path: root/lib/bch.c

/*
 * 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 <linux/kernel.h>
#include <linux/errno.h>
#include <linux/init.h>
#include <linux/module.h>
#include <linux/slab.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 =