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Linux/lib/bch.c

  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  */
 97 struct 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 */
106 struct 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  */
114 static 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  */
135 static 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  */
151 static 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  */
184 void 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 }
254 EXPORT_SYMBOL_GPL(encode_bch);
255 
256 static 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  */
269 static 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 
275 static inline int deg(unsigned int poly)
276 {
277         /* polynomial degree is the most-significant bit index */
278         return fls(poly)-1;
279 }
280 
281 static 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 
295 static 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 
302 static 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 
307 static 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 
314 static 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 
319 static inline unsigned int a_pow(struct bch_control *bch, int i)
320 {
321         return bch->a_pow_tab[modulo(bch, i)];
322 }
323 
324 static inline int a_log(struct bch_control *bch, unsigned int x)
325 {
326         return bch->a_log_tab[x];
327 }
328 
329 static 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  */
337 static 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 
371 static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
372 {
373         memcpy(dst, src, GF_POLY_SZ(src->deg));
374 }
375 
376 static 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  */
432 static 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  */
508 static 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  */
545 static 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  */
560 static 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  */
602 static 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  */
635 static 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  */
699 static 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  */
712 static 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  */
748 static 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  */
766 static 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  */
795 static 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  */
838 static 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  */
874 static 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  */
914 static 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  */
986 int 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 }
1046 EXPORT_SYMBOL_GPL(decode_bch);
1047 
1048 /*
1049  * generate Galois field lookup tables
1050  */
1051 static 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  */
1079 static 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  */
1113 static 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 
1151 static 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  */
1164 static 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 
1221 finish:
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  */
1249 struct 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 
1333 fail:
1334         free_bch(bch);
1335         return NULL;
1336 }
1337 EXPORT_SYMBOL_GPL(init_bch);
1338 
1339 /**
1340  *  free_bch - free the BCH control structure
1341  *  @bch:    BCH control structure to release
1342  */
1343 void 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 }
1364 EXPORT_SYMBOL_GPL(free_bch);
1365 
1366 MODULE_LICENSE("GPL");
1367 MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
1368 MODULE_DESCRIPTION("Binary BCH encoder/decoder");
1369 

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