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/*
* Copyright (C) 2013 Andrea Mazzoleni
*
* This program 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 of the License, or
* (at your option) any later version.
*
* This program 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.
*/
/* Matrix inversion test for the RAID library */
#include "internal.h"
#include "combo.h"
#include "gf.h"
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <inttypes.h>
/**
* Like raid_invert() but optimized to only check if the matrix is
* invertible.
*/
static __always_inline int raid_invert_fast(uint8_t *M, int n)
{
int i, j, k;
/* for each element in the diagonal */
for (k = 0; k < n; ++k) {
uint8_t f;
/* the diagonal element cannot be 0 because */
/* we are inverting matrices with all the square */
/* submatrices not singular */
if (M[k * n + k] == 0)
return -1;
/* make the diagonal element to be 1 */
f = inv(M[k * n + k]);
for (j = 0; j < n; ++j)
M[k * n + j] = mul(f, M[k * n + j]);
/* make all the elements over and under the diagonal */
/* to be zero */
for (i = 0; i < n; ++i) {
if (i == k)
continue;
f = M[i * n + k];
for (j = 0; j < n; ++j)
M[i * n + j] ^= mul(f, M[k * n + j]);
}
}
return 0;
}
#define TEST_REFRESH (4 * 1024 * 1024)
/**
* Precomputed number of square submatrices of size nr.
*
* It's bc(np,nr) * bc(nd,nr)
*
* With 1<=nr<=6 and bc(n, r) == binomial coefficient of (n over r).
*/
long long EXPECTED[RAID_PARITY_MAX] = {
1506LL,
470625LL,
52082500LL,
2421836250LL,
47855484300LL,
327012476050LL
};
static __always_inline int test_sub_matrix(int nr, long long *total)
{
uint8_t M[RAID_PARITY_MAX * RAID_PARITY_MAX];
int np = RAID_PARITY_MAX;
int nd = RAID_DATA_MAX;
int ip[RAID_PARITY_MAX];
int id[RAID_DATA_MAX];
long long count;
long long expected;
printf("\n%ux%u\n", nr, nr);
count = 0;
expected = EXPECTED[nr - 1];
/* all combinations (nr of nd) disks */
combination_first(nr, nd, id);
do {
/* all combinations (nr of np) parities */
combination_first(nr, np, ip);
do {
int i, j;
/* setup the submatrix */
for (i = 0; i < nr; ++i)
for (j = 0; j < nr; ++j)
M[i * nr + j] = gfgen[ip[i]][id[j]];
/* invert */
if (raid_invert_fast(M, nr) != 0)
return -1;
if (++count % TEST_REFRESH == 0) {
printf("\r%.3f %%", count * (double)100 / expected);
fflush(stdout);
}
} while (combination_next(nr, np, ip));
} while (combination_next(nr, nd, id));
if (count != expected)
return -1;
printf("\rTested %" PRIi64 " matrix\n", count);
*total += count;
return 0;
}
int test_all_sub_matrix(void)
{
long long total;
printf("Invert all square submatrices of the %dx%d Cauchy matrix\n",
RAID_PARITY_MAX, RAID_DATA_MAX);
printf("\nPlease wait about 2 days...\n");
total = 0;
/* force inlining of everything */
if (test_sub_matrix(1, &total) != 0)
return -1;
if (test_sub_matrix(2, &total) != 0)
return -1;
if (test_sub_matrix(3, &total) != 0)
return -1;
if (test_sub_matrix(4, &total) != 0)
return -1;
if (test_sub_matrix(5, &total) != 0)
return -1;
if (test_sub_matrix(6, &total) != 0)
return -1;
printf("\nTested in total %" PRIi64 " matrix\n", total);
return 0;
}
int main(void)
{
printf("Matrix inversion test for the RAID Cauchy library\n\n");
/* required to set the gfgen table */
raid_init();
if (test_all_sub_matrix() != 0) {
printf("FAILED!\n");
exit(EXIT_FAILURE);
}
printf("OK\n");
return 0;
}
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