) */
1283 if (prim_poly == 0)
1284 prim_poly = prim_poly_tab[m-min_m];
1285
1286 bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1287 if (bch == NULL)
1288 goto fail;
1289
1290 bch->m = m;
1291 bch->t = t;
1292 bch->n = (1 << m)-1;
1293 words = DIV_ROUND_UP(m*t, 32);
1294 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1295 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1296 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1297 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1298 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1299 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1300 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1301 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err);
1302 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err);
1303 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1304
1305 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1306 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1307
1308 if (err)
1309 goto fail;
1310
1311 err = build_gf_tables(bch, prim_poly);
1312 if (err)
1313 goto fail;
1314
1315 /* use generator polynomial for computing encoding tables */
1316 genpoly = compute_generator_polynomial(bch);
1317 if (genpoly == NULL)
1318 goto fail;
1319
1320 build_mod8_tables(bch, genpoly);
1321 kfree(genpoly);
1322
1323 err = build_deg2_base(bch);
1324 if (err)
1325 goto fail;
1326
1327 return bch;
1328
1329fail:
1330 free_bch(bch);
1331 return NULL;
1332}
1333
1334/**
1335 * free_bch - free the BCH control structure
1336 * @bch: BCH control structure to release
1337 */
1338void free_bch(struct bch_control *bch)
1339{
1340 unsigned int i;
1341
1342 if (bch) {
1343 kfree(bch->a_pow_tab);
1344 kfree(bch->a_log_tab);
1345 kfree(bch->mod8_tab);
1346 kfree(bch->ecc_buf);
1347 kfree(bch->ecc_buf2);
1348 kfree(bch->xi_tab);
1349 kfree(bch->syn);
1350 kfree(bch->cache);
1351 kfree(bch->elp);
1352
1353 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1354 kfree(bch->poly_2t[i]);
1355
1356 kfree(bch);
1357 }
1358}