1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
|
/*
* Reed-Solomon ECC handling for the Marvell Kirkwood SOC
* Copyright (C) 2009 Marvell Semiconductor, Inc.
*
* Authors: Lennert Buytenhek <buytenh@wantstofly.org>
* Nicolas Pitre <nico@cam.org>
*
* 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 <sys/types.h>
#include "nand.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_s *device, const u8 *data, u8 *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) {
u16 *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;
}
|
