/*
   * Generic binary BCH encoding/decoding library
   *
   * This program is free software; you can redistribute it and/or modify it
   * under the terms of the GNU General Public License version 2 as published by
   * the Free Software Foundation.
   *
   * This program is distributed in the hope that it will be useful, but WITHOUT
   * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
   * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
   * more details.
   *
   * You should have received a copy of the GNU General Public License along with
   * this program; if not, write to the Free Software Foundation, Inc., 51
   * Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
   *
   * Copyright © 2011 Parrot S.A.
   *
   * Author: Ivan Djelic <ivan.djelic@parrot.com>
   *
   * Description:
   *
   * This library provides runtime configurable encoding/decoding of binary
   * Bose-Chaudhuri-Hocquenghem (BCH) codes.
   *
   * Call init_bch to get a pointer to a newly allocated bch_control structure for
   * the given m (Galois field order), t (error correction capability) and
   * (optional) primitive polynomial parameters.
   *
   * Call encode_bch to compute and store ecc parity bytes to a given buffer.
   * Call decode_bch to detect and locate errors in received data.
   *
   * On systems supporting hw BCH features, intermediate results may be provided
   * to decode_bch in order to skip certain steps. See decode_bch() documentation
   * for details.
   *
   * Option CONFIG_BCH_CONST_PARAMS can be used to force fixed values of
   * parameters m and t; thus allowing extra compiler optimizations and providing
   * better (up to 2x) encoding performance. Using this option makes sense when
   * (m,t) are fixed and known in advance, e.g. when using BCH error correction
   * on a particular NAND flash device.
   *
   * Algorithmic details:
   *
   * Encoding is performed by processing 32 input bits in parallel, using 4
   * remainder lookup tables.
   *
   * The final stage of decoding involves the following internal steps:
   * a. Syndrome computation
   * b. Error locator polynomial computation using Berlekamp-Massey algorithm
   * c. Error locator root finding (by far the most expensive step)
   *
   * In this implementation, step c is not performed using the usual Chien search.
   * Instead, an alternative approach described in [1] is used. It consists in
   * factoring the error locator polynomial using the Berlekamp Trace algorithm
   * (BTA) down to a certain degree (4), after which ad hoc low-degree polynomial
   * solving techniques [2] are used. The resulting algorithm, called BTZ, yields
   * much better performance than Chien search for usual (m,t) values (typically
   * m >= 13, t < 32, see [1]).
   *
   * [1] B. Biswas, V. Herbert. Efficient root finding of polynomials over fields
   * of characteristic 2, in: Western European Workshop on Research in Cryptology
   * - WEWoRC 2009, Graz, Austria, LNCS, Springer, July 2009, to appear.
   * [2] [Zin96] V.A. Zinoviev. On the solution of equations of degree 10 over
   * finite fields GF(2^q). In Rapport de recherche INRIA no 2829, 1996.
   */
  
  #include <linux/kernel.h>
  #include <linux/errno.h>
  #include <linux/init.h>
  #include <linux/module.h>
  #include <linux/slab.h>
  #include <linux/bitops.h>
  #include <asm/byteorder.h>
  #include <linux/bch.h>
  
  #if defined(CONFIG_BCH_CONST_PARAMS)
  #define GF_M(_p)               (CONFIG_BCH_CONST_M)
  #define GF_T(_p)               (CONFIG_BCH_CONST_T)
  #define GF_N(_p)               ((1 << (CONFIG_BCH_CONST_M))-1)
  #else
  #define GF_M(_p)               ((_p)->m)
  #define GF_T(_p)               ((_p)->t)
  #define GF_N(_p)               ((_p)->n)
  #endif
  
  #define BCH_ECC_WORDS(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 32)
  #define BCH_ECC_BYTES(_p)      DIV_ROUND_UP(GF_M(_p)*GF_T(_p), 8)
  
  #ifndef dbg
  #define dbg(_fmt, args...)     do {} while (0)
  #endif
  
  /*
   * represent a polynomial over GF(2^m)
   */
  struct gf_poly {
  	unsigned int deg;    /* polynomial degree */
  	unsigned int c[0];   /* polynomial terms */
  };
  
  /* given its degree, compute a polynomial size in bytes */
  #define GF_POLY_SZ(_d) (sizeof(struct gf_poly)+((_d)+1)*sizeof(unsigned int))
  
  /* polynomial of degree 1 */
  struct gf_poly_deg1 {
  	struct gf_poly poly;
  	unsigned int   c[2];
  };
  
  /*
   * same as encode_bch(), but process input data one byte at a time
   */
  static void encode_bch_unaligned(struct bch_control *bch,
  				 const unsigned char *data, unsigned int len,
  				 uint32_t *ecc)
  {
  	int i;
  	const uint32_t *p;
  	const int l = 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
  ", 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
  ", 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
  ", 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...
  ", 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
  ", 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!
  ",
  		       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");