linux/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 */
  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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