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@@ -0,0 +1,1358 @@
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+/*
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+ * Generic binary BCH encoding/decoding library
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+ *
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+ * This program is free software; you can redistribute it and/or modify it
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+ * under the terms of the GNU General Public License version 2 as published by
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+ * the Free Software Foundation.
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+ *
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+ * This program is distributed in the hope that it will be useful, but WITHOUT
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+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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+ * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
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+ * more details.
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+ *
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+ * You should have received a copy of the GNU General Public License along with
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+ * this program; if not, write to the Free Software Foundation, Inc., 51
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+ * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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+ *
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+ * Copyright © 2011 Parrot S.A.
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+ *
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+ * Author: Ivan Djelic <ivan.djelic@parrot.com>
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+ *
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+ * Description:
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+ *
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+ * This library provides runtime configurable encoding/decoding of binary
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+ * Bose-Chaudhuri-Hocquenghem (BCH) codes.
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+ *
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+ * Call init_bch to get a pointer to a newly allocated bch_control structure for
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+ * the given m (Galois field order), t (error correction capability) and
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+ * (optional) primitive polynomial parameters.
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+ *
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+ * Call encode_bch to compute and store ecc parity bytes to a given buffer.
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+ * Call decode_bch to detect and locate errors in received data.
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+ *
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+ * On systems supporting hw BCH features, intermediate results may be provided
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+ * to decode_bch in order to skip certain steps. See decode_bch() documentation
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+ * for details.
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+ *
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+ * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
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+ * parameters m and t; thus allowing extra compiler optimizations and providing
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+ * better (up to 2x) encoding performance. Using this option makes sense when
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+ * (m,t) are fixed and known in advance, e.g. when using BCH error correction
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+ * on a particular NAND flash device.
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+ *
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+ * Algorithmic details:
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+ *
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+ * Encoding is performed by processing 32 input bits in parallel, using 4
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+ * remainder lookup tables.
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+ *
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+ * The final stage of decoding involves the following internal steps:
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+ * a. Syndrome computation
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+ * b. Error locator polynomial computation using Berlekamp-Massey algorithm
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+ * c. Error locator root finding (by far the most expensive step)
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+ *
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+ * In this implementation, step c is not performed using the usual Chien search.
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+ * Instead, an alternative approach described in [1] is used. It consists in
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+ * factoring the error locator polynomial using the Berlekamp Trace algorithm
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+ * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
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+ * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
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+ * much better performance than Chien search for usual (m,t) values (typically
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+ * m >= 13, t < 32, see [1]).
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+ *
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+ * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
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+ * of characteristic 2, in: Western European Workshop on Research in Cryptology
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+ * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
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+ * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
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+ * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
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+ */
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+
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+#include <common.h>
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+#include <ubi_uboot.h>
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+
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+#include <linux/bitops.h>
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+#include <asm/byteorder.h>
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+#include <linux/bch.h>
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+
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+#if defined(CONFIG_BCH_CONST_PARAMS)
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+#define GF_M(_p) (CONFIG_BCH_CONST_M)
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+#define GF_T(_p) (CONFIG_BCH_CONST_T)
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+#define GF_N(_p) ((1 << (CONFIG_BCH_CONST_M))-1)
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+#else
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+#define GF_M(_p) ((_p)->m)
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+#define GF_T(_p) ((_p)->t)
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+#define GF_N(_p) ((_p)->n)
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+#endif
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+
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+#define BCH_ECC_WORDS(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
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+#define BCH_ECC_BYTES(_p) DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
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+
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+#ifndef dbg
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+#define dbg(_fmt, args...) do {} while (0)
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+#endif
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+
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+/*
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+ * represent a polynomial over GF(2^m)
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+ */
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+struct gf_poly {
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+ unsigned int deg; /* polynomial degree */
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+ unsigned int c[0]; /* polynomial terms */
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+};
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+
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+/* given its degree, compute a polynomial size in bytes */
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+#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
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+
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+/* polynomial of degree 1 */
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+struct gf_poly_deg1 {
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+ struct gf_poly poly;
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+ unsigned int c[2];
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+};
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+
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+/*
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+ * same as encode_bch(), but process input data one byte at a time
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+ */
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+static void encode_bch_unaligned(struct bch_control *bch,
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+ const unsigned char *data, unsigned int len,
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+ uint32_t *ecc)
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+{
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+ int i;
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+ const uint32_t *p;
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+ const int l = BCH_ECC_WORDS(bch)-1;
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+
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+ while (len--) {
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+ p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
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+
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+ for (i = 0; i < l; i++)
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+ ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
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+
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+ ecc[l] = (ecc[l] << 8)^(*p);
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+ }
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+}
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+
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+/*
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+ * convert ecc bytes to aligned, zero-padded 32-bit ecc words
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+ */
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+static void load_ecc8(struct bch_control *bch, uint32_t *dst,
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+ const uint8_t *src)
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+{
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+ uint8_t pad[4] = {0, 0, 0, 0};
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+ unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
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+
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+ for (i = 0; i < nwords; i++, src += 4)
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+ dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
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+
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+ memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
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+ dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
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+}
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+
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+/*
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+ * convert 32-bit ecc words to ecc bytes
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+ */
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+static void store_ecc8(struct bch_control *bch, uint8_t *dst,
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+ const uint32_t *src)
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+{
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+ uint8_t pad[4];
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+ unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
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+
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+ for (i = 0; i < nwords; i++) {
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+ *dst++ = (src[i] >> 24);
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+ *dst++ = (src[i] >> 16) & 0xff;
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+ *dst++ = (src[i] >> 8) & 0xff;
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+ *dst++ = (src[i] >> 0) & 0xff;
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+ }
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+ pad[0] = (src[nwords] >> 24);
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+ pad[1] = (src[nwords] >> 16) & 0xff;
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+ pad[2] = (src[nwords] >> 8) & 0xff;
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+ pad[3] = (src[nwords] >> 0) & 0xff;
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+ memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
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+}
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+
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+/**
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+ * encode_bch - calculate BCH ecc parity of data
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+ * @bch: BCH control structure
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+ * @data: data to encode
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+ * @len: data length in bytes
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+ * @ecc: ecc parity data, must be initialized by caller
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+ *
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+ * The @ecc parity array is used both as input and output parameter, in order to
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+ * allow incremental computations. It should be of the size indicated by member
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+ * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
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+ *
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+ * The exact number of computed ecc parity bits is given by member @ecc_bits of
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+ * @bch; it may be less than m*t for large values of t.
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+ */
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+void encode_bch(struct bch_control *bch, const uint8_t *data,
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+ unsigned int len, uint8_t *ecc)
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+{
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+ const unsigned int l = BCH_ECC_WORDS(bch)-1;
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+ unsigned int i, mlen;
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+ unsigned long m;
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+ uint32_t w, r[l+1];
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+ const uint32_t * const tab0 = bch->mod8_tab;
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+ const uint32_t * const tab1 = tab0 + 256*(l+1);
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+ const uint32_t * const tab2 = tab1 + 256*(l+1);
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+ const uint32_t * const tab3 = tab2 + 256*(l+1);
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+ const uint32_t *pdata, *p0, *p1, *p2, *p3;
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+
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+ if (ecc) {
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+ /* load ecc parity bytes into internal 32-bit buffer */
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+ load_ecc8(bch, bch->ecc_buf, ecc);
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+ } else {
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+ memset(bch->ecc_buf, 0, sizeof(r));
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+ }
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+
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+ /* process first unaligned data bytes */
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+ m = ((unsigned long)data) & 3;
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+ if (m) {
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+ mlen = (len < (4-m)) ? len : 4-m;
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+ encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
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+ data += mlen;
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+ len -= mlen;
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+ }
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+
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+ /* process 32-bit aligned data words */
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+ pdata = (uint32_t *)data;
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+ mlen = len/4;
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+ data += 4*mlen;
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+ len -= 4*mlen;
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+ memcpy(r, bch->ecc_buf, sizeof(r));
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+
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+ /*
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+ * split each 32-bit word into 4 polynomials of weight 8 as follows:
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+ *
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+ * 31 ...24 23 ...16 15 ... 8 7 ... 0
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+ * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt
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+ * tttttttt mod g = r0 (precomputed)
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+ * zzzzzzzz 00000000 mod g = r1 (precomputed)
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+ * yyyyyyyy 00000000 00000000 mod g = r2 (precomputed)
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+ * xxxxxxxx 00000000 00000000 00000000 mod g = r3 (precomputed)
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+ * xxxxxxxx yyyyyyyy zzzzzzzz tttttttt mod g = r0^r1^r2^r3
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+ */
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+ while (mlen--) {
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+ /* input data is read in big-endian format */
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+ w = r[0]^cpu_to_be32(*pdata++);
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+ p0 = tab0 + (l+1)*((w >> 0) & 0xff);
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+ p1 = tab1 + (l+1)*((w >> 8) & 0xff);
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+ p2 = tab2 + (l+1)*((w >> 16) & 0xff);
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+ p3 = tab3 + (l+1)*((w >> 24) & 0xff);
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+
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+ for (i = 0; i < l; i++)
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+ r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
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+
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+ r[l] = p0[l]^p1[l]^p2[l]^p3[l];
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+ }
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+ memcpy(bch->ecc_buf, r, sizeof(r));
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+
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+ /* process last unaligned bytes */
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+ if (len)
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+ encode_bch_unaligned(bch, data, len, bch->ecc_buf);
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+
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+ /* store ecc parity bytes into original parity buffer */
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+ if (ecc)
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+ store_ecc8(bch, ecc, bch->ecc_buf);
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+}
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+
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+static inline int modulo(struct bch_control *bch, unsigned int v)
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+{
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+ const unsigned int n = GF_N(bch);
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+ while (v >= n) {
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+ v -= n;
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+ v = (v & n) + (v >> GF_M(bch));
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+ }
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+ return v;
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+}
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+
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+/*
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+ * shorter and faster modulo function, only works when v < 2N.
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+ */
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+static inline int mod_s(struct bch_control *bch, unsigned int v)
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+{
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+ const unsigned int n = GF_N(bch);
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+ return (v < n) ? v : v-n;
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+}
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+
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+static inline int deg(unsigned int poly)
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+{
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+ /* polynomial degree is the most-significant bit index */
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+ return fls(poly)-1;
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+}
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+
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+static inline int parity(unsigned int x)
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+{
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+ /*
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+ * public domain code snippet, lifted from
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+ * http://www-graphics.stanford.edu/~seander/bithacks.html
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+ */
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+ x ^= x >> 1;
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+ x ^= x >> 2;
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+ x = (x & 0x11111111U) * 0x11111111U;
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+ return (x >> 28) & 1;
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+}
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+
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+/* Galois field basic operations: multiply, divide, inverse, etc. */
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+
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+static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
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+ unsigned int b)
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+{
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+ return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
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+ bch->a_log_tab[b])] : 0;
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+}
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+
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+static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
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+{
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+ return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
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+}
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+
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+static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
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+ unsigned int b)
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+{
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+ return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
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+ GF_N(bch)-bch->a_log_tab[b])] : 0;
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+}
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+
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+static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
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+{
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+ return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
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+}
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+
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+static inline unsigned int a_pow(struct bch_control *bch, int i)
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+{
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+ return bch->a_pow_tab[modulo(bch, i)];
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+}
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+
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+static inline int a_log(struct bch_control *bch, unsigned int x)
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+{
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+ return bch->a_log_tab[x];
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+}
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+
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+static inline int a_ilog(struct bch_control *bch, unsigned int x)
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+{
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+ return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
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+}
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+
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+/*
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+ * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
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+ */
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+static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
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+ unsigned int *syn)
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+{
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+ int i, j, s;
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+ unsigned int m;
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+ uint32_t poly;
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+ const int t = GF_T(bch);
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+
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+ s = bch->ecc_bits;
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+
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+ /* make sure extra bits in last ecc word are cleared */
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+ m = ((unsigned int)s) & 31;
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+ if (m)
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+ ecc[s/32] &= ~((1u << (32-m))-1);
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+ memset(syn, 0, 2*t*sizeof(*syn));
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+
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+ /* compute v(a^j) for j=1 .. 2t-1 */
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+ do {
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+ poly = *ecc++;
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+ s -= 32;
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+ while (poly) {
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+ i = deg(poly);
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+ for (j = 0; j < 2*t; j += 2)
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+ syn[j] ^= a_pow(bch, (j+1)*(i+s));
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+
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+ poly ^= (1 << i);
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+ }
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+ } while (s > 0);
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+
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+ /* v(a^(2j)) = v(a^j)^2 */
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+ for (j = 0; j < t; j++)
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+ syn[2*j+1] = gf_sqr(bch, syn[j]);
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+}
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+
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+static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
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+{
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+ memcpy(dst, src, GF_POLY_SZ(src->deg));
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+}
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+
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+static int compute_error_locator_polynomial(struct bch_control *bch,
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+ const unsigned int *syn)
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|
+{
|
|
|
+ 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);
|
|
|
+ }
|
|
|
+}
|
Christian Hitz