[PATCH V2 1/3] lib: add BCH encoding/decoding

[Robert Jarzmik <robert.jarzmik@free.fr>]

As flash memories need BCH correcting codes, add the BCH
library, taken from the linux kernel.

Signed-off-by: Robert Jarzmik <robert.jarzmik@free.fr>
---
 include/linux/bch.h |   79 +++
 lib/Kconfig         |    4 +
 lib/Makefile        |    1 +
 lib/bch.c           | 1366 +++++++++++++++++++++++++++++++++++++++++++++++++++
 4 files changed, 1450 insertions(+), 0 deletions(-)
 create mode 100644 include/linux/bch.h
 create mode 100644 lib/bch.c

diff --git a/include/linux/bch.h b/include/linux/bch.h
new file mode 100644
index 0000000..295b4ef
--- /dev/null
+++ b/include/linux/bch.h
@@ -0,0 +1,79 @@
+/*
+ * 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.
+*/
+#ifndef _BCH_H
+#define _BCH_H
+
+#include <linux/types.h>
+
+/**
+ * struct bch_control - BCH control structure
+ * @m:          Galois field order
+ * @n:          maximum codeword size in bits (= 2^m-1)
+ * @t:          error correction capability in bits
+ * @ecc_bits:   ecc exact size in bits, i.e. generator polynomial degree (<=m*t)
+ * @ecc_bytes:  ecc max size (m*t bits) in bytes
+ * @a_pow_tab:  Galois field GF(2^m) exponentiation lookup table
+ * @a_log_tab:  Galois field GF(2^m) log lookup table
+ * @mod8_tab:   remainder generator polynomial lookup tables
+ * @ecc_buf:    ecc parity words buffer
+ * @ecc_buf2:   ecc parity words buffer
+ * @xi_tab:     GF(2^m) base for solving degree 2 polynomial roots
+ * @syn:        syndrome buffer
+ * @cache:      log-based polynomial representation buffer
+ * @elp:        error locator polynomial
+ * @poly_2t:    temporary polynomials of degree 2t
+ */
+struct bch_control {
+	unsigned int    m;
+	unsigned int    n;
+	unsigned int    t;
+	unsigned int    ecc_bits;
+	unsigned int    ecc_bytes;
+/* private: */
+	uint16_t       *a_pow_tab;
+	uint16_t       *a_log_tab;
+	uint32_t       *mod8_tab;
+	uint32_t       *ecc_buf;
+	uint32_t       *ecc_buf2;
+	unsigned int   *xi_tab;
+	unsigned int   *syn;
+	int            *cache;
+	struct gf_poly *elp;
+	struct gf_poly *poly_2t[4];
+};
+
+struct bch_control *init_bch(int m, int t, unsigned int prim_poly);
+
+void free_bch(struct bch_control *bch);
+
+void encode_bch(struct bch_control *bch, const uint8_t *data,
+		unsigned int len, uint8_t *ecc);
+
+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);
+
+#endif /* _BCH_H */
diff --git a/lib/Kconfig b/lib/Kconfig
index e16dd35..83ac1ac 100644
--- a/lib/Kconfig
+++ b/lib/Kconfig
@@ -19,4 +19,8 @@ config FDT
 config OFTREE
 	select FDT
 	bool
+
+config BCH
+       bool
+
 endmenu
diff --git a/lib/Makefile b/lib/Makefile
index ae76b4c..04c5487 100644
--- a/lib/Makefile
+++ b/lib/Makefile
@@ -31,3 +31,4 @@ obj-$(CONFIG_LZO_DECOMPRESS)		+= decompress_unlzo.o
 obj-$(CONFIG_PROCESS_ESCAPE_SEQUENCE)	+= process_escape_sequence.o
 obj-$(CONFIG_FDT)	+= fdt/
 obj-y			+= uncompress.o
+obj-$(CONFIG_BCH)	+= bch.o
diff --git a/lib/bch.c b/lib/bch.c
new file mode 100644
index 0000000..5797c3f
--- /dev/null
+++ b/lib/bch.c
@@ -0,0 +1,1366 @@
+/*
+ * 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.
+ *
+ * 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.
+ *
+ * Taken from the linux kernel.
+ */
+
+#include <common.h>
+#include <errno.h>
+#include <init.h>
+#include <malloc.h>
+#include <linux/kernel.h>
+#include <linux/bitops.h>
+#include <asm/byteorder.h>
+#include <linux/bch.h>
+
+#if defined(CONFIG_BCH_CONST_PARAMS)
+#define GF_M(_p)               (CONFIG_BCH_CONST_M)
+#define GF_T(_p)               (CONFIG_BCH_CONST_T)
+#define GF_N(_p)               ((1 << (CONFIG_BCH_CONST_M))-1)
+#else
+#define GF_M(_p)               ((_p)->m)
+#define GF_T(_p)               ((_p)->t)
+#define GF_N(_p)               ((_p)->n)
+#endif
+
+#define BCH_ECC_WORDS(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
+#define BCH_ECC_BYTES(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
+
+#ifndef dbg
+#define dbg(_fmt, args...)     do {} while (0)
+#endif
+
+/*
+ * represent a polynomial over GF(2^m)
+ */
+struct gf_poly {
+	unsigned int deg;    /* polynomial degree */
+	unsigned int c[0];   /* polynomial terms */
+};
+
+/* given its degree, compute a polynomial size in bytes */
+#define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
+
+/* polynomial of degree 1 */
+struct gf_poly_deg1 {
+	struct gf_poly poly;
+	unsigned int   c[2];
+};
+
+/*
+ * same as encode_bch(), but process input data one byte at a time
+ */
+static void encode_bch_unaligned(struct bch_control *bch,
+				 const unsigned char *data, unsigned int len,
+				 uint32_t *ecc)
+{
+	int i;
+	const uint32_t *p;
+	const int l = BCH_ECC_WORDS(bch)-1;
+
+	while (len--) {
+		p = bch->mod8_tab + (l+1)*(((ecc[0] >> 24)^(*data++)) & 0xff);
+
+		for (i = 0; i < l; i++)
+			ecc[i] = ((ecc[i] << 8)|(ecc[i+1] >> 24))^(*p++);
+
+		ecc[l] = (ecc[l] << 8)^(*p);
+	}
+}
+
+/*
+ * convert ecc bytes to aligned, zero-padded 32-bit ecc words
+ */
+static void load_ecc8(struct bch_control *bch, uint32_t *dst,
+		      const uint8_t *src)
+{
+	uint8_t pad[4] = {0, 0, 0, 0};
+	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
+
+	for (i = 0; i < nwords; i++, src += 4)
+		dst[i] = (src[0] << 24)|(src[1] << 16)|(src[2] << 8)|src[3];
+
+	memcpy(pad, src, BCH_ECC_BYTES(bch)-4*nwords);
+	dst[nwords] = (pad[0] << 24)|(pad[1] << 16)|(pad[2] << 8)|pad[3];
+}
+
+/*
+ * convert 32-bit ecc words to ecc bytes
+ */
+static void store_ecc8(struct bch_control *bch, uint8_t *dst,
+		       const uint32_t *src)
+{
+	uint8_t pad[4];
+	unsigned int i, nwords = BCH_ECC_WORDS(bch)-1;
+
+	for (i = 0; i < nwords; i++) {
+		*dst++ = (src[i] >> 24);
+		*dst++ = (src[i] >> 16) & 0xff;
+		*dst++ = (src[i] >>  8) & 0xff;
+		*dst++ = (src[i] >>  0) & 0xff;
+	}
+	pad[0] = (src[nwords] >> 24);
+	pad[1] = (src[nwords] >> 16) & 0xff;
+	pad[2] = (src[nwords] >>  8) & 0xff;
+	pad[3] = (src[nwords] >>  0) & 0xff;
+	memcpy(dst, pad, BCH_ECC_BYTES(bch)-4*nwords);
+}
+
+/**
+ * encode_bch - calculate BCH ecc parity of data
+ * @bch:   BCH control structure
+ * @data:  data to encode
+ * @len:   data length in bytes
+ * @ecc:   ecc parity data, must be initialized by caller
+ *
+ * The @ecc parity array is used both as input and output parameter, in order to
+ * allow incremental computations. It should be of the size indicated by member
+ * @ecc_bytes of @bch, and should be initialized to 0 before the first call.
+ *
+ * The exact number of computed ecc parity bits is given by member @ecc_bits of
+ * @bch; it may be less than m*t for large values of t.
+ */
+void encode_bch(struct bch_control *bch, const uint8_t *data,
+		unsigned int len, uint8_t *ecc)
+{
+	const unsigned int l = BCH_ECC_WORDS(bch)-1;
+	unsigned int i, mlen;
+	unsigned long m;
+	uint32_t w, r[l+1];
+	const uint32_t * const tab0 = bch->mod8_tab;
+	const uint32_t * const tab1 = tab0 + 256*(l+1);
+	const uint32_t * const tab2 = tab1 + 256*(l+1);
+	const uint32_t * const tab3 = tab2 + 256*(l+1);
+	const uint32_t *pdata, *p0, *p1, *p2, *p3;
+
+	if (ecc) {
+		/* load ecc parity bytes into internal 32-bit buffer */
+		load_ecc8(bch, bch->ecc_buf, ecc);
+	} else {
+		memset(bch->ecc_buf, 0, sizeof(r));
+	}
+
+	/* process first unaligned data bytes */
+	m = ((unsigned long)data) & 3;
+	if (m) {
+		mlen = (len < (4-m)) ? len : 4-m;
+		encode_bch_unaligned(bch, data, mlen, bch->ecc_buf);
+		data += mlen;
+		len  -= mlen;
+	}
+
+	/* process 32-bit aligned data words */
+	pdata = (uint32_t *)data;
+	mlen  = len/4;
+	data += 4*mlen;
+	len  -= 4*mlen;
+	memcpy(r, bch->ecc_buf, sizeof(r));
+
+	/*
+	 * split each 32-bit word into 4 polynomials of weight 8 as follows:
+	 *
+	 * 31 ...24  23 ...16  15 ... 8  7 ... 0
+	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt
+	 *                               tttttttt  mod g = r0 (precomputed)
+	 *                     zzzzzzzz  00000000  mod g = r1 (precomputed)
+	 *           yyyyyyyy  00000000  00000000  mod g = r2 (precomputed)
+	 * xxxxxxxx  00000000  00000000  00000000  mod g = r3 (precomputed)
+	 * xxxxxxxx  yyyyyyyy  zzzzzzzz  tttttttt  mod g = r0^r1^r2^r3
+	 */
+	while (mlen--) {
+		/* input data is read in big-endian format */
+		w = r[0]^cpu_to_be32(*pdata++);
+		p0 = tab0 + (l+1)*((w >>  0) & 0xff);
+		p1 = tab1 + (l+1)*((w >>  8) & 0xff);
+		p2 = tab2 + (l+1)*((w >> 16) & 0xff);
+		p3 = tab3 + (l+1)*((w >> 24) & 0xff);
+
+		for (i = 0; i < l; i++)
+			r[i] = r[i+1]^p0[i]^p1[i]^p2[i]^p3[i];
+
+		r[l] = p0[l]^p1[l]^p2[l]^p3[l];
+	}
+	memcpy(bch->ecc_buf, r, sizeof(r));
+
+	/* process last unaligned bytes */
+	if (len)
+		encode_bch_unaligned(bch, data, len, bch->ecc_buf);
+
+	/* store ecc parity bytes into original parity buffer */
+	if (ecc)
+		store_ecc8(bch, ecc, bch->ecc_buf);
+}
+EXPORT_SYMBOL_GPL(encode_bch);
+
+static inline int modulo(struct bch_control *bch, unsigned int v)
+{
+	const unsigned int n = GF_N(bch);
+	while (v >= n) {
+		v -= n;
+		v = (v & n) + (v >> GF_M(bch));
+	}
+	return v;
+}
+
+/*
+ * shorter and faster modulo function, only works when v < 2N.
+ */
+static inline int mod_s(struct bch_control *bch, unsigned int v)
+{
+	const unsigned int n = GF_N(bch);
+	return (v < n) ? v : v-n;
+}
+
+static inline int deg(unsigned int poly)
+{
+	/* polynomial degree is the most-significant bit index */
+	return fls(poly)-1;
+}
+
+static inline int parity(unsigned int x)
+{
+	/*
+	 * public domain code snippet, lifted from
+	 * http://www-graphics.stanford.edu/~seander/bithacks.html
+	 */
+	x ^= x >> 1;
+	x ^= x >> 2;
+	x = (x & 0x11111111U) * 0x11111111U;
+	return (x >> 28) & 1;
+}
+
+/* Galois field basic operations: multiply, divide, inverse, etc. */
+
+static inline unsigned int gf_mul(struct bch_control *bch, unsigned int a,
+				  unsigned int b)
+{
+	return (a && b) ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
+					       bch->a_log_tab[b])] : 0;
+}
+
+static inline unsigned int gf_sqr(struct bch_control *bch, unsigned int a)
+{
+	return a ? bch->a_pow_tab[mod_s(bch, 2*bch->a_log_tab[a])] : 0;
+}
+
+static inline unsigned int gf_div(struct bch_control *bch, unsigned int a,
+				  unsigned int b)
+{
+	return a ? bch->a_pow_tab[mod_s(bch, bch->a_log_tab[a]+
+					GF_N(bch)-bch->a_log_tab[b])] : 0;
+}
+
+static inline unsigned int gf_inv(struct bch_control *bch, unsigned int a)
+{
+	return bch->a_pow_tab[GF_N(bch)-bch->a_log_tab[a]];
+}
+
+static inline unsigned int a_pow(struct bch_control *bch, int i)
+{
+	return bch->a_pow_tab[modulo(bch, i)];
+}
+
+static inline int a_log(struct bch_control *bch, unsigned int x)
+{
+	return bch->a_log_tab[x];
+}
+
+static inline int a_ilog(struct bch_control *bch, unsigned int x)
+{
+	return mod_s(bch, GF_N(bch)-bch->a_log_tab[x]);
+}
+
+/*
+ * compute 2t syndromes of ecc polynomial, i.e. ecc(a^j) for j=1..2t
+ */
+static void compute_syndromes(struct bch_control *bch, uint32_t *ecc,
+			      unsigned int *syn)
+{
+	int i, j, s;
+	unsigned int m;
+	uint32_t poly;
+	const int t = GF_T(bch);
+
+	s = bch->ecc_bits;
+
+	/* make sure extra bits in last ecc word are cleared */
+	m = ((unsigned int)s) & 31;
+	if (m)
+		ecc[s/32] &= ~((1u << (32-m))-1);
+	memset(syn, 0, 2*t*sizeof(*syn));
+
+	/* compute v(a^j) for j=1 .. 2t-1 */
+	do {
+		poly = *ecc++;
+		s -= 32;
+		while (poly) {
+			i = deg(poly);
+			for (j = 0; j < 2*t; j += 2)
+				syn[j] ^= a_pow(bch, (j+1)*(i+s));
+
+			poly ^= (1 << i);
+		}
+	} while (s > 0);
+
+	/* v(a^(2j)) = v(a^j)^2 */
+	for (j = 0; j < t; j++)
+		syn[2*j+1] = gf_sqr(bch, syn[j]);
+}
+
+static void gf_poly_copy(struct gf_poly *dst, struct gf_poly *src)
+{
+	memcpy(dst, src, GF_POLY_SZ(src->deg));
+}
+
+static int compute_error_locator_polynomial(struct bch_control *bch,
+					    const unsigned int *syn)
+{
+	const unsigned int t = GF_T(bch);
+	const unsigned int n = GF_N(bch);
+	unsigned int i, j, tmp, l, pd = 1, d = syn[0];
+	struct gf_poly *elp = bch->elp;
+	struct gf_poly *pelp = bch->poly_2t[0];
+	struct gf_poly *elp_copy = bch->poly_2t[1];
+	int k, pp = -1;
+
+	memset(pelp, 0, GF_POLY_SZ(2*t));
+	memset(elp, 0, GF_POLY_SZ(2*t));
+
+	pelp->deg = 0;
+	pelp->c[0] = 1;
+	elp->deg = 0;
+	elp->c[0] = 1;
+
+	/* use simplified binary Berlekamp-Massey algorithm */
+	for (i = 0; (i < t) && (elp->deg <= t); i++) {
+		if (d) {
+			k = 2*i-pp;
+			gf_poly_copy(elp_copy, elp);
+			/* e[i+1](X) = e[i](X)+di*dp^-1*X^2(i-p)*e[p](X) */
+			tmp = a_log(bch, d)+n-a_log(bch, pd);
+			for (j = 0; j <= pelp->deg; j++) {
+				if (pelp->c[j]) {
+					l = a_log(bch, pelp->c[j]);
+					elp->c[j+k] ^= a_pow(bch, tmp+l);
+				}
+			}
+			/* compute l[i+1] = max(l[i]->c[l[p]+2*(i-p]) */
+			tmp = pelp->deg+k;
+			if (tmp > elp->deg) {
+				elp->deg = tmp;
+				gf_poly_copy(pelp, elp_copy);
+				pd = d;
+				pp = 2*i;
+			}
+		}
+		/* di+1 = S(2i+3)+elp[i+1].1*S(2i+2)+...+elp[i+1].lS(2i+3-l) */
+		if (i < t-1) {
+			d = syn[2*i+2];
+			for (j = 1; j <= elp->deg; j++)
+				d ^= gf_mul(bch, elp->c[j], syn[2*i+2-j]);
+		}
+	}
+	dbg("elp=%s\n", gf_poly_str(elp));
+	return (elp->deg > t) ? -1 : (int)elp->deg;
+}
+
+/*
+ * solve a m x m linear system in GF(2) with an expected number of solutions,
+ * and return the number of found solutions
+ */
+static int solve_linear_system(struct bch_control *bch, unsigned int *rows,
+			       unsigned int *sol, int nsol)
+{
+	const int m = GF_M(bch);
+	unsigned int tmp, mask;
+	int rem, c, r, p, k, param[m];
+
+	k = 0;
+	mask = 1 << m;
+
+	/* Gaussian elimination */
+	for (c = 0; c < m; c++) {
+		rem = 0;
+		p = c-k;
+		/* find suitable row for elimination */
+		for (r = p; r < m; r++) {
+			if (rows[r] & mask) {
+				if (r != p) {
+					tmp = rows[r];
+					rows[r] = rows[p];
+					rows[p] = tmp;
+				}
+				rem = r+1;
+				break;
+			}
+		}
+		if (rem) {
+			/* perform elimination on remaining rows */
+			tmp = rows[p];
+			for (r = rem; r < m; r++) {
+				if (rows[r] & mask)
+					rows[r] ^= tmp;
+			}
+		} else {
+			/* elimination not needed, store defective row index */
+			param[k++] = c;
+		}
+		mask >>= 1;
+	}
+	/* rewrite system, inserting fake parameter rows */
+	if (k > 0) {
+		p = k;
+		for (r = m-1; r >= 0; r--) {
+			if ((r > m-1-k) && rows[r])
+				/* system has no solution */
+				return 0;
+
+			rows[r] = (p && (r == param[p-1])) ?
+				p--, 1u << (m-r) : rows[r-p];
+		}
+	}
+
+	if (nsol != (1 << k))
+		/* unexpected number of solutions */
+		return 0;
+
+	for (p = 0; p < nsol; p++) {
+		/* set parameters for p-th solution */
+		for (c = 0; c < k; c++)
+			rows[param[c]] = (rows[param[c]] & ~1)|((p >> c) & 1);
+
+		/* compute unique solution */
+		tmp = 0;
+		for (r = m-1; r >= 0; r--) {
+			mask = rows[r] & (tmp|1);
+			tmp |= parity(mask) << (m-r);
+		}
+		sol[p] = tmp >> 1;
+	}
+	return nsol;
+}
+
+/*
+ * this function builds and solves a linear system for finding roots of a degree
+ * 4 affine monic polynomial X^4+aX^2+bX+c over GF(2^m).
+ */
+static int find_affine4_roots(struct bch_control *bch, unsigned int a,
+			      unsigned int b, unsigned int c,
+			      unsigned int *roots)
+{
+	int i, j, k;
+	const int m = GF_M(bch);
+	unsigned int mask = 0xff, t, rows[16] = {0,};
+
+	j = a_log(bch, b);
+	k = a_log(bch, a);
+	rows[0] = c;
+
+	/* buid linear system to solve X^4+aX^2+bX+c = 0 */
+	for (i = 0; i < m; i++) {
+		rows[i+1] = bch->a_pow_tab[4*i]^
+			(a ? bch->a_pow_tab[mod_s(bch, k)] : 0)^
+			(b ? bch->a_pow_tab[mod_s(bch, j)] : 0);
+		j++;
+		k += 2;
+	}
+	/*
+	 * transpose 16x16 matrix before passing it to linear solver
+	 * warning: this code assumes m < 16
+	 */
+	for (j = 8; j != 0; j >>= 1, mask ^= (mask << j)) {
+		for (k = 0; k < 16; k = (k+j+1) & ~j) {
+			t = ((rows[k] >> j)^rows[k+j]) & mask;
+			rows[k] ^= (t << j);
+			rows[k+j] ^= t;
+		}
+	}
+	return solve_linear_system(bch, rows, roots, 4);
+}
+
+/*
+ * compute root r of a degree 1 polynomial over GF(2^m) (returned as log(1/r))
+ */
+static int find_poly_deg1_roots(struct bch_control *bch, struct gf_poly *poly,
+				unsigned int *roots)
+{
+	int n = 0;
+
+	if (poly->c[0])
+		/* poly[X] = bX+c with c!=0, root=c/b */
+		roots[n++] = mod_s(bch, GF_N(bch)-bch->a_log_tab[poly->c[0]]+
+				   bch->a_log_tab[poly->c[1]]);
+	return n;
+}
+
+/*
+ * compute roots of a degree 2 polynomial over GF(2^m)
+ */
+static int find_poly_deg2_roots(struct bch_control *bch, struct gf_poly *poly,
+				unsigned int *roots)
+{
+	int n = 0, i, l0, l1, l2;
+	unsigned int u, v, r;
+
+	if (poly->c[0] && poly->c[1]) {
+
+		l0 = bch->a_log_tab[poly->c[0]];
+		l1 = bch->a_log_tab[poly->c[1]];
+		l2 = bch->a_log_tab[poly->c[2]];
+
+		/* using z=a/bX, transform aX^2+bX+c into z^2+z+u (u=ac/b^2) */
+		u = a_pow(bch, l0+l2+2*(GF_N(bch)-l1));
+		/*
+		 * let u = sum(li.a^i) i=0..m-1; then compute r = sum(li.xi):
+		 * r^2+r = sum(li.(xi^2+xi)) = sum(li.(a^i+Tr(a^i).a^k)) =
+		 * u + sum(li.Tr(a^i).a^k) = u+a^k.Tr(sum(li.a^i)) = u+a^k.Tr(u)
+		 * i.e. r and r+1 are roots iff Tr(u)=0
+		 */
+		r = 0;
+		v = u;
+		while (v) {
+			i = deg(v);
+			r ^= bch->xi_tab[i];
+			v ^= (1 << i);
+		}
+		/* verify root */
+		if ((gf_sqr(bch, r)^r) == u) {
+			/* reverse z=a/bX transformation and compute log(1/r) */
+			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
+					    bch->a_log_tab[r]+l2);
+			roots[n++] = modulo(bch, 2*GF_N(bch)-l1-
+					    bch->a_log_tab[r^1]+l2);
+		}
+	}
+	return n;
+}
+
+/*
+ * compute roots of a degree 3 polynomial over GF(2^m)
+ */
+static int find_poly_deg3_roots(struct bch_control *bch, struct gf_poly *poly,
+				unsigned int *roots)
+{
+	int i, n = 0;
+	unsigned int a, b, c, a2, b2, c2, e3, tmp[4];
+
+	if (poly->c[0]) {
+		/* transform polynomial into monic X^3 + a2X^2 + b2X + c2 */
+		e3 = poly->c[3];
+		c2 = gf_div(bch, poly->c[0], e3);
+		b2 = gf_div(bch, poly->c[1], e3);
+		a2 = gf_div(bch, poly->c[2], e3);
+
+		/* (X+a2)(X^3+a2X^2+b2X+c2) = X^4+aX^2+bX+c (affine) */
+		c = gf_mul(bch, a2, c2);           /* c = a2c2      */
+		b = gf_mul(bch, a2, b2)^c2;        /* b = a2b2 + c2 */
+		a = gf_sqr(bch, a2)^b2;            /* a = a2^2 + b2 */
+
+		/* find the 4 roots of this affine polynomial */
+		if (find_affine4_roots(bch, a, b, c, tmp) == 4) {
+			/* remove a2 from final list of roots */
+			for (i = 0; i < 4; i++) {
+				if (tmp[i] != a2)
+					roots[n++] = a_ilog(bch, tmp[i]);
+			}
+		}
+	}
+	return n;
+}
+
+/*
+ * compute roots of a degree 4 polynomial over GF(2^m)
+ */
+static int find_poly_deg4_roots(struct bch_control *bch, struct gf_poly *poly,
+				unsigned int *roots)
+{
+	int i, l, n = 0;
+	unsigned int a, b, c, d, e = 0, f, a2, b2, c2, e4;
+
+	if (poly->c[0] == 0)
+		return 0;
+
+	/* transform polynomial into monic X^4 + aX^3 + bX^2 + cX + d */
+	e4 = poly->c[4];
+	d = gf_div(bch, poly->c[0], e4);
+	c = gf_div(bch, poly->c[1], e4);
+	b = gf_div(bch, poly->c[2], e4);
+	a = gf_div(bch, poly->c[3], e4);
+
+	/* use Y=1/X transformation to get an affine polynomial */
+	if (a) {
+		/* first, eliminate cX by using z=X+e with ae^2+c=0 */
+		if (c) {
+			/* compute e such that e^2 = c/a */
+			f = gf_div(bch, c, a);
+			l = a_log(bch, f);
+			l += (l & 1) ? GF_N(bch) : 0;
+			e = a_pow(bch, l/2);
+			/*
+			 * use transformation z=X+e:
+			 * z^4+e^4 + a(z^3+ez^2+e^2z+e^3) + b(z^2+e^2) +cz+ce+d
+			 * z^4 + az^3 + (ae+b)z^2 + (ae^2+c)z+e^4+be^2+ae^3+ce+d
+			 * z^4 + az^3 + (ae+b)z^2 + e^4+be^2+d
+			 * z^4 + az^3 +     b'z^2 + d'
+			 */
+			d = a_pow(bch, 2*l)^gf_mul(bch, b, f)^d;
+			b = gf_mul(bch, a, e)^b;
+		}
+		/* now, use Y=1/X to get Y^4 + b/dY^2 + a/dY + 1/d */
+		if (d == 0)
+			/* assume all roots have multiplicity 1 */
+			return 0;
+
+		c2 = gf_inv(bch, d);
+		b2 = gf_div(bch, a, d);
+		a2 = gf_div(bch, b, d);
+	} else {
+		/* polynomial is already affine */
+		c2 = d;
+		b2 = c;
+		a2 = b;
+	}
+	/* find the 4 roots of this affine polynomial */
+	if (find_affine4_roots(bch, a2, b2, c2, roots) == 4) {
+		for (i = 0; i < 4; i++) {
+			/* post-process roots (reverse transformations) */
+			f = a ? gf_inv(bch, roots[i]) : roots[i];
+			roots[i] = a_ilog(bch, f^e);
+		}
+		n = 4;
+	}
+	return n;
+}
+
+/*
+ * build monic, log-based representation of a polynomial
+ */
+static void gf_poly_logrep(struct bch_control *bch,
+			   const struct gf_poly *a, int *rep)
+{
+	int i, d = a->deg, l = GF_N(bch)-a_log(bch, a->c[a->deg]);
+
+	/* represent 0 values with -1; warning, rep[d] is not set to 1 */
+	for (i = 0; i < d; i++)
+		rep[i] = a->c[i] ? mod_s(bch, a_log(bch, a->c[i])+l) : -1;
+}
+
+/*
+ * compute polynomial Euclidean division remainder in GF(2^m)[X]
+ */
+static void gf_poly_mod(struct bch_control *bch, struct gf_poly *a,
+			const struct gf_poly *b, int *rep)
+{
+	int la, p, m;
+	unsigned int i, j, *c = a->c;
+	const unsigned int d = b->deg;
+
+	if (a->deg < d)
+		return;
+
+	/* reuse or compute log representation of denominator */
+	if (!rep) {
+		rep = bch->cache;
+		gf_poly_logrep(bch, b, rep);
+	}
+
+	for (j = a->deg; j >= d; j--) {
+		if (c[j]) {
+			la = a_log(bch, c[j]);
+			p = j-d;
+			for (i = 0; i < d; i++, p++) {
+				m = rep[i];
+				if (m >= 0)
+					c[p] ^= bch->a_pow_tab[mod_s(bch,
+								     m+la)];
+			}
+		}
+	}
+	a->deg = d-1;
+	while (!c[a->deg] && a->deg)
+		a->deg--;
+}
+
+/*
+ * compute polynomial Euclidean division quotient in GF(2^m)[X]
+ */
+static void gf_poly_div(struct bch_control *bch, struct gf_poly *a,
+			const struct gf_poly *b, struct gf_poly *q)
+{
+	if (a->deg >= b->deg) {
+		q->deg = a->deg-b->deg;
+		/* compute a mod b (modifies a) */
+		gf_poly_mod(bch, a, b, NULL);
+		/* quotient is stored in upper part of polynomial a */
+		memcpy(q->c, &a->c[b->deg], (1+q->deg)*sizeof(unsigned int));
+	} else {
+		q->deg = 0;
+		q->c[0] = 0;
+	}
+}
+
+/*
+ * compute polynomial GCD (Greatest Common Divisor) in GF(2^m)[X]
+ */
+static struct gf_poly *gf_poly_gcd(struct bch_control *bch, struct gf_poly *a,
+				   struct gf_poly *b)
+{
+	struct gf_poly *tmp;
+
+	dbg("gcd(%s,%s)=", gf_poly_str(a), gf_poly_str(b));
+
+	if (a->deg < b->deg) {
+		tmp = b;
+		b = a;
+		a = tmp;
+	}
+
+	while (b->deg > 0) {
+		gf_poly_mod(bch, a, b, NULL);
+		tmp = b;
+		b = a;
+		a = tmp;
+	}
+
+	dbg("%s\n", gf_poly_str(a));
+
+	return a;
+}
+
+/*
+ * Given a polynomial f and an integer k, compute Tr(a^kX) mod f
+ * This is used in Berlekamp Trace algorithm for splitting polynomials
+ */
+static void compute_trace_bk_mod(struct bch_control *bch, int k,
+				 const struct gf_poly *f, struct gf_poly *z,
+				 struct gf_poly *out)
+{
+	const int m = GF_M(bch);
+	int i, j;
+
+	/* z contains z^2j mod f */
+	z->deg = 1;
+	z->c[0] = 0;
+	z->c[1] = bch->a_pow_tab[k];
+
+	out->deg = 0;
+	memset(out, 0, GF_POLY_SZ(f->deg));
+
+	/* compute f log representation only once */
+	gf_poly_logrep(bch, f, bch->cache);
+
+	for (i = 0; i < m; i++) {
+		/* add a^(k*2^i)(z^(2^i) mod f) and compute (z^(2^i) mod f)^2 */
+		for (j = z->deg; j >= 0; j--) {
+			out->c[j] ^= z->c[j];
+			z->c[2*j] = gf_sqr(bch, z->c[j]);
+			z->c[2*j+1] = 0;
+		}
+		if (z->deg > out->deg)
+			out->deg = z->deg;
+
+		if (i < m-1) {
+			z->deg *= 2;
+			/* z^(2(i+1)) mod f = (z^(2^i) mod f)^2 mod f */
+			gf_poly_mod(bch, z, f, bch->cache);
+		}
+	}
+	while (!out->c[out->deg] && out->deg)
+		out->deg--;
+
+	dbg("Tr(a^%d.X) mod f = %s\n", k, gf_poly_str(out));
+}
+
+/*
+ * factor a polynomial using Berlekamp Trace algorithm (BTA)
+ */
+static void factor_polynomial(struct bch_control *bch, int k, struct gf_poly *f,
+			      struct gf_poly **g, struct gf_poly **h)
+{
+	struct gf_poly *f2 = bch->poly_2t[0];
+	struct gf_poly *q  = bch->poly_2t[1];
+	struct gf_poly *tk = bch->poly_2t[2];
+	struct gf_poly *z  = bch->poly_2t[3];
+	struct gf_poly *gcd;
+
+	dbg("factoring %s...\n", gf_poly_str(f));
+
+	*g = f;
+	*h = NULL;
+
+	/* tk = Tr(a^k.X) mod f */
+	compute_trace_bk_mod(bch, k, f, z, tk);
+
+	if (tk->deg > 0) {
+		/* compute g = gcd(f, tk) (destructive operation) */
+		gf_poly_copy(f2, f);
+		gcd = gf_poly_gcd(bch, f2, tk);
+		if (gcd->deg < f->deg) {
+			/* compute h=f/gcd(f,tk); this will modify f and q */
+			gf_poly_div(bch, f, gcd, q);
+			/* store g and h in-place (clobbering f) */
+			*h = &((struct gf_poly_deg1 *)f)[gcd->deg].poly;
+			gf_poly_copy(*g, gcd);
+			gf_poly_copy(*h, q);
+		}
+	}
+}
+
+/*
+ * find roots of a polynomial, using BTZ algorithm; see the beginning of this
+ * file for details
+ */
+static int find_poly_roots(struct bch_control *bch, unsigned int k,
+			   struct gf_poly *poly, unsigned int *roots)
+{
+	int cnt;
+	struct gf_poly *f1, *f2;
+
+	switch (poly->deg) {
+		/* handle low degree polynomials with ad hoc techniques */
+	case 1:
+		cnt = find_poly_deg1_roots(bch, poly, roots);
+		break;
+	case 2:
+		cnt = find_poly_deg2_roots(bch, poly, roots);
+		break;
+	case 3:
+		cnt = find_poly_deg3_roots(bch, poly, roots);
+		break;
+	case 4:
+		cnt = find_poly_deg4_roots(bch, poly, roots);
+		break;
+	default:
+		/* factor polynomial using Berlekamp Trace Algorithm (BTA) */
+		cnt = 0;
+		if (poly->deg && (k <= GF_M(bch))) {
+			factor_polynomial(bch, k, poly, &f1, &f2);
+			if (f1)
+				cnt += find_poly_roots(bch, k+1, f1, roots);
+			if (f2)
+				cnt += find_poly_roots(bch, k+1, f2, roots+cnt);
+		}
+		break;
+	}
+	return cnt;
+}
+
+#if defined(USE_CHIEN_SEARCH)
+/*
+ * exhaustive root search (Chien) implementation - not used, included only for
+ * reference/comparison tests
+ */
+static int chien_search(struct bch_control *bch, unsigned int len,
+			struct gf_poly *p, unsigned int *roots)
+{
+	int m;
+	unsigned int i, j, syn, syn0, count = 0;
+	const unsigned int k = 8*len+bch->ecc_bits;
+
+	/* use a log-based representation of polynomial */
+	gf_poly_logrep(bch, p, bch->cache);
+	bch->cache[p->deg] = 0;
+	syn0 = gf_div(bch, p->c[0], p->c[p->deg]);
+
+	for (i = GF_N(bch)-k+1; i <= GF_N(bch); i++) {
+		/* compute elp(a^i) */
+		for (j = 1, syn = syn0; j <= p->deg; j++) {
+			m = bch->cache[j];
+			if (m >= 0)
+				syn ^= a_pow(bch, m+j*i);
+		}
+		if (syn == 0) {
+			roots[count++] = GF_N(bch)-i;
+			if (count == p->deg)
+				break;
+		}
+	}
+	return (count == p->deg) ? count : 0;
+}
+#define find_poly_roots(_p, _k, _elp, _loc) chien_search(_p, len, _elp, _loc)
+#endif /* USE_CHIEN_SEARCH */
+
+/**
+ * decode_bch - decode received codeword and find bit error locations
+ * @bch:      BCH control structure
+ * @data:     received data, ignored if @calc_ecc is provided
+ * @len:      data length in bytes, must always be provided
+ * @recv_ecc: received ecc, if NULL then assume it was XORed in @calc_ecc
+ * @calc_ecc: calculated ecc, if NULL then calc_ecc is computed from @data
+ * @syn:      hw computed syndrome data (if NULL, syndrome is calculated)
+ * @errloc:   output array of error locations
+ *
+ * Returns:
+ *  The number of errors found, or -EBADMSG if decoding failed, or -EINVAL if
+ *  invalid parameters were provided
+ *
+ * Depending on the available hw BCH support and the need to compute @calc_ecc
+ * separately (using encode_bch()), this function should be called with one of
+ * the following parameter configurations -
+ *
+ * by providing @data and @recv_ecc only:
+ *   decode_bch(@bch, @data, @len, @recv_ecc, NULL, NULL, @errloc)
+ *
+ * by providing @recv_ecc and @calc_ecc:
+ *   decode_bch(@bch, NULL, @len, @recv_ecc, @calc_ecc, NULL, @errloc)
+ *
+ * by providing ecc = recv_ecc XOR calc_ecc:
+ *   decode_bch(@bch, NULL, @len, NULL, ecc, NULL, @errloc)
+ *
+ * by providing syndrome results @syn:
+ *   decode_bch(@bch, NULL, @len, NULL, NULL, @syn, @errloc)
+ *
+ * Once decode_bch() has successfully returned with a positive value, error
+ * locations returned in array @errloc should be interpreted as follows -
+ *
+ * if (errloc[n] >= 8*len), then n-th error is located in ecc (no need for
+ * data correction)
+ *
+ * if (errloc[n] < 8*len), then n-th error is located in data and can be
+ * corrected with statement data[errloc[n]/8] ^= 1 << (errloc[n] % 8);
+ *
+ * Note that this function does not perform any data correction by itself, it
+ * merely indicates error locations.
+ */
+int decode_bch(struct bch_control *bch, const uint8_t *data, unsigned int len,
+	       const uint8_t *recv_ecc, const uint8_t *calc_ecc,
+	       const unsigned int *syn, unsigned int *errloc)
+{
+	const unsigned int ecc_words = BCH_ECC_WORDS(bch);
+	unsigned int nbits;
+	int i, err, nroots;
+	uint32_t sum;
+
+	/* sanity check: make sure data length can be handled */
+	if (8*len > (bch->n-bch->ecc_bits))
+		return -EINVAL;
+
+	/* if caller does not provide syndromes, compute them */
+	if (!syn) {
+		if (!calc_ecc) {
+			/* compute received data ecc into an internal buffer */
+			if (!data || !recv_ecc)
+				return -EINVAL;
+			encode_bch(bch, data, len, NULL);
+		} else {
+			/* load provided calculated ecc */
+			load_ecc8(bch, bch->ecc_buf, calc_ecc);
+		}
+		/* load received ecc or assume it was XORed in calc_ecc */
+		if (recv_ecc) {
+			load_ecc8(bch, bch->ecc_buf2, recv_ecc);
+			/* XOR received and calculated ecc */
+			for (i = 0, sum = 0; i < (int)ecc_words; i++) {
+				bch->ecc_buf[i] ^= bch->ecc_buf2[i];
+				sum |= bch->ecc_buf[i];
+			}
+			if (!sum)
+				/* no error found */
+				return 0;
+		}
+		compute_syndromes(bch, bch->ecc_buf, bch->syn);
+		syn = bch->syn;
+	}
+
+	err = compute_error_locator_polynomial(bch, syn);
+	if (err > 0) {
+		nroots = find_poly_roots(bch, 1, bch->elp, errloc);
+		if (err != nroots)
+			err = -1;
+	}
+	if (err > 0) {
+		/* post-process raw error locations for easier correction */
+		nbits = (len*8)+bch->ecc_bits;
+		for (i = 0; i < err; i++) {
+			if (errloc[i] >= nbits) {
+				err = -1;
+				break;
+			}
+			errloc[i] = nbits-1-errloc[i];
+			errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
+		}
+	}
+	return (err >= 0) ? err : -EBADMSG;
+}
+EXPORT_SYMBOL_GPL(decode_bch);
+
+/*
+ * 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;
+}
+EXPORT_SYMBOL_GPL(init_bch);
+
+/**
+ *  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);
+	}
+}
+EXPORT_SYMBOL_GPL(free_bch);
+
+MODULE_LICENSE("GPL");
+MODULE_AUTHOR("Ivan Djelic <ivan.djelic@parrot.com>");
+MODULE_DESCRIPTION("Binary BCH encoder/decoder");
-- 
1.7.5.4


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