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master ... lrc-matrix

Author SHA1 Message Date
Vitaliy Filippov 4bee7f7b78 WIP/experimental LRC matrix generator 2023-01-06 17:13:29 +03:00
2 changed files with 293 additions and 0 deletions

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src/lrc/Makefile Normal file
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mat: mat.c
gcc -O3 -I/usr/include/jerasure -o mat mat.c -lJerasure

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src/lrc/mat.c Normal file
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#include <jerasure/reed_sol.h>
#include <jerasure.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
// Generate LRC matrix: (groups*local + global) code rows with (data_drives) columns
// w should be >= log2(data_drives + groups*local + global), but not necessary 8/16/32
int* reed_sol_vandermonde_lrc_matrix(int data_drives, int groups, int local, int global, int w)
{
if (w < 0 || w > 32 || data_drives + groups*local + global > (1<<w))
{
return NULL;
}
int *lrc_matrix = (int*)malloc(sizeof(int) * (local*groups+global));
int *matrix = reed_sol_vandermonde_coding_matrix(data_drives, local+global, w);
// Enough to transform LRC 8+2+2 GF(8) matrix into MR-LRC
//for (int i = 0; i < local+global; i++)
//{
// int t = matrix[i*data_drives + 3];
// matrix[i*data_drives + 3] = matrix[i*data_drives + 7];
// matrix[i*data_drives + 7] = t;
//}
for (int gr = 0; gr < groups; gr++)
{
for (int l = 0; l < local; l++)
{
for (int j = 0; j < data_drives; j++)
{
lrc_matrix[(gr*local+l)*data_drives + j] = (j / (data_drives/groups)) == gr ? matrix[l*data_drives + j] : 0;
}
}
}
for (int i = 0; i < global; i++)
{
for (int j = 0; j < data_drives; j++)
{
lrc_matrix[(groups*local+i)*data_drives + j] = matrix[(local+i)*data_drives + j];
}
}
free(matrix);
return lrc_matrix;
}
struct lrc_test_result_t
{
int success, impossible, failures;
};
// Check if the generated LRC with given parameters is Maximally Reconstructible (MR-LRC)
// Example of a MR-LRC: (8, 2, 1, 2, 6, 8)
struct lrc_test_result_t check_mr_lrc(int *lrc_matrix, int data_drives, int groups, int local, int global, int w, int log_level)
{
int n = data_drives;
int total_rows = n + groups*local + global;
int impossible = 0, success = 0, failures = 0;
int *lost_per_group = (int*)malloc(sizeof(int) * groups);
int *recovered_per_group = (int*)malloc(sizeof(int) * groups);
int *selected_inverted = (int*)malloc(sizeof(int) * data_drives);
// global+1 is always recoverable
for (int lost = global+2; lost <= groups*local+global; lost++)
{
int *erased_matrix = (int*)malloc(sizeof(int) * (total_rows-lost)*n);
int *inverted_matrix = (int*)malloc(sizeof(int) * (total_rows-lost)*n);
int *p = (int*)malloc(sizeof(int) * (total_rows-lost));
for (int i = 0; i < n; i++)
p[i] = i;
int *p2 = (int*)malloc(sizeof(int) * n);
if (total_rows-lost > n)
{
p[n-1] = n; // skip combinations with all N data disks (0..n-1)
for (int i = n; i < total_rows-lost; i++)
p[i] = i+1;
p[total_rows-lost-1]--; // will be incremented on the first step
}
int inc = total_rows-lost-1;
while (1)
{
p[inc]++;
if (p[inc] >= n+groups*local+global)
{
if (inc == 0)
break;
inc--;
}
else if (inc+1 < total_rows-lost)
{
p[inc+1] = p[inc];
inc++;
}
else
{
// Check if it should be recoverable
// Calculate count of data chunks lost in each group
int nsel = 0;
for (int gr = 0; gr < groups; gr++)
{
lost_per_group[gr] = ((gr+1)*(n/groups) > n ? (n - gr*(n/groups)) : n/groups);
recovered_per_group[gr] = 0;
}
for (int j = 0; j < total_rows-lost; j++)
{
if (p[j] < n)
{
lost_per_group[(p[j] / (n/groups))]--;
selected_inverted[nsel++] = j;
}
}
// Every local parity chunk is supposed to restore 1 missing chunk inside its group
// So, subtract local parity chunk counts from each group lost chunk count
for (int j = 0; j < total_rows-lost; j++)
{
if (p[j] >= n && p[j] < n+groups*local)
{
int gr = (p[j]-n)/local;
if (lost_per_group[gr] > recovered_per_group[gr] && nsel < n)
{
selected_inverted[nsel++] = j;
}
recovered_per_group[gr]++;
}
}
// Every global parity chunk is supposed to restore 1 chunk of all that are still missing
int still_missing = 0;
for (int gr = 0; gr < groups; gr++)
{
int non_fixed = lost_per_group[gr] - recovered_per_group[gr];
still_missing += (non_fixed > 0 ? non_fixed : 0);
}
for (int j = 0; j < total_rows-lost; j++)
{
if (p[j] >= n+groups*local)
{
if (still_missing > 0 && nsel < n)
{
selected_inverted[nsel++] = j;
}
still_missing--;
}
}
if (still_missing <= 0)
{
// We hope it can be recoverable. Try to invert it
assert(nsel == n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
erased_matrix[i*n+j] = lrc_matrix[p[selected_inverted[i]]*n+j];
}
}
int invert_ok = jerasure_invert_matrix(erased_matrix, inverted_matrix, n, w);
if (invert_ok < 0)
{
failures++;
if (log_level > 0)
{
printf("\nFAIL: ");
for (int i = 0; i < total_rows-lost; i++)
{
printf("%d ", p[i]);
}
printf("\nDIRECT:\n");
for (int i = 0; i < total_rows-lost; i++)
{
for (int j = 0; j < n; j++)
printf("%d ", lrc_matrix[p[i]*n+j]);
printf("\n");
}
printf("INVERSE:\n");
for (int i = 0; i < total_rows-lost; i++)
{
for (int j = 0; j < n; j++)
printf("%d ", inverted_matrix[i*n+j]);
printf("\n");
}
}
}
else
{
success++;
if (log_level > 2)
{
printf("OK: ");
for (int i = 0; i < total_rows-lost; i++)
{
printf("%d ", p[i]);
}
printf("\n");
}
}
}
else
{
impossible++;
if (log_level > 1)
{
printf("IMPOSSIBLE: ");
for (int i = 0; i < total_rows-lost; i++)
{
printf("%d ", p[i]);
}
printf("\n");
}
}
}
}
free(p2);
free(p);
free(inverted_matrix);
free(erased_matrix);
}
free(lost_per_group);
free(recovered_per_group);
return (struct lrc_test_result_t){
.success = success,
.impossible = impossible,
.failures = failures,
};
}
int main()
{
int W = 8, MATRIX_W = 8;
int n = 8, groups = 2, local = 1, global = 2;
//n = 4, groups = 2, local = 1, global = 1;
int total_rows = n+groups*local+global;
int *matrix = reed_sol_vandermonde_lrc_matrix(n, groups, local, global, MATRIX_W);
int *lrc_matrix = (int*)malloc(sizeof(int) * total_rows*n);
// Fill identity+LRC matrix
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
lrc_matrix[i*n + j] = j == i ? 1 : 0;
memcpy(lrc_matrix + n*n, matrix, (total_rows-n)*n*sizeof(int));
free(matrix);
matrix = NULL;
// Print LRC matrix
for (int i = 0; i < total_rows; i++)
{
for (int j = 0; j < n; j++)
{
printf("%d ", lrc_matrix[i*n+j]);
}
printf("\n");
}
struct lrc_test_result_t t = check_mr_lrc(lrc_matrix, n, groups, local, global, W, 1);
printf("\n%d recovered, %d impossible, %d failures\n", t.success, t.impossible, t.failures);
return 0;
}
// 1 1 1 1 0 0 0 0
// 0 0 0 0 1 1 1 1
// 1 55 39 73 84 181 225 217
// 1 172 70 235 143 34 200 101
//
// Can't recover
// 1 2 4 5 8 9 10 11 -1
// 2 3 4 6 8 9 10 11 -1
// FULL:
// 1 0 0 0 0 0 0 0
// 0 1 0 0 0 0 0 0
// 0 0 1 0 0 0 0 0
// 0 0 0 1 0 0 0 0
// 0 0 0 0 1 0 0 0
// 0 0 0 0 0 1 0 0
// 0 0 0 0 0 0 1 0
// 0 0 0 0 0 0 0 1
// 1 1 1 1 0 0 0 0
// 0 0 0 0 1 1 1 1
// 1 55 39 73 84 181 225 217
// 1 172 70 235 143 34 200 101
// FIRST UNRECOVERABLE:
// 0 1 0 0 0 0 0 0
// 0 0 1 0 0 0 0 0
// 0 0 0 0 1 0 0 0
// 0 0 0 0 0 1 0 0
// 1 1 1 1 0 0 0 0
// 0 0 0 0 1 1 1 1
// 1 55 39 73 84 181 225 217
// 1 172 70 235 143 34 200 101
// SECOND UNRECOVERABLE:
// 0 0 1 0 0 0 0 0
// 0 0 0 1 0 0 0 0
// 0 0 0 0 1 0 0 0
// 0 0 0 0 0 0 1 0
// 1 1 1 1 0 0 0 0
// 0 0 0 0 1 1 1 1
// 1 55 39 73 84 181 225 217
// 1 172 70 235 143 34 200 101
// Ho ho ho