--- /dev/null
+/*
+ * GRUB -- GRand Unified Bootloader
+ * Copyright (C) 2010 Free Software Foundation, Inc.
+ *
+ * GRUB 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 3 of the License, or
+ * (at your option) any later version.
+ *
+ * GRUB 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.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with GRUB. If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifdef TEST
+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+typedef unsigned int grub_size_t;
+typedef unsigned char grub_uint8_t;
+typedef unsigned short grub_uint16_t;
+#define xmalloc malloc
+#define grub_memset memset
+#define grub_memcpy memcpy
+#else
+#include <grub/types.h>
+#include <grub/reed_solomon.h>
+#include <grub/util/misc.h>
+#include <grub/misc.h>
+#endif
+
+#define GF_SIZE 8
+typedef grub_uint8_t gf_single_t;
+typedef grub_uint16_t gf_double_t;
+const gf_single_t gf_polynomial = 0x1d;
+
+#define SECTOR_SIZE 512
+#define MAX_BLOCK_SIZE (200 * SECTOR_SIZE)
+
+static gf_single_t
+gf_reduce (gf_double_t a)
+{
+ int i;
+ for (i = GF_SIZE - 1; i >= 0; i--)
+ if (a & (1ULL << (i + GF_SIZE)))
+ a ^= (((gf_double_t) gf_polynomial) << i);
+ return a & ((1ULL << GF_SIZE) - 1);
+}
+
+static gf_single_t
+gf_mul (gf_single_t a, gf_single_t b)
+{
+ gf_double_t res = 0;
+ int i;
+ for (i = 0; i < GF_SIZE; i++)
+ if (b & (1 << i))
+ res ^= ((gf_double_t) a) << i;
+ return gf_reduce (res);
+}
+
+static int
+bin_log2 (gf_double_t a)
+{
+ int i = 0;
+ while (a)
+ {
+ a >>= 1;
+ i++;
+ }
+ return i - 1;
+}
+
+static gf_single_t
+gf_invert (gf_single_t a)
+{
+ /* We start with: */
+ /* 1 * a + 0 * p = a */
+ /* 0 * a + 1 * p = p */
+ gf_double_t x1 = 1, y1 = 0, z1 = a, x2 = 0, y2 = 1;
+ gf_double_t z2 = gf_polynomial | (1ULL << GF_SIZE), t;
+ /* invariant: z1 < z2*/
+ while (z1 != 0)
+ {
+ int k;
+ k = bin_log2 (z2) - bin_log2 (z1);
+ x2 ^= (x1 << k);
+ y2 ^= (y1 << k);
+ z2 ^= (z1 << k);
+
+ if (z1 >= z2)
+ {
+ t = x2;
+ x2 = x1;
+ x1 = t;
+ t = y2;
+ y2 = y1;
+ y1 = t;
+ t = z2;
+ z2 = z1;
+ z1 = t;
+ }
+ }
+
+ return gf_reduce (x2);
+}
+
+static gf_single_t
+pol_evaluate (gf_single_t *pol, grub_size_t degree, gf_single_t x)
+{
+ int i;
+ gf_single_t xn = 1, s = 0;
+ for (i = degree; i >= 0; i--)
+ {
+ s ^= gf_mul (pol[i], xn);
+ xn = gf_mul (x, xn);
+ }
+ return s;
+}
+
+static void
+rs_encode (gf_single_t *data, grub_size_t s, grub_size_t rs)
+{
+ gf_single_t *rs_polynomial, a = 1;
+ int i, j;
+ gf_single_t *m;
+ m = xmalloc ((s + rs) * sizeof (gf_single_t));
+ grub_memcpy (m, data, s * sizeof (gf_single_t));
+ grub_memset (m + s, 0, rs * sizeof (gf_single_t));
+ rs_polynomial = xmalloc ((rs + 1) * sizeof (gf_single_t));
+ grub_memset (rs_polynomial, 0, (rs + 1) * sizeof (gf_single_t));
+ rs_polynomial[rs] = 1;
+ /* Multiply with X - a^r */
+ for (j = 0; j < rs; j++)
+ {
+ if (a & (1 << (GF_SIZE - 1)))
+ {
+ a <<= 1;
+ a ^= gf_polynomial;
+ }
+ else
+ a <<= 1;
+ for (i = 0; i < rs; i++)
+ rs_polynomial[i] = rs_polynomial[i + 1] ^ gf_mul (a, rs_polynomial[i]);
+ rs_polynomial[rs] = gf_mul (a, rs_polynomial[rs]);
+ }
+ for (j = 0; j < s; j++)
+ if (m[j])
+ {
+ gf_single_t f = m[j];
+ for (i = 0; i <= rs; i++)
+ m[i+j] ^= gf_mul (rs_polynomial[i], f);
+ }
+ free (rs_polynomial);
+ grub_memcpy (data + s, m + s, rs * sizeof (gf_single_t));
+ free (m);
+
+}
+
+static void
+syndroms (gf_single_t *m, grub_size_t s, grub_size_t rs,
+ gf_single_t *sy)
+{
+ gf_single_t xn = 1;
+ int i;
+ for (i = 0; i < rs; i++)
+ {
+ if (xn & (1 << (GF_SIZE - 1)))
+ {
+ xn <<= 1;
+ xn ^= gf_polynomial;
+ }
+ else
+ xn <<= 1;
+ sy[i] = pol_evaluate (m, s + rs - 1, xn);
+ }
+}
+
+static void
+rs_recover (gf_single_t *m, grub_size_t s, grub_size_t rs)
+{
+ grub_size_t rs2 = rs / 2;
+ gf_single_t *sigma;
+ gf_single_t *errpot;
+ int *errpos;
+ gf_single_t *sy;
+ int errnum = 0;
+ int i, j;
+
+ sigma = xmalloc (rs2 * sizeof (gf_single_t));
+ errpot = xmalloc (rs2 * sizeof (gf_single_t));
+ errpos = xmalloc (rs2 * sizeof (int));
+ sy = xmalloc (rs * sizeof (gf_single_t));
+
+ syndroms (m, s, rs, sy);
+
+ {
+ gf_single_t *eq;
+ int *chosen;
+
+ eq = xmalloc (rs2 * (rs2 + 1) * sizeof (gf_single_t));
+ chosen = xmalloc (rs2 * sizeof (int));
+
+ for (i = 0; i < rs; i++)
+ if (sy[i] != 0)
+ break;
+
+ /* No error detected. */
+ if (i == rs)
+ return;
+
+ for (i = 0; i < rs2; i++)
+ for (j = 0; j < rs2 + 1; j++)
+ eq[i * (rs2 + 1) + j] = sy[i+j];
+
+ grub_memset (sigma, 0, rs2 * sizeof (gf_single_t));
+ grub_memset (chosen, -1, rs2 * sizeof (int));
+
+ for (i = 0 ; i < rs2; i++)
+ {
+ int nzidx;
+ int k;
+ gf_single_t r;
+ for (nzidx = 0; nzidx < rs2 && (eq[i * (rs2 + 1) + nzidx] == 0);
+ nzidx++);
+ if (nzidx == rs2)
+ {
+ break;
+ }
+ chosen[i] = nzidx;
+ r = gf_invert (eq[i * (rs2 + 1) + nzidx]);
+ for (j = 0; j < rs2 + 1; j++)
+ eq[i * (rs2 + 1) + j] = gf_mul (eq[i * (rs2 + 1) + j], r);
+ for (j = i + 1; j < rs2; j++)
+ {
+ gf_single_t rr = eq[j * (rs2 + 1) + nzidx];
+ for (k = 0; k < rs2 + 1; k++)
+ eq[j * (rs2 + 1) + k] ^= gf_mul (eq[i * (rs2 + 1) + k], rr);;
+ }
+ }
+ for (i = rs2 - 1; i >= 0; i--)
+ {
+ gf_single_t s = 0;
+ if (chosen[i] == -1)
+ continue;
+ for (j = 0; j < rs2; j++)
+ s ^= gf_mul (eq[i * (rs2 + 1) + j], sigma[j]);
+ s ^= eq[i * (rs2 + 1) + rs2];
+ sigma[chosen[i]] = s;
+ }
+
+ free (chosen);
+ free (eq);
+ }
+
+ {
+ gf_single_t xn = 1, xx = gf_invert (2), yn = 1;
+ int lp = 0;
+ for (i = 0; i < rs + s; i++)
+ {
+ gf_single_t ev = (gf_mul (pol_evaluate (sigma, rs2 - 1, xn), xn) ^ 1);
+ if (ev == 0)
+ {
+ errpot[errnum] = yn;
+ errpos[errnum++] = s + rs - i - 1;
+ }
+ yn = gf_mul (yn, 2);
+ xn = gf_mul (xn, xx);
+ }
+ }
+ {
+ gf_single_t *eq;
+ int *chosen;
+ gf_single_t *errvals;
+
+ eq = xmalloc (rs * (errnum + 1) * sizeof (gf_single_t));
+ chosen = xmalloc (rs * sizeof (int));
+ errvals = xmalloc (errnum * sizeof (int));
+
+ grub_memset (chosen, -1, rs * sizeof (int));
+ grub_memset (errvals, 0, errnum * sizeof (gf_single_t));
+
+ for (j = 0; j < errnum; j++)
+ eq[j] = errpot[j];
+ eq[errnum] = sy[0];
+ for (i = 1; i < rs; i++)
+ {
+ for (j = 0; j < errnum; j++)
+ eq[(errnum + 1) * i + j] = gf_mul (errpot[j],
+ eq[(errnum + 1) * (i - 1) + j]);
+ eq[(errnum + 1) * i + errnum] = sy[i];
+ }
+ for (i = 0 ; i < rs; i++)
+ {
+ int nzidx;
+ int k;
+ gf_single_t r;
+ for (nzidx = 0; nzidx < errnum && (eq[i * (errnum + 1) + nzidx] == 0);
+ nzidx++);
+ if (nzidx == errnum)
+ continue;
+ chosen[i] = nzidx;
+ r = gf_invert (eq[i * (errnum + 1) + nzidx]);
+ for (j = 0; j < errnum + 1; j++)
+ eq[i * (errnum + 1) + j] = gf_mul (eq[i * (errnum + 1) + j], r);
+ for (j = i + 1; j < rs; j++)
+ {
+ gf_single_t rr = eq[j * (errnum + 1) + nzidx];
+ for (k = 0; k < errnum + 1; k++)
+ eq[j * (errnum + 1) + k] ^= gf_mul (eq[i * (errnum + 1) + k], rr);
+ }
+ }
+ for (i = rs - 1; i >= 0; i--)
+ {
+ gf_single_t s = 0;
+ if (chosen[i] == -1)
+ continue;
+ for (j = 0; j < errnum; j++)
+ s ^= gf_mul (eq[i * (errnum + 1) + j], errvals[j]);
+ s ^= eq[i * (errnum + 1) + errnum];
+ errvals[chosen[i]] = s;
+ }
+ for (i = 0; i < errnum; i++)
+ m[errpos[i]] ^= errvals[i];
+ }
+ free (sy);
+}
+
+static void
+decode_block (gf_single_t *ptr, grub_size_t s,
+ gf_single_t *rptr, grub_size_t rs)
+{
+ grub_size_t ss;
+ int i, j, k;
+ for (i = 0; i < SECTOR_SIZE; i++)
+ {
+ grub_size_t ds = (s + SECTOR_SIZE - 1 - i) / SECTOR_SIZE;
+ grub_size_t rr = (rs + SECTOR_SIZE - 1 - i) / SECTOR_SIZE;
+ gf_single_t m[ds + rr];
+
+ for (j = 0; j < ds; j++)
+ m[j] = ptr[SECTOR_SIZE * j + i];
+ for (j = 0; j < rr; j++)
+ m[j + ds] = rptr[SECTOR_SIZE * j + i];
+
+ rs_recover (m, ds, rr);
+
+ for (j = 0; j < ds; j++)
+ ptr[SECTOR_SIZE * j + i] = m[j];
+ }
+}
+
+static void
+encode_block (gf_single_t *ptr, grub_size_t s,
+ gf_single_t *rptr, grub_size_t rs)
+{
+ grub_size_t ss;
+ int i, j;
+ for (i = 0; i < SECTOR_SIZE; i++)
+ {
+ grub_size_t ds = (s + SECTOR_SIZE - 1 - i) / SECTOR_SIZE;
+ grub_size_t rr = (rs + SECTOR_SIZE - 1 - i) / SECTOR_SIZE;
+ gf_single_t m[ds + rr];
+ for (j = 0; j < ds; j++)
+ m[j] = ptr[SECTOR_SIZE * j + i];
+ rs_encode (m, ds, rr);
+ for (j = 0; j < rr; j++)
+ rptr[SECTOR_SIZE * j + i] = m[j + ds];
+ }
+}
+
+void
+grub_reed_solomon_add_redundancy (void *buffer, grub_size_t data_size,
+ grub_size_t redundancy)
+{
+ grub_size_t s = data_size;
+ grub_size_t rs = redundancy;
+ gf_single_t *ptr = buffer;
+ gf_single_t *rptr = ptr + s;
+
+ while (s > 0)
+ {
+ grub_size_t tt;
+ grub_size_t cs, crs;
+ cs = s;
+ crs = rs;
+ tt = cs + crs;
+ if (tt > MAX_BLOCK_SIZE)
+ {
+ cs = (cs * MAX_BLOCK_SIZE) / tt;
+ crs = (crs * MAX_BLOCK_SIZE) / tt;
+ }
+ encode_block (ptr, cs, rptr, crs);
+ ptr += cs;
+ rptr += crs;
+ s -= cs;
+ rs -= crs;
+ }
+}
+
+void
+grub_reed_solomon_recover (void *ptr, grub_size_t s, grub_size_t rs)
+{
+ gf_single_t *rptr = ptr + s;
+ while (s > 0)
+ {
+ grub_size_t tt;
+ grub_size_t cs, crs;
+ cs = s;
+ crs = rs;
+ tt = cs + crs;
+ if (tt > MAX_BLOCK_SIZE)
+ {
+ cs = cs * MAX_BLOCK_SIZE / tt;
+ crs = crs * MAX_BLOCK_SIZE / tt;
+ }
+ decode_block (ptr, cs, rptr, crs);
+ ptr += cs;
+ rptr += crs;
+ s -= cs;
+ rs -= crs;
+ }
+}
+
+#ifdef TEST
+int
+main (int argc, char **argv)
+{
+ FILE *in, *out;
+ grub_size_t s, rs;
+ char *buf;
+ in = fopen ("tst.bin", "rb");
+ if (!in)
+ return 1;
+ fseek (in, 0, SEEK_END);
+ s = ftell (in);
+ fseek (in, 0, SEEK_SET);
+ rs = 1024 * ((s + MAX_BLOCK_SIZE - 1) / (MAX_BLOCK_SIZE - 1024));
+ buf = xmalloc (s + rs + SECTOR_SIZE);
+ fread (buf, 1, s, in);
+
+ grub_reed_solomon_add_redundancy (buf, s, rs);
+
+ out = fopen ("tst_rs.bin", "wb");
+ fwrite (buf, 1, s + rs, out);
+ fclose (out);
+
+ grub_memset (buf + 512 * 15, 0, 512);
+
+ out = fopen ("tst_dam.bin", "wb");
+ fwrite (buf, 1, s + rs, out);
+ fclose (out);
+
+ grub_reed_solomon_recover (buf, s, rs);
+
+ out = fopen ("tst_rec.bin", "wb");
+ fwrite (buf, 1, s, out);
+ fclose (out);
+
+ return 0;
+}
+#endif
projects / thirdparty / grub.git / commitdiff
