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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#else
82#define GF_M(_p) ((_p)->m)
83#define GF_T(_p) ((_p)->t)
84#define GF_N(_p) ((_p)->n)
85#endif
86
87#define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
88#define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
89
90#ifndef dbg
91#define dbg(_fmt, args...) do {} while (0)
92#endif
93
94/*
95 * represent a polynomial over GF(2^m)
96 */
97struct gf_poly {
98 unsigned int deg; /* polynomial degree */
99 unsigned int c[0]; /* polynomial terms */
100};
101
102/* given its degree, compute a polynomial size in bytes */
103#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
104
105/* polynomial of degree 1 */
106struct gf_poly_deg1 {
107 struct gf_poly poly;
108 unsigned int c[2];
109};
110
111/*
112 * same as encode_bch(), but process input data one byte at a time
113 */
114static void encode_bch_unaligned(struct bch_control *bch,
115 const unsigned char *data, unsigned int len,
116 uint32_t *ecc)
117{
118 int i;
119 const uint32_t *p;
120 const int l = BCH_ECC_WORDS(bch)-1;
121
122 while (len--) {
123 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
124
125 for (i = 0; i < l; i++)
126 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
127
128 ecc[l] = (ecc[l] << 8)^(*p);
129 }
130}
131
132/*
133 * convert ecc bytes to aligned, zero-padded 32-bit ecc words
134 */
135static void load_ecc8(struct bch_control *bch, uint32_t *dst,
136 const uint8_t *src)
137{
138 uint8_t pad[4] = {0, 0, 0, 0};
139 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
140
141 for (i = 0; i < nwords; i++, src += 4)
142 dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
143
144 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
145 dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
146}
147
148/*
149 * convert 32-bit ecc words to ecc bytes
150 */
151static void store_ecc8(struct bch_control *bch, uint8_t *dst,
152 const uint32_t *src)
153{
154 uint8_t pad[4];
155 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
156
157 for (i = 0; i < nwords; i++) {
158 *dst++ = (src[i] >> 24);
159 *dst++ = (src[i] >> 16) & 0xff;
160 *dst++ = (src[i] >> 8) & 0xff;
161 *dst++ = (src[i] >> 0) & 0xff;
162 }
163 pad[0] = (src[nwords] >> 24);
164 pad[1] = (src[nwords] >> 16) & 0xff;
165 pad[2] = (src[nwords] >> 8) & 0xff;
166 pad[3] = (src[nwords] >> 0) & 0xff;
167 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
168}
169
170/**
171 * encode_bch - calculate BCH ecc parity of data
172 * @bch: BCH control structure
173 * @data: data to encode
174 * @len: data length in bytes
175 * @ecc: ecc parity data, must be initialized by caller
176 *
177 * The @ecc parity array is used both as input and output parameter, in order to
178 * allow incremental computations. It should be of the size indicated by member
179 * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
180 *
181 * The exact number of computed ecc parity bits is given by member @ecc_bits of
182 * @bch; it may be less than m*t for large values of t.
183 */
184void encode_bch(struct bch_control *bch, const uint8_t *data,
185 unsigned int len, uint8_t *ecc)
186{
187 const unsigned int l = BCH_ECC_WORDS(bch)-1;
188 unsigned int i, mlen;
189 unsigned long m;
190 uint32_t w, r[l+1];
191 const uint32_t * const tab0 = bch->mod8_tab;
192 const uint32_t * const tab1 = tab0 + 256*(l+1);
193 const uint32_t * const tab2 = tab1 + 256*(l+1);
194 const uint32_t * const tab3 = tab2 + 256*(l+1);
195 const uint32_t *pdata, *p0, *p1, *p2, *p3;
196
197 if (ecc) {
198 /* load ecc parity bytes into internal 32-bit buffer */
199 load_ecc8(bch, bch->ecc_buf, ecc);
200 } else {
201 memset(bch->ecc_buf, 0, sizeof(r));
202 }
203
204 /* process first unaligned data bytes */
205 m = ((unsigned long)data) & 3;
206 if (m) {
207 mlen = (len < (4-m)) ? len : 4-m;
208 encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
209 data += mlen;
210 len -= mlen;
211 }
212
213 /* process 32-bit aligned data words */
214 pdata = (uint32_t *)data;
215 mlen = len/4;
216 data += 4*mlen;
217 len -= 4*mlen;
218 memcpy(r, bch->ecc_buf, sizeof(r));
219
220 /*
221 * split each 32-bit word into 4 polynomials of weight 8 as follows:
222 *
223 * 31 ...24 23 ...16 15 ... 8 7 ... 0
224 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt
225 * tttttttt mod g = r0 (precomputed)
226 * zzzzzzzz 00000000 mod g = r1 (precomputed)
227 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed)
228 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed)
229 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3
230 */
231 while (mlen--) {
232 /* input data is read in big-endian format */
233 w = r[0]^cpu_to_be32(*pdata++);
234 p0 = tab0 + (l+1)*((w >> 0) & 0xff);
235 p1 = tab1 + (l+1)*((w >> 8) & 0xff);
236 p2 = tab2 + (l+1)*((w >> 16) & 0xff);
237 p3 = tab3 + (l+1)*((w >> 24) & 0xff);
238
239 for (i = 0; i < l; i++)
240 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
241
242 r[l] = p0[l]^p1[l]^p2[l]^p3[l];
243 }
244 memcpy(bch->ecc_buf, r, sizeof(r));
245
246 /* process last unaligned bytes */
247 if (len)
248 encode_bch_unaligned(bch, data, len, bch->ecc_buf);
249
250 /* store ecc parity bytes into original parity buffer */
251 if (ecc)
252 store_ecc8(bch, ecc, bch->ecc_buf);
253}
254EXPORT_SYMBOL_GPL(encode_bch);
255
256static inline int modulo(struct bch_control *bch, unsigned int v)
257{
258 const unsigned int n = GF_N(bch);
259 while (v >= n) {
260 v -= n;
261 v = (v & n) + (v >> GF_M(bch));
262 }
263 return v;
264}
265
266/*
267 * shorter and faster modulo function, only works when v < 2N.
268 */
269static inline int mod_s(struct bch_control *bch, unsigned int v)
270{
271 const unsigned int n = GF_N(bch);
272 return (v < n) ? v : v-n;
273}
274
275static inline int deg(unsigned int poly)
276{
277 /* polynomial degree is the most-significant bit index */
278 return fls(poly)-1;
279}
280
281static inline int parity(unsigned int x)
282{
283 /*
284 * public domain code snippet, lifted from
285 * http://www-graphics.stanford.edu/~seander/bithacks.html
286 */
287 x ^= x >> 1;
288 x ^= x >> 2;
289 x = (x & 0x11111111U) * 0x11111111U;
290 return (x >> 28) & 1;
291}
292
293/* Galois field basic operations: multiply, divide, inverse, etc. */
294
295static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
296 unsigned int b)
297{
298 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
299 bch->a_log_tab[b])] : 0;
300}
301
302static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
303{
304 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
305}
306
307static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
308 unsigned int b)
309{
310 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
311 GF_N(bch)-bch->a_log_tab[b])] : 0;
312}
313
314static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
315{
316 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
317}
318
319static inline unsigned int a_pow(struct bch_control *bch, int i)
320{
321 return bch->a_pow_tab[modulo(bch, i)];
322}
323
324static inline int a_log(struct bch_control *bch, unsigned int x)
325{
326 return bch->a_log_tab[x];
327}
328
329static inline int a_ilog(struct bch_control *bch, unsigned int x)
330{
331 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
332}
333
334/*
335 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
336 */
337static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
338 unsigned int *syn)
339{
340 int i, j, s;
341 unsigned int m;
342 uint32_t poly;
343 const int t = GF_T(bch);
344
345 s = bch->ecc_bits;
346
347 /* make sure extra bits in last ecc word are cleared */
348 m = ((unsigned int)s) & 31;
349 if (m)
350 ecc[s/32] &= ~((1u << (32-m))-1);
351 memset(syn, 0, 2*t*sizeof(*syn));
352
353 /* compute v(a^j) for j=1 .. 2t-1 */
354 do {
355 poly = *ecc++;
356 s -= 32;
357 while (poly) {
358 i = deg(poly);
359 for (j = 0; j < 2*t; j += 2)
360 syn[j] ^= a_pow(bch, (j+1)*(i+s));
361
362 poly ^= (1 << i);
363 }
364 } while (s > 0);
365
366 /* v(a^(2j)) = v(a^j)^2 */
367 for (j = 0; j < t; j++)
368 syn[2*j+1] = gf_sqr(bch, syn[j]);
369}
370
371static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
372{
373 memcpy(dst, src, GF_POLY_SZ(src->deg));
374}
375
376static int compute_error_locator_polynomial(struct bch_control *bch,
377 const unsigned int *syn)
378{
379 const unsigned int t = GF_T(bch);
380 const unsigned int n = GF_N(bch);
381 unsigned int i, j, tmp, l, pd = 1, d = syn[0];
382 struct gf_poly *elp = bch->elp;
383 struct gf_poly *pelp = bch->poly_2t[0];
384 struct gf_poly *elp_copy = bch->poly_2t[1];
385 int k, pp = -1;
386
387 memset(pelp, 0, GF_POLY_SZ(2*t));
388 memset(elp, 0, GF_POLY_SZ(2*t));
389
390 pelp->deg = 0;
391 pelp->c[0] = 1;
392 elp->deg = 0;
393 elp->c[0] = 1;
394
395 /* use simplified binary Berlekamp-Massey algorithm */
396 for (i = 0; (i < t) && (elp->deg <= t); i++) {
397 if (d) {
398 k = 2*i-pp;
399 gf_poly_copy(elp_copy, elp);
400 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
401 tmp = a_log(bch, d)+n-a_log(bch, pd);
402 for (j = 0; j <= pelp->deg; j++) {
403 if (pelp->c[j]) {
404 l = a_log(bch, pelp->c[j]);
405 elp->c[j+k] ^= a_pow(bch, tmp+l);
406 }
407 }
408 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
409 tmp = pelp->deg+k;
410 if (tmp > elp->deg) {
411 elp->deg = tmp;
412 gf_poly_copy(pelp, elp_copy);
413 pd = d;
414 pp = 2*i;
415 }
416 }
417 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
418 if (i < t-1) {
419 d = syn[2*i+2];
420 for (j = 1; j <= elp->deg; j++)
421 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
422 }
423 }
424 dbg("elp=%s\n", gf_poly_str(elp));
425 return (elp->deg > t) ? -1 : (int)elp->deg;
426}
427
428/*
429 * solve a m x m linear system in GF(2) with an expected number of solutions,
430 * and return the number of found solutions
431 */
432static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
433 unsigned int *sol, int nsol)
434{
435 const int m = GF_M(bch);
436 unsigned int tmp, mask;
437 int rem, c, r, p, k, param[m];
438
439 k = 0;
440 mask = 1 << m;
441
442 /* Gaussian elimination */
443 for (c = 0; c < m; c++) {
444 rem = 0;
445 p = c-k;
446 /* find suitable row for elimination */
447 for (r = p; r < m; r++) {
448 if (rows[r] & mask) {
449 if (r != p) {
450 tmp = rows[r];
451 rows[r] = rows[p];
452 rows[p] = tmp;
453 }
454 rem = r+1;
455 break;
456 }
457 }
458 if (rem) {
459 /* perform elimination on remaining rows */
460 tmp = rows[p];
461 for (r = rem; r < m; r++) {
462 if (rows[r] & mask)
463 rows[r] ^= tmp;
464 }
465 } else {
466 /* elimination not needed, store defective row index */
467 param[k++] = c;
468 }
469 mask >>= 1;
470 }
471 /* rewrite system, inserting fake parameter rows */
472 if (k > 0) {
473 p = k;
474 for (r = m-1; r >= 0; r--) {
475 if ((r > m-1-k) && rows[r])
476 /* system has no solution */
477 return 0;
478
479 rows[r] = (p && (r == param[p-1])) ?
480 p--, 1u << (m-r) : rows[r-p];
481 }
482 }
483
484 if (nsol != (1 << k))
485 /* unexpected number of solutions */
486 return 0;
487
488 for (p = 0; p < nsol; p++) {
489 /* set parameters for p-th solution */
490 for (c = 0; c < k; c++)
491 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
492
493 /* compute unique solution */
494 tmp = 0;
495 for (r = m-1; r >= 0; r--) {
496 mask = rows[r] & (tmp|1);
497 tmp |= parity(mask) << (m-r);
498 }
499 sol[p] = tmp >> 1;
500 }
501 return nsol;
502}
503
504/*
505 * this function builds and solves a linear system for finding roots of a degree
506 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
507 */
508static int find_affine4_roots(struct bch_control *bch, unsigned int a,
509 unsigned int b, unsigned int c,
510 unsigned int *roots)
511{
512 int i, j, k;
513 const int m = GF_M(bch);
514 unsigned int mask = 0xff, t, rows[16] = {0,};
515
516 j = a_log(bch, b);
517 k = a_log(bch, a);
518 rows[0] = c;
519
520 /* buid linear system to solve X^4+aX^2+bX+c = 0 */
521 for (i = 0; i < m; i++) {
522 rows[i+1] = bch->a_pow_tab[4*i]^
523 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
524 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
525 j++;
526 k += 2;
527 }
528 /*
529 * transpose 16x16 matrix before passing it to linear solver
530 * warning: this code assumes m < 16
531 */
532 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
533 for (k = 0; k < 16; k = (k+j+1) & ~j) {
534 t = ((rows[k] >> j)^rows[k+j]) & mask;
535 rows[k] ^= (t << j);
536 rows[k+j] ^= t;
537 }
538 }
539 return solve_linear_system(bch, rows, roots, 4);
540}
541
542/*
543 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
544 */
545static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
546 unsigned int *roots)
547{
548 int n = 0;
549
550 if (poly->c[0])
551 /* poly[X] = bX+c with c!=0, root=c/b */
552 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
553 bch->a_log_tab[poly->c[1]]);
554 return n;
555}
556
557/*
558 * compute roots of a degree 2 polynomial over GF(2^m)
559 */
560static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
561 unsigned int *roots)
562{
563 int n = 0, i, l0, l1, l2;
564 unsigned int u, v, r;
565
566 if (poly->c[0] && poly->c[1]) {
567
568 l0 = bch->a_log_tab[poly->c[0]];
569 l1 = bch->a_log_tab[poly->c[1]];
570 l2 = bch->a_log_tab[poly->c[2]];
571
572 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
573 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
574 /*
575 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
576 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
577 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
578 * i.e. r and r+1 are roots iff Tr(u)=0
579 */
580 r = 0;
581 v = u;
582 while (v) {
583 i = deg(v);
584 r ^= bch->xi_tab[i];
585 v ^= (1 << i);
586 }
587 /* verify root */
588 if ((gf_sqr(bch, r)^r) == u) {
589 /* reverse z=a/bX transformation and compute log(1/r) */
590 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
591 bch->a_log_tab[r]+l2);
592 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
593 bch->a_log_tab[r^1]+l2);
594 }
595 }
596 return n;
597}
598
599/*
600 * compute roots of a degree 3 polynomial over GF(2^m)
601 */
602static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
603 unsigned int *roots)
604{
605 int i, n = 0;
606 unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
607
608 if (poly->c[0]) {
609 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
610 e3 = poly->c[3];
611 c2 = gf_div(bch, poly->c[0], e3);
612 b2 = gf_div(bch, poly->c[1], e3);
613 a2 = gf_div(bch, poly->c[2], e3);
614
615 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
616 c = gf_mul(bch, a2, c2); /* c = a2c2 */
617 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */
618 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */
619
620 /* find the 4 roots of this affine polynomial */
621 if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
622 /* remove a2 from final list of roots */
623 for (i = 0; i < 4; i++) {
624 if (tmp[i] != a2)
625 roots[n++] = a_ilog(bch, tmp[i]);
626 }
627 }
628 }
629 return n;
630}
631
632/*
633 * compute roots of a degree 4 polynomial over GF(2^m)
634 */
635static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
636 unsigned int *roots)
637{
638 int i, l, n = 0;
639 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
640
641 if (poly->c[0] == 0)
642 return 0;
643
644 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
645 e4 = poly->c[4];
646 d = gf_div(bch, poly->c[0], e4);
647 c = gf_div(bch, poly->c[1], e4);
648 b = gf_div(bch, poly->c[2], e4);
649 a = gf_div(bch, poly->c[3], e4);
650
651 /* use Y=1/X transformation to get an affine polynomial */
652 if (a) {
653 /* first, eliminate cX by using z=X+e with ae^2+c=0 */
654 if (c) {
655 /* compute e such that e^2 = c/a */
656 f = gf_div(bch, c, a);
657 l = a_log(bch, f);
658 l += (l & 1) ? GF_N(bch) : 0;
659 e = a_pow(bch, l/2);
660 /*
661 * use transformation z=X+e:
662 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
663 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
664 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
665 * z^4 + az^3 + b'z^2 + d'
666 */
667 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
668 b = gf_mul(bch, a, e)^b;
669 }
670 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
671 if (d == 0)
672 /* assume all roots have multiplicity 1 */
673 return 0;
674
675 c2 = gf_inv(bch, d);
676 b2 = gf_div(bch, a, d);
677 a2 = gf_div(bch, b, d);
678 } else {
679 /* polynomial is already affine */
680 c2 = d;
681 b2 = c;
682 a2 = b;
683 }
684 /* find the 4 roots of this affine polynomial */
685 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
686 for (i = 0; i < 4; i++) {
687 /* post-process roots (reverse transformations) */
688 f = a ? gf_inv(bch, roots[i]) : roots[i];
689 roots[i] = a_ilog(bch, f^e);
690 }
691 n = 4;
692 }
693 return n;
694}
695
696/*
697 * build monic, log-based representation of a polynomial
698 */
699static void gf_poly_logrep(struct bch_control *bch,
700 const struct gf_poly *a, int *rep)
701{
702 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
703
704 /* represent 0 values with -1; warning, rep[d] is not set to 1 */
705 for (i = 0; i < d; i++)
706 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
707}
708
709/*
710 * compute polynomial Euclidean division remainder in GF(2^m)[X]
711 */
712static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
713 const struct gf_poly *b, int *rep)
714{
715 int la, p, m;
716 unsigned int i, j, *c = a->c;
717 const unsigned int d = b->deg;
718
719 if (a->deg < d)
720 return;
721
722 /* reuse or compute log representation of denominator */
723 if (!rep) {
724 rep = bch->cache;
725 gf_poly_logrep(bch, b, rep);
726 }
727
728 for (j = a->deg; j >= d; j--) {
729 if (c[j]) {
730 la = a_log(bch, c[j]);
731 p = j-d;
732 for (i = 0; i < d; i++, p++) {
733 m = rep[i];
734 if (m >= 0)
735 c[p] ^= bch->a_pow_tab[mod_s(bch,
736 m+la)];
737 }
738 }
739 }
740 a->deg = d-1;
741 while (!c[a->deg] && a->deg)
742 a->deg--;
743}
744
745/*
746 * compute polynomial Euclidean division quotient in GF(2^m)[X]
747 */
748static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
749 const struct gf_poly *b, struct gf_poly *q)
750{
751 if (a->deg >= b->deg) {
752 q->deg = a->deg-b->deg;
753 /* compute a mod b (modifies a) */
754 gf_poly_mod(bch, a, b, NULL);
755 /* quotient is stored in upper part of polynomial a */
756 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
757 } else {
758 q->deg = 0;
759 q->c[0] = 0;
760 }
761}
762
763/*
764 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
765 */
766static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
767 struct gf_poly *b)
768{
769 struct gf_poly *tmp;
770
771 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
772
773 if (a->deg < b->deg) {
774 tmp = b;
775 b = a;
776 a = tmp;
777 }
778
779 while (b->deg > 0) {
780 gf_poly_mod(bch, a, b, NULL);
781 tmp = b;
782 b = a;
783 a = tmp;
784 }
785
786 dbg("%s\n", gf_poly_str(a));
787
788 return a;
789}
790
791/*
792 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
793 * This is used in Berlekamp Trace algorithm for splitting polynomials
794 */
795static void compute_trace_bk_mod(struct bch_control *bch, int k,
796 const struct gf_poly *f, struct gf_poly *z,
797 struct gf_poly *out)
798{
799 const int m = GF_M(bch);
800 int i, j;
801
802 /* z contains z^2j mod f */
803 z->deg = 1;
804 z->c[0] = 0;
805 z->c[1] = bch->a_pow_tab[k];
806
807 out->deg = 0;
808 memset(out, 0, GF_POLY_SZ(f->deg));
809
810 /* compute f log representation only once */
811 gf_poly_logrep(bch, f, bch->cache);
812
813 for (i = 0; i < m; i++) {
814 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
815 for (j = z->deg; j >= 0; j--) {
816 out->c[j] ^= z->c[j];
817 z->c[2*j] = gf_sqr(bch, z->c[j]);
818 z->c[2*j+1] = 0;
819 }
820 if (z->deg > out->deg)
821 out->deg = z->deg;
822
823 if (i < m-1) {
824 z->deg *= 2;
825 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
826 gf_poly_mod(bch, z, f, bch->cache);
827 }
828 }
829 while (!out->c[out->deg] && out->deg)
830 out->deg--;
831
832 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
833}
834
835/*
836 * factor a polynomial using Berlekamp Trace algorithm (BTA)
837 */
838static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
839 struct gf_poly **g, struct gf_poly **h)
840{
841 struct gf_poly *f2 = bch->poly_2t[0];
842 struct gf_poly *q = bch->poly_2t[1];
843 struct gf_poly *tk = bch->poly_2t[2];
844 struct gf_poly *z = bch->poly_2t[3];
845 struct gf_poly *gcd;
846
847 dbg("factoring %s...\n", gf_poly_str(f));
848
849 *g = f;
850 *h = NULL;
851
852 /* tk = Tr(a^k.X) mod f */
853 compute_trace_bk_mod(bch, k, f, z, tk);
854
855 if (tk->deg > 0) {
856 /* compute g = gcd(f, tk) (destructive operation) */
857 gf_poly_copy(f2, f);
858 gcd = gf_poly_gcd(bch, f2, tk);
859 if (gcd->deg < f->deg) {
860 /* compute h=f/gcd(f,tk); this will modify f and q */
861 gf_poly_div(bch, f, gcd, q);
862 /* store g and h in-place (clobbering f) */
863 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
864 gf_poly_copy(*g, gcd);
865 gf_poly_copy(*h, q);
866 }
867 }
868}
869
870/*
871 * find roots of a polynomial, using BTZ algorithm; see the beginning of this
872 * file for details
873 */
874static int find_poly_roots(struct bch_control *bch, unsigned int k,
875 struct gf_poly *poly, unsigned int *roots)
876{
877 int cnt;
878 struct gf_poly *f1, *f2;
879
880 switch (poly->deg) {
881 /* handle low degree polynomials with ad hoc techniques */
882 case 1:
883 cnt = find_poly_deg1_roots(bch, poly, roots);
884 break;
885 case 2:
886 cnt = find_poly_deg2_roots(bch, poly, roots);
887 break;
888 case 3:
889 cnt = find_poly_deg3_roots(bch, poly, roots);
890 break;
891 case 4:
892 cnt = find_poly_deg4_roots(bch, poly, roots);
893 break;
894 default:
895 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */
896 cnt = 0;
897 if (poly->deg && (k <= GF_M(bch))) {
898 factor_polynomial(bch, k, poly, &f1, &f2);
899 if (f1)
900 cnt += find_poly_roots(bch, k+1, f1, roots);
901 if (f2)
902 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
903 }
904 break;
905 }
906 return cnt;
907}
908
909#if defined(USE_CHIEN_SEARCH)
910/*
911 * exhaustive root search (Chien) implementation - not used, included only for
912 * reference/comparison tests
913 */
914static int chien_search(struct bch_control *bch, unsigned int len,
915 struct gf_poly *p, unsigned int *roots)
916{
917 int m;
918 unsigned int i, j, syn, syn0, count = 0;
919 const unsigned int k = 8*len+bch->ecc_bits;
920
921 /* use a log-based representation of polynomial */
922 gf_poly_logrep(bch, p, bch->cache);
923 bch->cache[p->deg] = 0;
924 syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
925
926 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
927 /* compute elp(a^i) */
928 for (j = 1, syn = syn0; j <= p->deg; j++) {
929 m = bch->cache[j];
930 if (m >= 0)
931 syn ^= a_pow(bch, m+j*i);
932 }
933 if (syn == 0) {
934 roots[count++] = GF_N(bch)-i;
935 if (count == p->deg)
936 break;
937 }
938 }
939 return (count == p->deg) ? count : 0;
940}
941#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
942#endif /* USE_CHIEN_SEARCH */
943
944/**
945 * decode_bch - decode received codeword and find bit error locations
946 * @bch: BCH control structure
947 * @data: received data, ignored if @calc_ecc is provided
948 * @len: data length in bytes, must always be provided
949 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
950 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
951 * @syn: hw computed syndrome data (if NULL, syndrome is calculated)
952 * @errloc: output array of error locations
953 *
954 * Returns:
955 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
956 * invalid parameters were provided
957 *
958 * Depending on the available hw BCH support and the need to compute @calc_ecc
959 * separately (using encode_bch()), this function should be called with one of
960 * the following parameter configurations -
961 *
962 * by providing @data and @recv_ecc only:
963 * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
964 *
965 * by providing @recv_ecc and @calc_ecc:
966 * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
967 *
968 * by providing ecc = recv_ecc XOR calc_ecc:
969 * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
970 *
971 * by providing syndrome results @syn:
972 * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
973 *
974 * Once decode_bch() has successfully returned with a positive value, error
975 * locations returned in array @errloc should be interpreted as follows -
976 *
977 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
978 * data correction)
979 *
980 * if (errloc[n] < 8*len), then n-th error is located in data and can be
981 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
982 *
983 * Note that this function does not perform any data correction by itself, it
984 * merely indicates error locations.
985 */
986int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
987 const uint8_t *recv_ecc, const uint8_t *calc_ecc,
988 const unsigned int *syn, unsigned int *errloc)
989{
990 const unsigned int ecc_words = BCH_ECC_WORDS(bch);
991 unsigned int nbits;
992 int i, err, nroots;
993 uint32_t sum;
994
995 /* sanity check: make sure data length can be handled */
996 if (8*len > (bch->n-bch->ecc_bits))
997 return -EINVAL;
998
999 /* if caller does not provide syndromes, compute them */
1000 if (!syn) {
1001 if (!calc_ecc) {
1002 /* compute received data ecc into an internal buffer */
1003 if (!data || !recv_ecc)
1004 return -EINVAL;
1005 encode_bch(bch, data, len, NULL);
1006 } else {
1007 /* load provided calculated ecc */
1008 load_ecc8(bch, bch->ecc_buf, calc_ecc);
1009 }
1010 /* load received ecc or assume it was XORed in calc_ecc */
1011 if (recv_ecc) {
1012 load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1013 /* XOR received and calculated ecc */
1014 for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1015 bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1016 sum |= bch->ecc_buf[i];
1017 }
1018 if (!sum)
1019 /* no error found */
1020 return 0;
1021 }
1022 compute_syndromes(bch, bch->ecc_buf, bch->syn);
1023 syn = bch->syn;
1024 }
1025
1026 err = compute_error_locator_polynomial(bch, syn);
1027 if (err > 0) {
1028 nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1029 if (err != nroots)
1030 err = -1;
1031 }
1032 if (err > 0) {
1033 /* post-process raw error locations for easier correction */
1034 nbits = (len*8)+bch->ecc_bits;
1035 for (i = 0; i < err; i++) {
1036 if (errloc[i] >= nbits) {
1037 err = -1;
1038 break;
1039 }
1040 errloc[i] = nbits-1-errloc[i];
1041 errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
1042 }
1043 }
1044 return (err >= 0) ? err : -EBADMSG;
1045}
1046EXPORT_SYMBOL_GPL(decode_bch);
1047
1048/*
1049 * generate Galois field lookup tables
1050 */
1051static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1052{
1053 unsigned int i, x = 1;
1054 const unsigned int k = 1 << deg(poly);
1055
1056 /* primitive polynomial must be of degree m */
1057 if (k != (1u << GF_M(bch)))
1058 return -1;
1059
1060 for (i = 0; i < GF_N(bch); i++) {
1061 bch->a_pow_tab[i] = x;
1062 bch->a_log_tab[x] = i;
1063 if (i && (x == 1))
1064 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1065 return -1;
1066 x <<= 1;
1067 if (x & k)
1068 x ^= poly;
1069 }
1070 bch->a_pow_tab[GF_N(bch)] = 1;
1071 bch->a_log_tab[0] = 0;
1072
1073 return 0;
1074}
1075
1076/*
1077 * compute generator polynomial remainder tables for fast encoding
1078 */
1079static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1080{
1081 int i, j, b, d;
1082 uint32_t data, hi, lo, *tab;
1083 const int l = BCH_ECC_WORDS(bch);
1084 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1085 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1086
1087 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1088
1089 for (i = 0; i < 256; i++) {
1090 /* p(X)=i is a small polynomial of weight <= 8 */
1091 for (b = 0; b < 4; b++) {
1092 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1093 tab = bch->mod8_tab + (b*256+i)*l;
1094 data = i << (8*b);
1095 while (data) {
1096 d = deg(data);
1097 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1098 data ^= g[0] >> (31-d);
1099 for (j = 0; j < ecclen; j++) {
1100 hi = (d < 31) ? g[j] << (d+1) : 0;
1101 lo = (j+1 < plen) ?
1102 g[j+1] >> (31-d) : 0;
1103 tab[j] ^= hi|lo;
1104 }
1105 }
1106 }
1107 }
1108}
1109
1110/*
1111 * build a base for factoring degree 2 polynomials
1112 */
1113static int build_deg2_base(struct bch_control *bch)
1114{
1115 const int m = GF_M(bch);
1116 int i, j, r;
1117 unsigned int sum, x, y, remaining, ak = 0, xi[m];
1118
1119 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1120 for (i = 0; i < m; i++) {
1121 for (j = 0, sum = 0; j < m; j++)
1122 sum ^= a_pow(bch, i*(1 << j));
1123
1124 if (sum) {
1125 ak = bch->a_pow_tab[i];
1126 break;
1127 }
1128 }
1129 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1130 remaining = m;
1131 memset(xi, 0, sizeof(xi));
1132
1133 for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1134 y = gf_sqr(bch, x)^x;
1135 for (i = 0; i < 2; i++) {
1136 r = a_log(bch, y);
1137 if (y && (r < m) && !xi[r]) {
1138 bch->xi_tab[r] = x;
1139 xi[r] = 1;
1140 remaining--;
1141 dbg("x%d = %x\n", r, x);
1142 break;
1143 }
1144 y ^= ak;
1145 }
1146 }
1147 /* should not happen but check anyway */
1148 return remaining ? -1 : 0;
1149}
1150
1151static void *bch_alloc(size_t size, int *err)
1152{
1153 void *ptr;
1154
1155 ptr = kmalloc(size, GFP_KERNEL);
1156 if (ptr == NULL)
1157 *err = 1;
1158 return ptr;
1159}
1160
1161/*
1162 * compute generator polynomial for given (m,t) parameters.
1163 */
1164static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1165{
1166 const unsigned int m = GF_M(bch);
1167 const unsigned int t = GF_T(bch);
1168 int n, err = 0;
1169 unsigned int i, j, nbits, r, word, *roots;
1170 struct gf_poly *g;
1171 uint32_t *genpoly;
1172
1173 g = bch_alloc(GF_POLY_SZ(m*t), &err);
1174 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1175 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1176
1177 if (err) {
1178 kfree(genpoly);
1179 genpoly = NULL;
1180 goto finish;
1181 }
1182
1183 /* enumerate all roots of g(X) */
1184 memset(roots , 0, (bch->n+1)*sizeof(*roots));
1185 for (i = 0; i < t; i++) {
1186 for (j = 0, r = 2*i+1; j < m; j++) {
1187 roots[r] = 1;
1188 r = mod_s(bch, 2*r);
1189 }
1190 }
1191 /* build generator polynomial g(X) */
1192 g->deg = 0;
1193 g->c[0] = 1;
1194 for (i = 0; i < GF_N(bch); i++) {
1195 if (roots[i]) {
1196 /* multiply g(X) by (X+root) */
1197 r = bch->a_pow_tab[i];
1198 g->c[g->deg+1] = 1;
1199 for (j = g->deg; j > 0; j--)
1200 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1201
1202 g->c[0] = gf_mul(bch, g->c[0], r);
1203 g->deg++;
1204 }
1205 }
1206 /* store left-justified binary representation of g(X) */
1207 n = g->deg+1;
1208 i = 0;
1209
1210 while (n > 0) {
1211 nbits = (n > 32) ? 32 : n;
1212 for (j = 0, word = 0; j < nbits; j++) {
1213 if (g->c[n-1-j])
1214 word |= 1u << (31-j);
1215 }
1216 genpoly[i++] = word;
1217 n -= nbits;
1218 }
1219 bch->ecc_bits = g->deg;
1220
1221finish:
1222 kfree(g);
1223 kfree(roots);
1224
1225 return genpoly;
1226}
1227
1228/**
1229 * init_bch - initialize a BCH encoder/decoder
1230 * @m: Galois field order, should be in the range 5-15
1231 * @t: maximum error correction capability, in bits
1232 * @prim_poly: user-provided primitive polynomial (or 0 to use default)
1233 *
1234 * Returns:
1235 * a newly allocated BCH control structure if successful, NULL otherwise
1236 *
1237 * This initialization can take some time, as lookup tables are built for fast
1238 * encoding/decoding; make sure not to call this function from a time critical
1239 * path. Usually, init_bch() should be called on module/driver init and
1240 * free_bch() should be called to release memory on exit.
1241 *
1242 * You may provide your own primitive polynomial of degree @m in argument
1243 * @prim_poly, or let init_bch() use its default polynomial.
1244 *
1245 * Once init_bch() has successfully returned a pointer to a newly allocated
1246 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1247 * the structure.
1248 */
1249struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
1250{
1251 int err = 0;
1252 unsigned int i, words;
1253 uint32_t *genpoly;
1254 struct bch_control *bch = NULL;
1255
1256 const int min_m = 5;
1257 const int max_m = 15;
1258
1259 /* default primitive polynomials */
1260 static const unsigned int prim_poly_tab[] = {
1261 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1262 0x402b, 0x8003,
1263 };
1264
1265#if defined(CONFIG_BCH_CONST_PARAMS)
1266 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1267 printk(KERN_ERR "bch encoder/decoder was configured to support "
1268 "parameters m=%d, t=%d only!\n",
1269 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1270 goto fail;
1271 }
1272#endif
1273 if ((m < min_m) || (m > max_m))
1274 /*
1275 * values of m greater than 15 are not currently supported;
1276 * supporting m > 15 would require changing table base type
1277 * (uint16_t) and a small patch in matrix transposition
1278 */
1279 goto fail;
1280
1281 /* sanity checks */
1282 if ((t < 1) || (m*t >= ((1 << m)-1)))
1283 /* invalid t value */
1284 goto fail;
1285
1286 /* select a primitive polynomial for generating GF(2^m) */
1287 if (prim_poly == 0)
1288 prim_poly = prim_poly_tab[m-min_m];
1289
1290 bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1291 if (bch == NULL)
1292 goto fail;
1293
1294 bch->m = m;
1295 bch->t = t;
1296 bch->n = (1 << m)-1;
1297 words = DIV_ROUND_UP(m*t, 32);
1298 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1299 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1300 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1301 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1302 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1303 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1304 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1305 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err);
1306 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err);
1307 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1308
1309 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1310 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1311
1312 if (err)
1313 goto fail;
1314
1315 err = build_gf_tables(bch, prim_poly);
1316 if (err)
1317 goto fail;
1318
1319 /* use generator polynomial for computing encoding tables */
1320 genpoly = compute_generator_polynomial(bch);
1321 if (genpoly == NULL)
1322 goto fail;
1323
1324 build_mod8_tables(bch, genpoly);
1325 kfree(genpoly);
1326
1327 err = build_deg2_base(bch);
1328 if (err)
1329 goto fail;
1330
1331 return bch;
1332
1333fail:
1334 free_bch(bch);
1335 return NULL;
1336}
1337EXPORT_SYMBOL_GPL(init_bch);
1338
1339/**
1340 * free_bch - free the BCH control structure
1341 * @bch: BCH control structure to release
1342 */
1343void free_bch(struct bch_control *bch)
1344{
1345 unsigned int i;
1346
1347 if (bch) {
1348 kfree(bch->a_pow_tab);
1349 kfree(bch->a_log_tab);
1350 kfree(bch->mod8_tab);
1351 kfree(bch->ecc_buf);
1352 kfree(bch->ecc_buf2);
1353 kfree(bch->xi_tab);
1354 kfree(bch->syn);
1355 kfree(bch->cache);
1356 kfree(bch->elp);
1357
1358 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1359 kfree(bch->poly_2t[i]);
1360
1361 kfree(bch);
1362 }
1363}
1364EXPORT_SYMBOL_GPL(free_bch);
1365
1366MODULE_LICENSE("GPL");
1367MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
1368MODULE_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 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 tmp = rows[r];
484 rows[r] = rows[p];
485 rows[p] = tmp;
486 }
487 rem = r+1;
488 break;
489 }
490 }
491 if (rem) {
492 /* perform elimination on remaining rows */
493 tmp = rows[p];
494 for (r = rem; r < m; r++) {
495 if (rows[r] & mask)
496 rows[r] ^= tmp;
497 }
498 } else {
499 /* elimination not needed, store defective row index */
500 param[k++] = c;
501 }
502 mask >>= 1;
503 }
504 /* rewrite system, inserting fake parameter rows */
505 if (k > 0) {
506 p = k;
507 for (r = m-1; r >= 0; r--) {
508 if ((r > m-1-k) && rows[r])
509 /* system has no solution */
510 return 0;
511
512 rows[r] = (p && (r == param[p-1])) ?
513 p--, 1u << (m-r) : rows[r-p];
514 }
515 }
516
517 if (nsol != (1 << k))
518 /* unexpected number of solutions */
519 return 0;
520
521 for (p = 0; p < nsol; p++) {
522 /* set parameters for p-th solution */
523 for (c = 0; c < k; c++)
524 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
525
526 /* compute unique solution */
527 tmp = 0;
528 for (r = m-1; r >= 0; r--) {
529 mask = rows[r] & (tmp|1);
530 tmp |= parity(mask) << (m-r);
531 }
532 sol[p] = tmp >> 1;
533 }
534 return nsol;
535}
536
537/*
538 * this function builds and solves a linear system for finding roots of a degree
539 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
540 */
541static int find_affine4_roots(struct bch_control *bch, unsigned int a,
542 unsigned int b, unsigned int c,
543 unsigned int *roots)
544{
545 int i, j, k;
546 const int m = GF_M(bch);
547 unsigned int mask = 0xff, t, rows[16] = {0,};
548
549 j = a_log(bch, b);
550 k = a_log(bch, a);
551 rows[0] = c;
552
553 /* build linear system to solve X^4+aX^2+bX+c = 0 */
554 for (i = 0; i < m; i++) {
555 rows[i+1] = bch->a_pow_tab[4*i]^
556 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
557 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
558 j++;
559 k += 2;
560 }
561 /*
562 * transpose 16x16 matrix before passing it to linear solver
563 * warning: this code assumes m < 16
564 */
565 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
566 for (k = 0; k < 16; k = (k+j+1) & ~j) {
567 t = ((rows[k] >> j)^rows[k+j]) & mask;
568 rows[k] ^= (t << j);
569 rows[k+j] ^= t;
570 }
571 }
572 return solve_linear_system(bch, rows, roots, 4);
573}
574
575/*
576 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
577 */
578static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
579 unsigned int *roots)
580{
581 int n = 0;
582
583 if (poly->c[0])
584 /* poly[X] = bX+c with c!=0, root=c/b */
585 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
586 bch->a_log_tab[poly->c[1]]);
587 return n;
588}
589
590/*
591 * compute roots of a degree 2 polynomial over GF(2^m)
592 */
593static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
594 unsigned int *roots)
595{
596 int n = 0, i, l0, l1, l2;
597 unsigned int u, v, r;
598
599 if (poly->c[0] && poly->c[1]) {
600
601 l0 = bch->a_log_tab[poly->c[0]];
602 l1 = bch->a_log_tab[poly->c[1]];
603 l2 = bch->a_log_tab[poly->c[2]];
604
605 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
606 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
607 /*
608 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
609 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
610 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
611 * i.e. r and r+1 are roots iff Tr(u)=0
612 */
613 r = 0;
614 v = u;
615 while (v) {
616 i = deg(v);
617 r ^= bch->xi_tab[i];
618 v ^= (1 << i);
619 }
620 /* verify root */
621 if ((gf_sqr(bch, r)^r) == u) {
622 /* reverse z=a/bX transformation and compute log(1/r) */
623 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
624 bch->a_log_tab[r]+l2);
625 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
626 bch->a_log_tab[r^1]+l2);
627 }
628 }
629 return n;
630}
631
632/*
633 * compute roots of a degree 3 polynomial over GF(2^m)
634 */
635static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
636 unsigned int *roots)
637{
638 int i, n = 0;
639 unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
640
641 if (poly->c[0]) {
642 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
643 e3 = poly->c[3];
644 c2 = gf_div(bch, poly->c[0], e3);
645 b2 = gf_div(bch, poly->c[1], e3);
646 a2 = gf_div(bch, poly->c[2], e3);
647
648 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
649 c = gf_mul(bch, a2, c2); /* c = a2c2 */
650 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */
651 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */
652
653 /* find the 4 roots of this affine polynomial */
654 if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
655 /* remove a2 from final list of roots */
656 for (i = 0; i < 4; i++) {
657 if (tmp[i] != a2)
658 roots[n++] = a_ilog(bch, tmp[i]);
659 }
660 }
661 }
662 return n;
663}
664
665/*
666 * compute roots of a degree 4 polynomial over GF(2^m)
667 */
668static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
669 unsigned int *roots)
670{
671 int i, l, n = 0;
672 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
673
674 if (poly->c[0] == 0)
675 return 0;
676
677 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
678 e4 = poly->c[4];
679 d = gf_div(bch, poly->c[0], e4);
680 c = gf_div(bch, poly->c[1], e4);
681 b = gf_div(bch, poly->c[2], e4);
682 a = gf_div(bch, poly->c[3], e4);
683
684 /* use Y=1/X transformation to get an affine polynomial */
685 if (a) {
686 /* first, eliminate cX by using z=X+e with ae^2+c=0 */
687 if (c) {
688 /* compute e such that e^2 = c/a */
689 f = gf_div(bch, c, a);
690 l = a_log(bch, f);
691 l += (l & 1) ? GF_N(bch) : 0;
692 e = a_pow(bch, l/2);
693 /*
694 * use transformation z=X+e:
695 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
696 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
697 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
698 * z^4 + az^3 + b'z^2 + d'
699 */
700 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
701 b = gf_mul(bch, a, e)^b;
702 }
703 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
704 if (d == 0)
705 /* assume all roots have multiplicity 1 */
706 return 0;
707
708 c2 = gf_inv(bch, d);
709 b2 = gf_div(bch, a, d);
710 a2 = gf_div(bch, b, d);
711 } else {
712 /* polynomial is already affine */
713 c2 = d;
714 b2 = c;
715 a2 = b;
716 }
717 /* find the 4 roots of this affine polynomial */
718 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
719 for (i = 0; i < 4; i++) {
720 /* post-process roots (reverse transformations) */
721 f = a ? gf_inv(bch, roots[i]) : roots[i];
722 roots[i] = a_ilog(bch, f^e);
723 }
724 n = 4;
725 }
726 return n;
727}
728
729/*
730 * build monic, log-based representation of a polynomial
731 */
732static void gf_poly_logrep(struct bch_control *bch,
733 const struct gf_poly *a, int *rep)
734{
735 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
736
737 /* represent 0 values with -1; warning, rep[d] is not set to 1 */
738 for (i = 0; i < d; i++)
739 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
740}
741
742/*
743 * compute polynomial Euclidean division remainder in GF(2^m)[X]
744 */
745static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
746 const struct gf_poly *b, int *rep)
747{
748 int la, p, m;
749 unsigned int i, j, *c = a->c;
750 const unsigned int d = b->deg;
751
752 if (a->deg < d)
753 return;
754
755 /* reuse or compute log representation of denominator */
756 if (!rep) {
757 rep = bch->cache;
758 gf_poly_logrep(bch, b, rep);
759 }
760
761 for (j = a->deg; j >= d; j--) {
762 if (c[j]) {
763 la = a_log(bch, c[j]);
764 p = j-d;
765 for (i = 0; i < d; i++, p++) {
766 m = rep[i];
767 if (m >= 0)
768 c[p] ^= bch->a_pow_tab[mod_s(bch,
769 m+la)];
770 }
771 }
772 }
773 a->deg = d-1;
774 while (!c[a->deg] && a->deg)
775 a->deg--;
776}
777
778/*
779 * compute polynomial Euclidean division quotient in GF(2^m)[X]
780 */
781static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
782 const struct gf_poly *b, struct gf_poly *q)
783{
784 if (a->deg >= b->deg) {
785 q->deg = a->deg-b->deg;
786 /* compute a mod b (modifies a) */
787 gf_poly_mod(bch, a, b, NULL);
788 /* quotient is stored in upper part of polynomial a */
789 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
790 } else {
791 q->deg = 0;
792 q->c[0] = 0;
793 }
794}
795
796/*
797 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
798 */
799static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
800 struct gf_poly *b)
801{
802 struct gf_poly *tmp;
803
804 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
805
806 if (a->deg < b->deg) {
807 tmp = b;
808 b = a;
809 a = tmp;
810 }
811
812 while (b->deg > 0) {
813 gf_poly_mod(bch, a, b, NULL);
814 tmp = b;
815 b = a;
816 a = tmp;
817 }
818
819 dbg("%s\n", gf_poly_str(a));
820
821 return a;
822}
823
824/*
825 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
826 * This is used in Berlekamp Trace algorithm for splitting polynomials
827 */
828static void compute_trace_bk_mod(struct bch_control *bch, int k,
829 const struct gf_poly *f, struct gf_poly *z,
830 struct gf_poly *out)
831{
832 const int m = GF_M(bch);
833 int i, j;
834
835 /* z contains z^2j mod f */
836 z->deg = 1;
837 z->c[0] = 0;
838 z->c[1] = bch->a_pow_tab[k];
839
840 out->deg = 0;
841 memset(out, 0, GF_POLY_SZ(f->deg));
842
843 /* compute f log representation only once */
844 gf_poly_logrep(bch, f, bch->cache);
845
846 for (i = 0; i < m; i++) {
847 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
848 for (j = z->deg; j >= 0; j--) {
849 out->c[j] ^= z->c[j];
850 z->c[2*j] = gf_sqr(bch, z->c[j]);
851 z->c[2*j+1] = 0;
852 }
853 if (z->deg > out->deg)
854 out->deg = z->deg;
855
856 if (i < m-1) {
857 z->deg *= 2;
858 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
859 gf_poly_mod(bch, z, f, bch->cache);
860 }
861 }
862 while (!out->c[out->deg] && out->deg)
863 out->deg--;
864
865 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
866}
867
868/*
869 * factor a polynomial using Berlekamp Trace algorithm (BTA)
870 */
871static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
872 struct gf_poly **g, struct gf_poly **h)
873{
874 struct gf_poly *f2 = bch->poly_2t[0];
875 struct gf_poly *q = bch->poly_2t[1];
876 struct gf_poly *tk = bch->poly_2t[2];
877 struct gf_poly *z = bch->poly_2t[3];
878 struct gf_poly *gcd;
879
880 dbg("factoring %s...\n", gf_poly_str(f));
881
882 *g = f;
883 *h = NULL;
884
885 /* tk = Tr(a^k.X) mod f */
886 compute_trace_bk_mod(bch, k, f, z, tk);
887
888 if (tk->deg > 0) {
889 /* compute g = gcd(f, tk) (destructive operation) */
890 gf_poly_copy(f2, f);
891 gcd = gf_poly_gcd(bch, f2, tk);
892 if (gcd->deg < f->deg) {
893 /* compute h=f/gcd(f,tk); this will modify f and q */
894 gf_poly_div(bch, f, gcd, q);
895 /* store g and h in-place (clobbering f) */
896 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
897 gf_poly_copy(*g, gcd);
898 gf_poly_copy(*h, q);
899 }
900 }
901}
902
903/*
904 * find roots of a polynomial, using BTZ algorithm; see the beginning of this
905 * file for details
906 */
907static int find_poly_roots(struct bch_control *bch, unsigned int k,
908 struct gf_poly *poly, unsigned int *roots)
909{
910 int cnt;
911 struct gf_poly *f1, *f2;
912
913 switch (poly->deg) {
914 /* handle low degree polynomials with ad hoc techniques */
915 case 1:
916 cnt = find_poly_deg1_roots(bch, poly, roots);
917 break;
918 case 2:
919 cnt = find_poly_deg2_roots(bch, poly, roots);
920 break;
921 case 3:
922 cnt = find_poly_deg3_roots(bch, poly, roots);
923 break;
924 case 4:
925 cnt = find_poly_deg4_roots(bch, poly, roots);
926 break;
927 default:
928 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */
929 cnt = 0;
930 if (poly->deg && (k <= GF_M(bch))) {
931 factor_polynomial(bch, k, poly, &f1, &f2);
932 if (f1)
933 cnt += find_poly_roots(bch, k+1, f1, roots);
934 if (f2)
935 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
936 }
937 break;
938 }
939 return cnt;
940}
941
942#if defined(USE_CHIEN_SEARCH)
943/*
944 * exhaustive root search (Chien) implementation - not used, included only for
945 * reference/comparison tests
946 */
947static int chien_search(struct bch_control *bch, unsigned int len,
948 struct gf_poly *p, unsigned int *roots)
949{
950 int m;
951 unsigned int i, j, syn, syn0, count = 0;
952 const unsigned int k = 8*len+bch->ecc_bits;
953
954 /* use a log-based representation of polynomial */
955 gf_poly_logrep(bch, p, bch->cache);
956 bch->cache[p->deg] = 0;
957 syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
958
959 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
960 /* compute elp(a^i) */
961 for (j = 1, syn = syn0; j <= p->deg; j++) {
962 m = bch->cache[j];
963 if (m >= 0)
964 syn ^= a_pow(bch, m+j*i);
965 }
966 if (syn == 0) {
967 roots[count++] = GF_N(bch)-i;
968 if (count == p->deg)
969 break;
970 }
971 }
972 return (count == p->deg) ? count : 0;
973}
974#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
975#endif /* USE_CHIEN_SEARCH */
976
977/**
978 * bch_decode - decode received codeword and find bit error locations
979 * @bch: BCH control structure
980 * @data: received data, ignored if @calc_ecc is provided
981 * @len: data length in bytes, must always be provided
982 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
983 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
984 * @syn: hw computed syndrome data (if NULL, syndrome is calculated)
985 * @errloc: output array of error locations
986 *
987 * Returns:
988 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
989 * invalid parameters were provided
990 *
991 * Depending on the available hw BCH support and the need to compute @calc_ecc
992 * separately (using bch_encode()), this function should be called with one of
993 * the following parameter configurations -
994 *
995 * by providing @data and @recv_ecc only:
996 * bch_decode(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
997 *
998 * by providing @recv_ecc and @calc_ecc:
999 * bch_decode(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
1000 *
1001 * by providing ecc = recv_ecc XOR calc_ecc:
1002 * bch_decode(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
1003 *
1004 * by providing syndrome results @syn:
1005 * bch_decode(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
1006 *
1007 * Once bch_decode() has successfully returned with a positive value, error
1008 * locations returned in array @errloc should be interpreted as follows -
1009 *
1010 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
1011 * data correction)
1012 *
1013 * if (errloc[n] < 8*len), then n-th error is located in data and can be
1014 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
1015 *
1016 * Note that this function does not perform any data correction by itself, it
1017 * merely indicates error locations.
1018 */
1019int bch_decode(struct bch_control *bch, const uint8_t *data, unsigned int len,
1020 const uint8_t *recv_ecc, const uint8_t *calc_ecc,
1021 const unsigned int *syn, unsigned int *errloc)
1022{
1023 const unsigned int ecc_words = BCH_ECC_WORDS(bch);
1024 unsigned int nbits;
1025 int i, err, nroots;
1026 uint32_t sum;
1027
1028 /* sanity check: make sure data length can be handled */
1029 if (8*len > (bch->n-bch->ecc_bits))
1030 return -EINVAL;
1031
1032 /* if caller does not provide syndromes, compute them */
1033 if (!syn) {
1034 if (!calc_ecc) {
1035 /* compute received data ecc into an internal buffer */
1036 if (!data || !recv_ecc)
1037 return -EINVAL;
1038 bch_encode(bch, data, len, NULL);
1039 } else {
1040 /* load provided calculated ecc */
1041 load_ecc8(bch, bch->ecc_buf, calc_ecc);
1042 }
1043 /* load received ecc or assume it was XORed in calc_ecc */
1044 if (recv_ecc) {
1045 load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1046 /* XOR received and calculated ecc */
1047 for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1048 bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1049 sum |= bch->ecc_buf[i];
1050 }
1051 if (!sum)
1052 /* no error found */
1053 return 0;
1054 }
1055 compute_syndromes(bch, bch->ecc_buf, bch->syn);
1056 syn = bch->syn;
1057 }
1058
1059 err = compute_error_locator_polynomial(bch, syn);
1060 if (err > 0) {
1061 nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1062 if (err != nroots)
1063 err = -1;
1064 }
1065 if (err > 0) {
1066 /* post-process raw error locations for easier correction */
1067 nbits = (len*8)+bch->ecc_bits;
1068 for (i = 0; i < err; i++) {
1069 if (errloc[i] >= nbits) {
1070 err = -1;
1071 break;
1072 }
1073 errloc[i] = nbits-1-errloc[i];
1074 if (!bch->swap_bits)
1075 errloc[i] = (errloc[i] & ~7) |
1076 (7-(errloc[i] & 7));
1077 }
1078 }
1079 return (err >= 0) ? err : -EBADMSG;
1080}
1081EXPORT_SYMBOL_GPL(bch_decode);
1082
1083/*
1084 * generate Galois field lookup tables
1085 */
1086static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1087{
1088 unsigned int i, x = 1;
1089 const unsigned int k = 1 << deg(poly);
1090
1091 /* primitive polynomial must be of degree m */
1092 if (k != (1u << GF_M(bch)))
1093 return -1;
1094
1095 for (i = 0; i < GF_N(bch); i++) {
1096 bch->a_pow_tab[i] = x;
1097 bch->a_log_tab[x] = i;
1098 if (i && (x == 1))
1099 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1100 return -1;
1101 x <<= 1;
1102 if (x & k)
1103 x ^= poly;
1104 }
1105 bch->a_pow_tab[GF_N(bch)] = 1;
1106 bch->a_log_tab[0] = 0;
1107
1108 return 0;
1109}
1110
1111/*
1112 * compute generator polynomial remainder tables for fast encoding
1113 */
1114static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1115{
1116 int i, j, b, d;
1117 uint32_t data, hi, lo, *tab;
1118 const int l = BCH_ECC_WORDS(bch);
1119 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1120 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1121
1122 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1123
1124 for (i = 0; i < 256; i++) {
1125 /* p(X)=i is a small polynomial of weight <= 8 */
1126 for (b = 0; b < 4; b++) {
1127 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1128 tab = bch->mod8_tab + (b*256+i)*l;
1129 data = i << (8*b);
1130 while (data) {
1131 d = deg(data);
1132 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1133 data ^= g[0] >> (31-d);
1134 for (j = 0; j < ecclen; j++) {
1135 hi = (d < 31) ? g[j] << (d+1) : 0;
1136 lo = (j+1 < plen) ?
1137 g[j+1] >> (31-d) : 0;
1138 tab[j] ^= hi|lo;
1139 }
1140 }
1141 }
1142 }
1143}
1144
1145/*
1146 * build a base for factoring degree 2 polynomials
1147 */
1148static int build_deg2_base(struct bch_control *bch)
1149{
1150 const int m = GF_M(bch);
1151 int i, j, r;
1152 unsigned int sum, x, y, remaining, ak = 0, xi[BCH_MAX_M];
1153
1154 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1155 for (i = 0; i < m; i++) {
1156 for (j = 0, sum = 0; j < m; j++)
1157 sum ^= a_pow(bch, i*(1 << j));
1158
1159 if (sum) {
1160 ak = bch->a_pow_tab[i];
1161 break;
1162 }
1163 }
1164 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1165 remaining = m;
1166 memset(xi, 0, sizeof(xi));
1167
1168 for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1169 y = gf_sqr(bch, x)^x;
1170 for (i = 0; i < 2; i++) {
1171 r = a_log(bch, y);
1172 if (y && (r < m) && !xi[r]) {
1173 bch->xi_tab[r] = x;
1174 xi[r] = 1;
1175 remaining--;
1176 dbg("x%d = %x\n", r, x);
1177 break;
1178 }
1179 y ^= ak;
1180 }
1181 }
1182 /* should not happen but check anyway */
1183 return remaining ? -1 : 0;
1184}
1185
1186static void *bch_alloc(size_t size, int *err)
1187{
1188 void *ptr;
1189
1190 ptr = kmalloc(size, GFP_KERNEL);
1191 if (ptr == NULL)
1192 *err = 1;
1193 return ptr;
1194}
1195
1196/*
1197 * compute generator polynomial for given (m,t) parameters.
1198 */
1199static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1200{
1201 const unsigned int m = GF_M(bch);
1202 const unsigned int t = GF_T(bch);
1203 int n, err = 0;
1204 unsigned int i, j, nbits, r, word, *roots;
1205 struct gf_poly *g;
1206 uint32_t *genpoly;
1207
1208 g = bch_alloc(GF_POLY_SZ(m*t), &err);
1209 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1210 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1211
1212 if (err) {
1213 kfree(genpoly);
1214 genpoly = NULL;
1215 goto finish;
1216 }
1217
1218 /* enumerate all roots of g(X) */
1219 memset(roots , 0, (bch->n+1)*sizeof(*roots));
1220 for (i = 0; i < t; i++) {
1221 for (j = 0, r = 2*i+1; j < m; j++) {
1222 roots[r] = 1;
1223 r = mod_s(bch, 2*r);
1224 }
1225 }
1226 /* build generator polynomial g(X) */
1227 g->deg = 0;
1228 g->c[0] = 1;
1229 for (i = 0; i < GF_N(bch); i++) {
1230 if (roots[i]) {
1231 /* multiply g(X) by (X+root) */
1232 r = bch->a_pow_tab[i];
1233 g->c[g->deg+1] = 1;
1234 for (j = g->deg; j > 0; j--)
1235 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1236
1237 g->c[0] = gf_mul(bch, g->c[0], r);
1238 g->deg++;
1239 }
1240 }
1241 /* store left-justified binary representation of g(X) */
1242 n = g->deg+1;
1243 i = 0;
1244
1245 while (n > 0) {
1246 nbits = (n > 32) ? 32 : n;
1247 for (j = 0, word = 0; j < nbits; j++) {
1248 if (g->c[n-1-j])
1249 word |= 1u << (31-j);
1250 }
1251 genpoly[i++] = word;
1252 n -= nbits;
1253 }
1254 bch->ecc_bits = g->deg;
1255
1256finish:
1257 kfree(g);
1258 kfree(roots);
1259
1260 return genpoly;
1261}
1262
1263/**
1264 * bch_init - initialize a BCH encoder/decoder
1265 * @m: Galois field order, should be in the range 5-15
1266 * @t: maximum error correction capability, in bits
1267 * @prim_poly: user-provided primitive polynomial (or 0 to use default)
1268 * @swap_bits: swap bits within data and syndrome bytes
1269 *
1270 * Returns:
1271 * a newly allocated BCH control structure if successful, NULL otherwise
1272 *
1273 * This initialization can take some time, as lookup tables are built for fast
1274 * encoding/decoding; make sure not to call this function from a time critical
1275 * path. Usually, bch_init() should be called on module/driver init and
1276 * bch_free() should be called to release memory on exit.
1277 *
1278 * You may provide your own primitive polynomial of degree @m in argument
1279 * @prim_poly, or let bch_init() use its default polynomial.
1280 *
1281 * Once bch_init() has successfully returned a pointer to a newly allocated
1282 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1283 * the structure.
1284 */
1285struct bch_control *bch_init(int m, int t, unsigned int prim_poly,
1286 bool swap_bits)
1287{
1288 int err = 0;
1289 unsigned int i, words;
1290 uint32_t *genpoly;
1291 struct bch_control *bch = NULL;
1292
1293 const int min_m = 5;
1294
1295 /* default primitive polynomials */
1296 static const unsigned int prim_poly_tab[] = {
1297 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1298 0x402b, 0x8003,
1299 };
1300
1301#if defined(CONFIG_BCH_CONST_PARAMS)
1302 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1303 printk(KERN_ERR "bch encoder/decoder was configured to support "
1304 "parameters m=%d, t=%d only!\n",
1305 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1306 goto fail;
1307 }
1308#endif
1309 if ((m < min_m) || (m > BCH_MAX_M))
1310 /*
1311 * values of m greater than 15 are not currently supported;
1312 * supporting m > 15 would require changing table base type
1313 * (uint16_t) and a small patch in matrix transposition
1314 */
1315 goto fail;
1316
1317 if (t > BCH_MAX_T)
1318 /*
1319 * we can support larger than 64 bits if necessary, at the
1320 * cost of higher stack usage.
1321 */
1322 goto fail;
1323
1324 /* sanity checks */
1325 if ((t < 1) || (m*t >= ((1 << m)-1)))
1326 /* invalid t value */
1327 goto fail;
1328
1329 /* select a primitive polynomial for generating GF(2^m) */
1330 if (prim_poly == 0)
1331 prim_poly = prim_poly_tab[m-min_m];
1332
1333 bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1334 if (bch == NULL)
1335 goto fail;
1336
1337 bch->m = m;
1338 bch->t = t;
1339 bch->n = (1 << m)-1;
1340 words = DIV_ROUND_UP(m*t, 32);
1341 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1342 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1343 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1344 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1345 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1346 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1347 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1348 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err);
1349 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err);
1350 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1351 bch->swap_bits = swap_bits;
1352
1353 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1354 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1355
1356 if (err)
1357 goto fail;
1358
1359 err = build_gf_tables(bch, prim_poly);
1360 if (err)
1361 goto fail;
1362
1363 /* use generator polynomial for computing encoding tables */
1364 genpoly = compute_generator_polynomial(bch);
1365 if (genpoly == NULL)
1366 goto fail;
1367
1368 build_mod8_tables(bch, genpoly);
1369 kfree(genpoly);
1370
1371 err = build_deg2_base(bch);
1372 if (err)
1373 goto fail;
1374
1375 return bch;
1376
1377fail:
1378 bch_free(bch);
1379 return NULL;
1380}
1381EXPORT_SYMBOL_GPL(bch_init);
1382
1383/**
1384 * bch_free - free the BCH control structure
1385 * @bch: BCH control structure to release
1386 */
1387void bch_free(struct bch_control *bch)
1388{
1389 unsigned int i;
1390
1391 if (bch) {
1392 kfree(bch->a_pow_tab);
1393 kfree(bch->a_log_tab);
1394 kfree(bch->mod8_tab);
1395 kfree(bch->ecc_buf);
1396 kfree(bch->ecc_buf2);
1397 kfree(bch->xi_tab);
1398 kfree(bch->syn);
1399 kfree(bch->cache);
1400 kfree(bch->elp);
1401
1402 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1403 kfree(bch->poly_2t[i]);
1404
1405 kfree(bch);
1406 }
1407}
1408EXPORT_SYMBOL_GPL(bch_free);
1409
1410MODULE_LICENSE("GPL");
1411MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
1412MODULE_DESCRIPTION("Binary BCH encoder/decoder");