Loading...
1/*
2 * Generic binary BCH encoding/decoding library
3 *
4 * This program is free software; you can redistribute it and/or modify it
5 * under the terms of the GNU General Public License version 2 as published by
6 * the Free Software Foundation.
7 *
8 * This program is distributed in the hope that it will be useful, but WITHOUT
9 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
10 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
11 * more details.
12 *
13 * You should have received a copy of the GNU General Public License along with
14 * this program; if not, write to the Free Software Foundation, Inc., 51
15 * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
16 *
17 * Copyright © 2011 Parrot S.A.
18 *
19 * Author: Ivan Djelic <ivan.djelic@parrot.com>
20 *
21 * Description:
22 *
23 * This library provides runtime configurable encoding/decoding of binary
24 * Bose-Chaudhuri-Hocquenghem (BCH) codes.
25 *
26 * Call bch_init to get a pointer to a newly allocated bch_control structure for
27 * the given m (Galois field order), t (error correction capability) and
28 * (optional) primitive polynomial parameters.
29 *
30 * Call bch_encode to compute and store ecc parity bytes to a given buffer.
31 * Call bch_decode to detect and locate errors in received data.
32 *
33 * On systems supporting hw BCH features, intermediate results may be provided
34 * to bch_decode in order to skip certain steps. See bch_decode() documentation
35 * for details.
36 *
37 * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
38 * parameters m and t; thus allowing extra compiler optimizations and providing
39 * better (up to 2x) encoding performance. Using this option makes sense when
40 * (m,t) are fixed and known in advance, e.g. when using BCH error correction
41 * on a particular NAND flash device.
42 *
43 * Algorithmic details:
44 *
45 * Encoding is performed by processing 32 input bits in parallel, using 4
46 * remainder lookup tables.
47 *
48 * The final stage of decoding involves the following internal steps:
49 * a. Syndrome computation
50 * b. Error locator polynomial computation using Berlekamp-Massey algorithm
51 * c. Error locator root finding (by far the most expensive step)
52 *
53 * In this implementation, step c is not performed using the usual Chien search.
54 * Instead, an alternative approach described in [1] is used. It consists in
55 * factoring the error locator polynomial using the Berlekamp Trace algorithm
56 * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
57 * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
58 * much better performance than Chien search for usual (m,t) values (typically
59 * m >= 13, t < 32, see [1]).
60 *
61 * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
62 * of characteristic 2, in: Western European Workshop on Research in Cryptology
63 * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
64 * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
65 * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
66 */
67
68#include <linux/kernel.h>
69#include <linux/errno.h>
70#include <linux/init.h>
71#include <linux/module.h>
72#include <linux/slab.h>
73#include <linux/bitops.h>
74#include <linux/bitrev.h>
75#include <asm/byteorder.h>
76#include <linux/bch.h>
77
78#if defined(CONFIG_BCH_CONST_PARAMS)
79#define GF_M(_p) (CONFIG_BCH_CONST_M)
80#define GF_T(_p) (CONFIG_BCH_CONST_T)
81#define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1)
82#define BCH_MAX_M (CONFIG_BCH_CONST_M)
83#define BCH_MAX_T (CONFIG_BCH_CONST_T)
84#else
85#define GF_M(_p) ((_p)->m)
86#define GF_T(_p) ((_p)->t)
87#define GF_N(_p) ((_p)->n)
88#define BCH_MAX_M 15 /* 2KB */
89#define BCH_MAX_T 64 /* 64 bit correction */
90#endif
91
92#define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
93#define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
94
95#define BCH_ECC_MAX_WORDS DIV_ROUND_UP(BCH_MAX_M * BCH_MAX_T, 32)
96
97#ifndef dbg
98#define dbg(_fmt, args...) do {} while (0)
99#endif
100
101/*
102 * represent a polynomial over GF(2^m)
103 */
104struct gf_poly {
105 unsigned int deg; /* polynomial degree */
106 unsigned int c[]; /* polynomial terms */
107};
108
109/* given its degree, compute a polynomial size in bytes */
110#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
111
112/* polynomial of degree 1 */
113struct gf_poly_deg1 {
114 struct gf_poly poly;
115 unsigned int c[2];
116};
117
118static u8 swap_bits(struct bch_control *bch, u8 in)
119{
120 if (!bch->swap_bits)
121 return in;
122
123 return bitrev8(in);
124}
125
126/*
127 * same as bch_encode(), but process input data one byte at a time
128 */
129static void bch_encode_unaligned(struct bch_control *bch,
130 const unsigned char *data, unsigned int len,
131 uint32_t *ecc)
132{
133 int i;
134 const uint32_t *p;
135 const int l = BCH_ECC_WORDS(bch)-1;
136
137 while (len--) {
138 u8 tmp = swap_bits(bch, *data++);
139
140 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(tmp)) & 0xff);
141
142 for (i = 0; i < l; i++)
143 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
144
145 ecc[l] = (ecc[l] << 8)^(*p);
146 }
147}
148
149/*
150 * convert ecc bytes to aligned, zero-padded 32-bit ecc words
151 */
152static void load_ecc8(struct bch_control *bch, uint32_t *dst,
153 const uint8_t *src)
154{
155 uint8_t pad[4] = {0, 0, 0, 0};
156 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
157
158 for (i = 0; i < nwords; i++, src += 4)
159 dst[i] = ((u32)swap_bits(bch, src[0]) << 24) |
160 ((u32)swap_bits(bch, src[1]) << 16) |
161 ((u32)swap_bits(bch, src[2]) << 8) |
162 swap_bits(bch, src[3]);
163
164 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
165 dst[nwords] = ((u32)swap_bits(bch, pad[0]) << 24) |
166 ((u32)swap_bits(bch, pad[1]) << 16) |
167 ((u32)swap_bits(bch, pad[2]) << 8) |
168 swap_bits(bch, pad[3]);
169}
170
171/*
172 * convert 32-bit ecc words to ecc bytes
173 */
174static void store_ecc8(struct bch_control *bch, uint8_t *dst,
175 const uint32_t *src)
176{
177 uint8_t pad[4];
178 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
179
180 for (i = 0; i < nwords; i++) {
181 *dst++ = swap_bits(bch, src[i] >> 24);
182 *dst++ = swap_bits(bch, src[i] >> 16);
183 *dst++ = swap_bits(bch, src[i] >> 8);
184 *dst++ = swap_bits(bch, src[i]);
185 }
186 pad[0] = swap_bits(bch, src[nwords] >> 24);
187 pad[1] = swap_bits(bch, src[nwords] >> 16);
188 pad[2] = swap_bits(bch, src[nwords] >> 8);
189 pad[3] = swap_bits(bch, src[nwords]);
190 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
191}
192
193/**
194 * bch_encode - calculate BCH ecc parity of data
195 * @bch: BCH control structure
196 * @data: data to encode
197 * @len: data length in bytes
198 * @ecc: ecc parity data, must be initialized by caller
199 *
200 * The @ecc parity array is used both as input and output parameter, in order to
201 * allow incremental computations. It should be of the size indicated by member
202 * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
203 *
204 * The exact number of computed ecc parity bits is given by member @ecc_bits of
205 * @bch; it may be less than m*t for large values of t.
206 */
207void bch_encode(struct bch_control *bch, const uint8_t *data,
208 unsigned int len, uint8_t *ecc)
209{
210 const unsigned int l = BCH_ECC_WORDS(bch)-1;
211 unsigned int i, mlen;
212 unsigned long m;
213 uint32_t w, r[BCH_ECC_MAX_WORDS];
214 const size_t r_bytes = BCH_ECC_WORDS(bch) * sizeof(*r);
215 const uint32_t * const tab0 = bch->mod8_tab;
216 const uint32_t * const tab1 = tab0 + 256*(l+1);
217 const uint32_t * const tab2 = tab1 + 256*(l+1);
218 const uint32_t * const tab3 = tab2 + 256*(l+1);
219 const uint32_t *pdata, *p0, *p1, *p2, *p3;
220
221 if (WARN_ON(r_bytes > sizeof(r)))
222 return;
223
224 if (ecc) {
225 /* load ecc parity bytes into internal 32-bit buffer */
226 load_ecc8(bch, bch->ecc_buf, ecc);
227 } else {
228 memset(bch->ecc_buf, 0, r_bytes);
229 }
230
231 /* process first unaligned data bytes */
232 m = ((unsigned long)data) & 3;
233 if (m) {
234 mlen = (len < (4-m)) ? len : 4-m;
235 bch_encode_unaligned(bch, data, mlen, bch->ecc_buf);
236 data += mlen;
237 len -= mlen;
238 }
239
240 /* process 32-bit aligned data words */
241 pdata = (uint32_t *)data;
242 mlen = len/4;
243 data += 4*mlen;
244 len -= 4*mlen;
245 memcpy(r, bch->ecc_buf, r_bytes);
246
247 /*
248 * split each 32-bit word into 4 polynomials of weight 8 as follows:
249 *
250 * 31 ...24 23 ...16 15 ... 8 7 ... 0
251 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt
252 * tttttttt mod g = r0 (precomputed)
253 * zzzzzzzz 00000000 mod g = r1 (precomputed)
254 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed)
255 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed)
256 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3
257 */
258 while (mlen--) {
259 /* input data is read in big-endian format */
260 w = cpu_to_be32(*pdata++);
261 if (bch->swap_bits)
262 w = (u32)swap_bits(bch, w) |
263 ((u32)swap_bits(bch, w >> 8) << 8) |
264 ((u32)swap_bits(bch, w >> 16) << 16) |
265 ((u32)swap_bits(bch, w >> 24) << 24);
266 w ^= r[0];
267 p0 = tab0 + (l+1)*((w >> 0) & 0xff);
268 p1 = tab1 + (l+1)*((w >> 8) & 0xff);
269 p2 = tab2 + (l+1)*((w >> 16) & 0xff);
270 p3 = tab3 + (l+1)*((w >> 24) & 0xff);
271
272 for (i = 0; i < l; i++)
273 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
274
275 r[l] = p0[l]^p1[l]^p2[l]^p3[l];
276 }
277 memcpy(bch->ecc_buf, r, r_bytes);
278
279 /* process last unaligned bytes */
280 if (len)
281 bch_encode_unaligned(bch, data, len, bch->ecc_buf);
282
283 /* store ecc parity bytes into original parity buffer */
284 if (ecc)
285 store_ecc8(bch, ecc, bch->ecc_buf);
286}
287EXPORT_SYMBOL_GPL(bch_encode);
288
289static inline int modulo(struct bch_control *bch, unsigned int v)
290{
291 const unsigned int n = GF_N(bch);
292 while (v >= n) {
293 v -= n;
294 v = (v & n) + (v >> GF_M(bch));
295 }
296 return v;
297}
298
299/*
300 * shorter and faster modulo function, only works when v < 2N.
301 */
302static inline int mod_s(struct bch_control *bch, unsigned int v)
303{
304 const unsigned int n = GF_N(bch);
305 return (v < n) ? v : v-n;
306}
307
308static inline int deg(unsigned int poly)
309{
310 /* polynomial degree is the most-significant bit index */
311 return fls(poly)-1;
312}
313
314static inline int parity(unsigned int x)
315{
316 /*
317 * public domain code snippet, lifted from
318 * http://www-graphics.stanford.edu/~seander/bithacks.html
319 */
320 x ^= x >> 1;
321 x ^= x >> 2;
322 x = (x & 0x11111111U) * 0x11111111U;
323 return (x >> 28) & 1;
324}
325
326/* Galois field basic operations: multiply, divide, inverse, etc. */
327
328static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
329 unsigned int b)
330{
331 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
332 bch->a_log_tab[b])] : 0;
333}
334
335static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
336{
337 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
338}
339
340static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
341 unsigned int b)
342{
343 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
344 GF_N(bch)-bch->a_log_tab[b])] : 0;
345}
346
347static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
348{
349 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
350}
351
352static inline unsigned int a_pow(struct bch_control *bch, int i)
353{
354 return bch->a_pow_tab[modulo(bch, i)];
355}
356
357static inline int a_log(struct bch_control *bch, unsigned int x)
358{
359 return bch->a_log_tab[x];
360}
361
362static inline int a_ilog(struct bch_control *bch, unsigned int x)
363{
364 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
365}
366
367/*
368 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
369 */
370static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
371 unsigned int *syn)
372{
373 int i, j, s;
374 unsigned int m;
375 uint32_t poly;
376 const int t = GF_T(bch);
377
378 s = bch->ecc_bits;
379
380 /* make sure extra bits in last ecc word are cleared */
381 m = ((unsigned int)s) & 31;
382 if (m)
383 ecc[s/32] &= ~((1u << (32-m))-1);
384 memset(syn, 0, 2*t*sizeof(*syn));
385
386 /* compute v(a^j) for j=1 .. 2t-1 */
387 do {
388 poly = *ecc++;
389 s -= 32;
390 while (poly) {
391 i = deg(poly);
392 for (j = 0; j < 2*t; j += 2)
393 syn[j] ^= a_pow(bch, (j+1)*(i+s));
394
395 poly ^= (1 << i);
396 }
397 } while (s > 0);
398
399 /* v(a^(2j)) = v(a^j)^2 */
400 for (j = 0; j < t; j++)
401 syn[2*j+1] = gf_sqr(bch, syn[j]);
402}
403
404static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
405{
406 memcpy(dst, src, GF_POLY_SZ(src->deg));
407}
408
409static int compute_error_locator_polynomial(struct bch_control *bch,
410 const unsigned int *syn)
411{
412 const unsigned int t = GF_T(bch);
413 const unsigned int n = GF_N(bch);
414 unsigned int i, j, tmp, l, pd = 1, d = syn[0];
415 struct gf_poly *elp = bch->elp;
416 struct gf_poly *pelp = bch->poly_2t[0];
417 struct gf_poly *elp_copy = bch->poly_2t[1];
418 int k, pp = -1;
419
420 memset(pelp, 0, GF_POLY_SZ(2*t));
421 memset(elp, 0, GF_POLY_SZ(2*t));
422
423 pelp->deg = 0;
424 pelp->c[0] = 1;
425 elp->deg = 0;
426 elp->c[0] = 1;
427
428 /* use simplified binary Berlekamp-Massey algorithm */
429 for (i = 0; (i < t) && (elp->deg <= t); i++) {
430 if (d) {
431 k = 2*i-pp;
432 gf_poly_copy(elp_copy, elp);
433 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
434 tmp = a_log(bch, d)+n-a_log(bch, pd);
435 for (j = 0; j <= pelp->deg; j++) {
436 if (pelp->c[j]) {
437 l = a_log(bch, pelp->c[j]);
438 elp->c[j+k] ^= a_pow(bch, tmp+l);
439 }
440 }
441 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
442 tmp = pelp->deg+k;
443 if (tmp > elp->deg) {
444 elp->deg = tmp;
445 gf_poly_copy(pelp, elp_copy);
446 pd = d;
447 pp = 2*i;
448 }
449 }
450 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
451 if (i < t-1) {
452 d = syn[2*i+2];
453 for (j = 1; j <= elp->deg; j++)
454 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
455 }
456 }
457 dbg("elp=%s\n", gf_poly_str(elp));
458 return (elp->deg > t) ? -1 : (int)elp->deg;
459}
460
461/*
462 * solve a m x m linear system in GF(2) with an expected number of solutions,
463 * and return the number of found solutions
464 */
465static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
466 unsigned int *sol, int nsol)
467{
468 const int m = GF_M(bch);
469 unsigned int tmp, mask;
470 int rem, c, r, p, k, param[BCH_MAX_M];
471
472 k = 0;
473 mask = 1 << m;
474
475 /* Gaussian elimination */
476 for (c = 0; c < m; c++) {
477 rem = 0;
478 p = c-k;
479 /* find suitable row for elimination */
480 for (r = p; r < m; r++) {
481 if (rows[r] & mask) {
482 if (r != p)
483 swap(rows[r], rows[p]);
484 rem = r+1;
485 break;
486 }
487 }
488 if (rem) {
489 /* perform elimination on remaining rows */
490 tmp = rows[p];
491 for (r = rem; r < m; r++) {
492 if (rows[r] & mask)
493 rows[r] ^= tmp;
494 }
495 } else {
496 /* elimination not needed, store defective row index */
497 param[k++] = c;
498 }
499 mask >>= 1;
500 }
501 /* rewrite system, inserting fake parameter rows */
502 if (k > 0) {
503 p = k;
504 for (r = m-1; r >= 0; r--) {
505 if ((r > m-1-k) && rows[r])
506 /* system has no solution */
507 return 0;
508
509 rows[r] = (p && (r == param[p-1])) ?
510 p--, 1u << (m-r) : rows[r-p];
511 }
512 }
513
514 if (nsol != (1 << k))
515 /* unexpected number of solutions */
516 return 0;
517
518 for (p = 0; p < nsol; p++) {
519 /* set parameters for p-th solution */
520 for (c = 0; c < k; c++)
521 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
522
523 /* compute unique solution */
524 tmp = 0;
525 for (r = m-1; r >= 0; r--) {
526 mask = rows[r] & (tmp|1);
527 tmp |= parity(mask) << (m-r);
528 }
529 sol[p] = tmp >> 1;
530 }
531 return nsol;
532}
533
534/*
535 * this function builds and solves a linear system for finding roots of a degree
536 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
537 */
538static int find_affine4_roots(struct bch_control *bch, unsigned int a,
539 unsigned int b, unsigned int c,
540 unsigned int *roots)
541{
542 int i, j, k;
543 const int m = GF_M(bch);
544 unsigned int mask = 0xff, t, rows[16] = {0,};
545
546 j = a_log(bch, b);
547 k = a_log(bch, a);
548 rows[0] = c;
549
550 /* build linear system to solve X^4+aX^2+bX+c = 0 */
551 for (i = 0; i < m; i++) {
552 rows[i+1] = bch->a_pow_tab[4*i]^
553 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
554 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
555 j++;
556 k += 2;
557 }
558 /*
559 * transpose 16x16 matrix before passing it to linear solver
560 * warning: this code assumes m < 16
561 */
562 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
563 for (k = 0; k < 16; k = (k+j+1) & ~j) {
564 t = ((rows[k] >> j)^rows[k+j]) & mask;
565 rows[k] ^= (t << j);
566 rows[k+j] ^= t;
567 }
568 }
569 return solve_linear_system(bch, rows, roots, 4);
570}
571
572/*
573 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
574 */
575static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
576 unsigned int *roots)
577{
578 int n = 0;
579
580 if (poly->c[0])
581 /* poly[X] = bX+c with c!=0, root=c/b */
582 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
583 bch->a_log_tab[poly->c[1]]);
584 return n;
585}
586
587/*
588 * compute roots of a degree 2 polynomial over GF(2^m)
589 */
590static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
591 unsigned int *roots)
592{
593 int n = 0, i, l0, l1, l2;
594 unsigned int u, v, r;
595
596 if (poly->c[0] && poly->c[1]) {
597
598 l0 = bch->a_log_tab[poly->c[0]];
599 l1 = bch->a_log_tab[poly->c[1]];
600 l2 = bch->a_log_tab[poly->c[2]];
601
602 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
603 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
604 /*
605 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
606 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
607 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
608 * i.e. r and r+1 are roots iff Tr(u)=0
609 */
610 r = 0;
611 v = u;
612 while (v) {
613 i = deg(v);
614 r ^= bch->xi_tab[i];
615 v ^= (1 << i);
616 }
617 /* verify root */
618 if ((gf_sqr(bch, r)^r) == u) {
619 /* reverse z=a/bX transformation and compute log(1/r) */
620 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
621 bch->a_log_tab[r]+l2);
622 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
623 bch->a_log_tab[r^1]+l2);
624 }
625 }
626 return n;
627}
628
629/*
630 * compute roots of a degree 3 polynomial over GF(2^m)
631 */
632static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
633 unsigned int *roots)
634{
635 int i, n = 0;
636 unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
637
638 if (poly->c[0]) {
639 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
640 e3 = poly->c[3];
641 c2 = gf_div(bch, poly->c[0], e3);
642 b2 = gf_div(bch, poly->c[1], e3);
643 a2 = gf_div(bch, poly->c[2], e3);
644
645 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
646 c = gf_mul(bch, a2, c2); /* c = a2c2 */
647 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */
648 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */
649
650 /* find the 4 roots of this affine polynomial */
651 if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
652 /* remove a2 from final list of roots */
653 for (i = 0; i < 4; i++) {
654 if (tmp[i] != a2)
655 roots[n++] = a_ilog(bch, tmp[i]);
656 }
657 }
658 }
659 return n;
660}
661
662/*
663 * compute roots of a degree 4 polynomial over GF(2^m)
664 */
665static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
666 unsigned int *roots)
667{
668 int i, l, n = 0;
669 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
670
671 if (poly->c[0] == 0)
672 return 0;
673
674 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
675 e4 = poly->c[4];
676 d = gf_div(bch, poly->c[0], e4);
677 c = gf_div(bch, poly->c[1], e4);
678 b = gf_div(bch, poly->c[2], e4);
679 a = gf_div(bch, poly->c[3], e4);
680
681 /* use Y=1/X transformation to get an affine polynomial */
682 if (a) {
683 /* first, eliminate cX by using z=X+e with ae^2+c=0 */
684 if (c) {
685 /* compute e such that e^2 = c/a */
686 f = gf_div(bch, c, a);
687 l = a_log(bch, f);
688 l += (l & 1) ? GF_N(bch) : 0;
689 e = a_pow(bch, l/2);
690 /*
691 * use transformation z=X+e:
692 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
693 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
694 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
695 * z^4 + az^3 + b'z^2 + d'
696 */
697 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
698 b = gf_mul(bch, a, e)^b;
699 }
700 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
701 if (d == 0)
702 /* assume all roots have multiplicity 1 */
703 return 0;
704
705 c2 = gf_inv(bch, d);
706 b2 = gf_div(bch, a, d);
707 a2 = gf_div(bch, b, d);
708 } else {
709 /* polynomial is already affine */
710 c2 = d;
711 b2 = c;
712 a2 = b;
713 }
714 /* find the 4 roots of this affine polynomial */
715 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
716 for (i = 0; i < 4; i++) {
717 /* post-process roots (reverse transformations) */
718 f = a ? gf_inv(bch, roots[i]) : roots[i];
719 roots[i] = a_ilog(bch, f^e);
720 }
721 n = 4;
722 }
723 return n;
724}
725
726/*
727 * build monic, log-based representation of a polynomial
728 */
729static void gf_poly_logrep(struct bch_control *bch,
730 const struct gf_poly *a, int *rep)
731{
732 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
733
734 /* represent 0 values with -1; warning, rep[d] is not set to 1 */
735 for (i = 0; i < d; i++)
736 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
737}
738
739/*
740 * compute polynomial Euclidean division remainder in GF(2^m)[X]
741 */
742static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
743 const struct gf_poly *b, int *rep)
744{
745 int la, p, m;
746 unsigned int i, j, *c = a->c;
747 const unsigned int d = b->deg;
748
749 if (a->deg < d)
750 return;
751
752 /* reuse or compute log representation of denominator */
753 if (!rep) {
754 rep = bch->cache;
755 gf_poly_logrep(bch, b, rep);
756 }
757
758 for (j = a->deg; j >= d; j--) {
759 if (c[j]) {
760 la = a_log(bch, c[j]);
761 p = j-d;
762 for (i = 0; i < d; i++, p++) {
763 m = rep[i];
764 if (m >= 0)
765 c[p] ^= bch->a_pow_tab[mod_s(bch,
766 m+la)];
767 }
768 }
769 }
770 a->deg = d-1;
771 while (!c[a->deg] && a->deg)
772 a->deg--;
773}
774
775/*
776 * compute polynomial Euclidean division quotient in GF(2^m)[X]
777 */
778static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
779 const struct gf_poly *b, struct gf_poly *q)
780{
781 if (a->deg >= b->deg) {
782 q->deg = a->deg-b->deg;
783 /* compute a mod b (modifies a) */
784 gf_poly_mod(bch, a, b, NULL);
785 /* quotient is stored in upper part of polynomial a */
786 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
787 } else {
788 q->deg = 0;
789 q->c[0] = 0;
790 }
791}
792
793/*
794 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
795 */
796static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
797 struct gf_poly *b)
798{
799 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
800
801 if (a->deg < b->deg)
802 swap(a, b);
803
804 while (b->deg > 0) {
805 gf_poly_mod(bch, a, b, NULL);
806 swap(a, b);
807 }
808
809 dbg("%s\n", gf_poly_str(a));
810
811 return a;
812}
813
814/*
815 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
816 * This is used in Berlekamp Trace algorithm for splitting polynomials
817 */
818static void compute_trace_bk_mod(struct bch_control *bch, int k,
819 const struct gf_poly *f, struct gf_poly *z,
820 struct gf_poly *out)
821{
822 const int m = GF_M(bch);
823 int i, j;
824
825 /* z contains z^2j mod f */
826 z->deg = 1;
827 z->c[0] = 0;
828 z->c[1] = bch->a_pow_tab[k];
829
830 out->deg = 0;
831 memset(out, 0, GF_POLY_SZ(f->deg));
832
833 /* compute f log representation only once */
834 gf_poly_logrep(bch, f, bch->cache);
835
836 for (i = 0; i < m; i++) {
837 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
838 for (j = z->deg; j >= 0; j--) {
839 out->c[j] ^= z->c[j];
840 z->c[2*j] = gf_sqr(bch, z->c[j]);
841 z->c[2*j+1] = 0;
842 }
843 if (z->deg > out->deg)
844 out->deg = z->deg;
845
846 if (i < m-1) {
847 z->deg *= 2;
848 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
849 gf_poly_mod(bch, z, f, bch->cache);
850 }
851 }
852 while (!out->c[out->deg] && out->deg)
853 out->deg--;
854
855 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
856}
857
858/*
859 * factor a polynomial using Berlekamp Trace algorithm (BTA)
860 */
861static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
862 struct gf_poly **g, struct gf_poly **h)
863{
864 struct gf_poly *f2 = bch->poly_2t[0];
865 struct gf_poly *q = bch->poly_2t[1];
866 struct gf_poly *tk = bch->poly_2t[2];
867 struct gf_poly *z = bch->poly_2t[3];
868 struct gf_poly *gcd;
869
870 dbg("factoring %s...\n", gf_poly_str(f));
871
872 *g = f;
873 *h = NULL;
874
875 /* tk = Tr(a^k.X) mod f */
876 compute_trace_bk_mod(bch, k, f, z, tk);
877
878 if (tk->deg > 0) {
879 /* compute g = gcd(f, tk) (destructive operation) */
880 gf_poly_copy(f2, f);
881 gcd = gf_poly_gcd(bch, f2, tk);
882 if (gcd->deg < f->deg) {
883 /* compute h=f/gcd(f,tk); this will modify f and q */
884 gf_poly_div(bch, f, gcd, q);
885 /* store g and h in-place (clobbering f) */
886 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
887 gf_poly_copy(*g, gcd);
888 gf_poly_copy(*h, q);
889 }
890 }
891}
892
893/*
894 * find roots of a polynomial, using BTZ algorithm; see the beginning of this
895 * file for details
896 */
897static int find_poly_roots(struct bch_control *bch, unsigned int k,
898 struct gf_poly *poly, unsigned int *roots)
899{
900 int cnt;
901 struct gf_poly *f1, *f2;
902
903 switch (poly->deg) {
904 /* handle low degree polynomials with ad hoc techniques */
905 case 1:
906 cnt = find_poly_deg1_roots(bch, poly, roots);
907 break;
908 case 2:
909 cnt = find_poly_deg2_roots(bch, poly, roots);
910 break;
911 case 3:
912 cnt = find_poly_deg3_roots(bch, poly, roots);
913 break;
914 case 4:
915 cnt = find_poly_deg4_roots(bch, poly, roots);
916 break;
917 default:
918 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */
919 cnt = 0;
920 if (poly->deg && (k <= GF_M(bch))) {
921 factor_polynomial(bch, k, poly, &f1, &f2);
922 if (f1)
923 cnt += find_poly_roots(bch, k+1, f1, roots);
924 if (f2)
925 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
926 }
927 break;
928 }
929 return cnt;
930}
931
932#if defined(USE_CHIEN_SEARCH)
933/*
934 * exhaustive root search (Chien) implementation - not used, included only for
935 * reference/comparison tests
936 */
937static int chien_search(struct bch_control *bch, unsigned int len,
938 struct gf_poly *p, unsigned int *roots)
939{
940 int m;
941 unsigned int i, j, syn, syn0, count = 0;
942 const unsigned int k = 8*len+bch->ecc_bits;
943
944 /* use a log-based representation of polynomial */
945 gf_poly_logrep(bch, p, bch->cache);
946 bch->cache[p->deg] = 0;
947 syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
948
949 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
950 /* compute elp(a^i) */
951 for (j = 1, syn = syn0; j <= p->deg; j++) {
952 m = bch->cache[j];
953 if (m >= 0)
954 syn ^= a_pow(bch, m+j*i);
955 }
956 if (syn == 0) {
957 roots[count++] = GF_N(bch)-i;
958 if (count == p->deg)
959 break;
960 }
961 }
962 return (count == p->deg) ? count : 0;
963}
964#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
965#endif /* USE_CHIEN_SEARCH */
966
967/**
968 * bch_decode - decode received codeword and find bit error locations
969 * @bch: BCH control structure
970 * @data: received data, ignored if @calc_ecc is provided
971 * @len: data length in bytes, must always be provided
972 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
973 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
974 * @syn: hw computed syndrome data (if NULL, syndrome is calculated)
975 * @errloc: output array of error locations
976 *
977 * Returns:
978 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
979 * invalid parameters were provided
980 *
981 * Depending on the available hw BCH support and the need to compute @calc_ecc
982 * separately (using bch_encode()), this function should be called with one of
983 * the following parameter configurations -
984 *
985 * by providing @data and @recv_ecc only:
986 * bch_decode(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
987 *
988 * by providing @recv_ecc and @calc_ecc:
989 * bch_decode(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
990 *
991 * by providing ecc = recv_ecc XOR calc_ecc:
992 * bch_decode(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
993 *
994 * by providing syndrome results @syn:
995 * bch_decode(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
996 *
997 * Once bch_decode() has successfully returned with a positive value, error
998 * locations returned in array @errloc should be interpreted as follows -
999 *
1000 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
1001 * data correction)
1002 *
1003 * if (errloc[n] < 8*len), then n-th error is located in data and can be
1004 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
1005 *
1006 * Note that this function does not perform any data correction by itself, it
1007 * merely indicates error locations.
1008 */
1009int bch_decode(struct bch_control *bch, const uint8_t *data, unsigned int len,
1010 const uint8_t *recv_ecc, const uint8_t *calc_ecc,
1011 const unsigned int *syn, unsigned int *errloc)
1012{
1013 const unsigned int ecc_words = BCH_ECC_WORDS(bch);
1014 unsigned int nbits;
1015 int i, err, nroots;
1016 uint32_t sum;
1017
1018 /* sanity check: make sure data length can be handled */
1019 if (8*len > (bch->n-bch->ecc_bits))
1020 return -EINVAL;
1021
1022 /* if caller does not provide syndromes, compute them */
1023 if (!syn) {
1024 if (!calc_ecc) {
1025 /* compute received data ecc into an internal buffer */
1026 if (!data || !recv_ecc)
1027 return -EINVAL;
1028 bch_encode(bch, data, len, NULL);
1029 } else {
1030 /* load provided calculated ecc */
1031 load_ecc8(bch, bch->ecc_buf, calc_ecc);
1032 }
1033 /* load received ecc or assume it was XORed in calc_ecc */
1034 if (recv_ecc) {
1035 load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1036 /* XOR received and calculated ecc */
1037 for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1038 bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1039 sum |= bch->ecc_buf[i];
1040 }
1041 if (!sum)
1042 /* no error found */
1043 return 0;
1044 }
1045 compute_syndromes(bch, bch->ecc_buf, bch->syn);
1046 syn = bch->syn;
1047 }
1048
1049 err = compute_error_locator_polynomial(bch, syn);
1050 if (err > 0) {
1051 nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1052 if (err != nroots)
1053 err = -1;
1054 }
1055 if (err > 0) {
1056 /* post-process raw error locations for easier correction */
1057 nbits = (len*8)+bch->ecc_bits;
1058 for (i = 0; i < err; i++) {
1059 if (errloc[i] >= nbits) {
1060 err = -1;
1061 break;
1062 }
1063 errloc[i] = nbits-1-errloc[i];
1064 if (!bch->swap_bits)
1065 errloc[i] = (errloc[i] & ~7) |
1066 (7-(errloc[i] & 7));
1067 }
1068 }
1069 return (err >= 0) ? err : -EBADMSG;
1070}
1071EXPORT_SYMBOL_GPL(bch_decode);
1072
1073/*
1074 * generate Galois field lookup tables
1075 */
1076static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1077{
1078 unsigned int i, x = 1;
1079 const unsigned int k = 1 << deg(poly);
1080
1081 /* primitive polynomial must be of degree m */
1082 if (k != (1u << GF_M(bch)))
1083 return -1;
1084
1085 for (i = 0; i < GF_N(bch); i++) {
1086 bch->a_pow_tab[i] = x;
1087 bch->a_log_tab[x] = i;
1088 if (i && (x == 1))
1089 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1090 return -1;
1091 x <<= 1;
1092 if (x & k)
1093 x ^= poly;
1094 }
1095 bch->a_pow_tab[GF_N(bch)] = 1;
1096 bch->a_log_tab[0] = 0;
1097
1098 return 0;
1099}
1100
1101/*
1102 * compute generator polynomial remainder tables for fast encoding
1103 */
1104static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1105{
1106 int i, j, b, d;
1107 uint32_t data, hi, lo, *tab;
1108 const int l = BCH_ECC_WORDS(bch);
1109 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1110 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1111
1112 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1113
1114 for (i = 0; i < 256; i++) {
1115 /* p(X)=i is a small polynomial of weight <= 8 */
1116 for (b = 0; b < 4; b++) {
1117 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1118 tab = bch->mod8_tab + (b*256+i)*l;
1119 data = i << (8*b);
1120 while (data) {
1121 d = deg(data);
1122 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1123 data ^= g[0] >> (31-d);
1124 for (j = 0; j < ecclen; j++) {
1125 hi = (d < 31) ? g[j] << (d+1) : 0;
1126 lo = (j+1 < plen) ?
1127 g[j+1] >> (31-d) : 0;
1128 tab[j] ^= hi|lo;
1129 }
1130 }
1131 }
1132 }
1133}
1134
1135/*
1136 * build a base for factoring degree 2 polynomials
1137 */
1138static int build_deg2_base(struct bch_control *bch)
1139{
1140 const int m = GF_M(bch);
1141 int i, j, r;
1142 unsigned int sum, x, y, remaining, ak = 0, xi[BCH_MAX_M];
1143
1144 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1145 for (i = 0; i < m; i++) {
1146 for (j = 0, sum = 0; j < m; j++)
1147 sum ^= a_pow(bch, i*(1 << j));
1148
1149 if (sum) {
1150 ak = bch->a_pow_tab[i];
1151 break;
1152 }
1153 }
1154 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1155 remaining = m;
1156 memset(xi, 0, sizeof(xi));
1157
1158 for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1159 y = gf_sqr(bch, x)^x;
1160 for (i = 0; i < 2; i++) {
1161 r = a_log(bch, y);
1162 if (y && (r < m) && !xi[r]) {
1163 bch->xi_tab[r] = x;
1164 xi[r] = 1;
1165 remaining--;
1166 dbg("x%d = %x\n", r, x);
1167 break;
1168 }
1169 y ^= ak;
1170 }
1171 }
1172 /* should not happen but check anyway */
1173 return remaining ? -1 : 0;
1174}
1175
1176static void *bch_alloc(size_t size, int *err)
1177{
1178 void *ptr;
1179
1180 ptr = kmalloc(size, GFP_KERNEL);
1181 if (ptr == NULL)
1182 *err = 1;
1183 return ptr;
1184}
1185
1186/*
1187 * compute generator polynomial for given (m,t) parameters.
1188 */
1189static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1190{
1191 const unsigned int m = GF_M(bch);
1192 const unsigned int t = GF_T(bch);
1193 int n, err = 0;
1194 unsigned int i, j, nbits, r, word, *roots;
1195 struct gf_poly *g;
1196 uint32_t *genpoly;
1197
1198 g = bch_alloc(GF_POLY_SZ(m*t), &err);
1199 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1200 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1201
1202 if (err) {
1203 kfree(genpoly);
1204 genpoly = NULL;
1205 goto finish;
1206 }
1207
1208 /* enumerate all roots of g(X) */
1209 memset(roots , 0, (bch->n+1)*sizeof(*roots));
1210 for (i = 0; i < t; i++) {
1211 for (j = 0, r = 2*i+1; j < m; j++) {
1212 roots[r] = 1;
1213 r = mod_s(bch, 2*r);
1214 }
1215 }
1216 /* build generator polynomial g(X) */
1217 g->deg = 0;
1218 g->c[0] = 1;
1219 for (i = 0; i < GF_N(bch); i++) {
1220 if (roots[i]) {
1221 /* multiply g(X) by (X+root) */
1222 r = bch->a_pow_tab[i];
1223 g->c[g->deg+1] = 1;
1224 for (j = g->deg; j > 0; j--)
1225 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1226
1227 g->c[0] = gf_mul(bch, g->c[0], r);
1228 g->deg++;
1229 }
1230 }
1231 /* store left-justified binary representation of g(X) */
1232 n = g->deg+1;
1233 i = 0;
1234
1235 while (n > 0) {
1236 nbits = (n > 32) ? 32 : n;
1237 for (j = 0, word = 0; j < nbits; j++) {
1238 if (g->c[n-1-j])
1239 word |= 1u << (31-j);
1240 }
1241 genpoly[i++] = word;
1242 n -= nbits;
1243 }
1244 bch->ecc_bits = g->deg;
1245
1246finish:
1247 kfree(g);
1248 kfree(roots);
1249
1250 return genpoly;
1251}
1252
1253/**
1254 * bch_init - initialize a BCH encoder/decoder
1255 * @m: Galois field order, should be in the range 5-15
1256 * @t: maximum error correction capability, in bits
1257 * @prim_poly: user-provided primitive polynomial (or 0 to use default)
1258 * @swap_bits: swap bits within data and syndrome bytes
1259 *
1260 * Returns:
1261 * a newly allocated BCH control structure if successful, NULL otherwise
1262 *
1263 * This initialization can take some time, as lookup tables are built for fast
1264 * encoding/decoding; make sure not to call this function from a time critical
1265 * path. Usually, bch_init() should be called on module/driver init and
1266 * bch_free() should be called to release memory on exit.
1267 *
1268 * You may provide your own primitive polynomial of degree @m in argument
1269 * @prim_poly, or let bch_init() use its default polynomial.
1270 *
1271 * Once bch_init() has successfully returned a pointer to a newly allocated
1272 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1273 * the structure.
1274 */
1275struct bch_control *bch_init(int m, int t, unsigned int prim_poly,
1276 bool swap_bits)
1277{
1278 int err = 0;
1279 unsigned int i, words;
1280 uint32_t *genpoly;
1281 struct bch_control *bch = NULL;
1282
1283 const int min_m = 5;
1284
1285 /* default primitive polynomials */
1286 static const unsigned int prim_poly_tab[] = {
1287 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1288 0x402b, 0x8003,
1289 };
1290
1291#if defined(CONFIG_BCH_CONST_PARAMS)
1292 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1293 printk(KERN_ERR "bch encoder/decoder was configured to support "
1294 "parameters m=%d, t=%d only!\n",
1295 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1296 goto fail;
1297 }
1298#endif
1299 if ((m < min_m) || (m > BCH_MAX_M))
1300 /*
1301 * values of m greater than 15 are not currently supported;
1302 * supporting m > 15 would require changing table base type
1303 * (uint16_t) and a small patch in matrix transposition
1304 */
1305 goto fail;
1306
1307 if (t > BCH_MAX_T)
1308 /*
1309 * we can support larger than 64 bits if necessary, at the
1310 * cost of higher stack usage.
1311 */
1312 goto fail;
1313
1314 /* sanity checks */
1315 if ((t < 1) || (m*t >= ((1 << m)-1)))
1316 /* invalid t value */
1317 goto fail;
1318
1319 /* select a primitive polynomial for generating GF(2^m) */
1320 if (prim_poly == 0)
1321 prim_poly = prim_poly_tab[m-min_m];
1322
1323 bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1324 if (bch == NULL)
1325 goto fail;
1326
1327 bch->m = m;
1328 bch->t = t;
1329 bch->n = (1 << m)-1;
1330 words = DIV_ROUND_UP(m*t, 32);
1331 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1332 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1333 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1334 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1335 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1336 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1337 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1338 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err);
1339 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err);
1340 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1341 bch->swap_bits = swap_bits;
1342
1343 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1344 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1345
1346 if (err)
1347 goto fail;
1348
1349 err = build_gf_tables(bch, prim_poly);
1350 if (err)
1351 goto fail;
1352
1353 /* use generator polynomial for computing encoding tables */
1354 genpoly = compute_generator_polynomial(bch);
1355 if (genpoly == NULL)
1356 goto fail;
1357
1358 build_mod8_tables(bch, genpoly);
1359 kfree(genpoly);
1360
1361 err = build_deg2_base(bch);
1362 if (err)
1363 goto fail;
1364
1365 return bch;
1366
1367fail:
1368 bch_free(bch);
1369 return NULL;
1370}
1371EXPORT_SYMBOL_GPL(bch_init);
1372
1373/**
1374 * bch_free - free the BCH control structure
1375 * @bch: BCH control structure to release
1376 */
1377void bch_free(struct bch_control *bch)
1378{
1379 unsigned int i;
1380
1381 if (bch) {
1382 kfree(bch->a_pow_tab);
1383 kfree(bch->a_log_tab);
1384 kfree(bch->mod8_tab);
1385 kfree(bch->ecc_buf);
1386 kfree(bch->ecc_buf2);
1387 kfree(bch->xi_tab);
1388 kfree(bch->syn);
1389 kfree(bch->cache);
1390 kfree(bch->elp);
1391
1392 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1393 kfree(bch->poly_2t[i]);
1394
1395 kfree(bch);
1396 }
1397}
1398EXPORT_SYMBOL_GPL(bch_free);
1399
1400MODULE_LICENSE("GPL");
1401MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
1402MODULE_DESCRIPTION("Binary BCH encoder/decoder");
1/*
2 * Generic binary BCH encoding/decoding library
3 *
4 * This program is free software; you can redistribute it and/or modify it
5 * under the terms of the GNU General Public License version 2 as published by
6 * the Free Software Foundation.
7 *
8 * This program is distributed in the hope that it will be useful, but WITHOUT
9 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
10 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
11 * more details.
12 *
13 * You should have received a copy of the GNU General Public License along with
14 * this program; if not, write to the Free Software Foundation, Inc., 51
15 * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
16 *
17 * Copyright © 2011 Parrot S.A.
18 *
19 * Author: Ivan Djelic <ivan.djelic@parrot.com>
20 *
21 * Description:
22 *
23 * This library provides runtime configurable encoding/decoding of binary
24 * Bose-Chaudhuri-Hocquenghem (BCH) codes.
25 *
26 * Call 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)
81#define BCH_MAX_M (CONFIG_BCH_CONST_M)
82#define BCH_MAX_T (CONFIG_BCH_CONST_T)
83#else
84#define GF_M(_p) ((_p)->m)
85#define GF_T(_p) ((_p)->t)
86#define GF_N(_p) ((_p)->n)
87#define BCH_MAX_M 15 /* 2KB */
88#define BCH_MAX_T 64 /* 64 bit correction */
89#endif
90
91#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
94#define BCH_ECC_MAX_WORDS DIV_ROUND_UP(BCH_MAX_M * BCH_MAX_T, 32)
95
96#ifndef dbg
97#define dbg(_fmt, args...) do {} while (0)
98#endif
99
100/*
101 * represent a polynomial over GF(2^m)
102 */
103struct gf_poly {
104 unsigned int deg; /* polynomial degree */
105 unsigned int c[0]; /* polynomial terms */
106};
107
108/* given its degree, compute a polynomial size in bytes */
109#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
110
111/* polynomial of degree 1 */
112struct gf_poly_deg1 {
113 struct gf_poly poly;
114 unsigned int c[2];
115};
116
117/*
118 * same as encode_bch(), but process input data one byte at a time
119 */
120static void encode_bch_unaligned(struct bch_control *bch,
121 const unsigned char *data, unsigned int len,
122 uint32_t *ecc)
123{
124 int i;
125 const uint32_t *p;
126 const int l = BCH_ECC_WORDS(bch)-1;
127
128 while (len--) {
129 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
130
131 for (i = 0; i < l; i++)
132 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
133
134 ecc[l] = (ecc[l] << 8)^(*p);
135 }
136}
137
138/*
139 * convert ecc bytes to aligned, zero-padded 32-bit ecc words
140 */
141static void load_ecc8(struct bch_control *bch, uint32_t *dst,
142 const uint8_t *src)
143{
144 uint8_t pad[4] = {0, 0, 0, 0};
145 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
146
147 for (i = 0; i < nwords; i++, src += 4)
148 dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
149
150 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
151 dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
152}
153
154/*
155 * convert 32-bit ecc words to ecc bytes
156 */
157static void store_ecc8(struct bch_control *bch, uint8_t *dst,
158 const uint32_t *src)
159{
160 uint8_t pad[4];
161 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
162
163 for (i = 0; i < nwords; i++) {
164 *dst++ = (src[i] >> 24);
165 *dst++ = (src[i] >> 16) & 0xff;
166 *dst++ = (src[i] >> 8) & 0xff;
167 *dst++ = (src[i] >> 0) & 0xff;
168 }
169 pad[0] = (src[nwords] >> 24);
170 pad[1] = (src[nwords] >> 16) & 0xff;
171 pad[2] = (src[nwords] >> 8) & 0xff;
172 pad[3] = (src[nwords] >> 0) & 0xff;
173 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
174}
175
176/**
177 * encode_bch - calculate BCH ecc parity of data
178 * @bch: BCH control structure
179 * @data: data to encode
180 * @len: data length in bytes
181 * @ecc: ecc parity data, must be initialized by caller
182 *
183 * The @ecc parity array is used both as input and output parameter, in order to
184 * allow incremental computations. It should be of the size indicated by member
185 * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
186 *
187 * The exact number of computed ecc parity bits is given by member @ecc_bits of
188 * @bch; it may be less than m*t for large values of t.
189 */
190void encode_bch(struct bch_control *bch, const uint8_t *data,
191 unsigned int len, uint8_t *ecc)
192{
193 const unsigned int l = BCH_ECC_WORDS(bch)-1;
194 unsigned int i, mlen;
195 unsigned long m;
196 uint32_t w, r[BCH_ECC_MAX_WORDS];
197 const size_t r_bytes = BCH_ECC_WORDS(bch) * sizeof(*r);
198 const uint32_t * const tab0 = bch->mod8_tab;
199 const uint32_t * const tab1 = tab0 + 256*(l+1);
200 const uint32_t * const tab2 = tab1 + 256*(l+1);
201 const uint32_t * const tab3 = tab2 + 256*(l+1);
202 const uint32_t *pdata, *p0, *p1, *p2, *p3;
203
204 if (WARN_ON(r_bytes > sizeof(r)))
205 return;
206
207 if (ecc) {
208 /* load ecc parity bytes into internal 32-bit buffer */
209 load_ecc8(bch, bch->ecc_buf, ecc);
210 } else {
211 memset(bch->ecc_buf, 0, r_bytes);
212 }
213
214 /* process first unaligned data bytes */
215 m = ((unsigned long)data) & 3;
216 if (m) {
217 mlen = (len < (4-m)) ? len : 4-m;
218 encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
219 data += mlen;
220 len -= mlen;
221 }
222
223 /* process 32-bit aligned data words */
224 pdata = (uint32_t *)data;
225 mlen = len/4;
226 data += 4*mlen;
227 len -= 4*mlen;
228 memcpy(r, bch->ecc_buf, r_bytes);
229
230 /*
231 * split each 32-bit word into 4 polynomials of weight 8 as follows:
232 *
233 * 31 ...24 23 ...16 15 ... 8 7 ... 0
234 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt
235 * tttttttt mod g = r0 (precomputed)
236 * zzzzzzzz 00000000 mod g = r1 (precomputed)
237 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed)
238 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed)
239 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3
240 */
241 while (mlen--) {
242 /* input data is read in big-endian format */
243 w = r[0]^cpu_to_be32(*pdata++);
244 p0 = tab0 + (l+1)*((w >> 0) & 0xff);
245 p1 = tab1 + (l+1)*((w >> 8) & 0xff);
246 p2 = tab2 + (l+1)*((w >> 16) & 0xff);
247 p3 = tab3 + (l+1)*((w >> 24) & 0xff);
248
249 for (i = 0; i < l; i++)
250 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
251
252 r[l] = p0[l]^p1[l]^p2[l]^p3[l];
253 }
254 memcpy(bch->ecc_buf, r, r_bytes);
255
256 /* process last unaligned bytes */
257 if (len)
258 encode_bch_unaligned(bch, data, len, bch->ecc_buf);
259
260 /* store ecc parity bytes into original parity buffer */
261 if (ecc)
262 store_ecc8(bch, ecc, bch->ecc_buf);
263}
264EXPORT_SYMBOL_GPL(encode_bch);
265
266static inline int modulo(struct bch_control *bch, unsigned int v)
267{
268 const unsigned int n = GF_N(bch);
269 while (v >= n) {
270 v -= n;
271 v = (v & n) + (v >> GF_M(bch));
272 }
273 return v;
274}
275
276/*
277 * shorter and faster modulo function, only works when v < 2N.
278 */
279static inline int mod_s(struct bch_control *bch, unsigned int v)
280{
281 const unsigned int n = GF_N(bch);
282 return (v < n) ? v : v-n;
283}
284
285static inline int deg(unsigned int poly)
286{
287 /* polynomial degree is the most-significant bit index */
288 return fls(poly)-1;
289}
290
291static inline int parity(unsigned int x)
292{
293 /*
294 * public domain code snippet, lifted from
295 * http://www-graphics.stanford.edu/~seander/bithacks.html
296 */
297 x ^= x >> 1;
298 x ^= x >> 2;
299 x = (x & 0x11111111U) * 0x11111111U;
300 return (x >> 28) & 1;
301}
302
303/* Galois field basic operations: multiply, divide, inverse, etc. */
304
305static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
306 unsigned int b)
307{
308 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
309 bch->a_log_tab[b])] : 0;
310}
311
312static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
313{
314 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
315}
316
317static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
318 unsigned int b)
319{
320 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
321 GF_N(bch)-bch->a_log_tab[b])] : 0;
322}
323
324static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
325{
326 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
327}
328
329static inline unsigned int a_pow(struct bch_control *bch, int i)
330{
331 return bch->a_pow_tab[modulo(bch, i)];
332}
333
334static inline int a_log(struct bch_control *bch, unsigned int x)
335{
336 return bch->a_log_tab[x];
337}
338
339static inline int a_ilog(struct bch_control *bch, unsigned int x)
340{
341 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
342}
343
344/*
345 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
346 */
347static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
348 unsigned int *syn)
349{
350 int i, j, s;
351 unsigned int m;
352 uint32_t poly;
353 const int t = GF_T(bch);
354
355 s = bch->ecc_bits;
356
357 /* make sure extra bits in last ecc word are cleared */
358 m = ((unsigned int)s) & 31;
359 if (m)
360 ecc[s/32] &= ~((1u << (32-m))-1);
361 memset(syn, 0, 2*t*sizeof(*syn));
362
363 /* compute v(a^j) for j=1 .. 2t-1 */
364 do {
365 poly = *ecc++;
366 s -= 32;
367 while (poly) {
368 i = deg(poly);
369 for (j = 0; j < 2*t; j += 2)
370 syn[j] ^= a_pow(bch, (j+1)*(i+s));
371
372 poly ^= (1 << i);
373 }
374 } while (s > 0);
375
376 /* v(a^(2j)) = v(a^j)^2 */
377 for (j = 0; j < t; j++)
378 syn[2*j+1] = gf_sqr(bch, syn[j]);
379}
380
381static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
382{
383 memcpy(dst, src, GF_POLY_SZ(src->deg));
384}
385
386static int compute_error_locator_polynomial(struct bch_control *bch,
387 const unsigned int *syn)
388{
389 const unsigned int t = GF_T(bch);
390 const unsigned int n = GF_N(bch);
391 unsigned int i, j, tmp, l, pd = 1, d = syn[0];
392 struct gf_poly *elp = bch->elp;
393 struct gf_poly *pelp = bch->poly_2t[0];
394 struct gf_poly *elp_copy = bch->poly_2t[1];
395 int k, pp = -1;
396
397 memset(pelp, 0, GF_POLY_SZ(2*t));
398 memset(elp, 0, GF_POLY_SZ(2*t));
399
400 pelp->deg = 0;
401 pelp->c[0] = 1;
402 elp->deg = 0;
403 elp->c[0] = 1;
404
405 /* use simplified binary Berlekamp-Massey algorithm */
406 for (i = 0; (i < t) && (elp->deg <= t); i++) {
407 if (d) {
408 k = 2*i-pp;
409 gf_poly_copy(elp_copy, elp);
410 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
411 tmp = a_log(bch, d)+n-a_log(bch, pd);
412 for (j = 0; j <= pelp->deg; j++) {
413 if (pelp->c[j]) {
414 l = a_log(bch, pelp->c[j]);
415 elp->c[j+k] ^= a_pow(bch, tmp+l);
416 }
417 }
418 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
419 tmp = pelp->deg+k;
420 if (tmp > elp->deg) {
421 elp->deg = tmp;
422 gf_poly_copy(pelp, elp_copy);
423 pd = d;
424 pp = 2*i;
425 }
426 }
427 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
428 if (i < t-1) {
429 d = syn[2*i+2];
430 for (j = 1; j <= elp->deg; j++)
431 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
432 }
433 }
434 dbg("elp=%s\n", gf_poly_str(elp));
435 return (elp->deg > t) ? -1 : (int)elp->deg;
436}
437
438/*
439 * solve a m x m linear system in GF(2) with an expected number of solutions,
440 * and return the number of found solutions
441 */
442static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
443 unsigned int *sol, int nsol)
444{
445 const int m = GF_M(bch);
446 unsigned int tmp, mask;
447 int rem, c, r, p, k, param[BCH_MAX_M];
448
449 k = 0;
450 mask = 1 << m;
451
452 /* Gaussian elimination */
453 for (c = 0; c < m; c++) {
454 rem = 0;
455 p = c-k;
456 /* find suitable row for elimination */
457 for (r = p; r < m; r++) {
458 if (rows[r] & mask) {
459 if (r != p) {
460 tmp = rows[r];
461 rows[r] = rows[p];
462 rows[p] = tmp;
463 }
464 rem = r+1;
465 break;
466 }
467 }
468 if (rem) {
469 /* perform elimination on remaining rows */
470 tmp = rows[p];
471 for (r = rem; r < m; r++) {
472 if (rows[r] & mask)
473 rows[r] ^= tmp;
474 }
475 } else {
476 /* elimination not needed, store defective row index */
477 param[k++] = c;
478 }
479 mask >>= 1;
480 }
481 /* rewrite system, inserting fake parameter rows */
482 if (k > 0) {
483 p = k;
484 for (r = m-1; r >= 0; r--) {
485 if ((r > m-1-k) && rows[r])
486 /* system has no solution */
487 return 0;
488
489 rows[r] = (p && (r == param[p-1])) ?
490 p--, 1u << (m-r) : rows[r-p];
491 }
492 }
493
494 if (nsol != (1 << k))
495 /* unexpected number of solutions */
496 return 0;
497
498 for (p = 0; p < nsol; p++) {
499 /* set parameters for p-th solution */
500 for (c = 0; c < k; c++)
501 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
502
503 /* compute unique solution */
504 tmp = 0;
505 for (r = m-1; r >= 0; r--) {
506 mask = rows[r] & (tmp|1);
507 tmp |= parity(mask) << (m-r);
508 }
509 sol[p] = tmp >> 1;
510 }
511 return nsol;
512}
513
514/*
515 * this function builds and solves a linear system for finding roots of a degree
516 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
517 */
518static int find_affine4_roots(struct bch_control *bch, unsigned int a,
519 unsigned int b, unsigned int c,
520 unsigned int *roots)
521{
522 int i, j, k;
523 const int m = GF_M(bch);
524 unsigned int mask = 0xff, t, rows[16] = {0,};
525
526 j = a_log(bch, b);
527 k = a_log(bch, a);
528 rows[0] = c;
529
530 /* buid linear system to solve X^4+aX^2+bX+c = 0 */
531 for (i = 0; i < m; i++) {
532 rows[i+1] = bch->a_pow_tab[4*i]^
533 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
534 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
535 j++;
536 k += 2;
537 }
538 /*
539 * transpose 16x16 matrix before passing it to linear solver
540 * warning: this code assumes m < 16
541 */
542 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
543 for (k = 0; k < 16; k = (k+j+1) & ~j) {
544 t = ((rows[k] >> j)^rows[k+j]) & mask;
545 rows[k] ^= (t << j);
546 rows[k+j] ^= t;
547 }
548 }
549 return solve_linear_system(bch, rows, roots, 4);
550}
551
552/*
553 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
554 */
555static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
556 unsigned int *roots)
557{
558 int n = 0;
559
560 if (poly->c[0])
561 /* poly[X] = bX+c with c!=0, root=c/b */
562 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
563 bch->a_log_tab[poly->c[1]]);
564 return n;
565}
566
567/*
568 * compute roots of a degree 2 polynomial over GF(2^m)
569 */
570static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
571 unsigned int *roots)
572{
573 int n = 0, i, l0, l1, l2;
574 unsigned int u, v, r;
575
576 if (poly->c[0] && poly->c[1]) {
577
578 l0 = bch->a_log_tab[poly->c[0]];
579 l1 = bch->a_log_tab[poly->c[1]];
580 l2 = bch->a_log_tab[poly->c[2]];
581
582 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
583 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
584 /*
585 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
586 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
587 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
588 * i.e. r and r+1 are roots iff Tr(u)=0
589 */
590 r = 0;
591 v = u;
592 while (v) {
593 i = deg(v);
594 r ^= bch->xi_tab[i];
595 v ^= (1 << i);
596 }
597 /* verify root */
598 if ((gf_sqr(bch, r)^r) == u) {
599 /* reverse z=a/bX transformation and compute log(1/r) */
600 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
601 bch->a_log_tab[r]+l2);
602 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
603 bch->a_log_tab[r^1]+l2);
604 }
605 }
606 return n;
607}
608
609/*
610 * compute roots of a degree 3 polynomial over GF(2^m)
611 */
612static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
613 unsigned int *roots)
614{
615 int i, n = 0;
616 unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
617
618 if (poly->c[0]) {
619 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
620 e3 = poly->c[3];
621 c2 = gf_div(bch, poly->c[0], e3);
622 b2 = gf_div(bch, poly->c[1], e3);
623 a2 = gf_div(bch, poly->c[2], e3);
624
625 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
626 c = gf_mul(bch, a2, c2); /* c = a2c2 */
627 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */
628 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */
629
630 /* find the 4 roots of this affine polynomial */
631 if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
632 /* remove a2 from final list of roots */
633 for (i = 0; i < 4; i++) {
634 if (tmp[i] != a2)
635 roots[n++] = a_ilog(bch, tmp[i]);
636 }
637 }
638 }
639 return n;
640}
641
642/*
643 * compute roots of a degree 4 polynomial over GF(2^m)
644 */
645static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
646 unsigned int *roots)
647{
648 int i, l, n = 0;
649 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
650
651 if (poly->c[0] == 0)
652 return 0;
653
654 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
655 e4 = poly->c[4];
656 d = gf_div(bch, poly->c[0], e4);
657 c = gf_div(bch, poly->c[1], e4);
658 b = gf_div(bch, poly->c[2], e4);
659 a = gf_div(bch, poly->c[3], e4);
660
661 /* use Y=1/X transformation to get an affine polynomial */
662 if (a) {
663 /* first, eliminate cX by using z=X+e with ae^2+c=0 */
664 if (c) {
665 /* compute e such that e^2 = c/a */
666 f = gf_div(bch, c, a);
667 l = a_log(bch, f);
668 l += (l & 1) ? GF_N(bch) : 0;
669 e = a_pow(bch, l/2);
670 /*
671 * use transformation z=X+e:
672 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
673 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
674 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
675 * z^4 + az^3 + b'z^2 + d'
676 */
677 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
678 b = gf_mul(bch, a, e)^b;
679 }
680 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
681 if (d == 0)
682 /* assume all roots have multiplicity 1 */
683 return 0;
684
685 c2 = gf_inv(bch, d);
686 b2 = gf_div(bch, a, d);
687 a2 = gf_div(bch, b, d);
688 } else {
689 /* polynomial is already affine */
690 c2 = d;
691 b2 = c;
692 a2 = b;
693 }
694 /* find the 4 roots of this affine polynomial */
695 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
696 for (i = 0; i < 4; i++) {
697 /* post-process roots (reverse transformations) */
698 f = a ? gf_inv(bch, roots[i]) : roots[i];
699 roots[i] = a_ilog(bch, f^e);
700 }
701 n = 4;
702 }
703 return n;
704}
705
706/*
707 * build monic, log-based representation of a polynomial
708 */
709static void gf_poly_logrep(struct bch_control *bch,
710 const struct gf_poly *a, int *rep)
711{
712 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
713
714 /* represent 0 values with -1; warning, rep[d] is not set to 1 */
715 for (i = 0; i < d; i++)
716 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
717}
718
719/*
720 * compute polynomial Euclidean division remainder in GF(2^m)[X]
721 */
722static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
723 const struct gf_poly *b, int *rep)
724{
725 int la, p, m;
726 unsigned int i, j, *c = a->c;
727 const unsigned int d = b->deg;
728
729 if (a->deg < d)
730 return;
731
732 /* reuse or compute log representation of denominator */
733 if (!rep) {
734 rep = bch->cache;
735 gf_poly_logrep(bch, b, rep);
736 }
737
738 for (j = a->deg; j >= d; j--) {
739 if (c[j]) {
740 la = a_log(bch, c[j]);
741 p = j-d;
742 for (i = 0; i < d; i++, p++) {
743 m = rep[i];
744 if (m >= 0)
745 c[p] ^= bch->a_pow_tab[mod_s(bch,
746 m+la)];
747 }
748 }
749 }
750 a->deg = d-1;
751 while (!c[a->deg] && a->deg)
752 a->deg--;
753}
754
755/*
756 * compute polynomial Euclidean division quotient in GF(2^m)[X]
757 */
758static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
759 const struct gf_poly *b, struct gf_poly *q)
760{
761 if (a->deg >= b->deg) {
762 q->deg = a->deg-b->deg;
763 /* compute a mod b (modifies a) */
764 gf_poly_mod(bch, a, b, NULL);
765 /* quotient is stored in upper part of polynomial a */
766 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
767 } else {
768 q->deg = 0;
769 q->c[0] = 0;
770 }
771}
772
773/*
774 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
775 */
776static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
777 struct gf_poly *b)
778{
779 struct gf_poly *tmp;
780
781 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
782
783 if (a->deg < b->deg) {
784 tmp = b;
785 b = a;
786 a = tmp;
787 }
788
789 while (b->deg > 0) {
790 gf_poly_mod(bch, a, b, NULL);
791 tmp = b;
792 b = a;
793 a = tmp;
794 }
795
796 dbg("%s\n", gf_poly_str(a));
797
798 return a;
799}
800
801/*
802 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
803 * This is used in Berlekamp Trace algorithm for splitting polynomials
804 */
805static void compute_trace_bk_mod(struct bch_control *bch, int k,
806 const struct gf_poly *f, struct gf_poly *z,
807 struct gf_poly *out)
808{
809 const int m = GF_M(bch);
810 int i, j;
811
812 /* z contains z^2j mod f */
813 z->deg = 1;
814 z->c[0] = 0;
815 z->c[1] = bch->a_pow_tab[k];
816
817 out->deg = 0;
818 memset(out, 0, GF_POLY_SZ(f->deg));
819
820 /* compute f log representation only once */
821 gf_poly_logrep(bch, f, bch->cache);
822
823 for (i = 0; i < m; i++) {
824 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
825 for (j = z->deg; j >= 0; j--) {
826 out->c[j] ^= z->c[j];
827 z->c[2*j] = gf_sqr(bch, z->c[j]);
828 z->c[2*j+1] = 0;
829 }
830 if (z->deg > out->deg)
831 out->deg = z->deg;
832
833 if (i < m-1) {
834 z->deg *= 2;
835 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
836 gf_poly_mod(bch, z, f, bch->cache);
837 }
838 }
839 while (!out->c[out->deg] && out->deg)
840 out->deg--;
841
842 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
843}
844
845/*
846 * factor a polynomial using Berlekamp Trace algorithm (BTA)
847 */
848static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
849 struct gf_poly **g, struct gf_poly **h)
850{
851 struct gf_poly *f2 = bch->poly_2t[0];
852 struct gf_poly *q = bch->poly_2t[1];
853 struct gf_poly *tk = bch->poly_2t[2];
854 struct gf_poly *z = bch->poly_2t[3];
855 struct gf_poly *gcd;
856
857 dbg("factoring %s...\n", gf_poly_str(f));
858
859 *g = f;
860 *h = NULL;
861
862 /* tk = Tr(a^k.X) mod f */
863 compute_trace_bk_mod(bch, k, f, z, tk);
864
865 if (tk->deg > 0) {
866 /* compute g = gcd(f, tk) (destructive operation) */
867 gf_poly_copy(f2, f);
868 gcd = gf_poly_gcd(bch, f2, tk);
869 if (gcd->deg < f->deg) {
870 /* compute h=f/gcd(f,tk); this will modify f and q */
871 gf_poly_div(bch, f, gcd, q);
872 /* store g and h in-place (clobbering f) */
873 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
874 gf_poly_copy(*g, gcd);
875 gf_poly_copy(*h, q);
876 }
877 }
878}
879
880/*
881 * find roots of a polynomial, using BTZ algorithm; see the beginning of this
882 * file for details
883 */
884static int find_poly_roots(struct bch_control *bch, unsigned int k,
885 struct gf_poly *poly, unsigned int *roots)
886{
887 int cnt;
888 struct gf_poly *f1, *f2;
889
890 switch (poly->deg) {
891 /* handle low degree polynomials with ad hoc techniques */
892 case 1:
893 cnt = find_poly_deg1_roots(bch, poly, roots);
894 break;
895 case 2:
896 cnt = find_poly_deg2_roots(bch, poly, roots);
897 break;
898 case 3:
899 cnt = find_poly_deg3_roots(bch, poly, roots);
900 break;
901 case 4:
902 cnt = find_poly_deg4_roots(bch, poly, roots);
903 break;
904 default:
905 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */
906 cnt = 0;
907 if (poly->deg && (k <= GF_M(bch))) {
908 factor_polynomial(bch, k, poly, &f1, &f2);
909 if (f1)
910 cnt += find_poly_roots(bch, k+1, f1, roots);
911 if (f2)
912 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
913 }
914 break;
915 }
916 return cnt;
917}
918
919#if defined(USE_CHIEN_SEARCH)
920/*
921 * exhaustive root search (Chien) implementation - not used, included only for
922 * reference/comparison tests
923 */
924static int chien_search(struct bch_control *bch, unsigned int len,
925 struct gf_poly *p, unsigned int *roots)
926{
927 int m;
928 unsigned int i, j, syn, syn0, count = 0;
929 const unsigned int k = 8*len+bch->ecc_bits;
930
931 /* use a log-based representation of polynomial */
932 gf_poly_logrep(bch, p, bch->cache);
933 bch->cache[p->deg] = 0;
934 syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
935
936 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
937 /* compute elp(a^i) */
938 for (j = 1, syn = syn0; j <= p->deg; j++) {
939 m = bch->cache[j];
940 if (m >= 0)
941 syn ^= a_pow(bch, m+j*i);
942 }
943 if (syn == 0) {
944 roots[count++] = GF_N(bch)-i;
945 if (count == p->deg)
946 break;
947 }
948 }
949 return (count == p->deg) ? count : 0;
950}
951#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
952#endif /* USE_CHIEN_SEARCH */
953
954/**
955 * decode_bch - decode received codeword and find bit error locations
956 * @bch: BCH control structure
957 * @data: received data, ignored if @calc_ecc is provided
958 * @len: data length in bytes, must always be provided
959 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
960 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
961 * @syn: hw computed syndrome data (if NULL, syndrome is calculated)
962 * @errloc: output array of error locations
963 *
964 * Returns:
965 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
966 * invalid parameters were provided
967 *
968 * Depending on the available hw BCH support and the need to compute @calc_ecc
969 * separately (using encode_bch()), this function should be called with one of
970 * the following parameter configurations -
971 *
972 * by providing @data and @recv_ecc only:
973 * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
974 *
975 * by providing @recv_ecc and @calc_ecc:
976 * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
977 *
978 * by providing ecc = recv_ecc XOR calc_ecc:
979 * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
980 *
981 * by providing syndrome results @syn:
982 * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
983 *
984 * Once decode_bch() has successfully returned with a positive value, error
985 * locations returned in array @errloc should be interpreted as follows -
986 *
987 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
988 * data correction)
989 *
990 * if (errloc[n] < 8*len), then n-th error is located in data and can be
991 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
992 *
993 * Note that this function does not perform any data correction by itself, it
994 * merely indicates error locations.
995 */
996int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
997 const uint8_t *recv_ecc, const uint8_t *calc_ecc,
998 const unsigned int *syn, unsigned int *errloc)
999{
1000 const unsigned int ecc_words = BCH_ECC_WORDS(bch);
1001 unsigned int nbits;
1002 int i, err, nroots;
1003 uint32_t sum;
1004
1005 /* sanity check: make sure data length can be handled */
1006 if (8*len > (bch->n-bch->ecc_bits))
1007 return -EINVAL;
1008
1009 /* if caller does not provide syndromes, compute them */
1010 if (!syn) {
1011 if (!calc_ecc) {
1012 /* compute received data ecc into an internal buffer */
1013 if (!data || !recv_ecc)
1014 return -EINVAL;
1015 encode_bch(bch, data, len, NULL);
1016 } else {
1017 /* load provided calculated ecc */
1018 load_ecc8(bch, bch->ecc_buf, calc_ecc);
1019 }
1020 /* load received ecc or assume it was XORed in calc_ecc */
1021 if (recv_ecc) {
1022 load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1023 /* XOR received and calculated ecc */
1024 for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1025 bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1026 sum |= bch->ecc_buf[i];
1027 }
1028 if (!sum)
1029 /* no error found */
1030 return 0;
1031 }
1032 compute_syndromes(bch, bch->ecc_buf, bch->syn);
1033 syn = bch->syn;
1034 }
1035
1036 err = compute_error_locator_polynomial(bch, syn);
1037 if (err > 0) {
1038 nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1039 if (err != nroots)
1040 err = -1;
1041 }
1042 if (err > 0) {
1043 /* post-process raw error locations for easier correction */
1044 nbits = (len*8)+bch->ecc_bits;
1045 for (i = 0; i < err; i++) {
1046 if (errloc[i] >= nbits) {
1047 err = -1;
1048 break;
1049 }
1050 errloc[i] = nbits-1-errloc[i];
1051 errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
1052 }
1053 }
1054 return (err >= 0) ? err : -EBADMSG;
1055}
1056EXPORT_SYMBOL_GPL(decode_bch);
1057
1058/*
1059 * generate Galois field lookup tables
1060 */
1061static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1062{
1063 unsigned int i, x = 1;
1064 const unsigned int k = 1 << deg(poly);
1065
1066 /* primitive polynomial must be of degree m */
1067 if (k != (1u << GF_M(bch)))
1068 return -1;
1069
1070 for (i = 0; i < GF_N(bch); i++) {
1071 bch->a_pow_tab[i] = x;
1072 bch->a_log_tab[x] = i;
1073 if (i && (x == 1))
1074 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1075 return -1;
1076 x <<= 1;
1077 if (x & k)
1078 x ^= poly;
1079 }
1080 bch->a_pow_tab[GF_N(bch)] = 1;
1081 bch->a_log_tab[0] = 0;
1082
1083 return 0;
1084}
1085
1086/*
1087 * compute generator polynomial remainder tables for fast encoding
1088 */
1089static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1090{
1091 int i, j, b, d;
1092 uint32_t data, hi, lo, *tab;
1093 const int l = BCH_ECC_WORDS(bch);
1094 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1095 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1096
1097 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1098
1099 for (i = 0; i < 256; i++) {
1100 /* p(X)=i is a small polynomial of weight <= 8 */
1101 for (b = 0; b < 4; b++) {
1102 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1103 tab = bch->mod8_tab + (b*256+i)*l;
1104 data = i << (8*b);
1105 while (data) {
1106 d = deg(data);
1107 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1108 data ^= g[0] >> (31-d);
1109 for (j = 0; j < ecclen; j++) {
1110 hi = (d < 31) ? g[j] << (d+1) : 0;
1111 lo = (j+1 < plen) ?
1112 g[j+1] >> (31-d) : 0;
1113 tab[j] ^= hi|lo;
1114 }
1115 }
1116 }
1117 }
1118}
1119
1120/*
1121 * build a base for factoring degree 2 polynomials
1122 */
1123static int build_deg2_base(struct bch_control *bch)
1124{
1125 const int m = GF_M(bch);
1126 int i, j, r;
1127 unsigned int sum, x, y, remaining, ak = 0, xi[BCH_MAX_M];
1128
1129 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1130 for (i = 0; i < m; i++) {
1131 for (j = 0, sum = 0; j < m; j++)
1132 sum ^= a_pow(bch, i*(1 << j));
1133
1134 if (sum) {
1135 ak = bch->a_pow_tab[i];
1136 break;
1137 }
1138 }
1139 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1140 remaining = m;
1141 memset(xi, 0, sizeof(xi));
1142
1143 for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1144 y = gf_sqr(bch, x)^x;
1145 for (i = 0; i < 2; i++) {
1146 r = a_log(bch, y);
1147 if (y && (r < m) && !xi[r]) {
1148 bch->xi_tab[r] = x;
1149 xi[r] = 1;
1150 remaining--;
1151 dbg("x%d = %x\n", r, x);
1152 break;
1153 }
1154 y ^= ak;
1155 }
1156 }
1157 /* should not happen but check anyway */
1158 return remaining ? -1 : 0;
1159}
1160
1161static void *bch_alloc(size_t size, int *err)
1162{
1163 void *ptr;
1164
1165 ptr = kmalloc(size, GFP_KERNEL);
1166 if (ptr == NULL)
1167 *err = 1;
1168 return ptr;
1169}
1170
1171/*
1172 * compute generator polynomial for given (m,t) parameters.
1173 */
1174static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1175{
1176 const unsigned int m = GF_M(bch);
1177 const unsigned int t = GF_T(bch);
1178 int n, err = 0;
1179 unsigned int i, j, nbits, r, word, *roots;
1180 struct gf_poly *g;
1181 uint32_t *genpoly;
1182
1183 g = bch_alloc(GF_POLY_SZ(m*t), &err);
1184 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1185 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1186
1187 if (err) {
1188 kfree(genpoly);
1189 genpoly = NULL;
1190 goto finish;
1191 }
1192
1193 /* enumerate all roots of g(X) */
1194 memset(roots , 0, (bch->n+1)*sizeof(*roots));
1195 for (i = 0; i < t; i++) {
1196 for (j = 0, r = 2*i+1; j < m; j++) {
1197 roots[r] = 1;
1198 r = mod_s(bch, 2*r);
1199 }
1200 }
1201 /* build generator polynomial g(X) */
1202 g->deg = 0;
1203 g->c[0] = 1;
1204 for (i = 0; i < GF_N(bch); i++) {
1205 if (roots[i]) {
1206 /* multiply g(X) by (X+root) */
1207 r = bch->a_pow_tab[i];
1208 g->c[g->deg+1] = 1;
1209 for (j = g->deg; j > 0; j--)
1210 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1211
1212 g->c[0] = gf_mul(bch, g->c[0], r);
1213 g->deg++;
1214 }
1215 }
1216 /* store left-justified binary representation of g(X) */
1217 n = g->deg+1;
1218 i = 0;
1219
1220 while (n > 0) {
1221 nbits = (n > 32) ? 32 : n;
1222 for (j = 0, word = 0; j < nbits; j++) {
1223 if (g->c[n-1-j])
1224 word |= 1u << (31-j);
1225 }
1226 genpoly[i++] = word;
1227 n -= nbits;
1228 }
1229 bch->ecc_bits = g->deg;
1230
1231finish:
1232 kfree(g);
1233 kfree(roots);
1234
1235 return genpoly;
1236}
1237
1238/**
1239 * init_bch - initialize a BCH encoder/decoder
1240 * @m: Galois field order, should be in the range 5-15
1241 * @t: maximum error correction capability, in bits
1242 * @prim_poly: user-provided primitive polynomial (or 0 to use default)
1243 *
1244 * Returns:
1245 * a newly allocated BCH control structure if successful, NULL otherwise
1246 *
1247 * This initialization can take some time, as lookup tables are built for fast
1248 * encoding/decoding; make sure not to call this function from a time critical
1249 * path. Usually, init_bch() should be called on module/driver init and
1250 * free_bch() should be called to release memory on exit.
1251 *
1252 * You may provide your own primitive polynomial of degree @m in argument
1253 * @prim_poly, or let init_bch() use its default polynomial.
1254 *
1255 * Once init_bch() has successfully returned a pointer to a newly allocated
1256 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1257 * the structure.
1258 */
1259struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
1260{
1261 int err = 0;
1262 unsigned int i, words;
1263 uint32_t *genpoly;
1264 struct bch_control *bch = NULL;
1265
1266 const int min_m = 5;
1267
1268 /* default primitive polynomials */
1269 static const unsigned int prim_poly_tab[] = {
1270 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1271 0x402b, 0x8003,
1272 };
1273
1274#if defined(CONFIG_BCH_CONST_PARAMS)
1275 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1276 printk(KERN_ERR "bch encoder/decoder was configured to support "
1277 "parameters m=%d, t=%d only!\n",
1278 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1279 goto fail;
1280 }
1281#endif
1282 if ((m < min_m) || (m > BCH_MAX_M))
1283 /*
1284 * values of m greater than 15 are not currently supported;
1285 * supporting m > 15 would require changing table base type
1286 * (uint16_t) and a small patch in matrix transposition
1287 */
1288 goto fail;
1289
1290 if (t > BCH_MAX_T)
1291 /*
1292 * we can support larger than 64 bits if necessary, at the
1293 * cost of higher stack usage.
1294 */
1295 goto fail;
1296
1297 /* sanity checks */
1298 if ((t < 1) || (m*t >= ((1 << m)-1)))
1299 /* invalid t value */
1300 goto fail;
1301
1302 /* select a primitive polynomial for generating GF(2^m) */
1303 if (prim_poly == 0)
1304 prim_poly = prim_poly_tab[m-min_m];
1305
1306 bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1307 if (bch == NULL)
1308 goto fail;
1309
1310 bch->m = m;
1311 bch->t = t;
1312 bch->n = (1 << m)-1;
1313 words = DIV_ROUND_UP(m*t, 32);
1314 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1315 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1316 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1317 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1318 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1319 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1320 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1321 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err);
1322 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err);
1323 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1324
1325 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1326 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1327
1328 if (err)
1329 goto fail;
1330
1331 err = build_gf_tables(bch, prim_poly);
1332 if (err)
1333 goto fail;
1334
1335 /* use generator polynomial for computing encoding tables */
1336 genpoly = compute_generator_polynomial(bch);
1337 if (genpoly == NULL)
1338 goto fail;
1339
1340 build_mod8_tables(bch, genpoly);
1341 kfree(genpoly);
1342
1343 err = build_deg2_base(bch);
1344 if (err)
1345 goto fail;
1346
1347 return bch;
1348
1349fail:
1350 free_bch(bch);
1351 return NULL;
1352}
1353EXPORT_SYMBOL_GPL(init_bch);
1354
1355/**
1356 * free_bch - free the BCH control structure
1357 * @bch: BCH control structure to release
1358 */
1359void free_bch(struct bch_control *bch)
1360{
1361 unsigned int i;
1362
1363 if (bch) {
1364 kfree(bch->a_pow_tab);
1365 kfree(bch->a_log_tab);
1366 kfree(bch->mod8_tab);
1367 kfree(bch->ecc_buf);
1368 kfree(bch->ecc_buf2);
1369 kfree(bch->xi_tab);
1370 kfree(bch->syn);
1371 kfree(bch->cache);
1372 kfree(bch->elp);
1373
1374 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1375 kfree(bch->poly_2t[i]);
1376
1377 kfree(bch);
1378 }
1379}
1380EXPORT_SYMBOL_GPL(free_bch);
1381
1382MODULE_LICENSE("GPL");
1383MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
1384MODULE_DESCRIPTION("Binary BCH encoder/decoder");