/*
* Reed-Solomon ECC handling for the Marvell Kirkwood SOC
* Copyright (C) 2009 Marvell Semiconductor, Inc.
*
* Authors: Lennert Buytenhek
* Nicolas Pitre
*
* This file is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation; either version 2 or (at your option) any
* later version.
*
* This file 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.
*/
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "core.h"
/*****************************************************************************
* Arithmetic in GF(2^10) ("F") modulo x^10 + x^3 + 1.
*
* For multiplication, a discrete log/exponent table is used, with
* primitive element x (F is a primitive field, so x is primitive).
*/
#define MODPOLY 0x409 /* x^10 + x^3 + 1 in binary */
/*
* Maps an integer a [0..1022] to a polynomial b = gf_exp[a] in
* GF(2^10) mod x^10 + x^3 + 1 such that b = x ^ a. There's two
* identical copies of this array back-to-back so that we can save
* the mod 1023 operation when doing a GF multiplication.
*/
static uint16_t gf_exp[1023 + 1023];
/*
* Maps a polynomial b in GF(2^10) mod x^10 + x^3 + 1 to an index
* a = gf_log[b] in [0..1022] such that b = x ^ a.
*/
static uint16_t gf_log[1024];
static void gf_build_log_exp_table(void)
{
int i;
int p_i;
/*
* p_i = x ^ i
*
* Initialise to 1 for i = 0.
*/
p_i = 1;
for (i = 0; i < 1023; i++) {
gf_exp[i] = p_i;
gf_exp[i + 1023] = p_i;
gf_log[p_i] = i;
/*
* p_i = p_i * x
*/
p_i <<= 1;
if (p_i & (1 << 10))
p_i ^= MODPOLY;
}
}
/*****************************************************************************
* Reed-Solomon code
*
* This implements a (1023,1015) Reed-Solomon ECC code over GF(2^10)
* mod x^10 + x^3 + 1, shortened to (520,512). The ECC data consists
* of 8 10-bit symbols, or 10 8-bit bytes.
*
* Given 512 bytes of data, computes 10 bytes of ECC.
*
* This is done by converting the 512 bytes to 512 10-bit symbols
* (elements of F), interpreting those symbols as a polynomial in F[X]
* by taking symbol 0 as the coefficient of X^8 and symbol 511 as the
* coefficient of X^519, and calculating the residue of that polynomial
* divided by the generator polynomial, which gives us the 8 ECC symbols
* as the remainder. Finally, we convert the 8 10-bit ECC symbols to 10
* 8-bit bytes.
*
* The generator polynomial is hardcoded, as that is faster, but it
* can be computed by taking the primitive element a = x (in F), and
* constructing a polynomial in F[X] with roots a, a^2, a^3, ..., a^8
* by multiplying the minimal polynomials for those roots (which are
* just 'x - a^i' for each i).
*
* Note: due to unfortunate circumstances, the bootrom in the Kirkwood SOC
* expects the ECC to be computed backward, i.e. from the last byte down
* to the first one.
*/
int nand_calculate_ecc_kw(struct nand_device *nand, const uint8_t *data, uint8_t *ecc)
{
unsigned int r7, r6, r5, r4, r3, r2, r1, r0;
int i;
static int tables_initialized = 0;
if (!tables_initialized) {
gf_build_log_exp_table();
tables_initialized = 1;
}
/*
* Load bytes 504..511 of the data into r.
*/
r0 = data[504];
r1 = data[505];
r2 = data[506];
r3 = data[507];
r4 = data[508];
r5 = data[509];
r6 = data[510];
r7 = data[511];
/*
* Shift bytes 503..0 (in that order) into r0, followed
* by eight zero bytes, while reducing the polynomial by the
* generator polynomial in every step.
*/
for (i = 503; i >= -8; i--) {
unsigned int d;
d = 0;
if (i >= 0)
d = data[i];
if (r7) {
uint16_t *t = gf_exp + gf_log[r7];
r7 = r6 ^ t[0x21c];
r6 = r5 ^ t[0x181];
r5 = r4 ^ t[0x18e];
r4 = r3 ^ t[0x25f];
r3 = r2 ^ t[0x197];
r2 = r1 ^ t[0x193];
r1 = r0 ^ t[0x237];
r0 = d ^ t[0x024];
} else {
r7 = r6;
r6 = r5;
r5 = r4;
r4 = r3;
r3 = r2;
r2 = r1;
r1 = r0;
r0 = d;
}
}
ecc[0] = r0;
ecc[1] = (r0 >> 8) | (r1 << 2);
ecc[2] = (r1 >> 6) | (r2 << 4);
ecc[3] = (r2 >> 4) | (r3 << 6);
ecc[4] = (r3 >> 2);
ecc[5] = r4;
ecc[6] = (r4 >> 8) | (r5 << 2);
ecc[7] = (r5 >> 6) | (r6 << 4);
ecc[8] = (r6 >> 4) | (r7 << 6);
ecc[9] = (r7 >> 2);
return 0;
}