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

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