src/flash/nand/ecc_kw.c

   1 // SPDX-License-Identifier: GPL-2.0-or-later
   2
   3 /*
   4  * Reed-Solomon ECC handling for the Marvell Kirkwood SOC
   5  * Copyright (C) 2009 Marvell Semiconductor, Inc.
   6  *
   7  * Authors: Lennert Buytenhek <buytenh@wantstofly.org>
   8  *          Nicolas Pitre <nico@fluxnic.net>
   9  */
  10
  11 #ifdef HAVE_CONFIG_H
  12 #include "config.h"
  13 #endif
  14
  15 #include "core.h"
  16
  17 /*****************************************************************************
  18  * Arithmetic in GF(2^10) ("F") modulo x^10 + x^3 + 1.
  19  *
  20  * For multiplication, a discrete log/exponent table is used, with
  21  * primitive element x (F is a primitive field, so x is primitive).
  22  */
  23 #define MODPOLY 0x409           /* x^10 + x^3 + 1 in binary */
  24
  25 /*
  26  * Maps an integer a [0..1022] to a polynomial b = gf_exp[a] in
  27  * GF(2^10) mod x^10 + x^3 + 1 such that b = x ^ a.  There's two
  28  * identical copies of this array back-to-back so that we can save
  29  * the mod 1023 operation when doing a GF multiplication.
  30  */
  31 static uint16_t gf_exp[1023 + 1023];
  32
  33 /*
  34  * Maps a polynomial b in GF(2^10) mod x^10 + x^3 + 1 to an index
  35  * a = gf_log[b] in [0..1022] such that b = x ^ a.
  36  */
  37 static uint16_t gf_log[1024];
  38
  39 static void gf_build_log_exp_table(void)
  40 {
  41         int i;
  42         int p_i;
  43
  44         /*
  45          * p_i = x ^ i
  46          *
  47          * Initialise to 1 for i = 0.
  48          */
  49         p_i = 1;
  50
  51         for (i = 0; i < 1023; i++) {
  52                 gf_exp[i] = p_i;
  53                 gf_exp[i + 1023] = p_i;
  54                 gf_log[p_i] = i;
  55
  56                 /*
  57                  * p_i = p_i * x
  58                  */
  59                 p_i <<= 1;
  60                 if (p_i & (1 << 10))
  61                         p_i ^= MODPOLY;
  62         }
  63 }
  64
  65
  66 /*****************************************************************************
  67  * Reed-Solomon code
  68  *
  69  * This implements a (1023,1015) Reed-Solomon ECC code over GF(2^10)
  70  * mod x^10 + x^3 + 1, shortened to (520,512).  The ECC data consists
  71  * of 8 10-bit symbols, or 10 8-bit bytes.
  72  *
  73  * Given 512 bytes of data, computes 10 bytes of ECC.
  74  *
  75  * This is done by converting the 512 bytes to 512 10-bit symbols
  76  * (elements of F), interpreting those symbols as a polynomial in F[X]
  77  * by taking symbol 0 as the coefficient of X^8 and symbol 511 as the
  78  * coefficient of X^519, and calculating the residue of that polynomial
  79  * divided by the generator polynomial, which gives us the 8 ECC symbols
  80  * as the remainder.  Finally, we convert the 8 10-bit ECC symbols to 10
  81  * 8-bit bytes.
  82  *
  83  * The generator polynomial is hardcoded, as that is faster, but it
  84  * can be computed by taking the primitive element a = x (in F), and
  85  * constructing a polynomial in F[X] with roots a, a^2, a^3, ..., a^8
  86  * by multiplying the minimal polynomials for those roots (which are
  87  * just 'x - a^i' for each i).
  88  *
  89  * Note: due to unfortunate circumstances, the bootrom in the Kirkwood SOC
  90  * expects the ECC to be computed backward, i.e. from the last byte down
  91  * to the first one.
  92  */
  93 int nand_calculate_ecc_kw(struct nand_device *nand, const uint8_t *data, uint8_t *ecc)
  94 {
  95         unsigned int r7, r6, r5, r4, r3, r2, r1, r0;
  96         int i;
  97         static int tables_initialized;
  98
  99         if (!tables_initialized) {
 100                 gf_build_log_exp_table();
 101                 tables_initialized = 1;
 102         }
 103
 104         /*
 105          * Load bytes 504..511 of the data into r.
 106          */
 107         r0 = data[504];
 108         r1 = data[505];
 109         r2 = data[506];
 110         r3 = data[507];
 111         r4 = data[508];
 112         r5 = data[509];
 113         r6 = data[510];
 114         r7 = data[511];
 115
 116         /*
 117          * Shift bytes 503..0 (in that order) into r0, followed
 118          * by eight zero bytes, while reducing the polynomial by the
 119          * generator polynomial in every step.
 120          */
 121         for (i = 503; i >= -8; i--) {
 122                 unsigned int d;
 123
 124                 d = 0;
 125                 if (i >= 0)
 126                         d = data[i];
 127
 128                 if (r7) {
 129                         uint16_t *t = gf_exp + gf_log[r7];
 130
 131                         r7 = r6 ^ t[0x21c];
 132                         r6 = r5 ^ t[0x181];
 133                         r5 = r4 ^ t[0x18e];
 134                         r4 = r3 ^ t[0x25f];
 135                         r3 = r2 ^ t[0x197];
 136                         r2 = r1 ^ t[0x193];
 137                         r1 = r0 ^ t[0x237];
 138                         r0 = d  ^ t[0x024];
 139                 } else {
 140                         r7 = r6;
 141                         r6 = r5;
 142                         r5 = r4;
 143                         r4 = r3;
 144                         r3 = r2;
 145                         r2 = r1;
 146                         r1 = r0;
 147                         r0 = d;
 148                 }
 149         }
 150
 151         ecc[0] = r0;
 152         ecc[1] = (r0 >> 8) | (r1 << 2);
 153         ecc[2] = (r1 >> 6) | (r2 << 4);
 154         ecc[3] = (r2 >> 4) | (r3 << 6);
 155         ecc[4] = (r3 >> 2);
 156         ecc[5] = r4;
 157         ecc[6] = (r4 >> 8) | (r5 << 2);
 158         ecc[7] = (r5 >> 6) | (r6 << 4);
 159         ecc[8] = (r6 >> 4) | (r7 << 6);
 160         ecc[9] = (r7 >> 2);
 161
 162         return 0;
 163 }