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0001 /*
0002  * Generic binary BCH encoding/decoding library
0003  *
0004  * This program is free software; you can redistribute it and/or modify it
0005  * under the terms of the GNU General Public License version 2 as published by
0006  * the Free Software Foundation.
0007  *
0008  * This program is distributed in the hope that it will be useful, but WITHOUT
0009  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
0010  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
0011  * more details.
0012  *
0013  * You should have received a copy of the GNU General Public License along with
0014  * this program; if not, write to the Free Software Foundation, Inc., 51
0015  * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
0016  *
0017  * Copyright © 2011 Parrot S.A.
0018  *
0019  * Author: Ivan Djelic <ivan.djelic@parrot.com>
0020  *
0021  * Description:
0022  *
0023  * This library provides runtime configurable encoding/decoding of binary
0024  * Bose-Chaudhuri-Hocquenghem (BCH) codes.
0025  *
0026  * Call init_bch to get a pointer to a newly allocated bch_control structure for
0027  * the given m (Galois field order), t (error correction capability) and
0028  * (optional) primitive polynomial parameters.
0029  *
0030  * Call encode_bch to compute and store ecc parity bytes to a given buffer.
0031  * Call decode_bch to detect and locate errors in received data.
0032  *
0033  * On systems supporting hw BCH features, intermediate results may be provided
0034  * to decode_bch in order to skip certain steps. See decode_bch() documentation
0035  * for details.
0036  *
0037  * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
0038  * parameters m and t; thus allowing extra compiler optimizations and providing
0039  * better (up to 2x) encoding performance. Using this option makes sense when
0040  * (m,t) are fixed and known in advance, e.g. when using BCH error correction
0041  * on a particular NAND flash device.
0042  *
0043  * Algorithmic details:
0044  *
0045  * Encoding is performed by processing 32 input bits in parallel, using 4
0046  * remainder lookup tables.
0047  *
0048  * The final stage of decoding involves the following internal steps:
0049  * a. Syndrome computation
0050  * b. Error locator polynomial computation using Berlekamp-Massey algorithm
0051  * c. Error locator root finding (by far the most expensive step)
0052  *
0053  * In this implementation, step c is not performed using the usual Chien search.
0054  * Instead, an alternative approach described in [1] is used. It consists in
0055  * factoring the error locator polynomial using the Berlekamp Trace algorithm
0056  * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
0057  * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
0058  * much better performance than Chien search for usual (m,t) values (typically
0059  * m >= 13, t < 32, see [1]).
0060  *
0061  * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
0062  * of characteristic 2, in: Western European Workshop on Research in Cryptology
0063  * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
0064  * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
0065  * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
0066  */
0067 
0068 #include <linux/kernel.h>
0069 #include <linux/errno.h>
0070 #include <linux/init.h>
0071 #include <linux/module.h>
0072 #include <linux/slab.h>
0073 #include <linux/bitops.h>
0074 #include <asm/byteorder.h>
0075 #include <linux/bch.h>
0076 
0077 #if defined(CONFIG_BCH_CONST_PARAMS)
0078 #define GF_M(_p)               (CONFIG_BCH_CONST_M)
0079 #define GF_T(_p)               (CONFIG_BCH_CONST_T)
0080 #define GF_N(_p)               ((1 << (CONFIG_BCH_CONST_M))-1)
0081 #else
0082 #define GF_M(_p)               ((_p)->m)
0083 #define GF_T(_p)               ((_p)->t)
0084 #define GF_N(_p)               ((_p)->n)
0085 #endif
0086 
0087 #define BCH_ECC_WORDS(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
0088 #define BCH_ECC_BYTES(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
0089 
0090 #ifndef dbg
0091 #define dbg(_fmt, args...)     do {} while (0)
0092 #endif
0093 
0094 /*
0095  * represent a polynomial over GF(2^m)
0096  */
0097 struct gf_poly {
0098     unsigned int deg;    /* polynomial degree */
0099     unsigned int c[0];   /* polynomial terms */
0100 };
0101 
0102 /* given its degree, compute a polynomial size in bytes */
0103 #define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
0104 
0105 /* polynomial of degree 1 */
0106 struct gf_poly_deg1 {
0107     struct gf_poly poly;
0108     unsigned int   c[2];
0109 };
0110 
0111 /*
0112  * same as encode_bch(), but process input data one byte at a time
0113  */
0114 static void encode_bch_unaligned(struct bch_control *bch,
0115                  const unsigned char *data, unsigned int len,
0116                  uint32_t *ecc)
0117 {
0118     int i;
0119     const uint32_t *p;
0120     const int l = BCH_ECC_WORDS(bch)-1;
0121 
0122     while (len--) {
0123         p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
0124 
0125         for (i = 0; i < l; i++)
0126             ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
0127 
0128         ecc[l] = (ecc[l] << 8)^(*p);
0129     }
0130 }
0131 
0132 /*
0133  * convert ecc bytes to aligned, zero-padded 32-bit ecc words
0134  */
0135 static void load_ecc8(struct bch_control *bch, uint32_t *dst,
0136               const uint8_t *src)
0137 {
0138     uint8_t pad[4] = {0, 0, 0, 0};
0139     unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
0140 
0141     for (i = 0; i < nwords; i++, src += 4)
0142         dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
0143 
0144     memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
0145     dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
0146 }
0147 
0148 /*
0149  * convert 32-bit ecc words to ecc bytes
0150  */
0151 static void store_ecc8(struct bch_control *bch, uint8_t *dst,
0152                const uint32_t *src)
0153 {
0154     uint8_t pad[4];
0155     unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
0156 
0157     for (i = 0; i < nwords; i++) {
0158         *dst++ = (src[i] >> 24);
0159         *dst++ = (src[i] >> 16) & 0xff;
0160         *dst++ = (src[i] >>  8) & 0xff;
0161         *dst++ = (src[i] >>  0) & 0xff;
0162     }
0163     pad[0] = (src[nwords] >> 24);
0164     pad[1] = (src[nwords] >> 16) & 0xff;
0165     pad[2] = (src[nwords] >>  8) & 0xff;
0166     pad[3] = (src[nwords] >>  0) & 0xff;
0167     memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
0168 }
0169 
0170 /**
0171  * encode_bch - calculate BCH ecc parity of data
0172  * @bch:   BCH control structure
0173  * @data:  data to encode
0174  * @len:   data length in bytes
0175  * @ecc:   ecc parity data, must be initialized by caller
0176  *
0177  * The @ecc parity array is used both as input and output parameter, in order to
0178  * allow incremental computations. It should be of the size indicated by member
0179  * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
0180  *
0181  * The exact number of computed ecc parity bits is given by member @ecc_bits of
0182  * @bch; it may be less than m*t for large values of t.
0183  */
0184 void encode_bch(struct bch_control *bch, const uint8_t *data,
0185         unsigned int len, uint8_t *ecc)
0186 {
0187     const unsigned int l = BCH_ECC_WORDS(bch)-1;
0188     unsigned int i, mlen;
0189     unsigned long m;
0190     uint32_t w, r[l+1];
0191     const uint32_t * const tab0 = bch->mod8_tab;
0192     const uint32_t * const tab1 = tab0 + 256*(l+1);
0193     const uint32_t * const tab2 = tab1 + 256*(l+1);
0194     const uint32_t * const tab3 = tab2 + 256*(l+1);
0195     const uint32_t *pdata, *p0, *p1, *p2, *p3;
0196 
0197     if (ecc) {
0198         /* load ecc parity bytes into internal 32-bit buffer */
0199         load_ecc8(bch, bch->ecc_buf, ecc);
0200     } else {
0201         memset(bch->ecc_buf, 0, sizeof(r));
0202     }
0203 
0204     /* process first unaligned data bytes */
0205     m = ((unsigned long)data) & 3;
0206     if (m) {
0207         mlen = (len < (4-m)) ? len : 4-m;
0208         encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
0209         data += mlen;
0210         len  -= mlen;
0211     }
0212 
0213     /* process 32-bit aligned data words */
0214     pdata = (uint32_t *)data;
0215     mlen  = len/4;
0216     data += 4*mlen;
0217     len  -= 4*mlen;
0218     memcpy(r, bch->ecc_buf, sizeof(r));
0219 
0220     /*
0221      * split each 32-bit word into 4 polynomials of weight 8 as follows:
0222      *
0223      * 31 ...24  23 ...16  15 ... 8  7 ... 0
0224      * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt
0225      *                               tttttttt  mod g = r0 (precomputed)
0226      *                     zzzzzzzz  00000000  mod g = r1 (precomputed)
0227      *           yyyyyyyy  00000000  00000000  mod g = r2 (precomputed)
0228      * xxxxxxxx  00000000  00000000  00000000  mod g = r3 (precomputed)
0229      * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt  mod g = r0^r1^r2^r3
0230      */
0231     while (mlen--) {
0232         /* input data is read in big-endian format */
0233         w = r[0]^cpu_to_be32(*pdata++);
0234         p0 = tab0 + (l+1)*((w >>  0) & 0xff);
0235         p1 = tab1 + (l+1)*((w >>  8) & 0xff);
0236         p2 = tab2 + (l+1)*((w >> 16) & 0xff);
0237         p3 = tab3 + (l+1)*((w >> 24) & 0xff);
0238 
0239         for (i = 0; i < l; i++)
0240             r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
0241 
0242         r[l] = p0[l]^p1[l]^p2[l]^p3[l];
0243     }
0244     memcpy(bch->ecc_buf, r, sizeof(r));
0245 
0246     /* process last unaligned bytes */
0247     if (len)
0248         encode_bch_unaligned(bch, data, len, bch->ecc_buf);
0249 
0250     /* store ecc parity bytes into original parity buffer */
0251     if (ecc)
0252         store_ecc8(bch, ecc, bch->ecc_buf);
0253 }
0254 EXPORT_SYMBOL_GPL(encode_bch);
0255 
0256 static inline int modulo(struct bch_control *bch, unsigned int v)
0257 {
0258     const unsigned int n = GF_N(bch);
0259     while (v >= n) {
0260         v -= n;
0261         v = (v & n) + (v >> GF_M(bch));
0262     }
0263     return v;
0264 }
0265 
0266 /*
0267  * shorter and faster modulo function, only works when v < 2N.
0268  */
0269 static inline int mod_s(struct bch_control *bch, unsigned int v)
0270 {
0271     const unsigned int n = GF_N(bch);
0272     return (v < n) ? v : v-n;
0273 }
0274 
0275 static inline int deg(unsigned int poly)
0276 {
0277     /* polynomial degree is the most-significant bit index */
0278     return fls(poly)-1;
0279 }
0280 
0281 static inline int parity(unsigned int x)
0282 {
0283     /*
0284      * public domain code snippet, lifted from
0285      * http://www-graphics.stanford.edu/~seander/bithacks.html
0286      */
0287     x ^= x >> 1;
0288     x ^= x >> 2;
0289     x = (x & 0x11111111U) * 0x11111111U;
0290     return (x >> 28) & 1;
0291 }
0292 
0293 /* Galois field basic operations: multiply, divide, inverse, etc. */
0294 
0295 static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
0296                   unsigned int b)
0297 {
0298     return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
0299                            bch->a_log_tab[b])] : 0;
0300 }
0301 
0302 static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
0303 {
0304     return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
0305 }
0306 
0307 static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
0308                   unsigned int b)
0309 {
0310     return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
0311                     GF_N(bch)-bch->a_log_tab[b])] : 0;
0312 }
0313 
0314 static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
0315 {
0316     return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
0317 }
0318 
0319 static inline unsigned int a_pow(struct bch_control *bch, int i)
0320 {
0321     return bch->a_pow_tab[modulo(bch, i)];
0322 }
0323 
0324 static inline int a_log(struct bch_control *bch, unsigned int x)
0325 {
0326     return bch->a_log_tab[x];
0327 }
0328 
0329 static inline int a_ilog(struct bch_control *bch, unsigned int x)
0330 {
0331     return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
0332 }
0333 
0334 /*
0335  * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
0336  */
0337 static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
0338                   unsigned int *syn)
0339 {
0340     int i, j, s;
0341     unsigned int m;
0342     uint32_t poly;
0343     const int t = GF_T(bch);
0344 
0345     s = bch->ecc_bits;
0346 
0347     /* make sure extra bits in last ecc word are cleared */
0348     m = ((unsigned int)s) & 31;
0349     if (m)
0350         ecc[s/32] &= ~((1u << (32-m))-1);
0351     memset(syn, 0, 2*t*sizeof(*syn));
0352 
0353     /* compute v(a^j) for j=1 .. 2t-1 */
0354     do {
0355         poly = *ecc++;
0356         s -= 32;
0357         while (poly) {
0358             i = deg(poly);
0359             for (j = 0; j < 2*t; j += 2)
0360                 syn[j] ^= a_pow(bch, (j+1)*(i+s));
0361 
0362             poly ^= (1 << i);
0363         }
0364     } while (s > 0);
0365 
0366     /* v(a^(2j)) = v(a^j)^2 */
0367     for (j = 0; j < t; j++)
0368         syn[2*j+1] = gf_sqr(bch, syn[j]);
0369 }
0370 
0371 static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
0372 {
0373     memcpy(dst, src, GF_POLY_SZ(src->deg));
0374 }
0375 
0376 static int compute_error_locator_polynomial(struct bch_control *bch,
0377                         const unsigned int *syn)
0378 {
0379     const unsigned int t = GF_T(bch);
0380     const unsigned int n = GF_N(bch);
0381     unsigned int i, j, tmp, l, pd = 1, d = syn[0];
0382     struct gf_poly *elp = bch->elp;
0383     struct gf_poly *pelp = bch->poly_2t[0];
0384     struct gf_poly *elp_copy = bch->poly_2t[1];
0385     int k, pp = -1;
0386 
0387     memset(pelp, 0, GF_POLY_SZ(2*t));
0388     memset(elp, 0, GF_POLY_SZ(2*t));
0389 
0390     pelp->deg = 0;
0391     pelp->c[0] = 1;
0392     elp->deg = 0;
0393     elp->c[0] = 1;
0394 
0395     /* use simplified binary Berlekamp-Massey algorithm */
0396     for (i = 0; (i < t) && (elp->deg <= t); i++) {
0397         if (d) {
0398             k = 2*i-pp;
0399             gf_poly_copy(elp_copy, elp);
0400             /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
0401             tmp = a_log(bch, d)+n-a_log(bch, pd);
0402             for (j = 0; j <= pelp->deg; j++) {
0403                 if (pelp->c[j]) {
0404                     l = a_log(bch, pelp->c[j]);
0405                     elp->c[j+k] ^= a_pow(bch, tmp+l);
0406                 }
0407             }
0408             /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
0409             tmp = pelp->deg+k;
0410             if (tmp > elp->deg) {
0411                 elp->deg = tmp;
0412                 gf_poly_copy(pelp, elp_copy);
0413                 pd = d;
0414                 pp = 2*i;
0415             }
0416         }
0417         /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
0418         if (i < t-1) {
0419             d = syn[2*i+2];
0420             for (j = 1; j <= elp->deg; j++)
0421                 d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
0422         }
0423     }
0424     dbg("elp=%s\n", gf_poly_str(elp));
0425     return (elp->deg > t) ? -1 : (int)elp->deg;
0426 }
0427 
0428 /*
0429  * solve a m x m linear system in GF(2) with an expected number of solutions,
0430  * and return the number of found solutions
0431  */
0432 static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
0433                    unsigned int *sol, int nsol)
0434 {
0435     const int m = GF_M(bch);
0436     unsigned int tmp, mask;
0437     int rem, c, r, p, k, param[m];
0438 
0439     k = 0;
0440     mask = 1 << m;
0441 
0442     /* Gaussian elimination */
0443     for (c = 0; c < m; c++) {
0444         rem = 0;
0445         p = c-k;
0446         /* find suitable row for elimination */
0447         for (r = p; r < m; r++) {
0448             if (rows[r] & mask) {
0449                 if (r != p) {
0450                     tmp = rows[r];
0451                     rows[r] = rows[p];
0452                     rows[p] = tmp;
0453                 }
0454                 rem = r+1;
0455                 break;
0456             }
0457         }
0458         if (rem) {
0459             /* perform elimination on remaining rows */
0460             tmp = rows[p];
0461             for (r = rem; r < m; r++) {
0462                 if (rows[r] & mask)
0463                     rows[r] ^= tmp;
0464             }
0465         } else {
0466             /* elimination not needed, store defective row index */
0467             param[k++] = c;
0468         }
0469         mask >>= 1;
0470     }
0471     /* rewrite system, inserting fake parameter rows */
0472     if (k > 0) {
0473         p = k;
0474         for (r = m-1; r >= 0; r--) {
0475             if ((r > m-1-k) && rows[r])
0476                 /* system has no solution */
0477                 return 0;
0478 
0479             rows[r] = (p && (r == param[p-1])) ?
0480                 p--, 1u << (m-r) : rows[r-p];
0481         }
0482     }
0483 
0484     if (nsol != (1 << k))
0485         /* unexpected number of solutions */
0486         return 0;
0487 
0488     for (p = 0; p < nsol; p++) {
0489         /* set parameters for p-th solution */
0490         for (c = 0; c < k; c++)
0491             rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
0492 
0493         /* compute unique solution */
0494         tmp = 0;
0495         for (r = m-1; r >= 0; r--) {
0496             mask = rows[r] & (tmp|1);
0497             tmp |= parity(mask) << (m-r);
0498         }
0499         sol[p] = tmp >> 1;
0500     }
0501     return nsol;
0502 }
0503 
0504 /*
0505  * this function builds and solves a linear system for finding roots of a degree
0506  * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
0507  */
0508 static int find_affine4_roots(struct bch_control *bch, unsigned int a,
0509                   unsigned int b, unsigned int c,
0510                   unsigned int *roots)
0511 {
0512     int i, j, k;
0513     const int m = GF_M(bch);
0514     unsigned int mask = 0xff, t, rows[16] = {0,};
0515 
0516     j = a_log(bch, b);
0517     k = a_log(bch, a);
0518     rows[0] = c;
0519 
0520     /* buid linear system to solve X^4+aX^2+bX+c = 0 */
0521     for (i = 0; i < m; i++) {
0522         rows[i+1] = bch->a_pow_tab[4*i]^
0523             (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
0524             (b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
0525         j++;
0526         k += 2;
0527     }
0528     /*
0529      * transpose 16x16 matrix before passing it to linear solver
0530      * warning: this code assumes m < 16
0531      */
0532     for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
0533         for (k = 0; k < 16; k = (k+j+1) & ~j) {
0534             t = ((rows[k] >> j)^rows[k+j]) & mask;
0535             rows[k] ^= (t << j);
0536             rows[k+j] ^= t;
0537         }
0538     }
0539     return solve_linear_system(bch, rows, roots, 4);
0540 }
0541 
0542 /*
0543  * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
0544  */
0545 static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
0546                 unsigned int *roots)
0547 {
0548     int n = 0;
0549 
0550     if (poly->c[0])
0551         /* poly[X] = bX+c with c!=0, root=c/b */
0552         roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
0553                    bch->a_log_tab[poly->c[1]]);
0554     return n;
0555 }
0556 
0557 /*
0558  * compute roots of a degree 2 polynomial over GF(2^m)
0559  */
0560 static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
0561                 unsigned int *roots)
0562 {
0563     int n = 0, i, l0, l1, l2;
0564     unsigned int u, v, r;
0565 
0566     if (poly->c[0] && poly->c[1]) {
0567 
0568         l0 = bch->a_log_tab[poly->c[0]];
0569         l1 = bch->a_log_tab[poly->c[1]];
0570         l2 = bch->a_log_tab[poly->c[2]];
0571 
0572         /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
0573         u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
0574         /*
0575          * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
0576          * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
0577          * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
0578          * i.e. r and r+1 are roots iff Tr(u)=0
0579          */
0580         r = 0;
0581         v = u;
0582         while (v) {
0583             i = deg(v);
0584             r ^= bch->xi_tab[i];
0585             v ^= (1 << i);
0586         }
0587         /* verify root */
0588         if ((gf_sqr(bch, r)^r) == u) {
0589             /* reverse z=a/bX transformation and compute log(1/r) */
0590             roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
0591                         bch->a_log_tab[r]+l2);
0592             roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
0593                         bch->a_log_tab[r^1]+l2);
0594         }
0595     }
0596     return n;
0597 }
0598 
0599 /*
0600  * compute roots of a degree 3 polynomial over GF(2^m)
0601  */
0602 static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
0603                 unsigned int *roots)
0604 {
0605     int i, n = 0;
0606     unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
0607 
0608     if (poly->c[0]) {
0609         /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
0610         e3 = poly->c[3];
0611         c2 = gf_div(bch, poly->c[0], e3);
0612         b2 = gf_div(bch, poly->c[1], e3);
0613         a2 = gf_div(bch, poly->c[2], e3);
0614 
0615         /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
0616         c = gf_mul(bch, a2, c2);           /* c = a2c2      */
0617         b = gf_mul(bch, a2, b2)^c2;        /* b = a2b2 + c2 */
0618         a = gf_sqr(bch, a2)^b2;            /* a = a2^2 + b2 */
0619 
0620         /* find the 4 roots of this affine polynomial */
0621         if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
0622             /* remove a2 from final list of roots */
0623             for (i = 0; i < 4; i++) {
0624                 if (tmp[i] != a2)
0625                     roots[n++] = a_ilog(bch, tmp[i]);
0626             }
0627         }
0628     }
0629     return n;
0630 }
0631 
0632 /*
0633  * compute roots of a degree 4 polynomial over GF(2^m)
0634  */
0635 static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
0636                 unsigned int *roots)
0637 {
0638     int i, l, n = 0;
0639     unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
0640 
0641     if (poly->c[0] == 0)
0642         return 0;
0643 
0644     /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
0645     e4 = poly->c[4];
0646     d = gf_div(bch, poly->c[0], e4);
0647     c = gf_div(bch, poly->c[1], e4);
0648     b = gf_div(bch, poly->c[2], e4);
0649     a = gf_div(bch, poly->c[3], e4);
0650 
0651     /* use Y=1/X transformation to get an affine polynomial */
0652     if (a) {
0653         /* first, eliminate cX by using z=X+e with ae^2+c=0 */
0654         if (c) {
0655             /* compute e such that e^2 = c/a */
0656             f = gf_div(bch, c, a);
0657             l = a_log(bch, f);
0658             l += (l & 1) ? GF_N(bch) : 0;
0659             e = a_pow(bch, l/2);
0660             /*
0661              * use transformation z=X+e:
0662              * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
0663              * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
0664              * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
0665              * z^4 + az^3 +     b'z^2 + d'
0666              */
0667             d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
0668             b = gf_mul(bch, a, e)^b;
0669         }
0670         /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
0671         if (d == 0)
0672             /* assume all roots have multiplicity 1 */
0673             return 0;
0674 
0675         c2 = gf_inv(bch, d);
0676         b2 = gf_div(bch, a, d);
0677         a2 = gf_div(bch, b, d);
0678     } else {
0679         /* polynomial is already affine */
0680         c2 = d;
0681         b2 = c;
0682         a2 = b;
0683     }
0684     /* find the 4 roots of this affine polynomial */
0685     if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
0686         for (i = 0; i < 4; i++) {
0687             /* post-process roots (reverse transformations) */
0688             f = a ? gf_inv(bch, roots[i]) : roots[i];
0689             roots[i] = a_ilog(bch, f^e);
0690         }
0691         n = 4;
0692     }
0693     return n;
0694 }
0695 
0696 /*
0697  * build monic, log-based representation of a polynomial
0698  */
0699 static void gf_poly_logrep(struct bch_control *bch,
0700                const struct gf_poly *a, int *rep)
0701 {
0702     int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
0703 
0704     /* represent 0 values with -1; warning, rep[d] is not set to 1 */
0705     for (i = 0; i < d; i++)
0706         rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
0707 }
0708 
0709 /*
0710  * compute polynomial Euclidean division remainder in GF(2^m)[X]
0711  */
0712 static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
0713             const struct gf_poly *b, int *rep)
0714 {
0715     int la, p, m;
0716     unsigned int i, j, *c = a->c;
0717     const unsigned int d = b->deg;
0718 
0719     if (a->deg < d)
0720         return;
0721 
0722     /* reuse or compute log representation of denominator */
0723     if (!rep) {
0724         rep = bch->cache;
0725         gf_poly_logrep(bch, b, rep);
0726     }
0727 
0728     for (j = a->deg; j >= d; j--) {
0729         if (c[j]) {
0730             la = a_log(bch, c[j]);
0731             p = j-d;
0732             for (i = 0; i < d; i++, p++) {
0733                 m = rep[i];
0734                 if (m >= 0)
0735                     c[p] ^= bch->a_pow_tab[mod_s(bch,
0736                                      m+la)];
0737             }
0738         }
0739     }
0740     a->deg = d-1;
0741     while (!c[a->deg] && a->deg)
0742         a->deg--;
0743 }
0744 
0745 /*
0746  * compute polynomial Euclidean division quotient in GF(2^m)[X]
0747  */
0748 static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
0749             const struct gf_poly *b, struct gf_poly *q)
0750 {
0751     if (a->deg >= b->deg) {
0752         q->deg = a->deg-b->deg;
0753         /* compute a mod b (modifies a) */
0754         gf_poly_mod(bch, a, b, NULL);
0755         /* quotient is stored in upper part of polynomial a */
0756         memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
0757     } else {
0758         q->deg = 0;
0759         q->c[0] = 0;
0760     }
0761 }
0762 
0763 /*
0764  * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
0765  */
0766 static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
0767                    struct gf_poly *b)
0768 {
0769     struct gf_poly *tmp;
0770 
0771     dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
0772 
0773     if (a->deg < b->deg) {
0774         tmp = b;
0775         b = a;
0776         a = tmp;
0777     }
0778 
0779     while (b->deg > 0) {
0780         gf_poly_mod(bch, a, b, NULL);
0781         tmp = b;
0782         b = a;
0783         a = tmp;
0784     }
0785 
0786     dbg("%s\n", gf_poly_str(a));
0787 
0788     return a;
0789 }
0790 
0791 /*
0792  * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
0793  * This is used in Berlekamp Trace algorithm for splitting polynomials
0794  */
0795 static void compute_trace_bk_mod(struct bch_control *bch, int k,
0796                  const struct gf_poly *f, struct gf_poly *z,
0797                  struct gf_poly *out)
0798 {
0799     const int m = GF_M(bch);
0800     int i, j;
0801 
0802     /* z contains z^2j mod f */
0803     z->deg = 1;
0804     z->c[0] = 0;
0805     z->c[1] = bch->a_pow_tab[k];
0806 
0807     out->deg = 0;
0808     memset(out, 0, GF_POLY_SZ(f->deg));
0809 
0810     /* compute f log representation only once */
0811     gf_poly_logrep(bch, f, bch->cache);
0812 
0813     for (i = 0; i < m; i++) {
0814         /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
0815         for (j = z->deg; j >= 0; j--) {
0816             out->c[j] ^= z->c[j];
0817             z->c[2*j] = gf_sqr(bch, z->c[j]);
0818             z->c[2*j+1] = 0;
0819         }
0820         if (z->deg > out->deg)
0821             out->deg = z->deg;
0822 
0823         if (i < m-1) {
0824             z->deg *= 2;
0825             /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
0826             gf_poly_mod(bch, z, f, bch->cache);
0827         }
0828     }
0829     while (!out->c[out->deg] && out->deg)
0830         out->deg--;
0831 
0832     dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
0833 }
0834 
0835 /*
0836  * factor a polynomial using Berlekamp Trace algorithm (BTA)
0837  */
0838 static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
0839                   struct gf_poly **g, struct gf_poly **h)
0840 {
0841     struct gf_poly *f2 = bch->poly_2t[0];
0842     struct gf_poly *q  = bch->poly_2t[1];
0843     struct gf_poly *tk = bch->poly_2t[2];
0844     struct gf_poly *z  = bch->poly_2t[3];
0845     struct gf_poly *gcd;
0846 
0847     dbg("factoring %s...\n", gf_poly_str(f));
0848 
0849     *g = f;
0850     *h = NULL;
0851 
0852     /* tk = Tr(a^k.X) mod f */
0853     compute_trace_bk_mod(bch, k, f, z, tk);
0854 
0855     if (tk->deg > 0) {
0856         /* compute g = gcd(f, tk) (destructive operation) */
0857         gf_poly_copy(f2, f);
0858         gcd = gf_poly_gcd(bch, f2, tk);
0859         if (gcd->deg < f->deg) {
0860             /* compute h=f/gcd(f,tk); this will modify f and q */
0861             gf_poly_div(bch, f, gcd, q);
0862             /* store g and h in-place (clobbering f) */
0863             *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
0864             gf_poly_copy(*g, gcd);
0865             gf_poly_copy(*h, q);
0866         }
0867     }
0868 }
0869 
0870 /*
0871  * find roots of a polynomial, using BTZ algorithm; see the beginning of this
0872  * file for details
0873  */
0874 static int find_poly_roots(struct bch_control *bch, unsigned int k,
0875                struct gf_poly *poly, unsigned int *roots)
0876 {
0877     int cnt;
0878     struct gf_poly *f1, *f2;
0879 
0880     switch (poly->deg) {
0881         /* handle low degree polynomials with ad hoc techniques */
0882     case 1:
0883         cnt = find_poly_deg1_roots(bch, poly, roots);
0884         break;
0885     case 2:
0886         cnt = find_poly_deg2_roots(bch, poly, roots);
0887         break;
0888     case 3:
0889         cnt = find_poly_deg3_roots(bch, poly, roots);
0890         break;
0891     case 4:
0892         cnt = find_poly_deg4_roots(bch, poly, roots);
0893         break;
0894     default:
0895         /* factor polynomial using Berlekamp Trace Algorithm (BTA) */
0896         cnt = 0;
0897         if (poly->deg && (k <= GF_M(bch))) {
0898             factor_polynomial(bch, k, poly, &f1, &f2);
0899             if (f1)
0900                 cnt += find_poly_roots(bch, k+1, f1, roots);
0901             if (f2)
0902                 cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
0903         }
0904         break;
0905     }
0906     return cnt;
0907 }
0908 
0909 #if defined(USE_CHIEN_SEARCH)
0910 /*
0911  * exhaustive root search (Chien) implementation - not used, included only for
0912  * reference/comparison tests
0913  */
0914 static int chien_search(struct bch_control *bch, unsigned int len,
0915             struct gf_poly *p, unsigned int *roots)
0916 {
0917     int m;
0918     unsigned int i, j, syn, syn0, count = 0;
0919     const unsigned int k = 8*len+bch->ecc_bits;
0920 
0921     /* use a log-based representation of polynomial */
0922     gf_poly_logrep(bch, p, bch->cache);
0923     bch->cache[p->deg] = 0;
0924     syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
0925 
0926     for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
0927         /* compute elp(a^i) */
0928         for (j = 1, syn = syn0; j <= p->deg; j++) {
0929             m = bch->cache[j];
0930             if (m >= 0)
0931                 syn ^= a_pow(bch, m+j*i);
0932         }
0933         if (syn == 0) {
0934             roots[count++] = GF_N(bch)-i;
0935             if (count == p->deg)
0936                 break;
0937         }
0938     }
0939     return (count == p->deg) ? count : 0;
0940 }
0941 #define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
0942 #endif /* USE_CHIEN_SEARCH */
0943 
0944 /**
0945  * decode_bch - decode received codeword and find bit error locations
0946  * @bch:      BCH control structure
0947  * @data:     received data, ignored if @calc_ecc is provided
0948  * @len:      data length in bytes, must always be provided
0949  * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
0950  * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
0951  * @syn:      hw computed syndrome data (if NULL, syndrome is calculated)
0952  * @errloc:   output array of error locations
0953  *
0954  * Returns:
0955  *  The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
0956  *  invalid parameters were provided
0957  *
0958  * Depending on the available hw BCH support and the need to compute @calc_ecc
0959  * separately (using encode_bch()), this function should be called with one of
0960  * the following parameter configurations -
0961  *
0962  * by providing @data and @recv_ecc only:
0963  *   decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
0964  *
0965  * by providing @recv_ecc and @calc_ecc:
0966  *   decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
0967  *
0968  * by providing ecc = recv_ecc XOR calc_ecc:
0969  *   decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
0970  *
0971  * by providing syndrome results @syn:
0972  *   decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
0973  *
0974  * Once decode_bch() has successfully returned with a positive value, error
0975  * locations returned in array @errloc should be interpreted as follows -
0976  *
0977  * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
0978  * data correction)
0979  *
0980  * if (errloc[n] < 8*len), then n-th error is located in data and can be
0981  * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
0982  *
0983  * Note that this function does not perform any data correction by itself, it
0984  * merely indicates error locations.
0985  */
0986 int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
0987            const uint8_t *recv_ecc, const uint8_t *calc_ecc,
0988            const unsigned int *syn, unsigned int *errloc)
0989 {
0990     const unsigned int ecc_words = BCH_ECC_WORDS(bch);
0991     unsigned int nbits;
0992     int i, err, nroots;
0993     uint32_t sum;
0994 
0995     /* sanity check: make sure data length can be handled */
0996     if (8*len > (bch->n-bch->ecc_bits))
0997         return -EINVAL;
0998 
0999     /* 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");