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/*
* Reed-Solomon decoder, based on libfec
*
* Copyright (C) 2002, Phil Karn, KA9Q
* libcryptsetup modifications
* Copyright (C) 2017-2023 Red Hat, Inc. All rights reserved.
*
* This file is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this file; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#include <string.h>
#include <stdlib.h>
#include "rs.h"
#define MAX_NR_BUF 256
int decode_rs_char(struct rs* rs, data_t* data)
{
int deg_lambda, el, deg_omega, syn_error, count;
int i, j, r, k;
data_t q, tmp, num1, num2, den, discr_r;
data_t lambda[MAX_NR_BUF], s[MAX_NR_BUF]; /* Err+Eras Locator poly and syndrome poly */
data_t b[MAX_NR_BUF], t[MAX_NR_BUF], omega[MAX_NR_BUF];
data_t root[MAX_NR_BUF], reg[MAX_NR_BUF], loc[MAX_NR_BUF];
if (rs->nroots >= MAX_NR_BUF)
return -1;
memset(s, 0, rs->nroots * sizeof(data_t));
memset(b, 0, (rs->nroots + 1) * sizeof(data_t));
/* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
for (i = 0; i < rs->nroots; i++)
s[i] = data[0];
for (j = 1; j < rs->nn - rs->pad; j++) {
for (i = 0; i < rs->nroots; i++) {
if (s[i] == 0) {
s[i] = data[j];
} else {
s[i] = data[j] ^ rs->alpha_to[modnn(rs, rs->index_of[s[i]] + (rs->fcr + i) * rs->prim)];
}
}
}
/* Convert syndromes to index form, checking for nonzero condition */
syn_error = 0;
for (i = 0; i < rs->nroots; i++) {
syn_error |= s[i];
s[i] = rs->index_of[s[i]];
}
/*
* if syndrome is zero, data[] is a codeword and there are no
* errors to correct. So return data[] unmodified
*/
if (!syn_error)
return 0;
memset(&lambda[1], 0, rs->nroots * sizeof(lambda[0]));
lambda[0] = 1;
for (i = 0; i < rs->nroots + 1; i++)
b[i] = rs->index_of[lambda[i]];
/*
* Begin Berlekamp-Massey algorithm to determine error+erasure
* locator polynomial
*/
r = 0;
el = 0;
while (++r <= rs->nroots) { /* r is the step number */
/* Compute discrepancy at the r-th step in poly-form */
discr_r = 0;
for (i = 0; i < r; i++) {
if ((lambda[i] != 0) && (s[r - i - 1] != A0)) {
discr_r ^= rs->alpha_to[modnn(rs, rs->index_of[lambda[i]] + s[r - i - 1])];
}
}
discr_r = rs->index_of[discr_r]; /* Index form */
if (discr_r == A0) {
/* 2 lines below: B(x) <-- x*B(x) */
memmove(&b[1], b, rs->nroots * sizeof(b[0]));
b[0] = A0;
} else {
/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
t[0] = lambda[0];
for (i = 0; i < rs->nroots; i++) {
if (b[i] != A0)
t[i + 1] = lambda[i + 1] ^ rs->alpha_to[modnn(rs, discr_r + b[i])];
else
t[i + 1] = lambda[i + 1];
}
if (2 * el <= r - 1) {
el = r - el;
/*
* 2 lines below: B(x) <-- inv(discr_r) *
* lambda(x)
*/
for (i = 0; i <= rs->nroots; i++)
b[i] = (lambda[i] == 0) ? A0 : modnn(rs, rs->index_of[lambda[i]] - discr_r + rs->nn);
} else {
/* 2 lines below: B(x) <-- x*B(x) */
memmove(&b[1], b, rs->nroots * sizeof(b[0]));
b[0] = A0;
}
memcpy(lambda, t, (rs->nroots + 1) * sizeof(t[0]));
}
}
/* Convert lambda to index form and compute deg(lambda(x)) */
deg_lambda = 0;
for (i = 0; i < rs->nroots + 1; i++) {
lambda[i] = rs->index_of[lambda[i]];
if (lambda[i] != A0)
deg_lambda = i;
}
/* Find roots of the error+erasure locator polynomial by Chien search */
memcpy(®[1], &lambda[1], rs->nroots * sizeof(reg[0]));
count = 0; /* Number of roots of lambda(x) */
for (i = 1, k = rs->iprim - 1; i <= rs->nn; i++, k = modnn(rs, k + rs->iprim)) {
q = 1; /* lambda[0] is always 0 */
for (j = deg_lambda; j > 0; j--) {
if (reg[j] != A0) {
reg[j] = modnn(rs, reg[j] + j);
q ^= rs->alpha_to[reg[j]];
}
}
if (q != 0)
continue; /* Not a root */
/* store root (index-form) and error location number */
root[count] = i;
loc[count] = k;
/* If we've already found max possible roots, abort the search to save time */
if (++count == deg_lambda)
break;
}
/*
* deg(lambda) unequal to number of roots => uncorrectable
* error detected
*/
if (deg_lambda != count)
return -1;
/*
* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
* x**rs->nroots). in index form. Also find deg(omega).
*/
deg_omega = deg_lambda - 1;
for (i = 0; i <= deg_omega; i++) {
tmp = 0;
for (j = i; j >= 0; j--) {
if ((s[i - j] != A0) && (lambda[j] != A0))
tmp ^= rs->alpha_to[modnn(rs, s[i - j] + lambda[j])];
}
omega[i] = rs->index_of[tmp];
}
/*
* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
* inv(X(l))**(rs->fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
*/
for (j = count - 1; j >= 0; j--) {
num1 = 0;
for (i = deg_omega; i >= 0; i--) {
if (omega[i] != A0)
num1 ^= rs->alpha_to[modnn(rs, omega[i] + i * root[j])];
}
num2 = rs->alpha_to[modnn(rs, root[j] * (rs->fcr - 1) + rs->nn)];
den = 0;
/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
for (i = RS_MIN(deg_lambda, rs->nroots - 1) & ~1; i >= 0; i -= 2) {
if (lambda[i + 1] != A0)
den ^= rs->alpha_to[modnn(rs, lambda[i + 1] + i * root[j])];
}
/* Apply error to data */
if (num1 != 0 && loc[j] >= rs->pad) {
data[loc[j] - rs->pad] ^= rs->alpha_to[modnn(rs, rs->index_of[num1] +
rs->index_of[num2] + rs->nn - rs->index_of[den])];
}
}
return count;
}
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