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Christian Hitz4c6de852011-10-12 09:31:59 +02001/*
2 * Generic binary BCH encoding/decoding library
3 *
Tom Rini5b8031c2016-01-14 22:05:13 -05004 * SPDX-License-Identifier: GPL-2.0
Christian Hitz4c6de852011-10-12 09:31:59 +02005 *
6 * Copyright © 2011 Parrot S.A.
7 *
8 * Author: Ivan Djelic <ivan.djelic@parrot.com>
9 *
10 * Description:
11 *
12 * This library provides runtime configurable encoding/decoding of binary
13 * Bose-Chaudhuri-Hocquenghem (BCH) codes.
14 *
15 * Call init_bch to get a pointer to a newly allocated bch_control structure for
16 * the given m (Galois field order), t (error correction capability) and
17 * (optional) primitive polynomial parameters.
18 *
19 * Call encode_bch to compute and store ecc parity bytes to a given buffer.
20 * Call decode_bch to detect and locate errors in received data.
21 *
22 * On systems supporting hw BCH features, intermediate results may be provided
23 * to decode_bch in order to skip certain steps. See decode_bch() documentation
24 * for details.
25 *
26 * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
27 * parameters m and t; thus allowing extra compiler optimizations and providing
28 * better (up to 2x) encoding performance. Using this option makes sense when
29 * (m,t) are fixed and known in advance, e.g. when using BCH error correction
30 * on a particular NAND flash device.
31 *
32 * Algorithmic details:
33 *
34 * Encoding is performed by processing 32 input bits in parallel, using 4
35 * remainder lookup tables.
36 *
37 * The final stage of decoding involves the following internal steps:
38 * a. Syndrome computation
39 * b. Error locator polynomial computation using Berlekamp-Massey algorithm
40 * c. Error locator root finding (by far the most expensive step)
41 *
42 * In this implementation, step c is not performed using the usual Chien search.
43 * Instead, an alternative approach described in [1] is used. It consists in
44 * factoring the error locator polynomial using the Berlekamp Trace algorithm
45 * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
46 * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
47 * much better performance than Chien search for usual (m,t) values (typically
48 * m >= 13, t < 32, see [1]).
49 *
50 * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
51 * of characteristic 2, in: Western European Workshop on Research in Cryptology
52 * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
53 * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
54 * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
55 */
56
57#include <common.h>
58#include <ubi_uboot.h>
59
60#include <linux/bitops.h>
61#include <asm/byteorder.h>
62#include <linux/bch.h>
63
64#if defined(CONFIG_BCH_CONST_PARAMS)
65#define GF_M(_p) (CONFIG_BCH_CONST_M)
66#define GF_T(_p) (CONFIG_BCH_CONST_T)
67#define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1)
68#else
69#define GF_M(_p) ((_p)->m)
70#define GF_T(_p) ((_p)->t)
71#define GF_N(_p) ((_p)->n)
72#endif
73
74#define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
75#define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
76
77#ifndef dbg
78#define dbg(_fmt, args...) do {} while (0)
79#endif
80
81/*
82 * represent a polynomial over GF(2^m)
83 */
84struct gf_poly {
85 unsigned int deg; /* polynomial degree */
86 unsigned int c[0]; /* polynomial terms */
87};
88
89/* given its degree, compute a polynomial size in bytes */
90#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
91
92/* polynomial of degree 1 */
93struct gf_poly_deg1 {
94 struct gf_poly poly;
95 unsigned int c[2];
96};
97
98/*
99 * same as encode_bch(), but process input data one byte at a time
100 */
101static void encode_bch_unaligned(struct bch_control *bch,
102 const unsigned char *data, unsigned int len,
103 uint32_t *ecc)
104{
105 int i;
106 const uint32_t *p;
107 const int l = BCH_ECC_WORDS(bch)-1;
108
109 while (len--) {
110 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
111
112 for (i = 0; i < l; i++)
113 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
114
115 ecc[l] = (ecc[l] << 8)^(*p);
116 }
117}
118
119/*
120 * convert ecc bytes to aligned, zero-padded 32-bit ecc words
121 */
122static void load_ecc8(struct bch_control *bch, uint32_t *dst,
123 const uint8_t *src)
124{
125 uint8_t pad[4] = {0, 0, 0, 0};
126 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
127
128 for (i = 0; i < nwords; i++, src += 4)
129 dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
130
131 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
132 dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
133}
134
135/*
136 * convert 32-bit ecc words to ecc bytes
137 */
138static void store_ecc8(struct bch_control *bch, uint8_t *dst,
139 const uint32_t *src)
140{
141 uint8_t pad[4];
142 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
143
144 for (i = 0; i < nwords; i++) {
145 *dst++ = (src[i] >> 24);
146 *dst++ = (src[i] >> 16) & 0xff;
147 *dst++ = (src[i] >> 8) & 0xff;
148 *dst++ = (src[i] >> 0) & 0xff;
149 }
150 pad[0] = (src[nwords] >> 24);
151 pad[1] = (src[nwords] >> 16) & 0xff;
152 pad[2] = (src[nwords] >> 8) & 0xff;
153 pad[3] = (src[nwords] >> 0) & 0xff;
154 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
155}
156
157/**
158 * encode_bch - calculate BCH ecc parity of data
159 * @bch: BCH control structure
160 * @data: data to encode
161 * @len: data length in bytes
162 * @ecc: ecc parity data, must be initialized by caller
163 *
164 * The @ecc parity array is used both as input and output parameter, in order to
165 * allow incremental computations. It should be of the size indicated by member
166 * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
167 *
168 * The exact number of computed ecc parity bits is given by member @ecc_bits of
169 * @bch; it may be less than m*t for large values of t.
170 */
171void encode_bch(struct bch_control *bch, const uint8_t *data,
172 unsigned int len, uint8_t *ecc)
173{
174 const unsigned int l = BCH_ECC_WORDS(bch)-1;
175 unsigned int i, mlen;
176 unsigned long m;
177 uint32_t w, r[l+1];
178 const uint32_t * const tab0 = bch->mod8_tab;
179 const uint32_t * const tab1 = tab0 + 256*(l+1);
180 const uint32_t * const tab2 = tab1 + 256*(l+1);
181 const uint32_t * const tab3 = tab2 + 256*(l+1);
182 const uint32_t *pdata, *p0, *p1, *p2, *p3;
183
184 if (ecc) {
185 /* load ecc parity bytes into internal 32-bit buffer */
186 load_ecc8(bch, bch->ecc_buf, ecc);
187 } else {
188 memset(bch->ecc_buf, 0, sizeof(r));
189 }
190
191 /* process first unaligned data bytes */
192 m = ((unsigned long)data) & 3;
193 if (m) {
194 mlen = (len < (4-m)) ? len : 4-m;
195 encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
196 data += mlen;
197 len -= mlen;
198 }
199
200 /* process 32-bit aligned data words */
201 pdata = (uint32_t *)data;
202 mlen = len/4;
203 data += 4*mlen;
204 len -= 4*mlen;
205 memcpy(r, bch->ecc_buf, sizeof(r));
206
207 /*
208 * split each 32-bit word into 4 polynomials of weight 8 as follows:
209 *
210 * 31 ...24 23 ...16 15 ... 8 7 ... 0
211 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt
212 * tttttttt mod g = r0 (precomputed)
213 * zzzzzzzz 00000000 mod g = r1 (precomputed)
214 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed)
215 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed)
216 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3
217 */
218 while (mlen--) {
219 /* input data is read in big-endian format */
220 w = r[0]^cpu_to_be32(*pdata++);
221 p0 = tab0 + (l+1)*((w >> 0) & 0xff);
222 p1 = tab1 + (l+1)*((w >> 8) & 0xff);
223 p2 = tab2 + (l+1)*((w >> 16) & 0xff);
224 p3 = tab3 + (l+1)*((w >> 24) & 0xff);
225
226 for (i = 0; i < l; i++)
227 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
228
229 r[l] = p0[l]^p1[l]^p2[l]^p3[l];
230 }
231 memcpy(bch->ecc_buf, r, sizeof(r));
232
233 /* process last unaligned bytes */
234 if (len)
235 encode_bch_unaligned(bch, data, len, bch->ecc_buf);
236
237 /* store ecc parity bytes into original parity buffer */
238 if (ecc)
239 store_ecc8(bch, ecc, bch->ecc_buf);
240}
241
242static inline int modulo(struct bch_control *bch, unsigned int v)
243{
244 const unsigned int n = GF_N(bch);
245 while (v >= n) {
246 v -= n;
247 v = (v & n) + (v >> GF_M(bch));
248 }
249 return v;
250}
251
252/*
253 * shorter and faster modulo function, only works when v < 2N.
254 */
255static inline int mod_s(struct bch_control *bch, unsigned int v)
256{
257 const unsigned int n = GF_N(bch);
258 return (v < n) ? v : v-n;
259}
260
261static inline int deg(unsigned int poly)
262{
263 /* polynomial degree is the most-significant bit index */
264 return fls(poly)-1;
265}
266
267static inline int parity(unsigned int x)
268{
269 /*
270 * public domain code snippet, lifted from
271 * http://www-graphics.stanford.edu/~seander/bithacks.html
272 */
273 x ^= x >> 1;
274 x ^= x >> 2;
275 x = (x & 0x11111111U) * 0x11111111U;
276 return (x >> 28) & 1;
277}
278
279/* Galois field basic operations: multiply, divide, inverse, etc. */
280
281static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
282 unsigned int b)
283{
284 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
285 bch->a_log_tab[b])] : 0;
286}
287
288static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
289{
290 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
291}
292
293static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
294 unsigned int b)
295{
296 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
297 GF_N(bch)-bch->a_log_tab[b])] : 0;
298}
299
300static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
301{
302 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
303}
304
305static inline unsigned int a_pow(struct bch_control *bch, int i)
306{
307 return bch->a_pow_tab[modulo(bch, i)];
308}
309
310static inline int a_log(struct bch_control *bch, unsigned int x)
311{
312 return bch->a_log_tab[x];
313}
314
315static inline int a_ilog(struct bch_control *bch, unsigned int x)
316{
317 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
318}
319
320/*
321 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
322 */
323static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
324 unsigned int *syn)
325{
326 int i, j, s;
327 unsigned int m;
328 uint32_t poly;
329 const int t = GF_T(bch);
330
331 s = bch->ecc_bits;
332
333 /* make sure extra bits in last ecc word are cleared */
334 m = ((unsigned int)s) & 31;
335 if (m)
336 ecc[s/32] &= ~((1u << (32-m))-1);
337 memset(syn, 0, 2*t*sizeof(*syn));
338
339 /* compute v(a^j) for j=1 .. 2t-1 */
340 do {
341 poly = *ecc++;
342 s -= 32;
343 while (poly) {
344 i = deg(poly);
345 for (j = 0; j < 2*t; j += 2)
346 syn[j] ^= a_pow(bch, (j+1)*(i+s));
347
348 poly ^= (1 << i);
349 }
350 } while (s > 0);
351
352 /* v(a^(2j)) = v(a^j)^2 */
353 for (j = 0; j < t; j++)
354 syn[2*j+1] = gf_sqr(bch, syn[j]);
355}
356
357static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
358{
359 memcpy(dst, src, GF_POLY_SZ(src->deg));
360}
361
362static int compute_error_locator_polynomial(struct bch_control *bch,
363 const unsigned int *syn)
364{
365 const unsigned int t = GF_T(bch);
366 const unsigned int n = GF_N(bch);
367 unsigned int i, j, tmp, l, pd = 1, d = syn[0];
368 struct gf_poly *elp = bch->elp;
369 struct gf_poly *pelp = bch->poly_2t[0];
370 struct gf_poly *elp_copy = bch->poly_2t[1];
371 int k, pp = -1;
372
373 memset(pelp, 0, GF_POLY_SZ(2*t));
374 memset(elp, 0, GF_POLY_SZ(2*t));
375
376 pelp->deg = 0;
377 pelp->c[0] = 1;
378 elp->deg = 0;
379 elp->c[0] = 1;
380
381 /* use simplified binary Berlekamp-Massey algorithm */
382 for (i = 0; (i < t) && (elp->deg <= t); i++) {
383 if (d) {
384 k = 2*i-pp;
385 gf_poly_copy(elp_copy, elp);
386 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
387 tmp = a_log(bch, d)+n-a_log(bch, pd);
388 for (j = 0; j <= pelp->deg; j++) {
389 if (pelp->c[j]) {
390 l = a_log(bch, pelp->c[j]);
391 elp->c[j+k] ^= a_pow(bch, tmp+l);
392 }
393 }
394 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
395 tmp = pelp->deg+k;
396 if (tmp > elp->deg) {
397 elp->deg = tmp;
398 gf_poly_copy(pelp, elp_copy);
399 pd = d;
400 pp = 2*i;
401 }
402 }
403 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
404 if (i < t-1) {
405 d = syn[2*i+2];
406 for (j = 1; j <= elp->deg; j++)
407 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
408 }
409 }
410 dbg("elp=%s\n", gf_poly_str(elp));
411 return (elp->deg > t) ? -1 : (int)elp->deg;
412}
413
414/*
415 * solve a m x m linear system in GF(2) with an expected number of solutions,
416 * and return the number of found solutions
417 */
418static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
419 unsigned int *sol, int nsol)
420{
421 const int m = GF_M(bch);
422 unsigned int tmp, mask;
423 int rem, c, r, p, k, param[m];
424
425 k = 0;
426 mask = 1 << m;
427
428 /* Gaussian elimination */
429 for (c = 0; c < m; c++) {
430 rem = 0;
431 p = c-k;
432 /* find suitable row for elimination */
433 for (r = p; r < m; r++) {
434 if (rows[r] & mask) {
435 if (r != p) {
436 tmp = rows[r];
437 rows[r] = rows[p];
438 rows[p] = tmp;
439 }
440 rem = r+1;
441 break;
442 }
443 }
444 if (rem) {
445 /* perform elimination on remaining rows */
446 tmp = rows[p];
447 for (r = rem; r < m; r++) {
448 if (rows[r] & mask)
449 rows[r] ^= tmp;
450 }
451 } else {
452 /* elimination not needed, store defective row index */
453 param[k++] = c;
454 }
455 mask >>= 1;
456 }
457 /* rewrite system, inserting fake parameter rows */
458 if (k > 0) {
459 p = k;
460 for (r = m-1; r >= 0; r--) {
461 if ((r > m-1-k) && rows[r])
462 /* system has no solution */
463 return 0;
464
465 rows[r] = (p && (r == param[p-1])) ?
466 p--, 1u << (m-r) : rows[r-p];
467 }
468 }
469
470 if (nsol != (1 << k))
471 /* unexpected number of solutions */
472 return 0;
473
474 for (p = 0; p < nsol; p++) {
475 /* set parameters for p-th solution */
476 for (c = 0; c < k; c++)
477 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
478
479 /* compute unique solution */
480 tmp = 0;
481 for (r = m-1; r >= 0; r--) {
482 mask = rows[r] & (tmp|1);
483 tmp |= parity(mask) << (m-r);
484 }
485 sol[p] = tmp >> 1;
486 }
487 return nsol;
488}
489
490/*
491 * this function builds and solves a linear system for finding roots of a degree
492 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
493 */
494static int find_affine4_roots(struct bch_control *bch, unsigned int a,
495 unsigned int b, unsigned int c,
496 unsigned int *roots)
497{
498 int i, j, k;
499 const int m = GF_M(bch);
500 unsigned int mask = 0xff, t, rows[16] = {0,};
501
502 j = a_log(bch, b);
503 k = a_log(bch, a);
504 rows[0] = c;
505
506 /* buid linear system to solve X^4+aX^2+bX+c = 0 */
507 for (i = 0; i < m; i++) {
508 rows[i+1] = bch->a_pow_tab[4*i]^
509 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
510 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
511 j++;
512 k += 2;
513 }
514 /*
515 * transpose 16x16 matrix before passing it to linear solver
516 * warning: this code assumes m < 16
517 */
518 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
519 for (k = 0; k < 16; k = (k+j+1) & ~j) {
520 t = ((rows[k] >> j)^rows[k+j]) & mask;
521 rows[k] ^= (t << j);
522 rows[k+j] ^= t;
523 }
524 }
525 return solve_linear_system(bch, rows, roots, 4);
526}
527
528/*
529 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
530 */
531static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
532 unsigned int *roots)
533{
534 int n = 0;
535
536 if (poly->c[0])
537 /* poly[X] = bX+c with c!=0, root=c/b */
538 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
539 bch->a_log_tab[poly->c[1]]);
540 return n;
541}
542
543/*
544 * compute roots of a degree 2 polynomial over GF(2^m)
545 */
546static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
547 unsigned int *roots)
548{
549 int n = 0, i, l0, l1, l2;
550 unsigned int u, v, r;
551
552 if (poly->c[0] && poly->c[1]) {
553
554 l0 = bch->a_log_tab[poly->c[0]];
555 l1 = bch->a_log_tab[poly->c[1]];
556 l2 = bch->a_log_tab[poly->c[2]];
557
558 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
559 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
560 /*
561 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
562 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
563 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
564 * i.e. r and r+1 are roots iff Tr(u)=0
565 */
566 r = 0;
567 v = u;
568 while (v) {
569 i = deg(v);
570 r ^= bch->xi_tab[i];
571 v ^= (1 << i);
572 }
573 /* verify root */
574 if ((gf_sqr(bch, r)^r) == u) {
575 /* reverse z=a/bX transformation and compute log(1/r) */
576 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
577 bch->a_log_tab[r]+l2);
578 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
579 bch->a_log_tab[r^1]+l2);
580 }
581 }
582 return n;
583}
584
585/*
586 * compute roots of a degree 3 polynomial over GF(2^m)
587 */
588static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
589 unsigned int *roots)
590{
591 int i, n = 0;
592 unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
593
594 if (poly->c[0]) {
595 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
596 e3 = poly->c[3];
597 c2 = gf_div(bch, poly->c[0], e3);
598 b2 = gf_div(bch, poly->c[1], e3);
599 a2 = gf_div(bch, poly->c[2], e3);
600
601 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
602 c = gf_mul(bch, a2, c2); /* c = a2c2 */
603 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */
604 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */
605
606 /* find the 4 roots of this affine polynomial */
607 if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
608 /* remove a2 from final list of roots */
609 for (i = 0; i < 4; i++) {
610 if (tmp[i] != a2)
611 roots[n++] = a_ilog(bch, tmp[i]);
612 }
613 }
614 }
615 return n;
616}
617
618/*
619 * compute roots of a degree 4 polynomial over GF(2^m)
620 */
621static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
622 unsigned int *roots)
623{
624 int i, l, n = 0;
625 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
626
627 if (poly->c[0] == 0)
628 return 0;
629
630 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
631 e4 = poly->c[4];
632 d = gf_div(bch, poly->c[0], e4);
633 c = gf_div(bch, poly->c[1], e4);
634 b = gf_div(bch, poly->c[2], e4);
635 a = gf_div(bch, poly->c[3], e4);
636
637 /* use Y=1/X transformation to get an affine polynomial */
638 if (a) {
639 /* first, eliminate cX by using z=X+e with ae^2+c=0 */
640 if (c) {
641 /* compute e such that e^2 = c/a */
642 f = gf_div(bch, c, a);
643 l = a_log(bch, f);
644 l += (l & 1) ? GF_N(bch) : 0;
645 e = a_pow(bch, l/2);
646 /*
647 * use transformation z=X+e:
648 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
649 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
650 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
651 * z^4 + az^3 + b'z^2 + d'
652 */
653 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
654 b = gf_mul(bch, a, e)^b;
655 }
656 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
657 if (d == 0)
658 /* assume all roots have multiplicity 1 */
659 return 0;
660
661 c2 = gf_inv(bch, d);
662 b2 = gf_div(bch, a, d);
663 a2 = gf_div(bch, b, d);
664 } else {
665 /* polynomial is already affine */
666 c2 = d;
667 b2 = c;
668 a2 = b;
669 }
670 /* find the 4 roots of this affine polynomial */
671 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
672 for (i = 0; i < 4; i++) {
673 /* post-process roots (reverse transformations) */
674 f = a ? gf_inv(bch, roots[i]) : roots[i];
675 roots[i] = a_ilog(bch, f^e);
676 }
677 n = 4;
678 }
679 return n;
680}
681
682/*
683 * build monic, log-based representation of a polynomial
684 */
685static void gf_poly_logrep(struct bch_control *bch,
686 const struct gf_poly *a, int *rep)
687{
688 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
689
690 /* represent 0 values with -1; warning, rep[d] is not set to 1 */
691 for (i = 0; i < d; i++)
692 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
693}
694
695/*
696 * compute polynomial Euclidean division remainder in GF(2^m)[X]
697 */
698static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
699 const struct gf_poly *b, int *rep)
700{
701 int la, p, m;
702 unsigned int i, j, *c = a->c;
703 const unsigned int d = b->deg;
704
705 if (a->deg < d)
706 return;
707
708 /* reuse or compute log representation of denominator */
709 if (!rep) {
710 rep = bch->cache;
711 gf_poly_logrep(bch, b, rep);
712 }
713
714 for (j = a->deg; j >= d; j--) {
715 if (c[j]) {
716 la = a_log(bch, c[j]);
717 p = j-d;
718 for (i = 0; i < d; i++, p++) {
719 m = rep[i];
720 if (m >= 0)
721 c[p] ^= bch->a_pow_tab[mod_s(bch,
722 m+la)];
723 }
724 }
725 }
726 a->deg = d-1;
727 while (!c[a->deg] && a->deg)
728 a->deg--;
729}
730
731/*
732 * compute polynomial Euclidean division quotient in GF(2^m)[X]
733 */
734static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
735 const struct gf_poly *b, struct gf_poly *q)
736{
737 if (a->deg >= b->deg) {
738 q->deg = a->deg-b->deg;
739 /* compute a mod b (modifies a) */
740 gf_poly_mod(bch, a, b, NULL);
741 /* quotient is stored in upper part of polynomial a */
742 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
743 } else {
744 q->deg = 0;
745 q->c[0] = 0;
746 }
747}
748
749/*
750 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
751 */
752static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
753 struct gf_poly *b)
754{
755 struct gf_poly *tmp;
756
757 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
758
759 if (a->deg < b->deg) {
760 tmp = b;
761 b = a;
762 a = tmp;
763 }
764
765 while (b->deg > 0) {
766 gf_poly_mod(bch, a, b, NULL);
767 tmp = b;
768 b = a;
769 a = tmp;
770 }
771
772 dbg("%s\n", gf_poly_str(a));
773
774 return a;
775}
776
777/*
778 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
779 * This is used in Berlekamp Trace algorithm for splitting polynomials
780 */
781static void compute_trace_bk_mod(struct bch_control *bch, int k,
782 const struct gf_poly *f, struct gf_poly *z,
783 struct gf_poly *out)
784{
785 const int m = GF_M(bch);
786 int i, j;
787
788 /* z contains z^2j mod f */
789 z->deg = 1;
790 z->c[0] = 0;
791 z->c[1] = bch->a_pow_tab[k];
792
793 out->deg = 0;
794 memset(out, 0, GF_POLY_SZ(f->deg));
795
796 /* compute f log representation only once */
797 gf_poly_logrep(bch, f, bch->cache);
798
799 for (i = 0; i < m; i++) {
800 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
801 for (j = z->deg; j >= 0; j--) {
802 out->c[j] ^= z->c[j];
803 z->c[2*j] = gf_sqr(bch, z->c[j]);
804 z->c[2*j+1] = 0;
805 }
806 if (z->deg > out->deg)
807 out->deg = z->deg;
808
809 if (i < m-1) {
810 z->deg *= 2;
811 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
812 gf_poly_mod(bch, z, f, bch->cache);
813 }
814 }
815 while (!out->c[out->deg] && out->deg)
816 out->deg--;
817
818 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
819}
820
821/*
822 * factor a polynomial using Berlekamp Trace algorithm (BTA)
823 */
824static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
825 struct gf_poly **g, struct gf_poly **h)
826{
827 struct gf_poly *f2 = bch->poly_2t[0];
828 struct gf_poly *q = bch->poly_2t[1];
829 struct gf_poly *tk = bch->poly_2t[2];
830 struct gf_poly *z = bch->poly_2t[3];
831 struct gf_poly *gcd;
832
833 dbg("factoring %s...\n", gf_poly_str(f));
834
835 *g = f;
836 *h = NULL;
837
838 /* tk = Tr(a^k.X) mod f */
839 compute_trace_bk_mod(bch, k, f, z, tk);
840
841 if (tk->deg > 0) {
842 /* compute g = gcd(f, tk) (destructive operation) */
843 gf_poly_copy(f2, f);
844 gcd = gf_poly_gcd(bch, f2, tk);
845 if (gcd->deg < f->deg) {
846 /* compute h=f/gcd(f,tk); this will modify f and q */
847 gf_poly_div(bch, f, gcd, q);
848 /* store g and h in-place (clobbering f) */
849 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
850 gf_poly_copy(*g, gcd);
851 gf_poly_copy(*h, q);
852 }
853 }
854}
855
856/*
857 * find roots of a polynomial, using BTZ algorithm; see the beginning of this
858 * file for details
859 */
860static int find_poly_roots(struct bch_control *bch, unsigned int k,
861 struct gf_poly *poly, unsigned int *roots)
862{
863 int cnt;
864 struct gf_poly *f1, *f2;
865
866 switch (poly->deg) {
867 /* handle low degree polynomials with ad hoc techniques */
868 case 1:
869 cnt = find_poly_deg1_roots(bch, poly, roots);
870 break;
871 case 2:
872 cnt = find_poly_deg2_roots(bch, poly, roots);
873 break;
874 case 3:
875 cnt = find_poly_deg3_roots(bch, poly, roots);
876 break;
877 case 4:
878 cnt = find_poly_deg4_roots(bch, poly, roots);
879 break;
880 default:
881 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */
882 cnt = 0;
883 if (poly->deg && (k <= GF_M(bch))) {
884 factor_polynomial(bch, k, poly, &f1, &f2);
885 if (f1)
886 cnt += find_poly_roots(bch, k+1, f1, roots);
887 if (f2)
888 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
889 }
890 break;
891 }
892 return cnt;
893}
894
895#if defined(USE_CHIEN_SEARCH)
896/*
897 * exhaustive root search (Chien) implementation - not used, included only for
898 * reference/comparison tests
899 */
900static int chien_search(struct bch_control *bch, unsigned int len,
901 struct gf_poly *p, unsigned int *roots)
902{
903 int m;
904 unsigned int i, j, syn, syn0, count = 0;
905 const unsigned int k = 8*len+bch->ecc_bits;
906
907 /* use a log-based representation of polynomial */
908 gf_poly_logrep(bch, p, bch->cache);
909 bch->cache[p->deg] = 0;
910 syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
911
912 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
913 /* compute elp(a^i) */
914 for (j = 1, syn = syn0; j <= p->deg; j++) {
915 m = bch->cache[j];
916 if (m >= 0)
917 syn ^= a_pow(bch, m+j*i);
918 }
919 if (syn == 0) {
920 roots[count++] = GF_N(bch)-i;
921 if (count == p->deg)
922 break;
923 }
924 }
925 return (count == p->deg) ? count : 0;
926}
927#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
928#endif /* USE_CHIEN_SEARCH */
929
930/**
931 * decode_bch - decode received codeword and find bit error locations
932 * @bch: BCH control structure
933 * @data: received data, ignored if @calc_ecc is provided
934 * @len: data length in bytes, must always be provided
935 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
936 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
937 * @syn: hw computed syndrome data (if NULL, syndrome is calculated)
938 * @errloc: output array of error locations
939 *
940 * Returns:
941 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
942 * invalid parameters were provided
943 *
944 * Depending on the available hw BCH support and the need to compute @calc_ecc
945 * separately (using encode_bch()), this function should be called with one of
946 * the following parameter configurations -
947 *
948 * by providing @data and @recv_ecc only:
949 * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
950 *
951 * by providing @recv_ecc and @calc_ecc:
952 * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
953 *
954 * by providing ecc = recv_ecc XOR calc_ecc:
955 * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
956 *
957 * by providing syndrome results @syn:
958 * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
959 *
960 * Once decode_bch() has successfully returned with a positive value, error
961 * locations returned in array @errloc should be interpreted as follows -
962 *
963 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
964 * data correction)
965 *
966 * if (errloc[n] < 8*len), then n-th error is located in data and can be
967 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
968 *
969 * Note that this function does not perform any data correction by itself, it
970 * merely indicates error locations.
971 */
972int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
973 const uint8_t *recv_ecc, const uint8_t *calc_ecc,
974 const unsigned int *syn, unsigned int *errloc)
975{
976 const unsigned int ecc_words = BCH_ECC_WORDS(bch);
977 unsigned int nbits;
978 int i, err, nroots;
979 uint32_t sum;
980
981 /* sanity check: make sure data length can be handled */
982 if (8*len > (bch->n-bch->ecc_bits))
983 return -EINVAL;
984
985 /* if caller does not provide syndromes, compute them */
986 if (!syn) {
987 if (!calc_ecc) {
988 /* compute received data ecc into an internal buffer */
989 if (!data || !recv_ecc)
990 return -EINVAL;
991 encode_bch(bch, data, len, NULL);
992 } else {
993 /* load provided calculated ecc */
994 load_ecc8(bch, bch->ecc_buf, calc_ecc);
995 }
996 /* load received ecc or assume it was XORed in calc_ecc */
997 if (recv_ecc) {
998 load_ecc8(bch, bch->ecc_buf2, recv_ecc);
999 /* XOR received and calculated ecc */
1000 for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1001 bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1002 sum |= bch->ecc_buf[i];
1003 }
1004 if (!sum)
1005 /* no error found */
1006 return 0;
1007 }
1008 compute_syndromes(bch, bch->ecc_buf, bch->syn);
1009 syn = bch->syn;
1010 }
1011
1012 err = compute_error_locator_polynomial(bch, syn);
1013 if (err > 0) {
1014 nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1015 if (err != nroots)
1016 err = -1;
1017 }
1018 if (err > 0) {
1019 /* post-process raw error locations for easier correction */
1020 nbits = (len*8)+bch->ecc_bits;
1021 for (i = 0; i < err; i++) {
1022 if (errloc[i] >= nbits) {
1023 err = -1;
1024 break;
1025 }
1026 errloc[i] = nbits-1-errloc[i];
1027 errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
1028 }
1029 }
1030 return (err >= 0) ? err : -EBADMSG;
1031}
1032
1033/*
1034 * generate Galois field lookup tables
1035 */
1036static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1037{
1038 unsigned int i, x = 1;
1039 const unsigned int k = 1 << deg(poly);
1040
1041 /* primitive polynomial must be of degree m */
1042 if (k != (1u << GF_M(bch)))
1043 return -1;
1044
1045 for (i = 0; i < GF_N(bch); i++) {
1046 bch->a_pow_tab[i] = x;
1047 bch->a_log_tab[x] = i;
1048 if (i && (x == 1))
1049 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1050 return -1;
1051 x <<= 1;
1052 if (x & k)
1053 x ^= poly;
1054 }
1055 bch->a_pow_tab[GF_N(bch)] = 1;
1056 bch->a_log_tab[0] = 0;
1057
1058 return 0;
1059}
1060
1061/*
1062 * compute generator polynomial remainder tables for fast encoding
1063 */
1064static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1065{
1066 int i, j, b, d;
1067 uint32_t data, hi, lo, *tab;
1068 const int l = BCH_ECC_WORDS(bch);
1069 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1070 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1071
1072 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1073
1074 for (i = 0; i < 256; i++) {
1075 /* p(X)=i is a small polynomial of weight <= 8 */
1076 for (b = 0; b < 4; b++) {
1077 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1078 tab = bch->mod8_tab + (b*256+i)*l;
1079 data = i << (8*b);
1080 while (data) {
1081 d = deg(data);
1082 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1083 data ^= g[0] >> (31-d);
1084 for (j = 0; j < ecclen; j++) {
1085 hi = (d < 31) ? g[j] << (d+1) : 0;
1086 lo = (j+1 < plen) ?
1087 g[j+1] >> (31-d) : 0;
1088 tab[j] ^= hi|lo;
1089 }
1090 }
1091 }
1092 }
1093}
1094
1095/*
1096 * build a base for factoring degree 2 polynomials
1097 */
1098static int build_deg2_base(struct bch_control *bch)
1099{
1100 const int m = GF_M(bch);
1101 int i, j, r;
1102 unsigned int sum, x, y, remaining, ak = 0, xi[m];
1103
1104 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1105 for (i = 0; i < m; i++) {
1106 for (j = 0, sum = 0; j < m; j++)
1107 sum ^= a_pow(bch, i*(1 << j));
1108
1109 if (sum) {
1110 ak = bch->a_pow_tab[i];
1111 break;
1112 }
1113 }
1114 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1115 remaining = m;
1116 memset(xi, 0, sizeof(xi));
1117
1118 for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1119 y = gf_sqr(bch, x)^x;
1120 for (i = 0; i < 2; i++) {
1121 r = a_log(bch, y);
1122 if (y && (r < m) && !xi[r]) {
1123 bch->xi_tab[r] = x;
1124 xi[r] = 1;
1125 remaining--;
1126 dbg("x%d = %x\n", r, x);
1127 break;
1128 }
1129 y ^= ak;
1130 }
1131 }
1132 /* should not happen but check anyway */
1133 return remaining ? -1 : 0;
1134}
1135
1136static void *bch_alloc(size_t size, int *err)
1137{
1138 void *ptr;
1139
1140 ptr = kmalloc(size, GFP_KERNEL);
1141 if (ptr == NULL)
1142 *err = 1;
1143 return ptr;
1144}
1145
1146/*
1147 * compute generator polynomial for given (m,t) parameters.
1148 */
1149static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1150{
1151 const unsigned int m = GF_M(bch);
1152 const unsigned int t = GF_T(bch);
1153 int n, err = 0;
1154 unsigned int i, j, nbits, r, word, *roots;
1155 struct gf_poly *g;
1156 uint32_t *genpoly;
1157
1158 g = bch_alloc(GF_POLY_SZ(m*t), &err);
1159 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1160 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1161
1162 if (err) {
1163 kfree(genpoly);
1164 genpoly = NULL;
1165 goto finish;
1166 }
1167
1168 /* enumerate all roots of g(X) */
1169 memset(roots , 0, (bch->n+1)*sizeof(*roots));
1170 for (i = 0; i < t; i++) {
1171 for (j = 0, r = 2*i+1; j < m; j++) {
1172 roots[r] = 1;
1173 r = mod_s(bch, 2*r);
1174 }
1175 }
1176 /* build generator polynomial g(X) */
1177 g->deg = 0;
1178 g->c[0] = 1;
1179 for (i = 0; i < GF_N(bch); i++) {
1180 if (roots[i]) {
1181 /* multiply g(X) by (X+root) */
1182 r = bch->a_pow_tab[i];
1183 g->c[g->deg+1] = 1;
1184 for (j = g->deg; j > 0; j--)
1185 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1186
1187 g->c[0] = gf_mul(bch, g->c[0], r);
1188 g->deg++;
1189 }
1190 }
1191 /* store left-justified binary representation of g(X) */
1192 n = g->deg+1;
1193 i = 0;
1194
1195 while (n > 0) {
1196 nbits = (n > 32) ? 32 : n;
1197 for (j = 0, word = 0; j < nbits; j++) {
1198 if (g->c[n-1-j])
1199 word |= 1u << (31-j);
1200 }
1201 genpoly[i++] = word;
1202 n -= nbits;
1203 }
1204 bch->ecc_bits = g->deg;
1205
1206finish:
1207 kfree(g);
1208 kfree(roots);
1209
1210 return genpoly;
1211}
1212
1213/**
1214 * init_bch - initialize a BCH encoder/decoder
1215 * @m: Galois field order, should be in the range 5-15
1216 * @t: maximum error correction capability, in bits
1217 * @prim_poly: user-provided primitive polynomial (or 0 to use default)
1218 *
1219 * Returns:
1220 * a newly allocated BCH control structure if successful, NULL otherwise
1221 *
1222 * This initialization can take some time, as lookup tables are built for fast
1223 * encoding/decoding; make sure not to call this function from a time critical
1224 * path. Usually, init_bch() should be called on module/driver init and
1225 * free_bch() should be called to release memory on exit.
1226 *
1227 * You may provide your own primitive polynomial of degree @m in argument
1228 * @prim_poly, or let init_bch() use its default polynomial.
1229 *
1230 * Once init_bch() has successfully returned a pointer to a newly allocated
1231 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1232 * the structure.
1233 */
1234struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
1235{
1236 int err = 0;
1237 unsigned int i, words;
1238 uint32_t *genpoly;
1239 struct bch_control *bch = NULL;
1240
1241 const int min_m = 5;
1242 const int max_m = 15;
1243
1244 /* default primitive polynomials */
1245 static const unsigned int prim_poly_tab[] = {
1246 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1247 0x402b, 0x8003,
1248 };
1249
1250#if defined(CONFIG_BCH_CONST_PARAMS)
1251 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1252 printk(KERN_ERR "bch encoder/decoder was configured to support "
1253 "parameters m=%d, t=%d only!\n",
1254 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1255 goto fail;
1256 }
1257#endif
1258 if ((m < min_m) || (m > max_m))
1259 /*
1260 * values of m greater than 15 are not currently supported;
1261 * supporting m > 15 would require changing table base type
1262 * (uint16_t) and a small patch in matrix transposition
1263 */
1264 goto fail;
1265
1266 /* sanity checks */
1267 if ((t < 1) || (m*t >= ((1 << m)-1)))
1268 /* invalid t value */
1269 goto fail;
1270
1271 /* select a primitive polynomial for generating GF(2^m) */
1272 if (prim_poly == 0)
1273 prim_poly = prim_poly_tab[m-min_m];
1274
1275 bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1276 if (bch == NULL)
1277 goto fail;
1278
1279 bch->m = m;
1280 bch->t = t;
1281 bch->n = (1 << m)-1;
1282 words = DIV_ROUND_UP(m*t, 32);
1283 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1284 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1285 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1286 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1287 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1288 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1289 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1290 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err);
1291 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err);
1292 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1293
1294 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1295 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1296
1297 if (err)
1298 goto fail;
1299
1300 err = build_gf_tables(bch, prim_poly);
1301 if (err)
1302 goto fail;
1303
1304 /* use generator polynomial for computing encoding tables */
1305 genpoly = compute_generator_polynomial(bch);
1306 if (genpoly == NULL)
1307 goto fail;
1308
1309 build_mod8_tables(bch, genpoly);
1310 kfree(genpoly);
1311
1312 err = build_deg2_base(bch);
1313 if (err)
1314 goto fail;
1315
1316 return bch;
1317
1318fail:
1319 free_bch(bch);
1320 return NULL;
1321}
1322
1323/**
1324 * free_bch - free the BCH control structure
1325 * @bch: BCH control structure to release
1326 */
1327void free_bch(struct bch_control *bch)
1328{
1329 unsigned int i;
1330
1331 if (bch) {
1332 kfree(bch->a_pow_tab);
1333 kfree(bch->a_log_tab);
1334 kfree(bch->mod8_tab);
1335 kfree(bch->ecc_buf);
1336 kfree(bch->ecc_buf2);
1337 kfree(bch->xi_tab);
1338 kfree(bch->syn);
1339 kfree(bch->cache);
1340 kfree(bch->elp);
1341
1342 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1343 kfree(bch->poly_2t[i]);
1344
1345 kfree(bch);
1346 }
1347}