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(I'm so sorry!) Linux kernel mirror (for testing) git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux.git
kernel os linux
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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 bch_init 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 bch_encode to compute and store ecc parity bytes to a given buffer. * Call bch_decode to detect and locate errors in received data. * * On systems supporting hw BCH features, intermediate results may be provided * to bch_decode in order to skip certain steps. See bch_decode() 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 <linux/kernel.h>#include <linux/errno.h>#include <linux/init.h>#include <linux/module.h>#include <linux/slab.h>#include <linux/bitops.h>#include <linux/bitrev.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)#define BCH_MAX_M (CONFIG_BCH_CONST_M)#define BCH_MAX_T (CONFIG_BCH_CONST_T)#else#define GF_M(_p) ((_p)->m)#define GF_T(_p) ((_p)->t)#define GF_N(_p) ((_p)->n)#define BCH_MAX_M 15 /* 2KB */#define BCH_MAX_T 64 /* 64 bit correction */#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)
#define BCH_ECC_MAX_WORDS DIV_ROUND_UP(BCH_MAX_M * BCH_MAX_T, 32)
#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[]; /* 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];};
static u8 swap_bits(struct bch_control *bch, u8 in){ if (!bch->swap_bits) return in;
return bitrev8(in);}
/* * same as bch_encode(), but process input data one byte at a time */static void bch_encode_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--) { u8 tmp = swap_bits(bch, *data++);
p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(tmp)) & 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] = ((u32)swap_bits(bch, src[0]) << 24) | ((u32)swap_bits(bch, src[1]) << 16) | ((u32)swap_bits(bch, src[2]) << 8) | swap_bits(bch, src[3]);
memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords); dst[nwords] = ((u32)swap_bits(bch, pad[0]) << 24) | ((u32)swap_bits(bch, pad[1]) << 16) | ((u32)swap_bits(bch, pad[2]) << 8) | swap_bits(bch, 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++ = swap_bits(bch, src[i] >> 24); *dst++ = swap_bits(bch, src[i] >> 16); *dst++ = swap_bits(bch, src[i] >> 8); *dst++ = swap_bits(bch, src[i]); } pad[0] = swap_bits(bch, src[nwords] >> 24); pad[1] = swap_bits(bch, src[nwords] >> 16); pad[2] = swap_bits(bch, src[nwords] >> 8); pad[3] = swap_bits(bch, src[nwords]); memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);}
/** * bch_encode - 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 bch_encode(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[BCH_ECC_MAX_WORDS]; const size_t r_bytes = BCH_ECC_WORDS(bch) * sizeof(*r); 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 (WARN_ON(r_bytes > sizeof(r))) return;
if (ecc) { /* load ecc parity bytes into internal 32-bit buffer */ load_ecc8(bch, bch->ecc_buf, ecc); } else { memset(bch->ecc_buf, 0, r_bytes); }
/* process first unaligned data bytes */ m = ((unsigned long)data) & 3; if (m) { mlen = (len < (4-m)) ? len : 4-m; bch_encode_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, r_bytes);
/* * 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 = cpu_to_be32(*pdata++); if (bch->swap_bits) w = (u32)swap_bits(bch, w) | ((u32)swap_bits(bch, w >> 8) << 8) | ((u32)swap_bits(bch, w >> 16) << 16) | ((u32)swap_bits(bch, w >> 24) << 24); w ^= r[0]; 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, r_bytes);
/* process last unaligned bytes */ if (len) bch_encode_unaligned(bch, data, len, bch->ecc_buf);
/* store ecc parity bytes into original parity buffer */ if (ecc) store_ecc8(bch, ecc, bch->ecc_buf);}EXPORT_SYMBOL_GPL(bch_encode);
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 ^= (1u << 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[BCH_MAX_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) swap(rows[r], rows[p]); 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;
/* build 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 ^= (1u << 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){ dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
if (a->deg < b->deg) swap(a, b);
while (b->deg > 0) { gf_poly_mod(bch, a, b, NULL); swap(a, b); }
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 */
/** * bch_decode - 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 bch_encode()), this function should be called with one of * the following parameter configurations - * * by providing @data and @recv_ecc only: * bch_decode(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc) * * by providing @recv_ecc and @calc_ecc: * bch_decode(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc) * * by providing ecc = recv_ecc XOR calc_ecc: * bch_decode(@bch, NULL, @len, NULL, ecc, NULL, @errloc) * * by providing syndrome results @syn: * bch_decode(@bch, NULL, @len, NULL, NULL, @syn, @errloc) * * Once bch_decode() 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 bch_decode(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; bch_encode(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]; if (!bch->swap_bits) errloc[i] = (errloc[i] & ~7) | (7-(errloc[i] & 7)); } } return (err >= 0) ? err : -EBADMSG;}EXPORT_SYMBOL_GPL(bch_decode);
/* * 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 = (unsigned int)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[BCH_MAX_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;}
/** * bch_init - 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) * @swap_bits: swap bits within data and syndrome bytes * * 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, bch_init() should be called on module/driver init and * bch_free() should be called to release memory on exit. * * You may provide your own primitive polynomial of degree @m in argument * @prim_poly, or let bch_init() use its default polynomial. * * Once bch_init() 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 *bch_init(int m, int t, unsigned int prim_poly, bool swap_bits){ int err = 0; unsigned int i, words; uint32_t *genpoly; struct bch_control *bch = NULL;
const int min_m = 5;
/* 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 > BCH_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;
if (t > BCH_MAX_T) /* * we can support larger than 64 bits if necessary, at the * cost of higher stack usage. */ 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_obj(*bch); 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); bch->swap_bits = swap_bits;
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: bch_free(bch); return NULL;}EXPORT_SYMBOL_GPL(bch_init);
/** * bch_free - free the BCH control structure * @bch: BCH control structure to release */void bch_free(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); }}EXPORT_SYMBOL_GPL(bch_free);
MODULE_LICENSE("GPL");MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");MODULE_DESCRIPTION("Binary BCH encoder/decoder");