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Diffstat (limited to '')
| -rw-r--r-- | lib/verity/rs_decode_char.c | 197 |
1 files changed, 197 insertions, 0 deletions
diff --git a/lib/verity/rs_decode_char.c b/lib/verity/rs_decode_char.c new file mode 100644 index 0000000..aa27a64 --- /dev/null +++ b/lib/verity/rs_decode_char.c @@ -0,0 +1,197 @@ +/* + * Reed-Solomon decoder, based on libfec + * + * Copyright (C) 2002, Phil Karn, KA9Q + * libcryptsetup modifications + * Copyright (C) 2017-2021 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" + +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; + /* FIXME: remove VLAs here */ + data_t lambda[rs->nroots + 1], s[rs->nroots]; /* Err+Eras Locator poly and syndrome poly */ + data_t b[rs->nroots + 1], t[rs->nroots + 1], omega[rs->nroots + 1]; + data_t root[rs->nroots], reg[rs->nroots + 1], loc[rs->nroots]; + + 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; +} |