The Design and Implementation of the FreeBSD Operating System, Second Edition
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sys/lib/bch.c

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    1 /*
    2  * Generic binary BCH encoding/decoding library
    3  *
    4  * This program is free software; you can redistribute it and/or modify it
    5  * under the terms of the GNU General Public License version 2 as published by
    6  * the Free Software Foundation.
    7  *
    8  * This program is distributed in the hope that it will be useful, but WITHOUT
    9  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
   10  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
   11  * more details.
   12  *
   13  * You should have received a copy of the GNU General Public License along with
   14  * this program; if not, write to the Free Software Foundation, Inc., 51
   15  * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
   16  *
   17  * Copyright © 2011 Parrot S.A.
   18  *
   19  * Author: Ivan Djelic <ivan.djelic@parrot.com>
   20  *
   21  * Description:
   22  *
   23  * This library provides runtime configurable encoding/decoding of binary
   24  * Bose-Chaudhuri-Hocquenghem (BCH) codes.
   25  *
   26  * Call init_bch to get a pointer to a newly allocated bch_control structure for
   27  * the given m (Galois field order), t (error correction capability) and
   28  * (optional) primitive polynomial parameters.
   29  *
   30  * Call encode_bch to compute and store ecc parity bytes to a given buffer.
   31  * Call decode_bch to detect and locate errors in received data.
   32  *
   33  * On systems supporting hw BCH features, intermediate results may be provided
   34  * to decode_bch in order to skip certain steps. See decode_bch() documentation
   35  * for details.
   36  *
   37  * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
   38  * parameters m and t; thus allowing extra compiler optimizations and providing
   39  * better (up to 2x) encoding performance. Using this option makes sense when
   40  * (m,t) are fixed and known in advance, e.g. when using BCH error correction
   41  * on a particular NAND flash device.
   42  *
   43  * Algorithmic details:
   44  *
   45  * Encoding is performed by processing 32 input bits in parallel, using 4
   46  * remainder lookup tables.
   47  *
   48  * The final stage of decoding involves the following internal steps:
   49  * a. Syndrome computation
   50  * b. Error locator polynomial computation using Berlekamp-Massey algorithm
   51  * c. Error locator root finding (by far the most expensive step)
   52  *
   53  * In this implementation, step c is not performed using the usual Chien search.
   54  * Instead, an alternative approach described in [1] is used. It consists in
   55  * factoring the error locator polynomial using the Berlekamp Trace algorithm
   56  * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
   57  * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
   58  * much better performance than Chien search for usual (m,t) values (typically
   59  * m >= 13, t < 32, see [1]).
   60  *
   61  * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
   62  * of characteristic 2, in: Western European Workshop on Research in Cryptology
   63  * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
   64  * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
   65  * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
   66  */
   67 
   68 #include <linux/kernel.h>
   69 #include <linux/errno.h>
   70 #include <linux/init.h>
   71 #include <linux/module.h>
   72 #include <linux/slab.h>
   73 #include <linux/bitops.h>
   74 #include <asm/byteorder.h>
   75 #include <linux/bch.h>
   76 
   77 #if defined(CONFIG_BCH_CONST_PARAMS)
   78 #define GF_M(_p)               (CONFIG_BCH_CONST_M)
   79 #define GF_T(_p)               (CONFIG_BCH_CONST_T)
   80 #define GF_N(_p)               ((1 << (CONFIG_BCH_CONST_M))-1)
   81 #else
   82 #define GF_M(_p)               ((_p)->m)
   83 #define GF_T(_p)               ((_p)->t)
   84 #define GF_N(_p)               ((_p)->n)
   85 #endif
   86 
   87 #define BCH_ECC_WORDS(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
   88 #define BCH_ECC_BYTES(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
   89 
   90 #ifndef dbg
   91 #define dbg(_fmt, args...)     do {} while (0)
   92 #endif
   93 
   94 /*
   95  * represent a polynomial over GF(2^m)
   96  */
   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");

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