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Tom Rini83d290c2018-05-06 17:58:06 -04001// SPDX-License-Identifier: GPL-2.0
Christian Hitz4c6de852011-10-12 09:31:59 +02002/*
3 * Generic binary BCH encoding/decoding library
4 *
Christian Hitz4c6de852011-10-12 09:31:59 +02005 * Copyright © 2011 Parrot S.A.
6 *
7 * Author: Ivan Djelic <ivan.djelic@parrot.com>
8 *
9 * Description:
10 *
11 * This library provides runtime configurable encoding/decoding of binary
12 * Bose-Chaudhuri-Hocquenghem (BCH) codes.
13 *
14 * Call init_bch to get a pointer to a newly allocated bch_control structure for
15 * the given m (Galois field order), t (error correction capability) and
16 * (optional) primitive polynomial parameters.
17 *
18 * Call encode_bch to compute and store ecc parity bytes to a given buffer.
19 * Call decode_bch to detect and locate errors in received data.
20 *
21 * On systems supporting hw BCH features, intermediate results may be provided
22 * to decode_bch in order to skip certain steps. See decode_bch() documentation
23 * for details.
24 *
25 * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
26 * parameters m and t; thus allowing extra compiler optimizations and providing
27 * better (up to 2x) encoding performance. Using this option makes sense when
28 * (m,t) are fixed and known in advance, e.g. when using BCH error correction
29 * on a particular NAND flash device.
30 *
31 * Algorithmic details:
32 *
33 * Encoding is performed by processing 32 input bits in parallel, using 4
34 * remainder lookup tables.
35 *
36 * The final stage of decoding involves the following internal steps:
37 * a. Syndrome computation
38 * b. Error locator polynomial computation using Berlekamp-Massey algorithm
39 * c. Error locator root finding (by far the most expensive step)
40 *
41 * In this implementation, step c is not performed using the usual Chien search.
42 * Instead, an alternative approach described in [1] is used. It consists in
43 * factoring the error locator polynomial using the Berlekamp Trace algorithm
44 * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
45 * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
46 * much better performance than Chien search for usual (m,t) values (typically
47 * m >= 13, t < 32, see [1]).
48 *
49 * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
50 * of characteristic 2, in: Western European Workshop on Research in Cryptology
51 * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
52 * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
53 * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
54 */
55
Maxime Ripard71d2c072017-02-27 18:22:01 +010056#ifndef USE_HOSTCC
Christian Hitz4c6de852011-10-12 09:31:59 +020057#include <common.h>
Simon Glassf7ae49f2020-05-10 11:40:05 -060058#include <log.h>
Simon Glass336d4612020-02-03 07:36:16 -070059#include <malloc.h>
Christian Hitz4c6de852011-10-12 09:31:59 +020060#include <ubi_uboot.h>
Simon Glass61b29b82020-02-03 07:36:15 -070061#include <dm/devres.h>
Christian Hitz4c6de852011-10-12 09:31:59 +020062
63#include <linux/bitops.h>
Maxime Ripard71d2c072017-02-27 18:22:01 +010064#else
65#include <errno.h>
Emmanuel Vadot4ecc9882017-06-20 09:02:29 +020066#if defined(__FreeBSD__)
67#include <sys/endian.h>
默默ab8fc412019-03-31 16:07:03 +080068#elif defined(__APPLE__)
69#include <machine/endian.h>
70#include <libkern/OSByteOrder.h>
Emmanuel Vadot4ecc9882017-06-20 09:02:29 +020071#else
Maxime Ripard71d2c072017-02-27 18:22:01 +010072#include <endian.h>
Emmanuel Vadot4ecc9882017-06-20 09:02:29 +020073#endif
Maxime Ripard71d2c072017-02-27 18:22:01 +010074#include <stdint.h>
75#include <stdlib.h>
76#include <string.h>
77
78#undef cpu_to_be32
默默ab8fc412019-03-31 16:07:03 +080079#if defined(__APPLE__)
80#define cpu_to_be32 OSSwapHostToBigInt32
81#else
Maxime Ripard71d2c072017-02-27 18:22:01 +010082#define cpu_to_be32 htobe32
默默ab8fc412019-03-31 16:07:03 +080083#endif
Maxime Ripard71d2c072017-02-27 18:22:01 +010084#define DIV_ROUND_UP(n,d) (((n) + (d) - 1) / (d))
85#define kmalloc(size, flags) malloc(size)
86#define kzalloc(size, flags) calloc(1, size)
87#define kfree free
88#define ARRAY_SIZE(arr) (sizeof(arr) / sizeof((arr)[0]))
89#endif
90
Christian Hitz4c6de852011-10-12 09:31:59 +020091#include <asm/byteorder.h>
92#include <linux/bch.h>
93
94#if defined(CONFIG_BCH_CONST_PARAMS)
95#define GF_M(_p) (CONFIG_BCH_CONST_M)
96#define GF_T(_p) (CONFIG_BCH_CONST_T)
97#define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1)
98#else
99#define GF_M(_p) ((_p)->m)
100#define GF_T(_p) ((_p)->t)
101#define GF_N(_p) ((_p)->n)
102#endif
103
104#define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
105#define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
106
107#ifndef dbg
108#define dbg(_fmt, args...) do {} while (0)
109#endif
110
111/*
112 * represent a polynomial over GF(2^m)
113 */
114struct gf_poly {
115 unsigned int deg; /* polynomial degree */
116 unsigned int c[0]; /* polynomial terms */
117};
118
119/* given its degree, compute a polynomial size in bytes */
120#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
121
122/* polynomial of degree 1 */
123struct gf_poly_deg1 {
124 struct gf_poly poly;
125 unsigned int c[2];
126};
127
Maxime Ripard71d2c072017-02-27 18:22:01 +0100128#ifdef USE_HOSTCC
默默ab8fc412019-03-31 16:07:03 +0800129#if !defined(__DragonFly__) && !defined(__FreeBSD__) && !defined(__APPLE__)
Maxime Ripard71d2c072017-02-27 18:22:01 +0100130static int fls(int x)
131{
132 int r = 32;
133
134 if (!x)
135 return 0;
136 if (!(x & 0xffff0000u)) {
137 x <<= 16;
138 r -= 16;
139 }
140 if (!(x & 0xff000000u)) {
141 x <<= 8;
142 r -= 8;
143 }
144 if (!(x & 0xf0000000u)) {
145 x <<= 4;
146 r -= 4;
147 }
148 if (!(x & 0xc0000000u)) {
149 x <<= 2;
150 r -= 2;
151 }
152 if (!(x & 0x80000000u)) {
153 x <<= 1;
154 r -= 1;
155 }
156 return r;
157}
158#endif
Emmanuel Vadot4ecc9882017-06-20 09:02:29 +0200159#endif
Maxime Ripard71d2c072017-02-27 18:22:01 +0100160
Christian Hitz4c6de852011-10-12 09:31:59 +0200161/*
162 * same as encode_bch(), but process input data one byte at a time
163 */
164static void encode_bch_unaligned(struct bch_control *bch,
165 const unsigned char *data, unsigned int len,
166 uint32_t *ecc)
167{
168 int i;
169 const uint32_t *p;
170 const int l = BCH_ECC_WORDS(bch)-1;
171
172 while (len--) {
173 p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
174
175 for (i = 0; i < l; i++)
176 ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
177
178 ecc[l] = (ecc[l] << 8)^(*p);
179 }
180}
181
182/*
183 * convert ecc bytes to aligned, zero-padded 32-bit ecc words
184 */
185static void load_ecc8(struct bch_control *bch, uint32_t *dst,
186 const uint8_t *src)
187{
188 uint8_t pad[4] = {0, 0, 0, 0};
189 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
190
191 for (i = 0; i < nwords; i++, src += 4)
192 dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
193
194 memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
195 dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
196}
197
198/*
199 * convert 32-bit ecc words to ecc bytes
200 */
201static void store_ecc8(struct bch_control *bch, uint8_t *dst,
202 const uint32_t *src)
203{
204 uint8_t pad[4];
205 unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
206
207 for (i = 0; i < nwords; i++) {
208 *dst++ = (src[i] >> 24);
209 *dst++ = (src[i] >> 16) & 0xff;
210 *dst++ = (src[i] >> 8) & 0xff;
211 *dst++ = (src[i] >> 0) & 0xff;
212 }
213 pad[0] = (src[nwords] >> 24);
214 pad[1] = (src[nwords] >> 16) & 0xff;
215 pad[2] = (src[nwords] >> 8) & 0xff;
216 pad[3] = (src[nwords] >> 0) & 0xff;
217 memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
218}
219
220/**
221 * encode_bch - calculate BCH ecc parity of data
222 * @bch: BCH control structure
223 * @data: data to encode
224 * @len: data length in bytes
225 * @ecc: ecc parity data, must be initialized by caller
226 *
227 * The @ecc parity array is used both as input and output parameter, in order to
228 * allow incremental computations. It should be of the size indicated by member
229 * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
230 *
231 * The exact number of computed ecc parity bits is given by member @ecc_bits of
232 * @bch; it may be less than m*t for large values of t.
233 */
234void encode_bch(struct bch_control *bch, const uint8_t *data,
235 unsigned int len, uint8_t *ecc)
236{
237 const unsigned int l = BCH_ECC_WORDS(bch)-1;
238 unsigned int i, mlen;
239 unsigned long m;
240 uint32_t w, r[l+1];
241 const uint32_t * const tab0 = bch->mod8_tab;
242 const uint32_t * const tab1 = tab0 + 256*(l+1);
243 const uint32_t * const tab2 = tab1 + 256*(l+1);
244 const uint32_t * const tab3 = tab2 + 256*(l+1);
245 const uint32_t *pdata, *p0, *p1, *p2, *p3;
246
247 if (ecc) {
248 /* load ecc parity bytes into internal 32-bit buffer */
249 load_ecc8(bch, bch->ecc_buf, ecc);
250 } else {
251 memset(bch->ecc_buf, 0, sizeof(r));
252 }
253
254 /* process first unaligned data bytes */
255 m = ((unsigned long)data) & 3;
256 if (m) {
257 mlen = (len < (4-m)) ? len : 4-m;
258 encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
259 data += mlen;
260 len -= mlen;
261 }
262
263 /* process 32-bit aligned data words */
264 pdata = (uint32_t *)data;
265 mlen = len/4;
266 data += 4*mlen;
267 len -= 4*mlen;
268 memcpy(r, bch->ecc_buf, sizeof(r));
269
270 /*
271 * split each 32-bit word into 4 polynomials of weight 8 as follows:
272 *
273 * 31 ...24 23 ...16 15 ... 8 7 ... 0
274 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt
275 * tttttttt mod g = r0 (precomputed)
276 * zzzzzzzz 00000000 mod g = r1 (precomputed)
277 * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed)
278 * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed)
279 * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3
280 */
281 while (mlen--) {
282 /* input data is read in big-endian format */
283 w = r[0]^cpu_to_be32(*pdata++);
284 p0 = tab0 + (l+1)*((w >> 0) & 0xff);
285 p1 = tab1 + (l+1)*((w >> 8) & 0xff);
286 p2 = tab2 + (l+1)*((w >> 16) & 0xff);
287 p3 = tab3 + (l+1)*((w >> 24) & 0xff);
288
289 for (i = 0; i < l; i++)
290 r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
291
292 r[l] = p0[l]^p1[l]^p2[l]^p3[l];
293 }
294 memcpy(bch->ecc_buf, r, sizeof(r));
295
296 /* process last unaligned bytes */
297 if (len)
298 encode_bch_unaligned(bch, data, len, bch->ecc_buf);
299
300 /* store ecc parity bytes into original parity buffer */
301 if (ecc)
302 store_ecc8(bch, ecc, bch->ecc_buf);
303}
304
305static inline int modulo(struct bch_control *bch, unsigned int v)
306{
307 const unsigned int n = GF_N(bch);
308 while (v >= n) {
309 v -= n;
310 v = (v & n) + (v >> GF_M(bch));
311 }
312 return v;
313}
314
315/*
316 * shorter and faster modulo function, only works when v < 2N.
317 */
318static inline int mod_s(struct bch_control *bch, unsigned int v)
319{
320 const unsigned int n = GF_N(bch);
321 return (v < n) ? v : v-n;
322}
323
324static inline int deg(unsigned int poly)
325{
326 /* polynomial degree is the most-significant bit index */
327 return fls(poly)-1;
328}
329
330static inline int parity(unsigned int x)
331{
332 /*
333 * public domain code snippet, lifted from
334 * http://www-graphics.stanford.edu/~seander/bithacks.html
335 */
336 x ^= x >> 1;
337 x ^= x >> 2;
338 x = (x & 0x11111111U) * 0x11111111U;
339 return (x >> 28) & 1;
340}
341
342/* Galois field basic operations: multiply, divide, inverse, etc. */
343
344static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
345 unsigned int b)
346{
347 return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
348 bch->a_log_tab[b])] : 0;
349}
350
351static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
352{
353 return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
354}
355
356static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
357 unsigned int b)
358{
359 return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
360 GF_N(bch)-bch->a_log_tab[b])] : 0;
361}
362
363static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
364{
365 return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
366}
367
368static inline unsigned int a_pow(struct bch_control *bch, int i)
369{
370 return bch->a_pow_tab[modulo(bch, i)];
371}
372
373static inline int a_log(struct bch_control *bch, unsigned int x)
374{
375 return bch->a_log_tab[x];
376}
377
378static inline int a_ilog(struct bch_control *bch, unsigned int x)
379{
380 return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
381}
382
383/*
384 * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
385 */
386static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
387 unsigned int *syn)
388{
389 int i, j, s;
390 unsigned int m;
391 uint32_t poly;
392 const int t = GF_T(bch);
393
394 s = bch->ecc_bits;
395
396 /* make sure extra bits in last ecc word are cleared */
397 m = ((unsigned int)s) & 31;
398 if (m)
399 ecc[s/32] &= ~((1u << (32-m))-1);
400 memset(syn, 0, 2*t*sizeof(*syn));
401
402 /* compute v(a^j) for j=1 .. 2t-1 */
403 do {
404 poly = *ecc++;
405 s -= 32;
406 while (poly) {
407 i = deg(poly);
408 for (j = 0; j < 2*t; j += 2)
409 syn[j] ^= a_pow(bch, (j+1)*(i+s));
410
411 poly ^= (1 << i);
412 }
413 } while (s > 0);
414
415 /* v(a^(2j)) = v(a^j)^2 */
416 for (j = 0; j < t; j++)
417 syn[2*j+1] = gf_sqr(bch, syn[j]);
418}
419
420static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
421{
422 memcpy(dst, src, GF_POLY_SZ(src->deg));
423}
424
425static int compute_error_locator_polynomial(struct bch_control *bch,
426 const unsigned int *syn)
427{
428 const unsigned int t = GF_T(bch);
429 const unsigned int n = GF_N(bch);
430 unsigned int i, j, tmp, l, pd = 1, d = syn[0];
431 struct gf_poly *elp = bch->elp;
432 struct gf_poly *pelp = bch->poly_2t[0];
433 struct gf_poly *elp_copy = bch->poly_2t[1];
434 int k, pp = -1;
435
436 memset(pelp, 0, GF_POLY_SZ(2*t));
437 memset(elp, 0, GF_POLY_SZ(2*t));
438
439 pelp->deg = 0;
440 pelp->c[0] = 1;
441 elp->deg = 0;
442 elp->c[0] = 1;
443
444 /* use simplified binary Berlekamp-Massey algorithm */
445 for (i = 0; (i < t) && (elp->deg <= t); i++) {
446 if (d) {
447 k = 2*i-pp;
448 gf_poly_copy(elp_copy, elp);
449 /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
450 tmp = a_log(bch, d)+n-a_log(bch, pd);
451 for (j = 0; j <= pelp->deg; j++) {
452 if (pelp->c[j]) {
453 l = a_log(bch, pelp->c[j]);
454 elp->c[j+k] ^= a_pow(bch, tmp+l);
455 }
456 }
457 /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
458 tmp = pelp->deg+k;
459 if (tmp > elp->deg) {
460 elp->deg = tmp;
461 gf_poly_copy(pelp, elp_copy);
462 pd = d;
463 pp = 2*i;
464 }
465 }
466 /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
467 if (i < t-1) {
468 d = syn[2*i+2];
469 for (j = 1; j <= elp->deg; j++)
470 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
471 }
472 }
473 dbg("elp=%s\n", gf_poly_str(elp));
474 return (elp->deg > t) ? -1 : (int)elp->deg;
475}
476
477/*
478 * solve a m x m linear system in GF(2) with an expected number of solutions,
479 * and return the number of found solutions
480 */
481static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
482 unsigned int *sol, int nsol)
483{
484 const int m = GF_M(bch);
485 unsigned int tmp, mask;
486 int rem, c, r, p, k, param[m];
487
488 k = 0;
489 mask = 1 << m;
490
491 /* Gaussian elimination */
492 for (c = 0; c < m; c++) {
493 rem = 0;
494 p = c-k;
495 /* find suitable row for elimination */
496 for (r = p; r < m; r++) {
497 if (rows[r] & mask) {
498 if (r != p) {
499 tmp = rows[r];
500 rows[r] = rows[p];
501 rows[p] = tmp;
502 }
503 rem = r+1;
504 break;
505 }
506 }
507 if (rem) {
508 /* perform elimination on remaining rows */
509 tmp = rows[p];
510 for (r = rem; r < m; r++) {
511 if (rows[r] & mask)
512 rows[r] ^= tmp;
513 }
514 } else {
515 /* elimination not needed, store defective row index */
516 param[k++] = c;
517 }
518 mask >>= 1;
519 }
520 /* rewrite system, inserting fake parameter rows */
521 if (k > 0) {
522 p = k;
523 for (r = m-1; r >= 0; r--) {
524 if ((r > m-1-k) && rows[r])
525 /* system has no solution */
526 return 0;
527
528 rows[r] = (p && (r == param[p-1])) ?
529 p--, 1u << (m-r) : rows[r-p];
530 }
531 }
532
533 if (nsol != (1 << k))
534 /* unexpected number of solutions */
535 return 0;
536
537 for (p = 0; p < nsol; p++) {
538 /* set parameters for p-th solution */
539 for (c = 0; c < k; c++)
540 rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
541
542 /* compute unique solution */
543 tmp = 0;
544 for (r = m-1; r >= 0; r--) {
545 mask = rows[r] & (tmp|1);
546 tmp |= parity(mask) << (m-r);
547 }
548 sol[p] = tmp >> 1;
549 }
550 return nsol;
551}
552
553/*
554 * this function builds and solves a linear system for finding roots of a degree
555 * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
556 */
557static int find_affine4_roots(struct bch_control *bch, unsigned int a,
558 unsigned int b, unsigned int c,
559 unsigned int *roots)
560{
561 int i, j, k;
562 const int m = GF_M(bch);
563 unsigned int mask = 0xff, t, rows[16] = {0,};
564
565 j = a_log(bch, b);
566 k = a_log(bch, a);
567 rows[0] = c;
568
569 /* buid linear system to solve X^4+aX^2+bX+c = 0 */
570 for (i = 0; i < m; i++) {
571 rows[i+1] = bch->a_pow_tab[4*i]^
572 (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
573 (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
574 j++;
575 k += 2;
576 }
577 /*
578 * transpose 16x16 matrix before passing it to linear solver
579 * warning: this code assumes m < 16
580 */
581 for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
582 for (k = 0; k < 16; k = (k+j+1) & ~j) {
583 t = ((rows[k] >> j)^rows[k+j]) & mask;
584 rows[k] ^= (t << j);
585 rows[k+j] ^= t;
586 }
587 }
588 return solve_linear_system(bch, rows, roots, 4);
589}
590
591/*
592 * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
593 */
594static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
595 unsigned int *roots)
596{
597 int n = 0;
598
599 if (poly->c[0])
600 /* poly[X] = bX+c with c!=0, root=c/b */
601 roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
602 bch->a_log_tab[poly->c[1]]);
603 return n;
604}
605
606/*
607 * compute roots of a degree 2 polynomial over GF(2^m)
608 */
609static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
610 unsigned int *roots)
611{
612 int n = 0, i, l0, l1, l2;
613 unsigned int u, v, r;
614
615 if (poly->c[0] && poly->c[1]) {
616
617 l0 = bch->a_log_tab[poly->c[0]];
618 l1 = bch->a_log_tab[poly->c[1]];
619 l2 = bch->a_log_tab[poly->c[2]];
620
621 /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
622 u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
623 /*
624 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
625 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
626 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
627 * i.e. r and r+1 are roots iff Tr(u)=0
628 */
629 r = 0;
630 v = u;
631 while (v) {
632 i = deg(v);
633 r ^= bch->xi_tab[i];
634 v ^= (1 << i);
635 }
636 /* verify root */
637 if ((gf_sqr(bch, r)^r) == u) {
638 /* reverse z=a/bX transformation and compute log(1/r) */
639 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
640 bch->a_log_tab[r]+l2);
641 roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
642 bch->a_log_tab[r^1]+l2);
643 }
644 }
645 return n;
646}
647
648/*
649 * compute roots of a degree 3 polynomial over GF(2^m)
650 */
651static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
652 unsigned int *roots)
653{
654 int i, n = 0;
655 unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
656
657 if (poly->c[0]) {
658 /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
659 e3 = poly->c[3];
660 c2 = gf_div(bch, poly->c[0], e3);
661 b2 = gf_div(bch, poly->c[1], e3);
662 a2 = gf_div(bch, poly->c[2], e3);
663
664 /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
665 c = gf_mul(bch, a2, c2); /* c = a2c2 */
666 b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */
667 a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */
668
669 /* find the 4 roots of this affine polynomial */
670 if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
671 /* remove a2 from final list of roots */
672 for (i = 0; i < 4; i++) {
673 if (tmp[i] != a2)
674 roots[n++] = a_ilog(bch, tmp[i]);
675 }
676 }
677 }
678 return n;
679}
680
681/*
682 * compute roots of a degree 4 polynomial over GF(2^m)
683 */
684static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
685 unsigned int *roots)
686{
687 int i, l, n = 0;
688 unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
689
690 if (poly->c[0] == 0)
691 return 0;
692
693 /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
694 e4 = poly->c[4];
695 d = gf_div(bch, poly->c[0], e4);
696 c = gf_div(bch, poly->c[1], e4);
697 b = gf_div(bch, poly->c[2], e4);
698 a = gf_div(bch, poly->c[3], e4);
699
700 /* use Y=1/X transformation to get an affine polynomial */
701 if (a) {
702 /* first, eliminate cX by using z=X+e with ae^2+c=0 */
703 if (c) {
704 /* compute e such that e^2 = c/a */
705 f = gf_div(bch, c, a);
706 l = a_log(bch, f);
707 l += (l & 1) ? GF_N(bch) : 0;
708 e = a_pow(bch, l/2);
709 /*
710 * use transformation z=X+e:
711 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
712 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
713 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
714 * z^4 + az^3 + b'z^2 + d'
715 */
716 d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
717 b = gf_mul(bch, a, e)^b;
718 }
719 /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
720 if (d == 0)
721 /* assume all roots have multiplicity 1 */
722 return 0;
723
724 c2 = gf_inv(bch, d);
725 b2 = gf_div(bch, a, d);
726 a2 = gf_div(bch, b, d);
727 } else {
728 /* polynomial is already affine */
729 c2 = d;
730 b2 = c;
731 a2 = b;
732 }
733 /* find the 4 roots of this affine polynomial */
734 if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
735 for (i = 0; i < 4; i++) {
736 /* post-process roots (reverse transformations) */
737 f = a ? gf_inv(bch, roots[i]) : roots[i];
738 roots[i] = a_ilog(bch, f^e);
739 }
740 n = 4;
741 }
742 return n;
743}
744
745/*
746 * build monic, log-based representation of a polynomial
747 */
748static void gf_poly_logrep(struct bch_control *bch,
749 const struct gf_poly *a, int *rep)
750{
751 int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
752
753 /* represent 0 values with -1; warning, rep[d] is not set to 1 */
754 for (i = 0; i < d; i++)
755 rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
756}
757
758/*
759 * compute polynomial Euclidean division remainder in GF(2^m)[X]
760 */
761static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
762 const struct gf_poly *b, int *rep)
763{
764 int la, p, m;
765 unsigned int i, j, *c = a->c;
766 const unsigned int d = b->deg;
767
768 if (a->deg < d)
769 return;
770
771 /* reuse or compute log representation of denominator */
772 if (!rep) {
773 rep = bch->cache;
774 gf_poly_logrep(bch, b, rep);
775 }
776
777 for (j = a->deg; j >= d; j--) {
778 if (c[j]) {
779 la = a_log(bch, c[j]);
780 p = j-d;
781 for (i = 0; i < d; i++, p++) {
782 m = rep[i];
783 if (m >= 0)
784 c[p] ^= bch->a_pow_tab[mod_s(bch,
785 m+la)];
786 }
787 }
788 }
789 a->deg = d-1;
790 while (!c[a->deg] && a->deg)
791 a->deg--;
792}
793
794/*
795 * compute polynomial Euclidean division quotient in GF(2^m)[X]
796 */
797static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
798 const struct gf_poly *b, struct gf_poly *q)
799{
800 if (a->deg >= b->deg) {
801 q->deg = a->deg-b->deg;
802 /* compute a mod b (modifies a) */
803 gf_poly_mod(bch, a, b, NULL);
804 /* quotient is stored in upper part of polynomial a */
805 memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
806 } else {
807 q->deg = 0;
808 q->c[0] = 0;
809 }
810}
811
812/*
813 * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
814 */
815static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
816 struct gf_poly *b)
817{
818 struct gf_poly *tmp;
819
820 dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
821
822 if (a->deg < b->deg) {
823 tmp = b;
824 b = a;
825 a = tmp;
826 }
827
828 while (b->deg > 0) {
829 gf_poly_mod(bch, a, b, NULL);
830 tmp = b;
831 b = a;
832 a = tmp;
833 }
834
835 dbg("%s\n", gf_poly_str(a));
836
837 return a;
838}
839
840/*
841 * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
842 * This is used in Berlekamp Trace algorithm for splitting polynomials
843 */
844static void compute_trace_bk_mod(struct bch_control *bch, int k,
845 const struct gf_poly *f, struct gf_poly *z,
846 struct gf_poly *out)
847{
848 const int m = GF_M(bch);
849 int i, j;
850
851 /* z contains z^2j mod f */
852 z->deg = 1;
853 z->c[0] = 0;
854 z->c[1] = bch->a_pow_tab[k];
855
856 out->deg = 0;
857 memset(out, 0, GF_POLY_SZ(f->deg));
858
859 /* compute f log representation only once */
860 gf_poly_logrep(bch, f, bch->cache);
861
862 for (i = 0; i < m; i++) {
863 /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
864 for (j = z->deg; j >= 0; j--) {
865 out->c[j] ^= z->c[j];
866 z->c[2*j] = gf_sqr(bch, z->c[j]);
867 z->c[2*j+1] = 0;
868 }
869 if (z->deg > out->deg)
870 out->deg = z->deg;
871
872 if (i < m-1) {
873 z->deg *= 2;
874 /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
875 gf_poly_mod(bch, z, f, bch->cache);
876 }
877 }
878 while (!out->c[out->deg] && out->deg)
879 out->deg--;
880
881 dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
882}
883
884/*
885 * factor a polynomial using Berlekamp Trace algorithm (BTA)
886 */
887static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
888 struct gf_poly **g, struct gf_poly **h)
889{
890 struct gf_poly *f2 = bch->poly_2t[0];
891 struct gf_poly *q = bch->poly_2t[1];
892 struct gf_poly *tk = bch->poly_2t[2];
893 struct gf_poly *z = bch->poly_2t[3];
894 struct gf_poly *gcd;
895
896 dbg("factoring %s...\n", gf_poly_str(f));
897
898 *g = f;
899 *h = NULL;
900
901 /* tk = Tr(a^k.X) mod f */
902 compute_trace_bk_mod(bch, k, f, z, tk);
903
904 if (tk->deg > 0) {
905 /* compute g = gcd(f, tk) (destructive operation) */
906 gf_poly_copy(f2, f);
907 gcd = gf_poly_gcd(bch, f2, tk);
908 if (gcd->deg < f->deg) {
909 /* compute h=f/gcd(f,tk); this will modify f and q */
910 gf_poly_div(bch, f, gcd, q);
911 /* store g and h in-place (clobbering f) */
912 *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
913 gf_poly_copy(*g, gcd);
914 gf_poly_copy(*h, q);
915 }
916 }
917}
918
919/*
920 * find roots of a polynomial, using BTZ algorithm; see the beginning of this
921 * file for details
922 */
923static int find_poly_roots(struct bch_control *bch, unsigned int k,
924 struct gf_poly *poly, unsigned int *roots)
925{
926 int cnt;
927 struct gf_poly *f1, *f2;
928
929 switch (poly->deg) {
930 /* handle low degree polynomials with ad hoc techniques */
931 case 1:
932 cnt = find_poly_deg1_roots(bch, poly, roots);
933 break;
934 case 2:
935 cnt = find_poly_deg2_roots(bch, poly, roots);
936 break;
937 case 3:
938 cnt = find_poly_deg3_roots(bch, poly, roots);
939 break;
940 case 4:
941 cnt = find_poly_deg4_roots(bch, poly, roots);
942 break;
943 default:
944 /* factor polynomial using Berlekamp Trace Algorithm (BTA) */
945 cnt = 0;
946 if (poly->deg && (k <= GF_M(bch))) {
947 factor_polynomial(bch, k, poly, &f1, &f2);
948 if (f1)
949 cnt += find_poly_roots(bch, k+1, f1, roots);
950 if (f2)
951 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
952 }
953 break;
954 }
955 return cnt;
956}
957
958#if defined(USE_CHIEN_SEARCH)
959/*
960 * exhaustive root search (Chien) implementation - not used, included only for
961 * reference/comparison tests
962 */
963static int chien_search(struct bch_control *bch, unsigned int len,
964 struct gf_poly *p, unsigned int *roots)
965{
966 int m;
967 unsigned int i, j, syn, syn0, count = 0;
968 const unsigned int k = 8*len+bch->ecc_bits;
969
970 /* use a log-based representation of polynomial */
971 gf_poly_logrep(bch, p, bch->cache);
972 bch->cache[p->deg] = 0;
973 syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
974
975 for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
976 /* compute elp(a^i) */
977 for (j = 1, syn = syn0; j <= p->deg; j++) {
978 m = bch->cache[j];
979 if (m >= 0)
980 syn ^= a_pow(bch, m+j*i);
981 }
982 if (syn == 0) {
983 roots[count++] = GF_N(bch)-i;
984 if (count == p->deg)
985 break;
986 }
987 }
988 return (count == p->deg) ? count : 0;
989}
990#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
991#endif /* USE_CHIEN_SEARCH */
992
993/**
994 * decode_bch - decode received codeword and find bit error locations
995 * @bch: BCH control structure
996 * @data: received data, ignored if @calc_ecc is provided
997 * @len: data length in bytes, must always be provided
998 * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
999 * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
1000 * @syn: hw computed syndrome data (if NULL, syndrome is calculated)
1001 * @errloc: output array of error locations
1002 *
1003 * Returns:
1004 * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
1005 * invalid parameters were provided
1006 *
1007 * Depending on the available hw BCH support and the need to compute @calc_ecc
1008 * separately (using encode_bch()), this function should be called with one of
1009 * the following parameter configurations -
1010 *
1011 * by providing @data and @recv_ecc only:
1012 * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
1013 *
1014 * by providing @recv_ecc and @calc_ecc:
1015 * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
1016 *
1017 * by providing ecc = recv_ecc XOR calc_ecc:
1018 * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
1019 *
1020 * by providing syndrome results @syn:
1021 * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
1022 *
1023 * Once decode_bch() has successfully returned with a positive value, error
1024 * locations returned in array @errloc should be interpreted as follows -
1025 *
1026 * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
1027 * data correction)
1028 *
1029 * if (errloc[n] < 8*len), then n-th error is located in data and can be
1030 * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
1031 *
1032 * Note that this function does not perform any data correction by itself, it
1033 * merely indicates error locations.
1034 */
1035int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
1036 const uint8_t *recv_ecc, const uint8_t *calc_ecc,
1037 const unsigned int *syn, unsigned int *errloc)
1038{
1039 const unsigned int ecc_words = BCH_ECC_WORDS(bch);
1040 unsigned int nbits;
1041 int i, err, nroots;
1042 uint32_t sum;
1043
1044 /* sanity check: make sure data length can be handled */
1045 if (8*len > (bch->n-bch->ecc_bits))
1046 return -EINVAL;
1047
1048 /* if caller does not provide syndromes, compute them */
1049 if (!syn) {
1050 if (!calc_ecc) {
1051 /* compute received data ecc into an internal buffer */
1052 if (!data || !recv_ecc)
1053 return -EINVAL;
1054 encode_bch(bch, data, len, NULL);
1055 } else {
1056 /* load provided calculated ecc */
1057 load_ecc8(bch, bch->ecc_buf, calc_ecc);
1058 }
1059 /* load received ecc or assume it was XORed in calc_ecc */
1060 if (recv_ecc) {
1061 load_ecc8(bch, bch->ecc_buf2, recv_ecc);
1062 /* XOR received and calculated ecc */
1063 for (i = 0, sum = 0; i < (int)ecc_words; i++) {
1064 bch->ecc_buf[i] ^= bch->ecc_buf2[i];
1065 sum |= bch->ecc_buf[i];
1066 }
1067 if (!sum)
1068 /* no error found */
1069 return 0;
1070 }
1071 compute_syndromes(bch, bch->ecc_buf, bch->syn);
1072 syn = bch->syn;
1073 }
1074
1075 err = compute_error_locator_polynomial(bch, syn);
1076 if (err > 0) {
1077 nroots = find_poly_roots(bch, 1, bch->elp, errloc);
1078 if (err != nroots)
1079 err = -1;
1080 }
1081 if (err > 0) {
1082 /* post-process raw error locations for easier correction */
1083 nbits = (len*8)+bch->ecc_bits;
1084 for (i = 0; i < err; i++) {
1085 if (errloc[i] >= nbits) {
1086 err = -1;
1087 break;
1088 }
1089 errloc[i] = nbits-1-errloc[i];
1090 errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
1091 }
1092 }
1093 return (err >= 0) ? err : -EBADMSG;
1094}
1095
1096/*
1097 * generate Galois field lookup tables
1098 */
1099static int build_gf_tables(struct bch_control *bch, unsigned int poly)
1100{
1101 unsigned int i, x = 1;
1102 const unsigned int k = 1 << deg(poly);
1103
1104 /* primitive polynomial must be of degree m */
1105 if (k != (1u << GF_M(bch)))
1106 return -1;
1107
1108 for (i = 0; i < GF_N(bch); i++) {
1109 bch->a_pow_tab[i] = x;
1110 bch->a_log_tab[x] = i;
1111 if (i && (x == 1))
1112 /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */
1113 return -1;
1114 x <<= 1;
1115 if (x & k)
1116 x ^= poly;
1117 }
1118 bch->a_pow_tab[GF_N(bch)] = 1;
1119 bch->a_log_tab[0] = 0;
1120
1121 return 0;
1122}
1123
1124/*
1125 * compute generator polynomial remainder tables for fast encoding
1126 */
1127static void build_mod8_tables(struct bch_control *bch, const uint32_t *g)
1128{
1129 int i, j, b, d;
1130 uint32_t data, hi, lo, *tab;
1131 const int l = BCH_ECC_WORDS(bch);
1132 const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32);
1133 const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32);
1134
1135 memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab));
1136
1137 for (i = 0; i < 256; i++) {
1138 /* p(X)=i is a small polynomial of weight <= 8 */
1139 for (b = 0; b < 4; b++) {
1140 /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */
1141 tab = bch->mod8_tab + (b*256+i)*l;
1142 data = i << (8*b);
1143 while (data) {
1144 d = deg(data);
1145 /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */
1146 data ^= g[0] >> (31-d);
1147 for (j = 0; j < ecclen; j++) {
1148 hi = (d < 31) ? g[j] << (d+1) : 0;
1149 lo = (j+1 < plen) ?
1150 g[j+1] >> (31-d) : 0;
1151 tab[j] ^= hi|lo;
1152 }
1153 }
1154 }
1155 }
1156}
1157
1158/*
1159 * build a base for factoring degree 2 polynomials
1160 */
1161static int build_deg2_base(struct bch_control *bch)
1162{
1163 const int m = GF_M(bch);
1164 int i, j, r;
1165 unsigned int sum, x, y, remaining, ak = 0, xi[m];
1166
1167 /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */
1168 for (i = 0; i < m; i++) {
1169 for (j = 0, sum = 0; j < m; j++)
1170 sum ^= a_pow(bch, i*(1 << j));
1171
1172 if (sum) {
1173 ak = bch->a_pow_tab[i];
1174 break;
1175 }
1176 }
1177 /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */
1178 remaining = m;
1179 memset(xi, 0, sizeof(xi));
1180
1181 for (x = 0; (x <= GF_N(bch)) && remaining; x++) {
1182 y = gf_sqr(bch, x)^x;
1183 for (i = 0; i < 2; i++) {
1184 r = a_log(bch, y);
1185 if (y && (r < m) && !xi[r]) {
1186 bch->xi_tab[r] = x;
1187 xi[r] = 1;
1188 remaining--;
1189 dbg("x%d = %x\n", r, x);
1190 break;
1191 }
1192 y ^= ak;
1193 }
1194 }
1195 /* should not happen but check anyway */
1196 return remaining ? -1 : 0;
1197}
1198
1199static void *bch_alloc(size_t size, int *err)
1200{
1201 void *ptr;
1202
1203 ptr = kmalloc(size, GFP_KERNEL);
1204 if (ptr == NULL)
1205 *err = 1;
1206 return ptr;
1207}
1208
1209/*
1210 * compute generator polynomial for given (m,t) parameters.
1211 */
1212static uint32_t *compute_generator_polynomial(struct bch_control *bch)
1213{
1214 const unsigned int m = GF_M(bch);
1215 const unsigned int t = GF_T(bch);
1216 int n, err = 0;
1217 unsigned int i, j, nbits, r, word, *roots;
1218 struct gf_poly *g;
1219 uint32_t *genpoly;
1220
1221 g = bch_alloc(GF_POLY_SZ(m*t), &err);
1222 roots = bch_alloc((bch->n+1)*sizeof(*roots), &err);
1223 genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err);
1224
1225 if (err) {
1226 kfree(genpoly);
1227 genpoly = NULL;
1228 goto finish;
1229 }
1230
1231 /* enumerate all roots of g(X) */
1232 memset(roots , 0, (bch->n+1)*sizeof(*roots));
1233 for (i = 0; i < t; i++) {
1234 for (j = 0, r = 2*i+1; j < m; j++) {
1235 roots[r] = 1;
1236 r = mod_s(bch, 2*r);
1237 }
1238 }
1239 /* build generator polynomial g(X) */
1240 g->deg = 0;
1241 g->c[0] = 1;
1242 for (i = 0; i < GF_N(bch); i++) {
1243 if (roots[i]) {
1244 /* multiply g(X) by (X+root) */
1245 r = bch->a_pow_tab[i];
1246 g->c[g->deg+1] = 1;
1247 for (j = g->deg; j > 0; j--)
1248 g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1];
1249
1250 g->c[0] = gf_mul(bch, g->c[0], r);
1251 g->deg++;
1252 }
1253 }
1254 /* store left-justified binary representation of g(X) */
1255 n = g->deg+1;
1256 i = 0;
1257
1258 while (n > 0) {
1259 nbits = (n > 32) ? 32 : n;
1260 for (j = 0, word = 0; j < nbits; j++) {
1261 if (g->c[n-1-j])
1262 word |= 1u << (31-j);
1263 }
1264 genpoly[i++] = word;
1265 n -= nbits;
1266 }
1267 bch->ecc_bits = g->deg;
1268
1269finish:
1270 kfree(g);
1271 kfree(roots);
1272
1273 return genpoly;
1274}
1275
1276/**
1277 * init_bch - initialize a BCH encoder/decoder
1278 * @m: Galois field order, should be in the range 5-15
1279 * @t: maximum error correction capability, in bits
1280 * @prim_poly: user-provided primitive polynomial (or 0 to use default)
1281 *
1282 * Returns:
1283 * a newly allocated BCH control structure if successful, NULL otherwise
1284 *
1285 * This initialization can take some time, as lookup tables are built for fast
1286 * encoding/decoding; make sure not to call this function from a time critical
1287 * path. Usually, init_bch() should be called on module/driver init and
1288 * free_bch() should be called to release memory on exit.
1289 *
1290 * You may provide your own primitive polynomial of degree @m in argument
1291 * @prim_poly, or let init_bch() use its default polynomial.
1292 *
1293 * Once init_bch() has successfully returned a pointer to a newly allocated
1294 * BCH control structure, ecc length in bytes is given by member @ecc_bytes of
1295 * the structure.
1296 */
1297struct bch_control *init_bch(int m, int t, unsigned int prim_poly)
1298{
1299 int err = 0;
1300 unsigned int i, words;
1301 uint32_t *genpoly;
1302 struct bch_control *bch = NULL;
1303
1304 const int min_m = 5;
1305 const int max_m = 15;
1306
1307 /* default primitive polynomials */
1308 static const unsigned int prim_poly_tab[] = {
1309 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b,
1310 0x402b, 0x8003,
1311 };
1312
1313#if defined(CONFIG_BCH_CONST_PARAMS)
1314 if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) {
1315 printk(KERN_ERR "bch encoder/decoder was configured to support "
1316 "parameters m=%d, t=%d only!\n",
1317 CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T);
1318 goto fail;
1319 }
1320#endif
1321 if ((m < min_m) || (m > max_m))
1322 /*
1323 * values of m greater than 15 are not currently supported;
1324 * supporting m > 15 would require changing table base type
1325 * (uint16_t) and a small patch in matrix transposition
1326 */
1327 goto fail;
1328
1329 /* sanity checks */
1330 if ((t < 1) || (m*t >= ((1 << m)-1)))
1331 /* invalid t value */
1332 goto fail;
1333
1334 /* select a primitive polynomial for generating GF(2^m) */
1335 if (prim_poly == 0)
1336 prim_poly = prim_poly_tab[m-min_m];
1337
1338 bch = kzalloc(sizeof(*bch), GFP_KERNEL);
1339 if (bch == NULL)
1340 goto fail;
1341
1342 bch->m = m;
1343 bch->t = t;
1344 bch->n = (1 << m)-1;
1345 words = DIV_ROUND_UP(m*t, 32);
1346 bch->ecc_bytes = DIV_ROUND_UP(m*t, 8);
1347 bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err);
1348 bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err);
1349 bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err);
1350 bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err);
1351 bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err);
1352 bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err);
1353 bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err);
1354 bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err);
1355 bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err);
1356
1357 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1358 bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err);
1359
1360 if (err)
1361 goto fail;
1362
1363 err = build_gf_tables(bch, prim_poly);
1364 if (err)
1365 goto fail;
1366
1367 /* use generator polynomial for computing encoding tables */
1368 genpoly = compute_generator_polynomial(bch);
1369 if (genpoly == NULL)
1370 goto fail;
1371
1372 build_mod8_tables(bch, genpoly);
1373 kfree(genpoly);
1374
1375 err = build_deg2_base(bch);
1376 if (err)
1377 goto fail;
1378
1379 return bch;
1380
1381fail:
1382 free_bch(bch);
1383 return NULL;
1384}
1385
1386/**
1387 * free_bch - free the BCH control structure
1388 * @bch: BCH control structure to release
1389 */
1390void free_bch(struct bch_control *bch)
1391{
1392 unsigned int i;
1393
1394 if (bch) {
1395 kfree(bch->a_pow_tab);
1396 kfree(bch->a_log_tab);
1397 kfree(bch->mod8_tab);
1398 kfree(bch->ecc_buf);
1399 kfree(bch->ecc_buf2);
1400 kfree(bch->xi_tab);
1401 kfree(bch->syn);
1402 kfree(bch->cache);
1403 kfree(bch->elp);
1404
1405 for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++)
1406 kfree(bch->poly_2t[i]);
1407
1408 kfree(bch);
1409 }
1410}