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Ivan Djelic437aa562011-03-11 11:05:32 +01001/*
2 * Generic binary BCH encoding/decoding library
3 *
4 * This program is free software; you can redistribute it and/or modify it
5 * under the terms of the GNU General Public License version 2 as published by
6 * the Free Software Foundation.
7 *
8 * This program is distributed in the hope that it will be useful, but WITHOUT
9 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
10 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
11 * more details.
12 *
13 * You should have received a copy of the GNU General Public License along with
14 * this program; if not, write to the Free Software Foundation, Inc., 51
15 * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
16 *
17 * Copyright © 2011 Parrot S.A.
18 *
19 * Author: Ivan Djelic <ivan.djelic@parrot.com>
20 *
21 * Description:
22 *
23 * This library provides runtime configurable encoding/decoding of binary
24 * Bose-Chaudhuri-Hocquenghem (BCH) codes.
25 *
26 * Call init_bch to get a pointer to a newly allocated bch_control structure for
27 * the given m (Galois field order), t (error correction capability) and
28 * (optional) primitive polynomial parameters.
29 *
30 * Call encode_bch to compute and store ecc parity bytes to a given buffer.
31 * Call decode_bch to detect and locate errors in received data.
32 *
33 * On systems supporting hw BCH features, intermediate results may be provided
34 * to decode_bch in order to skip certain steps. See decode_bch() documentation
35 * for details.
36 *
37 * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
38 * parameters m and t; thus allowing extra compiler optimizations and providing
39 * better (up to 2x) encoding performance. Using this option makes sense when
40 * (m,t) are fixed and known in advance, e.g. when using BCH error correction
41 * on a particular NAND flash device.
42 *
43 * Algorithmic details:
44 *
45 * Encoding is performed by processing 32 input bits in parallel, using 4
46 * remainder lookup tables.
47 *
48 * The final stage of decoding involves the following internal steps:
49 * a. Syndrome computation
50 * b. Error locator polynomial computation using Berlekamp-Massey algorithm
51 * c. Error locator root finding (by far the most expensive step)
52 *
53 * In this implementation, step c is not performed using the usual Chien search.
54 * Instead, an alternative approach described in [1] is used. It consists in
55 * factoring the error locator polynomial using the Berlekamp Trace algorithm
56 * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
57 * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
58 * much better performance than Chien search for usual (m,t) values (typically
59 * m >= 13, t < 32, see [1]).
60 *
61 * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
62 * of characteristic 2, in: Western European Workshop on Research in Cryptology
63 * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
64 * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
65 * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
66 */
67
68#include <linux/kernel.h>
69#include <linux/errno.h>
70#include <linux/init.h>
71#include <linux/module.h>
72#include <linux/slab.h>
73#include <linux/bitops.h>
74#include <asm/byteorder.h>
75#include <linux/bch.h>
76
77#if defined(CONFIG_BCH_CONST_PARAMS)
78#define GF_M(_p) (CONFIG_BCH_CONST_M)
79#define GF_T(_p) (CONFIG_BCH_CONST_T)
80#define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1)
Kees Cook02361bc2018-05-31 11:45:25 -070081#define BCH_MAX_M (CONFIG_BCH_CONST_M)
Ivan Djelic437aa562011-03-11 11:05:32 +010082#else
83#define GF_M(_p) ((_p)->m)
84#define GF_T(_p) ((_p)->t)
85#define GF_N(_p) ((_p)->n)
Kees Cook02361bc2018-05-31 11:45:25 -070086#define BCH_MAX_M 15
Ivan Djelic437aa562011-03-11 11:05:32 +010087#endif
88
Kees Cook02361bc2018-05-31 11:45:25 -070089#define BCH_MAX_T (((1 << BCH_MAX_M) - 1) / BCH_MAX_M)
90
Ivan Djelic437aa562011-03-11 11:05:32 +010091#define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
92#define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
93
Kees Cook02361bc2018-05-31 11:45:25 -070094#define BCH_ECC_MAX_WORDS DIV_ROUND_UP(BCH_MAX_M * BCH_MAX_T, 32)
95#define BCH_ECC_MAX_BYTES DIV_ROUND_UP(BCH_MAX_M * BCH_MAX_T, 8)
96
Ivan Djelic437aa562011-03-11 11:05:32 +010097#ifndef dbg
98#define dbg(_fmt, args...) do {} while (0)
99#endif
100
101/*
102 * represent a polynomial over GF(2^m)
103 */
104struct gf_poly {
105 unsigned int deg; /* polynomial degree */
106 unsigned int c[0]; /* 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
118/*
119 * same as encode_bch(), but process input data one byte at a time
120 */
121static void encode_bch_unaligned(struct bch_control *bch,
122 const unsigned char *data, unsigned int len,
123 uint32_t *ecc)
124{
125 int i;
126 const uint32_t *p;
127 const int l = BCH_ECC_WORDS(bch)-1;
128
129 while (len--) {
130 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
131
132 for (i = 0; i < l; i++)
133 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
134
135 ecc[l] = (ecc[l] << 8)^(*p);
136 }
137}
138
139/*
140 * convert ecc bytes to aligned, zero-padded 32-bit ecc words
141 */
142static void load_ecc8(struct bch_control *bch, uint32_t *dst,
143 const uint8_t *src)
144{
145 uint8_t pad[4] = {0, 0, 0, 0};
146 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
147
148 for (i = 0; i < nwords; i++, src += 4)
149 dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
150
151 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
152 dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
153}
154
155/*
156 * convert 32-bit ecc words to ecc bytes
157 */
158static void store_ecc8(struct bch_control *bch, uint8_t *dst,
159 const uint32_t *src)
160{
161 uint8_t pad[4];
162 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
163
164 for (i = 0; i < nwords; i++) {
165 *dst++ = (src[i] >> 24);
166 *dst++ = (src[i] >> 16) & 0xff;
167 *dst++ = (src[i] >> 8) & 0xff;
168 *dst++ = (src[i] >> 0) & 0xff;
169 }
170 pad[0] = (src[nwords] >> 24);
171 pad[1] = (src[nwords] >> 16) & 0xff;
172 pad[2] = (src[nwords] >> 8) & 0xff;
173 pad[3] = (src[nwords] >> 0) & 0xff;
174 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
175}
176
177/**
178 * encode_bch - calculate BCH ecc parity of data
179 * @bch: BCH control structure
180 * @data: data to encode
181 * @len: data length in bytes
182 * @ecc: ecc parity data, must be initialized by caller
183 *
184 * The @ecc parity array is used both as input and output parameter, in order to
185 * allow incremental computations. It should be of the size indicated by member
186 * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
187 *
188 * The exact number of computed ecc parity bits is given by member @ecc_bits of
189 * @bch; it may be less than m*t for large values of t.
190 */
191void encode_bch(struct bch_control *bch, const uint8_t *data,
192 unsigned int len, uint8_t *ecc)
193{
194 const unsigned int l = BCH_ECC_WORDS(bch)-1;
195 unsigned int i, mlen;
196 unsigned long m;
Kees Cook02361bc2018-05-31 11:45:25 -0700197 uint32_t w, r[BCH_ECC_MAX_WORDS];
198 const size_t r_bytes = BCH_ECC_WORDS(bch) * sizeof(*r);
Ivan Djelic437aa562011-03-11 11:05:32 +0100199 const uint32_t * const tab0 = bch->mod8_tab;
200 const uint32_t * const tab1 = tab0 + 256*(l+1);
201 const uint32_t * const tab2 = tab1 + 256*(l+1);
202 const uint32_t * const tab3 = tab2 + 256*(l+1);
203 const uint32_t *pdata, *p0, *p1, *p2, *p3;
204
205 if (ecc) {
206 /* load ecc parity bytes into internal 32-bit buffer */
207 load_ecc8(bch, bch->ecc_buf, ecc);
208 } else {
Kees Cook02361bc2018-05-31 11:45:25 -0700209 memset(bch->ecc_buf, 0, r_bytes);
Ivan Djelic437aa562011-03-11 11:05:32 +0100210 }
211
212 /* process first unaligned data bytes */
213 m = ((unsigned long)data) & 3;
214 if (m) {
215 mlen = (len < (4-m)) ? len : 4-m;
216 encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
217 data += mlen;
218 len -= mlen;
219 }
220
221 /* process 32-bit aligned data words */
222 pdata = (uint32_t *)data;
223 mlen = len/4;
224 data += 4*mlen;
225 len -= 4*mlen;
Kees Cook02361bc2018-05-31 11:45:25 -0700226 memcpy(r, bch->ecc_buf, r_bytes);
Ivan Djelic437aa562011-03-11 11:05:32 +0100227
228 /*
229 * split each 32-bit word into 4 polynomials of weight 8 as follows:
230 *
231 * 31 ...24 23 ...16 15 ... 8 7 ... 0
232 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt
233 * tttttttt mod g = r0 (precomputed)
234 * zzzzzzzz 00000000 mod g = r1 (precomputed)
235 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed)
236 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed)
237 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3
238 */
239 while (mlen--) {
240 /* input data is read in big-endian format */
241 w = r[0]^cpu_to_be32(*pdata++);
242 p0 = tab0 + (l+1)*((w >> 0) & 0xff);
243 p1 = tab1 + (l+1)*((w >> 8) & 0xff);
244 p2 = tab2 + (l+1)*((w >> 16) & 0xff);
245 p3 = tab3 + (l+1)*((w >> 24) & 0xff);
246
247 for (i = 0; i < l; i++)
248 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
249
250 r[l] = p0[l]^p1[l]^p2[l]^p3[l];
251 }
Kees Cook02361bc2018-05-31 11:45:25 -0700252 memcpy(bch->ecc_buf, r, r_bytes);
Ivan Djelic437aa562011-03-11 11:05:32 +0100253
254 /* process last unaligned bytes */
255 if (len)
256 encode_bch_unaligned(bch, data, len, bch->ecc_buf);
257
258 /* store ecc parity bytes into original parity buffer */
259 if (ecc)
260 store_ecc8(bch, ecc, bch->ecc_buf);
261}
262EXPORT_SYMBOL_GPL(encode_bch);
263
264static inline int modulo(struct bch_control *bch, unsigned int v)
265{
266 const unsigned int n = GF_N(bch);
267 while (v >= n) {
268 v -= n;
269 v = (v & n) + (v >> GF_M(bch));
270 }
271 return v;
272}
273
274/*
275 * shorter and faster modulo function, only works when v < 2N.
276 */
277static inline int mod_s(struct bch_control *bch, unsigned int v)
278{
279 const unsigned int n = GF_N(bch);
280 return (v < n) ? v : v-n;
281}
282
283static inline int deg(unsigned int poly)
284{
285 /* polynomial degree is the most-significant bit index */
286 return fls(poly)-1;
287}
288
289static inline int parity(unsigned int x)
290{
291 /*
292 * public domain code snippet, lifted from
293 * http://www-graphics.stanford.edu/~seander/bithacks.html
294 */
295 x ^= x >> 1;
296 x ^= x >> 2;
297 x = (x & 0x11111111U) * 0x11111111U;
298 return (x >> 28) & 1;
299}
300
301/* Galois field basic operations: multiply, divide, inverse, etc. */
302
303static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
304 unsigned int b)
305{
306 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
307 bch->a_log_tab[b])] : 0;
308}
309
310static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
311{
312 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
313}
314
315static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
316 unsigned int b)
317{
318 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
319 GF_N(bch)-bch->a_log_tab[b])] : 0;
320}
321
322static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
323{
324 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
325}
326
327static inline unsigned int a_pow(struct bch_control *bch, int i)
328{
329 return bch->a_pow_tab[modulo(bch, i)];
330}
331
332static inline int a_log(struct bch_control *bch, unsigned int x)
333{
334 return bch->a_log_tab[x];
335}
336
337static inline int a_ilog(struct bch_control *bch, unsigned int x)
338{
339 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
340}
341
342/*
343 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
344 */
345static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
346 unsigned int *syn)
347{
348 int i, j, s;
349 unsigned int m;
350 uint32_t poly;
351 const int t = GF_T(bch);
352
353 s = bch->ecc_bits;
354
355 /* make sure extra bits in last ecc word are cleared */
356 m = ((unsigned int)s) & 31;
357 if (m)
358 ecc[s/32] &= ~((1u << (32-m))-1);
359 memset(syn, 0, 2*t*sizeof(*syn));
360
361 /* compute v(a^j) for j=1 .. 2t-1 */
362 do {
363 poly = *ecc++;
364 s -= 32;
365 while (poly) {
366 i = deg(poly);
367 for (j = 0; j < 2*t; j += 2)
368 syn[j] ^= a_pow(bch, (j+1)*(i+s));
369
370 poly ^= (1 << i);
371 }
372 } while (s > 0);
373
374 /* v(a^(2j)) = v(a^j)^2 */
375 for (j = 0; j < t; j++)
376 syn[2*j+1] = gf_sqr(bch, syn[j]);
377}
378
379static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
380{
381 memcpy(dst, src, GF_POLY_SZ(src->deg));
382}
383
384static int compute_error_locator_polynomial(struct bch_control *bch,
385 const unsigned int *syn)
386{
387 const unsigned int t = GF_T(bch);
388 const unsigned int n = GF_N(bch);
389 unsigned int i, j, tmp, l, pd = 1, d = syn[0];
390 struct gf_poly *elp = bch->elp;
391 struct gf_poly *pelp = bch->poly_2t[0];
392 struct gf_poly *elp_copy = bch->poly_2t[1];
393 int k, pp = -1;
394
395 memset(pelp, 0, GF_POLY_SZ(2*t));
396 memset(elp, 0, GF_POLY_SZ(2*t));
397
398 pelp->deg = 0;
399 pelp->c[0] = 1;
400 elp->deg = 0;
401 elp->c[0] = 1;
402
403 /* use simplified binary Berlekamp-Massey algorithm */
404 for (i = 0; (i < t) && (elp->deg <= t); i++) {
405 if (d) {
406 k = 2*i-pp;
407 gf_poly_copy(elp_copy, elp);
408 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
409 tmp = a_log(bch, d)+n-a_log(bch, pd);
410 for (j = 0; j <= pelp->deg; j++) {
411 if (pelp->c[j]) {
412 l = a_log(bch, pelp->c[j]);
413 elp->c[j+k] ^= a_pow(bch, tmp+l);
414 }
415 }
416 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
417 tmp = pelp->deg+k;
418 if (tmp > elp->deg) {
419 elp->deg = tmp;
420 gf_poly_copy(pelp, elp_copy);
421 pd = d;
422 pp = 2*i;
423 }
424 }
425 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
426 if (i < t-1) {
427 d = syn[2*i+2];
428 for (j = 1; j <= elp->deg; j++)
429 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
430 }
431 }
432 dbg("elp=%s\n", gf_poly_str(elp));
433 return (elp->deg > t) ? -1 : (int)elp->deg;
434}
435
436/*
437 * solve a m x m linear system in GF(2) with an expected number of solutions,
438 * and return the number of found solutions
439 */
440static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
441 unsigned int *sol, int nsol)
442{
443 const int m = GF_M(bch);
444 unsigned int tmp, mask;
Kees Cook02361bc2018-05-31 11:45:25 -0700445 int rem, c, r, p, k, param[BCH_MAX_M];
Ivan Djelic437aa562011-03-11 11:05:32 +0100446
447 k = 0;
448 mask = 1 << m;
449
450 /* Gaussian elimination */
451 for (c = 0; c < m; c++) {
452 rem = 0;
453 p = c-k;
454 /* find suitable row for elimination */
455 for (r = p; r < m; r++) {
456 if (rows[r] & mask) {
457 if (r != p) {
458 tmp = rows[r];
459 rows[r] = rows[p];
460 rows[p] = tmp;
461 }
462 rem = r+1;
463 break;
464 }
465 }
466 if (rem) {
467 /* perform elimination on remaining rows */
468 tmp = rows[p];
469 for (r = rem; r < m; r++) {
470 if (rows[r] & mask)
471 rows[r] ^= tmp;
472 }
473 } else {
474 /* elimination not needed, store defective row index */
475 param[k++] = c;
476 }
477 mask >>= 1;
478 }
479 /* rewrite system, inserting fake parameter rows */
480 if (k > 0) {
481 p = k;
482 for (r = m-1; r >= 0; r--) {
483 if ((r > m-1-k) && rows[r])
484 /* system has no solution */
485 return 0;
486
487 rows[r] = (p && (r == param[p-1])) ?
488 p--, 1u << (m-r) : rows[r-p];
489 }
490 }
491
492 if (nsol != (1 << k))
493 /* unexpected number of solutions */
494 return 0;
495
496 for (p = 0; p < nsol; p++) {
497 /* set parameters for p-th solution */
498 for (c = 0; c < k; c++)
499 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
500
501 /* compute unique solution */
502 tmp = 0;
503 for (r = m-1; r >= 0; r--) {
504 mask = rows[r] & (tmp|1);
505 tmp |= parity(mask) << (m-r);
506 }
507 sol[p] = tmp >> 1;
508 }
509 return nsol;
510}
511
512/*
513 * this function builds and solves a linear system for finding roots of a degree
514 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
515 */
516static int find_affine4_roots(struct bch_control *bch, unsigned int a,
517 unsigned int b, unsigned int c,
518 unsigned int *roots)
519{
520 int i, j, k;
521 const int m = GF_M(bch);
522 unsigned int mask = 0xff, t, rows[16] = {0,};
523
524 j = a_log(bch, b);
525 k = a_log(bch, a);
526 rows[0] = c;
527
528 /* buid linear system to solve X^4+aX^2+bX+c = 0 */
529 for (i = 0; i < m; i++) {
530 rows[i+1] = bch->a_pow_tab[4*i]^
531 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
532 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
533 j++;
534 k += 2;
535 }
536 /*
537 * transpose 16x16 matrix before passing it to linear solver
538 * warning: this code assumes m < 16
539 */
540 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
541 for (k = 0; k < 16; k = (k+j+1) & ~j) {
542 t = ((rows[k] >> j)^rows[k+j]) & mask;
543 rows[k] ^= (t << j);
544 rows[k+j] ^= t;
545 }
546 }
547 return solve_linear_system(bch, rows, roots, 4);
548}
549
550/*
551 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
552 */
553static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
554 unsigned int *roots)
555{
556 int n = 0;
557
558 if (poly->c[0])
559 /* poly[X] = bX+c with c!=0, root=c/b */
560 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
561 bch->a_log_tab[poly->c[1]]);
562 return n;
563}
564
565/*
566 * compute roots of a degree 2 polynomial over GF(2^m)
567 */
568static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
569 unsigned int *roots)
570{
571 int n = 0, i, l0, l1, l2;
572 unsigned int u, v, r;
573
574 if (poly->c[0] && poly->c[1]) {
575
576 l0 = bch->a_log_tab[poly->c[0]];
577 l1 = bch->a_log_tab[poly->c[1]];
578 l2 = bch->a_log_tab[poly->c[2]];
579
580 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
581 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
582 /*
583 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
584 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
585 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
586 * i.e. r and r+1 are roots iff Tr(u)=0
587 */
588 r = 0;
589 v = u;
590 while (v) {
591 i = deg(v);
592 r ^= bch->xi_tab[i];
593 v ^= (1 << i);
594 }
595 /* verify root */
596 if ((gf_sqr(bch, r)^r) == u) {
597 /* reverse z=a/bX transformation and compute log(1/r) */
598 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
599 bch->a_log_tab[r]+l2);
600 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
601 bch->a_log_tab[r^1]+l2);
602 }
603 }
604 return n;
605}
606
607/*
608 * compute roots of a degree 3 polynomial over GF(2^m)
609 */
610static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
611 unsigned int *roots)
612{
613 int i, n = 0;
614 unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
615
616 if (poly->c[0]) {
617 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
618 e3 = poly->c[3];
619 c2 = gf_div(bch, poly->c[0], e3);
620 b2 = gf_div(bch, poly->c[1], e3);
621 a2 = gf_div(bch, poly->c[2], e3);
622
623 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
624 c = gf_mul(bch, a2, c2); /* c = a2c2 */
625 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */
626 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */
627
628 /* find the 4 roots of this affine polynomial */
629 if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
630 /* remove a2 from final list of roots */
631 for (i = 0; i < 4; i++) {
632 if (tmp[i] != a2)
633 roots[n++] = a_ilog(bch, tmp[i]);
634 }
635 }
636 }
637 return n;
638}
639
640/*
641 * compute roots of a degree 4 polynomial over GF(2^m)
642 */
643static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
644 unsigned int *roots)
645{
646 int i, l, n = 0;
647 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
648
649 if (poly->c[0] == 0)
650 return 0;
651
652 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
653 e4 = poly->c[4];
654 d = gf_div(bch, poly->c[0], e4);
655 c = gf_div(bch, poly->c[1], e4);
656 b = gf_div(bch, poly->c[2], e4);
657 a = gf_div(bch, poly->c[3], e4);
658
659 /* use Y=1/X transformation to get an affine polynomial */
660 if (a) {
661 /* first, eliminate cX by using z=X+e with ae^2+c=0 */
662 if (c) {
663 /* compute e such that e^2 = c/a */
664 f = gf_div(bch, c, a);
665 l = a_log(bch, f);
666 l += (l & 1) ? GF_N(bch) : 0;
667 e = a_pow(bch, l/2);
668 /*
669 * use transformation z=X+e:
670 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
671 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
672 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
673 * z^4 + az^3 + b'z^2 + d'
674 */
675 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
676 b = gf_mul(bch, a, e)^b;
677 }
678 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
679 if (d == 0)
680 /* assume all roots have multiplicity 1 */
681 return 0;
682
683 c2 = gf_inv(bch, d);
684 b2 = gf_div(bch, a, d);
685 a2 = gf_div(bch, b, d);
686 } else {
687 /* polynomial is already affine */
688 c2 = d;
689 b2 = c;
690 a2 = b;
691 }
692 /* find the 4 roots of this affine polynomial */
693 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
694 for (i = 0; i < 4; i++) {
695 /* post-process roots (reverse transformations) */
696 f = a ? gf_inv(bch, roots[i]) : roots[i];
697 roots[i] = a_ilog(bch, f^e);
698 }
699 n = 4;
700 }
701 return n;
702}
703
704/*
705 * build monic, log-based representation of a polynomial
706 */
707static void gf_poly_logrep(struct bch_control *bch,
708 const struct gf_poly *a, int *rep)
709{
710 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
711
712 /* represent 0 values with -1; warning, rep[d] is not set to 1 */
713 for (i = 0; i < d; i++)
714 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
715}
716
717/*
718 * compute polynomial Euclidean division remainder in GF(2^m)[X]
719 */
720static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
721 const struct gf_poly *b, int *rep)
722{
723 int la, p, m;
724 unsigned int i, j, *c = a->c;
725 const unsigned int d = b->deg;
726
727 if (a->deg < d)
728 return;
729
730 /* reuse or compute log representation of denominator */
731 if (!rep) {
732 rep = bch->cache;
733 gf_poly_logrep(bch, b, rep);
734 }
735
736 for (j = a->deg; j >= d; j--) {
737 if (c[j]) {
738 la = a_log(bch, c[j]);
739 p = j-d;
740 for (i = 0; i < d; i++, p++) {
741 m = rep[i];
742 if (m >= 0)
743 c[p] ^= bch->a_pow_tab[mod_s(bch,
744 m+la)];
745 }
746 }
747 }
748 a->deg = d-1;
749 while (!c[a->deg] && a->deg)
750 a->deg--;
751}
752
753/*
754 * compute polynomial Euclidean division quotient in GF(2^m)[X]
755 */
756static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
757 const struct gf_poly *b, struct gf_poly *q)
758{
759 if (a->deg >= b->deg) {
760 q->deg = a->deg-b->deg;
761 /* compute a mod b (modifies a) */
762 gf_poly_mod(bch, a, b, NULL);
763 /* quotient is stored in upper part of polynomial a */
764 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
765 } else {
766 q->deg = 0;
767 q->c[0] = 0;
768 }
769}
770
771/*
772 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
773 */
774static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
775 struct gf_poly *b)
776{
777 struct gf_poly *tmp;
778
779 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
780
781 if (a->deg < b->deg) {
782 tmp = b;
783 b = a;
784 a = tmp;
785 }
786
787 while (b->deg > 0) {
788 gf_poly_mod(bch, a, b, NULL);
789 tmp = b;
790 b = a;
791 a = tmp;
792 }
793
794 dbg("%s\n", gf_poly_str(a));
795
796 return a;
797}
798
799/*
800 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
801 * This is used in Berlekamp Trace algorithm for splitting polynomials
802 */
803static void compute_trace_bk_mod(struct bch_control *bch, int k,
804 const struct gf_poly *f, struct gf_poly *z,
805 struct gf_poly *out)
806{
807 const int m = GF_M(bch);
808 int i, j;
809
810 /* z contains z^2j mod f */
811 z->deg = 1;
812 z->c[0] = 0;
813 z->c[1] = bch->a_pow_tab[k];
814
815 out->deg = 0;
816 memset(out, 0, GF_POLY_SZ(f->deg));
817
818 /* compute f log representation only once */
819 gf_poly_logrep(bch, f, bch->cache);
820
821 for (i = 0; i < m; i++) {
822 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
823 for (j = z->deg; j >= 0; j--) {
824 out->c[j] ^= z->c[j];
825 z->c[2*j] = gf_sqr(bch, z->c[j]);
826 z->c[2*j+1] = 0;
827 }
828 if (z->deg > out->deg)
829 out->deg = z->deg;
830
831 if (i < m-1) {
832 z->deg *= 2;
833 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
834 gf_poly_mod(bch, z, f, bch->cache);
835 }
836 }
837 while (!out->c[out->deg] && out->deg)
838 out->deg--;
839
840 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
841}
842
843/*
844 * factor a polynomial using Berlekamp Trace algorithm (BTA)
845 */
846static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
847 struct gf_poly **g, struct gf_poly **h)
848{
849 struct gf_poly *f2 = bch->poly_2t[0];
850 struct gf_poly *q = bch->poly_2t[1];
851 struct gf_poly *tk = bch->poly_2t[2];
852 struct gf_poly *z = bch->poly_2t[3];
853 struct gf_poly *gcd;
854
855 dbg("factoring %s...\n", gf_poly_str(f));
856
857 *g = f;
858 *h = NULL;
859
860 /* tk = Tr(a^k.X) mod f */
861 compute_trace_bk_mod(bch, k, f, z, tk);
862
863 if (tk->deg > 0) {
864 /* compute g = gcd(f, tk) (destructive operation) */
865 gf_poly_copy(f2, f);
866 gcd = gf_poly_gcd(bch, f2, tk);
867 if (gcd->deg < f->deg) {
868 /* compute h=f/gcd(f,tk); this will modify f and q */
869 gf_poly_div(bch, f, gcd, q);
870 /* store g and h in-place (clobbering f) */
871 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
872 gf_poly_copy(*g, gcd);
873 gf_poly_copy(*h, q);
874 }
875 }
876}
877
878/*
879 * find roots of a polynomial, using BTZ algorithm; see the beginning of this
880 * file for details
881 */
882static int find_poly_roots(struct bch_control *bch, unsigned int k,
883 struct gf_poly *poly, unsigned int *roots)
884{
885 int cnt;
886 struct gf_poly *f1, *f2;
887
888 switch (poly->deg) {
889 /* handle low degree polynomials with ad hoc techniques */
890 case 1:
891 cnt = find_poly_deg1_roots(bch, poly, roots);
892 break;
893 case 2:
894 cnt = find_poly_deg2_roots(bch, poly, roots);
895 break;
896 case 3:
897 cnt = find_poly_deg3_roots(bch, poly, roots);
898 break;
899 case 4:
900 cnt = find_poly_deg4_roots(bch, poly, roots);
901 break;
902 default:
903 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */
904 cnt = 0;
905 if (poly->deg && (k <= GF_M(bch))) {
906 factor_polynomial(bch, k, poly, &f1, &f2);
907 if (f1)
908 cnt += find_poly_roots(bch, k+1, f1, roots);
909 if (f2)
910 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
911 }
912 break;
913 }
914 return cnt;
915}
916
917#if defined(USE_CHIEN_SEARCH)
918/*
919 * exhaustive root search (Chien) implementation - not used, included only for
920 * reference/comparison tests
921 */
922static int chien_search(struct bch_control *bch, unsigned int len,
923 struct gf_poly *p, unsigned int *roots)
924{
925 int m;
926 unsigned int i, j, syn, syn0, count = 0;
927 const unsigned int k = 8*len+bch->ecc_bits;
928
929 /* use a log-based representation of polynomial */
930 gf_poly_logrep(bch, p, bch->cache);
931 bch->cache[p->deg] = 0;
932 syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
933
934 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
935 /* compute elp(a^i) */
936 for (j = 1, syn = syn0; j <= p->deg; j++) {
937 m = bch->cache[j];
938 if (m >= 0)
939 syn ^= a_pow(bch, m+j*i);
940 }
941 if (syn == 0) {
942 roots[count++] = GF_N(bch)-i;
943 if (count == p->deg)
944 break;
945 }
946 }
947 return (count == p->deg) ? count : 0;
948}
949#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
950#endif /* USE_CHIEN_SEARCH */
951
952/**
953 * decode_bch - decode received codeword and find bit error locations
954 * @bch: BCH control structure
955 * @data: received data, ignored if @calc_ecc is provided
956 * @len: data length in bytes, must always be provided
957 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
958 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
959 * @syn: hw computed syndrome data (if NULL, syndrome is calculated)
960 * @errloc: output array of error locations
961 *
962 * Returns:
963 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
964 * invalid parameters were provided
965 *
966 * Depending on the available hw BCH support and the need to compute @calc_ecc
967 * separately (using encode_bch()), this function should be called with one of
968 * the following parameter configurations -
969 *
970 * by providing @data and @recv_ecc only:
971 * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
972 *
973 * by providing @recv_ecc and @calc_ecc:
974 * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
975 *
976 * by providing ecc = recv_ecc XOR calc_ecc:
977 * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
978 *
979 * by providing syndrome results @syn:
980 * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
981 *
982 * Once decode_bch() has successfully returned with a positive value, error
983 * locations returned in array @errloc should be interpreted as follows -
984 *
985 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
986 * data correction)
987 *
988 * if (errloc[n] < 8*len), then n-th error is located in data and can be
989 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
990 *
991 * Note that this function does not perform any data correction by itself, it
992 * merely indicates error locations.
993 */
994int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
995 const uint8_t *recv_ecc, const uint8_t *calc_ecc,
996 const unsigned int *syn, unsigned int *errloc)
997{
998 const unsigned int ecc_words = BCH_ECC_WORDS(bch);
999 unsigned int nbits;
1000 int i, err, nroots;
1001 uint32_t sum;
1002
1003 /* sanity check: make sure data length can be handled */
1004 if (8*len > (bch->n-bch->ecc_bits))
1005 return -EINVAL;
1006
1007 /* if caller does not provide syndromes, compute them */
1008 if (!syn) {
1009 if (!calc_ecc) {
1010 /* compute received data ecc into an internal buffer */
1011 if (!data || !recv_ecc)
1012 return -EINVAL;
1013 encode_bch(bch, data, len, NULL);
1014 } else {
1015 /* load provided calculated ecc */
1016 load_ecc8(bch, bch->ecc_buf, calc_ecc);
1017 }
1018 /* load received ecc or assume it was XORed in calc_ecc */
1019 if (recv_ecc) {
1020 load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1021 /* XOR received and calculated ecc */
1022 for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1023 bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1024 sum |= bch->ecc_buf[i];
1025 }
1026 if (!sum)
1027 /* no error found */
1028 return 0;
1029 }
1030 compute_syndromes(bch, bch->ecc_buf, bch->syn);
1031 syn = bch->syn;
1032 }
1033
1034 err = compute_error_locator_polynomial(bch, syn);
1035 if (err > 0) {
1036 nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1037 if (err != nroots)
1038 err = -1;
1039 }
1040 if (err > 0) {
1041 /* post-process raw error locations for easier correction */
1042 nbits = (len*8)+bch->ecc_bits;
1043 for (i = 0; i < err; i++) {
1044 if (errloc[i] >= nbits) {
1045 err = -1;
1046 break;
1047 }
1048 errloc[i] = nbits-1-errloc[i];
1049 errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
1050 }
1051 }
1052 return (err >= 0) ? err : -EBADMSG;
1053}
1054EXPORT_SYMBOL_GPL(decode_bch);
1055
1056/*
1057 * generate Galois field lookup tables
1058 */
1059static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1060{
1061 unsigned int i, x = 1;
1062 const unsigned int k = 1 << deg(poly);
1063
1064 /* primitive polynomial must be of degree m */
1065 if (k != (1u << GF_M(bch)))
1066 return -1;
1067
1068 for (i = 0; i < GF_N(bch); i++) {
1069 bch->a_pow_tab[i] = x;
1070 bch->a_log_tab[x] = i;
1071 if (i && (x == 1))
1072 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1073 return -1;
1074 x <<= 1;
1075 if (x & k)
1076 x ^= poly;
1077 }
1078 bch->a_pow_tab[GF_N(bch)] = 1;
1079 bch->a_log_tab[0] = 0;
1080
1081 return 0;
1082}
1083
1084/*
1085 * compute generator polynomial remainder tables for fast encoding
1086 */
1087static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1088{
1089 int i, j, b, d;
1090 uint32_t data, hi, lo, *tab;
1091 const int l = BCH_ECC_WORDS(bch);
1092 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1093 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1094
1095 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1096
1097 for (i = 0; i < 256; i++) {
1098 /* p(X)=i is a small polynomial of weight <= 8 */
1099 for (b = 0; b < 4; b++) {
1100 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1101 tab = bch->mod8_tab + (b*256+i)*l;
1102 data = i << (8*b);
1103 while (data) {
1104 d = deg(data);
1105 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1106 data ^= g[0] >> (31-d);
1107 for (j = 0; j < ecclen; j++) {
1108 hi = (d < 31) ? g[j] << (d+1) : 0;
1109 lo = (j+1 < plen) ?
1110 g[j+1] >> (31-d) : 0;
1111 tab[j] ^= hi|lo;
1112 }
1113 }
1114 }
1115 }
1116}
1117
1118/*
1119 * build a base for factoring degree 2 polynomials
1120 */
1121static int build_deg2_base(struct bch_control *bch)
1122{
1123 const int m = GF_M(bch);
1124 int i, j, r;
Kees Cook02361bc2018-05-31 11:45:25 -07001125 unsigned int sum, x, y, remaining, ak = 0, xi[BCH_MAX_M];
Ivan Djelic437aa562011-03-11 11:05:32 +01001126
1127 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1128 for (i = 0; i < m; i++) {
1129 for (j = 0, sum = 0; j < m; j++)
1130 sum ^= a_pow(bch, i*(1 << j));
1131
1132 if (sum) {
1133 ak = bch->a_pow_tab[i];
1134 break;
1135 }
1136 }
1137 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1138 remaining = m;
1139 memset(xi, 0, sizeof(xi));
1140
1141 for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1142 y = gf_sqr(bch, x)^x;
1143 for (i = 0; i < 2; i++) {
1144 r = a_log(bch, y);
1145 if (y && (r < m) && !xi[r]) {
1146 bch->xi_tab[r] = x;
1147 xi[r] = 1;
1148 remaining--;
1149 dbg("x%d = %x\n", r, x);
1150 break;
1151 }
1152 y ^= ak;
1153 }
1154 }
1155 /* should not happen but check anyway */
1156 return remaining ? -1 : 0;
1157}
1158
1159static void *bch_alloc(size_t size, int *err)
1160{
1161 void *ptr;
1162
1163 ptr = kmalloc(size, GFP_KERNEL);
1164 if (ptr == NULL)
1165 *err = 1;
1166 return ptr;
1167}
1168
1169/*
1170 * compute generator polynomial for given (m,t) parameters.
1171 */
1172static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1173{
1174 const unsigned int m = GF_M(bch);
1175 const unsigned int t = GF_T(bch);
1176 int n, err = 0;
1177 unsigned int i, j, nbits, r, word, *roots;
1178 struct gf_poly *g;
1179 uint32_t *genpoly;
1180
1181 g = bch_alloc(GF_POLY_SZ(m*t), &err);
1182 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1183 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1184
1185 if (err) {
1186 kfree(genpoly);
1187 genpoly = NULL;
1188 goto finish;
1189 }
1190
1191 /* enumerate all roots of g(X) */
1192 memset(roots , 0, (bch->n+1)*sizeof(*roots));
1193 for (i = 0; i < t; i++) {
1194 for (j = 0, r = 2*i+1; j < m; j++) {
1195 roots[r] = 1;
1196 r = mod_s(bch, 2*r);
1197 }
1198 }
1199 /* build generator polynomial g(X) */
1200 g->deg = 0;
1201 g->c[0] = 1;
1202 for (i = 0; i < GF_N(bch); i++) {
1203 if (roots[i]) {
1204 /* multiply g(X) by (X+root) */
1205 r = bch->a_pow_tab[i];
1206 g->c[g->deg+1] = 1;
1207 for (j = g->deg; j > 0; j--)
1208 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1209
1210 g->c[0] = gf_mul(bch, g->c[0], r);
1211 g->deg++;
1212 }
1213 }
1214 /* store left-justified binary representation of g(X) */
1215 n = g->deg+1;
1216 i = 0;
1217
1218 while (n > 0) {
1219 nbits = (n > 32) ? 32 : n;
1220 for (j = 0, word = 0; j < nbits; j++) {
1221 if (g->c[n-1-j])
1222 word |= 1u << (31-j);
1223 }
1224 genpoly[i++] = word;
1225 n -= nbits;
1226 }
1227 bch->ecc_bits = g->deg;
1228
1229finish:
1230 kfree(g);
1231 kfree(roots);
1232
1233 return genpoly;
1234}
1235
1236/**
1237 * init_bch - initialize a BCH encoder/decoder
1238 * @m: Galois field order, should be in the range 5-15
1239 * @t: maximum error correction capability, in bits
1240 * @prim_poly: user-provided primitive polynomial (or 0 to use default)
1241 *
1242 * Returns:
1243 * a newly allocated BCH control structure if successful, NULL otherwise
1244 *
1245 * This initialization can take some time, as lookup tables are built for fast
1246 * encoding/decoding; make sure not to call this function from a time critical
1247 * path. Usually, init_bch() should be called on module/driver init and
1248 * free_bch() should be called to release memory on exit.
1249 *
1250 * You may provide your own primitive polynomial of degree @m in argument
1251 * @prim_poly, or let init_bch() use its default polynomial.
1252 *
1253 * Once init_bch() has successfully returned a pointer to a newly allocated
1254 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1255 * the structure.
1256 */
1257struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
1258{
1259 int err = 0;
1260 unsigned int i, words;
1261 uint32_t *genpoly;
1262 struct bch_control *bch = NULL;
1263
1264 const int min_m = 5;
Ivan Djelic437aa562011-03-11 11:05:32 +01001265
1266 /* default primitive polynomials */
1267 static const unsigned int prim_poly_tab[] = {
1268 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1269 0x402b, 0x8003,
1270 };
1271
1272#if defined(CONFIG_BCH_CONST_PARAMS)
1273 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1274 printk(KERN_ERR "bch encoder/decoder was configured to support "
1275 "parameters m=%d, t=%d only!\n",
1276 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1277 goto fail;
1278 }
1279#endif
Kees Cook02361bc2018-05-31 11:45:25 -07001280 if ((m < min_m) || (m > BCH_MAX_M))
Ivan Djelic437aa562011-03-11 11:05:32 +01001281 /*
1282 * values of m greater than 15 are not currently supported;
1283 * supporting m > 15 would require changing table base type
1284 * (uint16_t) and a small patch in matrix transposition
1285 */
1286 goto fail;
1287
1288 /* sanity checks */
1289 if ((t < 1) || (m*t >= ((1 << m)-1)))
1290 /* invalid t value */
1291 goto fail;
1292
1293 /* select a primitive polynomial for generating GF(2^m) */
1294 if (prim_poly == 0)
1295 prim_poly = prim_poly_tab[m-min_m];
1296
1297 bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1298 if (bch == NULL)
1299 goto fail;
1300
1301 bch->m = m;
1302 bch->t = t;
1303 bch->n = (1 << m)-1;
1304 words = DIV_ROUND_UP(m*t, 32);
1305 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1306 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1307 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1308 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1309 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1310 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1311 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1312 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err);
1313 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err);
1314 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1315
1316 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1317 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1318
1319 if (err)
1320 goto fail;
1321
1322 err = build_gf_tables(bch, prim_poly);
1323 if (err)
1324 goto fail;
1325
1326 /* use generator polynomial for computing encoding tables */
1327 genpoly = compute_generator_polynomial(bch);
1328 if (genpoly == NULL)
1329 goto fail;
1330
1331 build_mod8_tables(bch, genpoly);
1332 kfree(genpoly);
1333
1334 err = build_deg2_base(bch);
1335 if (err)
1336 goto fail;
1337
1338 return bch;
1339
1340fail:
1341 free_bch(bch);
1342 return NULL;
1343}
1344EXPORT_SYMBOL_GPL(init_bch);
1345
1346/**
1347 * free_bch - free the BCH control structure
1348 * @bch: BCH control structure to release
1349 */
1350void free_bch(struct bch_control *bch)
1351{
1352 unsigned int i;
1353
1354 if (bch) {
1355 kfree(bch->a_pow_tab);
1356 kfree(bch->a_log_tab);
1357 kfree(bch->mod8_tab);
1358 kfree(bch->ecc_buf);
1359 kfree(bch->ecc_buf2);
1360 kfree(bch->xi_tab);
1361 kfree(bch->syn);
1362 kfree(bch->cache);
1363 kfree(bch->elp);
1364
1365 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1366 kfree(bch->poly_2t[i]);
1367
1368 kfree(bch);
1369 }
1370}
1371EXPORT_SYMBOL_GPL(free_bch);
1372
1373MODULE_LICENSE("GPL");
1374MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
1375MODULE_DESCRIPTION("Binary BCH encoder/decoder");