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diff --git a/lib/bch.c b/lib/bch.c new file mode 100644 index 0000000..7f4ca92 --- /dev/null +++ b/lib/bch.c @@ -0,0 +1,1358 @@ +/* + * Generic binary BCH encoding/decoding library + * + * This program is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 as published by + * the Free Software Foundation. + * + * This program is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for + * more details. + * + * You should have received a copy of the GNU General Public License along with + * this program; if not, write to the Free Software Foundation, Inc., 51 + * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Copyright © 2011 Parrot S.A. + * + * Author: Ivan Djelic <ivan.djelic@parrot.com> + * + * Description: + * + * This library provides runtime configurable encoding/decoding of binary + * Bose-Chaudhuri-Hocquenghem (BCH) codes. + * + * Call init_bch to get a pointer to a newly allocated bch_control structure for + * the given m (Galois field order), t (error correction capability) and + * (optional) primitive polynomial parameters. + * + * Call encode_bch to compute and store ecc parity bytes to a given buffer. + * Call decode_bch to detect and locate errors in received data. + * + * On systems supporting hw BCH features, intermediate results may be provided + * to decode_bch in order to skip certain steps. See decode_bch() documentation + * for details. + * + * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of + * parameters m and t; thus allowing extra compiler optimizations and providing + * better (up to 2x) encoding performance. Using this option makes sense when + * (m,t) are fixed and known in advance, e.g. when using BCH error correction + * on a particular NAND flash device. + * + * Algorithmic details: + * + * Encoding is performed by processing 32 input bits in parallel, using 4 + * remainder lookup tables. + * + * The final stage of decoding involves the following internal steps: + * a. Syndrome computation + * b. Error locator polynomial computation using Berlekamp-Massey algorithm + * c. Error locator root finding (by far the most expensive step) + * + * In this implementation, step c is not performed using the usual Chien search. + * Instead, an alternative approach described in [1] is used. It consists in + * factoring the error locator polynomial using the Berlekamp Trace algorithm + * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial + * solving techniques [2] are used. The resulting algorithm, called BTZ, yields + * much better performance than Chien search for usual (m,t) values (typically + * m >= 13, t < 32, see [1]). + * + * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields + * of characteristic 2, in: Western European Workshop on Research in Cryptology + * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear. + * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over + * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996. + */ + +#include <common.h> +#include <ubi_uboot.h> + +#include <linux/bitops.h> +#include <asm/byteorder.h> +#include <linux/bch.h> + +#if defined(CONFIG_BCH_CONST_PARAMS) +#define GF_M(_p) (CONFIG_BCH_CONST_M) +#define GF_T(_p) (CONFIG_BCH_CONST_T) +#define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1) +#else +#define GF_M(_p) ((_p)->m) +#define GF_T(_p) ((_p)->t) +#define GF_N(_p) ((_p)->n) +#endif + +#define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32) +#define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8) + +#ifndef dbg +#define dbg(_fmt, args...) do {} while (0) +#endif + +/* + * represent a polynomial over GF(2^m) + */ +struct gf_poly { + unsigned int deg; /* polynomial degree */ + unsigned int c[0]; /* polynomial terms */ +}; + +/* given its degree, compute a polynomial size in bytes */ +#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int)) + +/* polynomial of degree 1 */ +struct gf_poly_deg1 { + struct gf_poly poly; + unsigned int c[2]; +}; + +/* + * same as encode_bch(), but process input data one byte at a time + */ +static void encode_bch_unaligned(struct bch_control *bch, + const unsigned char *data, unsigned int len, + uint32_t *ecc) +{ + int i; + const uint32_t *p; + const int l = BCH_ECC_WORDS(bch)-1; + + while (len--) { + p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff); + + for (i = 0; i < l; i++) + ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++); + + ecc[l] = (ecc[l] << 8)^(*p); + } +} + +/* + * convert ecc bytes to aligned, zero-padded 32-bit ecc words + */ +static void load_ecc8(struct bch_control *bch, uint32_t *dst, + const uint8_t *src) +{ + uint8_t pad[4] = {0, 0, 0, 0}; + unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; + + for (i = 0; i < nwords; i++, src += 4) + dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3]; + + memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords); + dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3]; +} + +/* + * convert 32-bit ecc words to ecc bytes + */ +static void store_ecc8(struct bch_control *bch, uint8_t *dst, + const uint32_t *src) +{ + uint8_t pad[4]; + unsigned int i, nwords = BCH_ECC_WORDS(bch)-1; + + for (i = 0; i < nwords; i++) { + *dst++ = (src[i] >> 24); + *dst++ = (src[i] >> 16) & 0xff; + *dst++ = (src[i] >> 8) & 0xff; + *dst++ = (src[i] >> 0) & 0xff; + } + pad[0] = (src[nwords] >> 24); + pad[1] = (src[nwords] >> 16) & 0xff; + pad[2] = (src[nwords] >> 8) & 0xff; + pad[3] = (src[nwords] >> 0) & 0xff; + memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords); +} + +/** + * encode_bch - calculate BCH ecc parity of data + * @bch: BCH control structure + * @data: data to encode + * @len: data length in bytes + * @ecc: ecc parity data, must be initialized by caller + * + * The @ecc parity array is used both as input and output parameter, in order to + * allow incremental computations. It should be of the size indicated by member + * @ecc_bytes of @bch, and should be initialized to 0 before the first call. + * + * The exact number of computed ecc parity bits is given by member @ecc_bits of + * @bch; it may be less than m*t for large values of t. + */ +void encode_bch(struct bch_control *bch, const uint8_t *data, + unsigned int len, uint8_t *ecc) +{ + const unsigned int l = BCH_ECC_WORDS(bch)-1; + unsigned int i, mlen; + unsigned long m; + uint32_t w, r[l+1]; + const uint32_t * const tab0 = bch->mod8_tab; + const uint32_t * const tab1 = tab0 + 256*(l+1); + const uint32_t * const tab2 = tab1 + 256*(l+1); + const uint32_t * const tab3 = tab2 + 256*(l+1); + const uint32_t *pdata, *p0, *p1, *p2, *p3; + + if (ecc) { + /* load ecc parity bytes into internal 32-bit buffer */ + load_ecc8(bch, bch->ecc_buf, ecc); + } else { + memset(bch->ecc_buf, 0, sizeof(r)); + } + + /* process first unaligned data bytes */ + m = ((unsigned long)data) & 3; + if (m) { + mlen = (len < (4-m)) ? len : 4-m; + encode_bch_unaligned(bch, data, mlen, bch->ecc_buf); + data += mlen; + len -= mlen; + } + + /* process 32-bit aligned data words */ + pdata = (uint32_t *)data; + mlen = len/4; + data += 4*mlen; + len -= 4*mlen; + memcpy(r, bch->ecc_buf, sizeof(r)); + + /* + * split each 32-bit word into 4 polynomials of weight 8 as follows: + * + * 31 ...24 23 ...16 15 ... 8 7 ... 0 + * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt + * tttttttt mod g = r0 (precomputed) + * zzzzzzzz 00000000 mod g = r1 (precomputed) + * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed) + * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed) + * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3 + */ + while (mlen--) { + /* input data is read in big-endian format */ + w = r[0]^cpu_to_be32(*pdata++); + p0 = tab0 + (l+1)*((w >> 0) & 0xff); + p1 = tab1 + (l+1)*((w >> 8) & 0xff); + p2 = tab2 + (l+1)*((w >> 16) & 0xff); + p3 = tab3 + (l+1)*((w >> 24) & 0xff); + + for (i = 0; i < l; i++) + r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i]; + + r[l] = p0[l]^p1[l]^p2[l]^p3[l]; + } + memcpy(bch->ecc_buf, r, sizeof(r)); + + /* process last unaligned bytes */ + if (len) + encode_bch_unaligned(bch, data, len, bch->ecc_buf); + + /* store ecc parity bytes into original parity buffer */ + if (ecc) + store_ecc8(bch, ecc, bch->ecc_buf); +} + +static inline int modulo(struct bch_control *bch, unsigned int v) +{ + const unsigned int n = GF_N(bch); + while (v >= n) { + v -= n; + v = (v & n) + (v >> GF_M(bch)); + } + return v; +} + +/* + * shorter and faster modulo function, only works when v < 2N. + */ +static inline int mod_s(struct bch_control *bch, unsigned int v) +{ + const unsigned int n = GF_N(bch); + return (v < n) ? v : v-n; +} + +static inline int deg(unsigned int poly) +{ + /* polynomial degree is the most-significant bit index */ + return fls(poly)-1; +} + +static inline int parity(unsigned int x) +{ + /* + * public domain code snippet, lifted from + * http://www-graphics.stanford.edu/~seander/bithacks.html + */ + x ^= x >> 1; + x ^= x >> 2; + x = (x & 0x11111111U) * 0x11111111U; + return (x >> 28) & 1; +} + +/* Galois field basic operations: multiply, divide, inverse, etc. */ + +static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a, + unsigned int b) +{ + return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ + bch->a_log_tab[b])] : 0; +} + +static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a) +{ + return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0; +} + +static inline unsigned int gf_div(struct bch_control *bch, unsigned int a, + unsigned int b) +{ + return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+ + GF_N(bch)-bch->a_log_tab[b])] : 0; +} + +static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a) +{ + return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]]; +} + +static inline unsigned int a_pow(struct bch_control *bch, int i) +{ + return bch->a_pow_tab[modulo(bch, i)]; +} + +static inline int a_log(struct bch_control *bch, unsigned int x) +{ + return bch->a_log_tab[x]; +} + +static inline int a_ilog(struct bch_control *bch, unsigned int x) +{ + return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]); +} + +/* + * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t + */ +static void compute_syndromes(struct bch_control *bch, uint32_t *ecc, + unsigned int *syn) +{ + int i, j, s; + unsigned int m; + uint32_t poly; + const int t = GF_T(bch); + + s = bch->ecc_bits; + + /* make sure extra bits in last ecc word are cleared */ + m = ((unsigned int)s) & 31; + if (m) + ecc[s/32] &= ~((1u << (32-m))-1); + memset(syn, 0, 2*t*sizeof(*syn)); + + /* compute v(a^j) for j=1 .. 2t-1 */ + do { + poly = *ecc++; + s -= 32; + while (poly) { + i = deg(poly); + for (j = 0; j < 2*t; j += 2) + syn[j] ^= a_pow(bch, (j+1)*(i+s)); + + poly ^= (1 << i); + } + } while (s > 0); + + /* v(a^(2j)) = v(a^j)^2 */ + for (j = 0; j < t; j++) + syn[2*j+1] = gf_sqr(bch, syn[j]); +} + +static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src) +{ + memcpy(dst, src, GF_POLY_SZ(src->deg)); +} + +static int compute_error_locator_polynomial(struct bch_control *bch, + const unsigned int *syn) +{ + const unsigned int t = GF_T(bch); + const unsigned int n = GF_N(bch); + unsigned int i, j, tmp, l, pd = 1, d = syn[0]; + struct gf_poly *elp = bch->elp; + struct gf_poly *pelp = bch->poly_2t[0]; + struct gf_poly *elp_copy = bch->poly_2t[1]; + int k, pp = -1; + + memset(pelp, 0, GF_POLY_SZ(2*t)); + memset(elp, 0, GF_POLY_SZ(2*t)); + + pelp->deg = 0; + pelp->c[0] = 1; + elp->deg = 0; + elp->c[0] = 1; + + /* use simplified binary Berlekamp-Massey algorithm */ + for (i = 0; (i < t) && (elp->deg <= t); i++) { + if (d) { + k = 2*i-pp; + gf_poly_copy(elp_copy, elp); + /* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */ + tmp = a_log(bch, d)+n-a_log(bch, pd); + for (j = 0; j <= pelp->deg; j++) { + if (pelp->c[j]) { + l = a_log(bch, pelp->c[j]); + elp->c[j+k] ^= a_pow(bch, tmp+l); + } + } + /* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */ + tmp = pelp->deg+k; + if (tmp > elp->deg) { + elp->deg = tmp; + gf_poly_copy(pelp, elp_copy); + pd = d; + pp = 2*i; + } + } + /* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */ + if (i < t-1) { + d = syn[2*i+2]; + for (j = 1; j <= elp->deg; j++) + d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]); + } + } + dbg("elp=%s\n", gf_poly_str(elp)); + return (elp->deg > t) ? -1 : (int)elp->deg; +} + +/* + * solve a m x m linear system in GF(2) with an expected number of solutions, + * and return the number of found solutions + */ +static int solve_linear_system(struct bch_control *bch, unsigned int *rows, + unsigned int *sol, int nsol) +{ + const int m = GF_M(bch); + unsigned int tmp, mask; + int rem, c, r, p, k, param[m]; + + k = 0; + mask = 1 << m; + + /* Gaussian elimination */ + for (c = 0; c < m; c++) { + rem = 0; + p = c-k; + /* find suitable row for elimination */ + for (r = p; r < m; r++) { + if (rows[r] & mask) { + if (r != p) { + tmp = rows[r]; + rows[r] = rows[p]; + rows[p] = tmp; + } + rem = r+1; + break; + } + } + if (rem) { + /* perform elimination on remaining rows */ + tmp = rows[p]; + for (r = rem; r < m; r++) { + if (rows[r] & mask) + rows[r] ^= tmp; + } + } else { + /* elimination not needed, store defective row index */ + param[k++] = c; + } + mask >>= 1; + } + /* rewrite system, inserting fake parameter rows */ + if (k > 0) { + p = k; + for (r = m-1; r >= 0; r--) { + if ((r > m-1-k) && rows[r]) + /* system has no solution */ + return 0; + + rows[r] = (p && (r == param[p-1])) ? + p--, 1u << (m-r) : rows[r-p]; + } + } + + if (nsol != (1 << k)) + /* unexpected number of solutions */ + return 0; + + for (p = 0; p < nsol; p++) { + /* set parameters for p-th solution */ + for (c = 0; c < k; c++) + rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1); + + /* compute unique solution */ + tmp = 0; + for (r = m-1; r >= 0; r--) { + mask = rows[r] & (tmp|1); + tmp |= parity(mask) << (m-r); + } + sol[p] = tmp >> 1; + } + return nsol; +} + +/* + * this function builds and solves a linear system for finding roots of a degree + * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m). + */ +static int find_affine4_roots(struct bch_control *bch, unsigned int a, + unsigned int b, unsigned int c, + unsigned int *roots) +{ + int i, j, k; + const int m = GF_M(bch); + unsigned int mask = 0xff, t, rows[16] = {0,}; + + j = a_log(bch, b); + k = a_log(bch, a); + rows[0] = c; + + /* buid linear system to solve X^4+aX^2+bX+c = 0 */ + for (i = 0; i < m; i++) { + rows[i+1] = bch->a_pow_tab[4*i]^ + (a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^ + (b ? bch->a_pow_tab[mod_s(bch, j)] : 0); + j++; + k += 2; + } + /* + * transpose 16x16 matrix before passing it to linear solver + * warning: this code assumes m < 16 + */ + for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) { + for (k = 0; k < 16; k = (k+j+1) & ~j) { + t = ((rows[k] >> j)^rows[k+j]) & mask; + rows[k] ^= (t << j); + rows[k+j] ^= t; + } + } + return solve_linear_system(bch, rows, roots, 4); +} + +/* + * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r)) + */ +static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly, + unsigned int *roots) +{ + int n = 0; + + if (poly->c[0]) + /* poly[X] = bX+c with c!=0, root=c/b */ + roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+ + bch->a_log_tab[poly->c[1]]); + return n; +} + +/* + * compute roots of a degree 2 polynomial over GF(2^m) + */ +static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly, + unsigned int *roots) +{ + int n = 0, i, l0, l1, l2; + unsigned int u, v, r; + + if (poly->c[0] && poly->c[1]) { + + l0 = bch->a_log_tab[poly->c[0]]; + l1 = bch->a_log_tab[poly->c[1]]; + l2 = bch->a_log_tab[poly->c[2]]; + + /* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */ + u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1)); + /* + * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi): + * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) = + * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u) + * i.e. r and r+1 are roots iff Tr(u)=0 + */ + r = 0; + v = u; + while (v) { + i = deg(v); + r ^= bch->xi_tab[i]; + v ^= (1 << i); + } + /* verify root */ + if ((gf_sqr(bch, r)^r) == u) { + /* reverse z=a/bX transformation and compute log(1/r) */ + roots[n++] = modulo(bch, 2*GF_N(bch)-l1- + bch->a_log_tab[r]+l2); + roots[n++] = modulo(bch, 2*GF_N(bch)-l1- + bch->a_log_tab[r^1]+l2); + } + } + return n; +} + +/* + * compute roots of a degree 3 polynomial over GF(2^m) + */ +static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly, + unsigned int *roots) +{ + int i, n = 0; + unsigned int a, b, c, a2, b2, c2, e3, tmp[4]; + + if (poly->c[0]) { + /* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */ + e3 = poly->c[3]; + c2 = gf_div(bch, poly->c[0], e3); + b2 = gf_div(bch, poly->c[1], e3); + a2 = gf_div(bch, poly->c[2], e3); + + /* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */ + c = gf_mul(bch, a2, c2); /* c = a2c2 */ + b = gf_mul(bch, a2, b2)^c2; /* b = a2b2 + c2 */ + a = gf_sqr(bch, a2)^b2; /* a = a2^2 + b2 */ + + /* find the 4 roots of this affine polynomial */ + if (find_affine4_roots(bch, a, b, c, tmp) == 4) { + /* remove a2 from final list of roots */ + for (i = 0; i < 4; i++) { + if (tmp[i] != a2) + roots[n++] = a_ilog(bch, tmp[i]); + } + } + } + return n; +} + +/* + * compute roots of a degree 4 polynomial over GF(2^m) + */ +static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly, + unsigned int *roots) +{ + int i, l, n = 0; + unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4; + + if (poly->c[0] == 0) + return 0; + + /* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */ + e4 = poly->c[4]; + d = gf_div(bch, poly->c[0], e4); + c = gf_div(bch, poly->c[1], e4); + b = gf_div(bch, poly->c[2], e4); + a = gf_div(bch, poly->c[3], e4); + + /* use Y=1/X transformation to get an affine polynomial */ + if (a) { + /* first, eliminate cX by using z=X+e with ae^2+c=0 */ + if (c) { + /* compute e such that e^2 = c/a */ + f = gf_div(bch, c, a); + l = a_log(bch, f); + l += (l & 1) ? GF_N(bch) : 0; + e = a_pow(bch, l/2); + /* + * use transformation z=X+e: + * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d + * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d + * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d + * z^4 + az^3 + b'z^2 + d' + */ + d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d; + b = gf_mul(bch, a, e)^b; + } + /* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */ + if (d == 0) + /* assume all roots have multiplicity 1 */ + return 0; + + c2 = gf_inv(bch, d); + b2 = gf_div(bch, a, d); + a2 = gf_div(bch, b, d); + } else { + /* polynomial is already affine */ + c2 = d; + b2 = c; + a2 = b; + } + /* find the 4 roots of this affine polynomial */ + if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) { + for (i = 0; i < 4; i++) { + /* post-process roots (reverse transformations) */ + f = a ? gf_inv(bch, roots[i]) : roots[i]; + roots[i] = a_ilog(bch, f^e); + } + n = 4; + } + return n; +} + +/* + * build monic, log-based representation of a polynomial + */ +static void gf_poly_logrep(struct bch_control *bch, + const struct gf_poly *a, int *rep) +{ + int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]); + + /* represent 0 values with -1; warning, rep[d] is not set to 1 */ + for (i = 0; i < d; i++) + rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1; +} + +/* + * compute polynomial Euclidean division remainder in GF(2^m)[X] + */ +static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a, + const struct gf_poly *b, int *rep) +{ + int la, p, m; + unsigned int i, j, *c = a->c; + const unsigned int d = b->deg; + + if (a->deg < d) + return; + + /* reuse or compute log representation of denominator */ + if (!rep) { + rep = bch->cache; + gf_poly_logrep(bch, b, rep); + } + + for (j = a->deg; j >= d; j--) { + if (c[j]) { + la = a_log(bch, c[j]); + p = j-d; + for (i = 0; i < d; i++, p++) { + m = rep[i]; + if (m >= 0) + c[p] ^= bch->a_pow_tab[mod_s(bch, + m+la)]; + } + } + } + a->deg = d-1; + while (!c[a->deg] && a->deg) + a->deg--; +} + +/* + * compute polynomial Euclidean division quotient in GF(2^m)[X] + */ +static void gf_poly_div(struct bch_control *bch, struct gf_poly *a, + const struct gf_poly *b, struct gf_poly *q) +{ + if (a->deg >= b->deg) { + q->deg = a->deg-b->deg; + /* compute a mod b (modifies a) */ + gf_poly_mod(bch, a, b, NULL); + /* quotient is stored in upper part of polynomial a */ + memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int)); + } else { + q->deg = 0; + q->c[0] = 0; + } +} + +/* + * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X] + */ +static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a, + struct gf_poly *b) +{ + struct gf_poly *tmp; + + dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b)); + + if (a->deg < b->deg) { + tmp = b; + b = a; + a = tmp; + } + + while (b->deg > 0) { + gf_poly_mod(bch, a, b, NULL); + tmp = b; + b = a; + a = tmp; + } + + dbg("%s\n", gf_poly_str(a)); + + return a; +} + +/* + * Given a polynomial f and an integer k, compute Tr(a^kX) mod f + * This is used in Berlekamp Trace algorithm for splitting polynomials + */ +static void compute_trace_bk_mod(struct bch_control *bch, int k, + const struct gf_poly *f, struct gf_poly *z, + struct gf_poly *out) +{ + const int m = GF_M(bch); + int i, j; + + /* z contains z^2j mod f */ + z->deg = 1; + z->c[0] = 0; + z->c[1] = bch->a_pow_tab[k]; + + out->deg = 0; + memset(out, 0, GF_POLY_SZ(f->deg)); + + /* compute f log representation only once */ + gf_poly_logrep(bch, f, bch->cache); + + for (i = 0; i < m; i++) { + /* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */ + for (j = z->deg; j >= 0; j--) { + out->c[j] ^= z->c[j]; + z->c[2*j] = gf_sqr(bch, z->c[j]); + z->c[2*j+1] = 0; + } + if (z->deg > out->deg) + out->deg = z->deg; + + if (i < m-1) { + z->deg *= 2; + /* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */ + gf_poly_mod(bch, z, f, bch->cache); + } + } + while (!out->c[out->deg] && out->deg) + out->deg--; + + dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out)); +} + +/* + * factor a polynomial using Berlekamp Trace algorithm (BTA) + */ +static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f, + struct gf_poly **g, struct gf_poly **h) +{ + struct gf_poly *f2 = bch->poly_2t[0]; + struct gf_poly *q = bch->poly_2t[1]; + struct gf_poly *tk = bch->poly_2t[2]; + struct gf_poly *z = bch->poly_2t[3]; + struct gf_poly *gcd; + + dbg("factoring %s...\n", gf_poly_str(f)); + + *g = f; + *h = NULL; + + /* tk = Tr(a^k.X) mod f */ + compute_trace_bk_mod(bch, k, f, z, tk); + + if (tk->deg > 0) { + /* compute g = gcd(f, tk) (destructive operation) */ + gf_poly_copy(f2, f); + gcd = gf_poly_gcd(bch, f2, tk); + if (gcd->deg < f->deg) { + /* compute h=f/gcd(f,tk); this will modify f and q */ + gf_poly_div(bch, f, gcd, q); + /* store g and h in-place (clobbering f) */ + *h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly; + gf_poly_copy(*g, gcd); + gf_poly_copy(*h, q); + } + } +} + +/* + * find roots of a polynomial, using BTZ algorithm; see the beginning of this + * file for details + */ +static int find_poly_roots(struct bch_control *bch, unsigned int k, + struct gf_poly *poly, unsigned int *roots) +{ + int cnt; + struct gf_poly *f1, *f2; + + switch (poly->deg) { + /* handle low degree polynomials with ad hoc techniques */ + case 1: + cnt = find_poly_deg1_roots(bch, poly, roots); + break; + case 2: + cnt = find_poly_deg2_roots(bch, poly, roots); + break; + case 3: + cnt = find_poly_deg3_roots(bch, poly, roots); + break; + case 4: + cnt = find_poly_deg4_roots(bch, poly, roots); + break; + default: + /* factor polynomial using Berlekamp Trace Algorithm (BTA) */ + cnt = 0; + if (poly->deg && (k <= GF_M(bch))) { + factor_polynomial(bch, k, poly, &f1, &f2); + if (f1) + cnt += find_poly_roots(bch, k+1, f1, roots); + if (f2) + cnt += find_poly_roots(bch, k+1, f2, roots+cnt); + } + break; + } + return cnt; +} + +#if defined(USE_CHIEN_SEARCH) +/* + * exhaustive root search (Chien) implementation - not used, included only for + * reference/comparison tests + */ +static int chien_search(struct bch_control *bch, unsigned int len, + struct gf_poly *p, unsigned int *roots) +{ + int m; + unsigned int i, j, syn, syn0, count = 0; + const unsigned int k = 8*len+bch->ecc_bits; + + /* use a log-based representation of polynomial */ + gf_poly_logrep(bch, p, bch->cache); + bch->cache[p->deg] = 0; + syn0 = gf_div(bch, p->c[0], p->c[p->deg]); + + for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) { + /* compute elp(a^i) */ + for (j = 1, syn = syn0; j <= p->deg; j++) { + m = bch->cache[j]; + if (m >= 0) + syn ^= a_pow(bch, m+j*i); + } + if (syn == 0) { + roots[count++] = GF_N(bch)-i; + if (count == p->deg) + break; + } + } + return (count == p->deg) ? count : 0; +} +#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc) +#endif /* USE_CHIEN_SEARCH */ + +/** + * decode_bch - decode received codeword and find bit error locations + * @bch: BCH control structure + * @data: received data, ignored if @calc_ecc is provided + * @len: data length in bytes, must always be provided + * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc + * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data + * @syn: hw computed syndrome data (if NULL, syndrome is calculated) + * @errloc: output array of error locations + * + * Returns: + * The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if + * invalid parameters were provided + * + * Depending on the available hw BCH support and the need to compute @calc_ecc + * separately (using encode_bch()), this function should be called with one of + * the following parameter configurations - + * + * by providing @data and @recv_ecc only: + * decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc) + * + * by providing @recv_ecc and @calc_ecc: + * decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc) + * + * by providing ecc = recv_ecc XOR calc_ecc: + * decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc) + * + * by providing syndrome results @syn: + * decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc) + * + * Once decode_bch() has successfully returned with a positive value, error + * locations returned in array @errloc should be interpreted as follows - + * + * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for + * data correction) + * + * if (errloc[n] < 8*len), then n-th error is located in data and can be + * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8); + * + * Note that this function does not perform any data correction by itself, it + * merely indicates error locations. + */ +int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len, + const uint8_t *recv_ecc, const uint8_t *calc_ecc, + const unsigned int *syn, unsigned int *errloc) +{ + const unsigned int ecc_words = BCH_ECC_WORDS(bch); + unsigned int nbits; + int i, err, nroots; + uint32_t sum; + + /* sanity check: make sure data length can be handled */ + if (8*len > (bch->n-bch->ecc_bits)) + return -EINVAL; + + /* if caller does not provide syndromes, compute them */ + if (!syn) { + if (!calc_ecc) { + /* compute received data ecc into an internal buffer */ + if (!data || !recv_ecc) + return -EINVAL; + encode_bch(bch, data, len, NULL); + } else { + /* load provided calculated ecc */ + load_ecc8(bch, bch->ecc_buf, calc_ecc); + } + /* load received ecc or assume it was XORed in calc_ecc */ + if (recv_ecc) { + load_ecc8(bch, bch->ecc_buf2, recv_ecc); + /* XOR received and calculated ecc */ + for (i = 0, sum = 0; i < (int)ecc_words; i++) { + bch->ecc_buf[i] ^= bch->ecc_buf2[i]; + sum |= bch->ecc_buf[i]; + } + if (!sum) + /* no error found */ + return 0; + } + compute_syndromes(bch, bch->ecc_buf, bch->syn); + syn = bch->syn; + } + + err = compute_error_locator_polynomial(bch, syn); + if (err > 0) { + nroots = find_poly_roots(bch, 1, bch->elp, errloc); + if (err != nroots) + err = -1; + } + if (err > 0) { + /* post-process raw error locations for easier correction */ + nbits = (len*8)+bch->ecc_bits; + for (i = 0; i < err; i++) { + if (errloc[i] >= nbits) { + err = -1; + break; + } + errloc[i] = nbits-1-errloc[i]; + errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7)); + } + } + return (err >= 0) ? err : -EBADMSG; +} + +/* + * generate Galois field lookup tables + */ +static int build_gf_tables(struct bch_control *bch, unsigned int poly) +{ + unsigned int i, x = 1; + const unsigned int k = 1 << deg(poly); + + /* primitive polynomial must be of degree m */ + if (k != (1u << GF_M(bch))) + return -1; + + for (i = 0; i < GF_N(bch); i++) { + bch->a_pow_tab[i] = x; + bch->a_log_tab[x] = i; + if (i && (x == 1)) + /* polynomial is not primitive (a^i=1 with 0<i<2^m-1) */ + return -1; + x <<= 1; + if (x & k) + x ^= poly; + } + bch->a_pow_tab[GF_N(bch)] = 1; + bch->a_log_tab[0] = 0; + + return 0; +} + +/* + * compute generator polynomial remainder tables for fast encoding + */ +static void build_mod8_tables(struct bch_control *bch, const uint32_t *g) +{ + int i, j, b, d; + uint32_t data, hi, lo, *tab; + const int l = BCH_ECC_WORDS(bch); + const int plen = DIV_ROUND_UP(bch->ecc_bits+1, 32); + const int ecclen = DIV_ROUND_UP(bch->ecc_bits, 32); + + memset(bch->mod8_tab, 0, 4*256*l*sizeof(*bch->mod8_tab)); + + for (i = 0; i < 256; i++) { + /* p(X)=i is a small polynomial of weight <= 8 */ + for (b = 0; b < 4; b++) { + /* we want to compute (p(X).X^(8*b+deg(g))) mod g(X) */ + tab = bch->mod8_tab + (b*256+i)*l; + data = i << (8*b); + while (data) { + d = deg(data); + /* subtract X^d.g(X) from p(X).X^(8*b+deg(g)) */ + data ^= g[0] >> (31-d); + for (j = 0; j < ecclen; j++) { + hi = (d < 31) ? g[j] << (d+1) : 0; + lo = (j+1 < plen) ? + g[j+1] >> (31-d) : 0; + tab[j] ^= hi|lo; + } + } + } + } +} + +/* + * build a base for factoring degree 2 polynomials + */ +static int build_deg2_base(struct bch_control *bch) +{ + const int m = GF_M(bch); + int i, j, r; + unsigned int sum, x, y, remaining, ak = 0, xi[m]; + + /* find k s.t. Tr(a^k) = 1 and 0 <= k < m */ + for (i = 0; i < m; i++) { + for (j = 0, sum = 0; j < m; j++) + sum ^= a_pow(bch, i*(1 << j)); + + if (sum) { + ak = bch->a_pow_tab[i]; + break; + } + } + /* find xi, i=0..m-1 such that xi^2+xi = a^i+Tr(a^i).a^k */ + remaining = m; + memset(xi, 0, sizeof(xi)); + + for (x = 0; (x <= GF_N(bch)) && remaining; x++) { + y = gf_sqr(bch, x)^x; + for (i = 0; i < 2; i++) { + r = a_log(bch, y); + if (y && (r < m) && !xi[r]) { + bch->xi_tab[r] = x; + xi[r] = 1; + remaining--; + dbg("x%d = %x\n", r, x); + break; + } + y ^= ak; + } + } + /* should not happen but check anyway */ + return remaining ? -1 : 0; +} + +static void *bch_alloc(size_t size, int *err) +{ + void *ptr; + + ptr = kmalloc(size, GFP_KERNEL); + if (ptr == NULL) + *err = 1; + return ptr; +} + +/* + * compute generator polynomial for given (m,t) parameters. + */ +static uint32_t *compute_generator_polynomial(struct bch_control *bch) +{ + const unsigned int m = GF_M(bch); + const unsigned int t = GF_T(bch); + int n, err = 0; + unsigned int i, j, nbits, r, word, *roots; + struct gf_poly *g; + uint32_t *genpoly; + + g = bch_alloc(GF_POLY_SZ(m*t), &err); + roots = bch_alloc((bch->n+1)*sizeof(*roots), &err); + genpoly = bch_alloc(DIV_ROUND_UP(m*t+1, 32)*sizeof(*genpoly), &err); + + if (err) { + kfree(genpoly); + genpoly = NULL; + goto finish; + } + + /* enumerate all roots of g(X) */ + memset(roots , 0, (bch->n+1)*sizeof(*roots)); + for (i = 0; i < t; i++) { + for (j = 0, r = 2*i+1; j < m; j++) { + roots[r] = 1; + r = mod_s(bch, 2*r); + } + } + /* build generator polynomial g(X) */ + g->deg = 0; + g->c[0] = 1; + for (i = 0; i < GF_N(bch); i++) { + if (roots[i]) { + /* multiply g(X) by (X+root) */ + r = bch->a_pow_tab[i]; + g->c[g->deg+1] = 1; + for (j = g->deg; j > 0; j--) + g->c[j] = gf_mul(bch, g->c[j], r)^g->c[j-1]; + + g->c[0] = gf_mul(bch, g->c[0], r); + g->deg++; + } + } + /* store left-justified binary representation of g(X) */ + n = g->deg+1; + i = 0; + + while (n > 0) { + nbits = (n > 32) ? 32 : n; + for (j = 0, word = 0; j < nbits; j++) { + if (g->c[n-1-j]) + word |= 1u << (31-j); + } + genpoly[i++] = word; + n -= nbits; + } + bch->ecc_bits = g->deg; + +finish: + kfree(g); + kfree(roots); + + return genpoly; +} + +/** + * init_bch - initialize a BCH encoder/decoder + * @m: Galois field order, should be in the range 5-15 + * @t: maximum error correction capability, in bits + * @prim_poly: user-provided primitive polynomial (or 0 to use default) + * + * Returns: + * a newly allocated BCH control structure if successful, NULL otherwise + * + * This initialization can take some time, as lookup tables are built for fast + * encoding/decoding; make sure not to call this function from a time critical + * path. Usually, init_bch() should be called on module/driver init and + * free_bch() should be called to release memory on exit. + * + * You may provide your own primitive polynomial of degree @m in argument + * @prim_poly, or let init_bch() use its default polynomial. + * + * Once init_bch() has successfully returned a pointer to a newly allocated + * BCH control structure, ecc length in bytes is given by member @ecc_bytes of + * the structure. + */ +struct bch_control *init_bch(int m, int t, unsigned int prim_poly) +{ + int err = 0; + unsigned int i, words; + uint32_t *genpoly; + struct bch_control *bch = NULL; + + const int min_m = 5; + const int max_m = 15; + + /* default primitive polynomials */ + static const unsigned int prim_poly_tab[] = { + 0x25, 0x43, 0x83, 0x11d, 0x211, 0x409, 0x805, 0x1053, 0x201b, + 0x402b, 0x8003, + }; + +#if defined(CONFIG_BCH_CONST_PARAMS) + if ((m != (CONFIG_BCH_CONST_M)) || (t != (CONFIG_BCH_CONST_T))) { + printk(KERN_ERR "bch encoder/decoder was configured to support " + "parameters m=%d, t=%d only!\n", + CONFIG_BCH_CONST_M, CONFIG_BCH_CONST_T); + goto fail; + } +#endif + if ((m < min_m) || (m > max_m)) + /* + * values of m greater than 15 are not currently supported; + * supporting m > 15 would require changing table base type + * (uint16_t) and a small patch in matrix transposition + */ + goto fail; + + /* sanity checks */ + if ((t < 1) || (m*t >= ((1 << m)-1))) + /* invalid t value */ + goto fail; + + /* select a primitive polynomial for generating GF(2^m) */ + if (prim_poly == 0) + prim_poly = prim_poly_tab[m-min_m]; + + bch = kzalloc(sizeof(*bch), GFP_KERNEL); + if (bch == NULL) + goto fail; + + bch->m = m; + bch->t = t; + bch->n = (1 << m)-1; + words = DIV_ROUND_UP(m*t, 32); + bch->ecc_bytes = DIV_ROUND_UP(m*t, 8); + bch->a_pow_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_pow_tab), &err); + bch->a_log_tab = bch_alloc((1+bch->n)*sizeof(*bch->a_log_tab), &err); + bch->mod8_tab = bch_alloc(words*1024*sizeof(*bch->mod8_tab), &err); + bch->ecc_buf = bch_alloc(words*sizeof(*bch->ecc_buf), &err); + bch->ecc_buf2 = bch_alloc(words*sizeof(*bch->ecc_buf2), &err); + bch->xi_tab = bch_alloc(m*sizeof(*bch->xi_tab), &err); + bch->syn = bch_alloc(2*t*sizeof(*bch->syn), &err); + bch->cache = bch_alloc(2*t*sizeof(*bch->cache), &err); + bch->elp = bch_alloc((t+1)*sizeof(struct gf_poly_deg1), &err); + + for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) + bch->poly_2t[i] = bch_alloc(GF_POLY_SZ(2*t), &err); + + if (err) + goto fail; + + err = build_gf_tables(bch, prim_poly); + if (err) + goto fail; + + /* use generator polynomial for computing encoding tables */ + genpoly = compute_generator_polynomial(bch); + if (genpoly == NULL) + goto fail; + + build_mod8_tables(bch, genpoly); + kfree(genpoly); + + err = build_deg2_base(bch); + if (err) + goto fail; + + return bch; + +fail: + free_bch(bch); + return NULL; +} + +/** + * free_bch - free the BCH control structure + * @bch: BCH control structure to release + */ +void free_bch(struct bch_control *bch) +{ + unsigned int i; + + if (bch) { + kfree(bch->a_pow_tab); + kfree(bch->a_log_tab); + kfree(bch->mod8_tab); + kfree(bch->ecc_buf); + kfree(bch->ecc_buf2); + kfree(bch->xi_tab); + kfree(bch->syn); + kfree(bch->cache); + kfree(bch->elp); + + for (i = 0; i < ARRAY_SIZE(bch->poly_2t); i++) + kfree(bch->poly_2t[i]); + + kfree(bch); + } +} |