rk27utils: Add nandextract utility

This quick and dirty utility allows to extract nand bootloader
from raw 1st nand block dump. I post it mainly to somewhat
document how BCH error correction engine of the rk27xx works.

Change-Id: I37ca91add7d372e3576d2722afc946d0f08971a9

5 files changed, 1782 insertions, 0 deletions

diff --git a/utils/rk27utils/README b/utils/rk27utils/README
index a43d69a88f..d0343580b8 100644
--- a/utils/rk27utils/README
+++ b/utils/rk27utils/README
@@ -35,3 +35,37 @@ This directory contains tool which sends custom scsi commands to the
 rockchip player.
 
 You need libusb-1.0 + header files in order to compile this utility.
+
+nandextract
+This directory contains quick and dirty tool which allows to extract
+nand bootloader from raw dump of the first nand block. The main reason
+I post this tool is to somewhat document error correction scheme used by
+rk27xx chip. The tool implements BCH error correction processing with
+help of bch library taken from linux kernel (and slightly modified to
+compile standalone). Error correction is SUPER important as the nands used
+in cheap rk27 players have quite high error rates.
+
+Nand controler in rk27xx chip implements hw BCH error correction engine.
+The documentation is lacking so this info was obtained from RE and
+various other sources.
+The data on the nand is stored in 528 bytes long chunks - 512 bytes
+of actual data followed by 3 bytes of metadata (used by FTL layer to mark
+special sectors) followed by 13 bytes of BCH ECC. BCH algorithm
+uses m=13, t=8 and primitive polynomial 0x25af. Special masking
+is used such as empty sector (with all 0xff) gives all 0xff ECC bytes.
+Quoting e-mail from Ivan Djelic (the author of bch lib in linux):
+To summarize, the steps needed to compute the rk27xx ecc are the following:
+1. Reverse bits in each input byte
+2. Call encode_bch()
+3. Reverse output bits in each computed ecc byte
+4. Add a polynomial in order to get only 0xff ecc bytes for a blank page
+For more details you need to read the code.
+
+Another quirk is that rom loader assumes that there are 4 sectors in each
+nand page. This is actually not true for newer nand chips with page size
+bigger then 2k. That means that on newer 4k page chips only first half of
+every page is used in nand bootloader area. This is for compatibility reasons
+most probably.
+
+Finally, every 512 bytes block of data is encoded with rc4 algorithm.
+The key and routine were recovered from rk27xx rom dump by AleMaxx.
diff --git a/utils/rk27utils/nandextract/Makefile b/utils/rk27utils/nandextract/Makefile
new file mode 100644
index 0000000000..096b26e893
--- /dev/null
+++ b/utils/rk27utils/nandextract/Makefile
@@ -0,0 +1,7 @@
+all: nandextract
+
+nandextract: nandextract.c libbch.c
+        gcc -g -std=c99 -o $@ -W -Wall $^
+
+clean:
+        rm -fr nandextract
diff --git a/utils/rk27utils/nandextract/libbch.c b/utils/rk27utils/nandextract/libbch.c
new file mode 100644
index 0000000000..04485f3512
--- /dev/null
+++ b/utils/rk27utils/nandextract/libbch.c
@@ -0,0 +1,1393 @@
+/*
+ * 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 <stdlib.h>
+#include <string.h>
+#include <errno.h>
+#include "libbch.h"
+
+/* glue code */
+#define kmalloc(x,y) malloc(x)
+#define kfree(x) free(x)
+
+static void *kzalloc(size_t size, int flags)
+{
+        (void)flags;
+        void *p = malloc(size);
+        
+        if (p)
+                memset(p, 0, size);
+                
+        return p;
+}
+
+#define EXPORT_SYMBOL_GPL(x)
+#define MODULE_LICENSE(x)
+#define MODULE_AUTHOR(x)
+#define MODULE_DESCRIPTION(x)
+
+#define DIV_ROUND_UP(n,d) (((n) + (d) - 1)/(d))
+
+#include <arpa/inet.h>
+#define cpu_to_be32(x) htonl(x)
+
+static inline int fls(int x)
+{
+        int r = 32;
+        if (!x)
+                return 0;
+ 
+        if (!(x & 0xffff0000u)) {
+                x <<= 16;
+                r -= 16;
+        }
+        
+        if (!(x & 0xff000000u)) {
+                x <<= 8;
+                r -= 8;
+        }
+        
+        if (!(x & 0xf0000000u)) {
+                x <<= 4;
+                r -= 4;
+        }
+        
+        if (!(x & 0xc0000000u)) {
+                x <<= 2;
+                r -= 2;
+        }
+        
+        if (!(x & 0x80000000u)) {
+                x <<= 1;
+                r -= 1;
+        }
+ 
+        return r;
+}
+ 
+#define ARRAY_SIZE(x) (sizeof(x) / sizeof((x)[0]))
+#define GFP_KERNEL 0
+/* end of glue code */
+
+/*
+ * 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 = -2;
+                                break;
+                        }
+                        errloc[i] = nbits-1-errloc[i];
+                        errloc[i] = (errloc[i] & ~7)|(7-(errloc[i] & 7));
+                }
+        }
+        return err;
+}
+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");
diff --git a/utils/rk27utils/nandextract/libbch.h b/utils/rk27utils/nandextract/libbch.h
new file mode 100644
index 0000000000..b4c779e815
--- /dev/null
+++ b/utils/rk27utils/nandextract/libbch.h
@@ -0,0 +1,113 @@
+/*
+ * 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 <stdint.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];
+};
+
+/**
+ * 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/utils/rk27utils/nandextract/nandextract.c b/utils/rk27utils/nandextract/nandextract.c
new file mode 100644
index 0000000000..c9b41d26e3
--- /dev/null
+++ b/utils/rk27utils/nandextract/nandextract.c
@@ -0,0 +1,235 @@
+#include <stdio.h>
+#include <stdint.h>
+#include <stdbool.h>
+#include <stdlib.h>
+#include <string.h>
+#include "libbch.h"
+
+#define SECTOR_DATA_SIZE 512
+#define SECTOR_META_SIZE 3
+#define SECTOR_ECC_SIZE 13
+#define SECTOR_SIZE (SECTOR_DATA_SIZE + SECTOR_META_SIZE + SECTOR_ECC_SIZE)
+
+/* scramble mode */
+enum {
+      CONTINOUS_ENC, /* scramble whole block at once */
+      PAGE_ENC       /* nand bootloader is scrambled in 0x200 chunks */
+};
+
+static uint8_t reverse_bits(uint8_t b)
+{
+        return (((b & 0x80) >> 7)|
+                ((b & 0x40) >> 5)|
+                ((b & 0x20) >> 3)|
+                ((b & 0x10) >> 1)|
+                ((b & 0x08) << 1)|
+                ((b & 0x04) << 3)|
+                ((b & 0x02) << 5)|
+                ((b & 0x01) << 7));
+}
+
+static int libbch_decode_sec(struct bch_control *bch, uint8_t *inbuf, uint8_t *outbuf)
+{
+        unsigned int errloc[8];
+        static const uint8_t mask[13] = {
+                0x4e, 0x8c, 0x9d, 0x52,
+                0x2d, 0x6c, 0x7c, 0xcb,
+                0xc3, 0x12, 0x14, 0x19,
+                0x37,
+        };
+        
+        int i, err_num = 0;
+        
+        /* ecc masking polynomial */
+        for (i=0; i<SECTOR_ECC_SIZE; i++)
+                inbuf[SECTOR_DATA_SIZE+SECTOR_META_SIZE+i] ^= mask[i];
+                
+        /* fix ordering of input bits */
+        for (i = 0; i < SECTOR_SIZE; i++)
+                inbuf[i] = reverse_bits(inbuf[i]);
+
+        err_num = decode_bch(bch, inbuf,
+                             (SECTOR_SIZE - SECTOR_ECC_SIZE),
+                             &inbuf[SECTOR_SIZE - SECTOR_ECC_SIZE],
+                             NULL, NULL, errloc);
+        
+        /* apply fixups */
+        for(i=0; i<err_num; i++)
+                inbuf[errloc[i]/8] ^= 1 << (errloc[i] % 8);
+
+        /* reverse bits back (data part only), remining bytes are scratched */          
+        for (i = 0; i < SECTOR_DATA_SIZE; i++)
+                outbuf[i] = reverse_bits(inbuf[i]);
+                
+        return err_num;
+}
+
+/* scrambling/descrambling reverse engineered by AleMaxx */
+static void encode_page(uint8_t *inpg, uint8_t *outpg, const int size)
+{
+
+uint8_t key[] = {
+        0x7C, 0x4E, 0x03, 0x04,
+        0x55, 0x05, 0x09, 0x07,
+        0x2D, 0x2C, 0x7B, 0x38,
+        0x17, 0x0D, 0x17, 0x11
+};
+        int i, i3, x, val, idx;
+
+        uint8_t key1[0x100];
+        uint8_t key2[0x100];
+
+        for (i=0; i<0x100; i++) {
+                key1[i] = i;
+                key2[i] = key[i&0xf];
+        }
+
+        i3 = 0;
+        for (i=0; i<0x100; i++) {
+                x = key1[i];
+                i3 = key1[i] + i3;
+                i3 += key2[i];
+                i3 &= 0xff;
+                key1[i] = key1[i3];
+                key1[i3] = x;
+        }
+
+        idx = 0;
+        for (i=0; i<size; i++) {
+                x = key1[(i+1) & 0xff];
+                val = x;
+                idx = (x + idx) & 0xff;
+                key1[(i+1) & 0xff] = key1[idx];
+                key1[idx] = (x & 0xff);
+                val = (key1[(i+1)&0xff] + x) & 0xff;
+                val = key1[val];
+                outpg[i] = val ^ inpg[i];
+        }
+}
+
+/* returns offset in bytes of the sector
+ * NOTE: bootrom assumes 4 secs per page (regardles of actual pagesize)
+ */
+static int offset(int sec_num, int page_size, int rom)
+{
+    int sec_per_page, page_num, page_offset;
+
+    if (rom)
+        sec_per_page = 4;
+    else
+        sec_per_page = page_size / SECTOR_SIZE;
+
+    page_num = sec_num / sec_per_page;
+    page_offset = sec_num % sec_per_page;
+
+    printf("Sec per page: %d\n", sec_per_page);
+    printf("Page num: %d\n", page_num);
+    printf("Offset in page (sec): %d\n", page_offset);
+    printf("Offset in file (bytes): %d (0x%0x)\n", (page_num * page_size) +
+                                                   (page_offset * SECTOR_SIZE),
+                                                   (page_num * page_size) +
+                                                   (page_offset * SECTOR_SIZE));
+
+    return ((page_num * page_size) + (page_offset * SECTOR_SIZE));
+}
+
+static int sector_read(FILE *fp, void *buff, int sec_num, int nand_page_size, struct bch_control *bch)
+{
+    int ret;
+    int file_offset = offset(sec_num, nand_page_size, 1);
+    uint8_t inbuf[SECTOR_SIZE];  
+    uint8_t outbuf[SECTOR_SIZE];
+
+    if (fp == NULL)
+        return -1;
+
+   /* seek to the begining of the data */
+    fseek(fp, file_offset, SEEK_SET);
+
+    /* read into the buffer */
+    ret = fread(inbuf, 1, SECTOR_SIZE, fp);
+
+    if (ret != SECTOR_SIZE)
+    {
+        return -2;
+    }
+        
+    ret = libbch_decode_sec(bch, inbuf, outbuf);
+    
+    if (ret)
+    {
+                printf("LIBBCH Data %d error(s) in sector %d\n", ret, sec_num);
+        }
+                
+    memcpy(buff, outbuf, SECTOR_DATA_SIZE);
+    return ret;
+}
+
+int main (int argc, char **argv)
+{
+    FILE *ifp, *ofp;
+    void *obuf;
+    int i, size, sector, num_sectors, nand_page_size;
+    char *infile, *outfile, *ptr;
+
+        struct bch_control *bch;
+        
+    if (argc < 6)
+    {
+        printf("Usage: %s infile outfile start_sector num_sectors nand_page_size\n", argv[0]);
+        return 0;
+    }
+    
+    infile = argv[1];
+    outfile = argv[2];
+    sector = atoi(argv[3]);
+    num_sectors = atoi(argv[4]);
+    nand_page_size = atoi(argv[5]);
+
+    size = SECTOR_DATA_SIZE * num_sectors;    
+    obuf = malloc(size);
+    
+    if (obuf == NULL)
+    {
+                printf("Error allocating %d bytes of buffer\n", size);
+                return -1;
+    }
+    
+    ifp = fopen(infile, "rb");
+    
+    if (ifp == NULL)
+    {
+                printf("Cannot open %s file\n", infile);
+                free(obuf);
+                return -2;
+    }
+    
+    ofp = fopen(outfile, "wb");    
+    
+    if (ifp == NULL)
+    {
+                printf("Cannot open %s file\n", outfile);
+                fclose(ifp);
+                free(obuf);
+                return -3;
+    }
+
+    bch = init_bch(13, 8, 0x25af);
+     
+    ptr = (char *)obuf;
+    for(i=0; i<num_sectors; i++)
+    {
+                sector_read(ifp, ptr, sector++, nand_page_size, bch);
+                encode_page((uint8_t *)ptr, (uint8_t *)ptr, SECTOR_DATA_SIZE);
+                ptr += SECTOR_DATA_SIZE;
+    }
+
+    fwrite(obuf, 1, size, ofp);
+
+    fclose(ifp);
+    fclose(ofp);
+    free(obuf);
+    
+    free_bch(bch); 
+    return 0;
+}