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lrc-matrix
| Author | SHA1 | Date |
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 Vitaliy Filippov
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42ae8f91ee |
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@ -0,0 +1,2 @@
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mat: mat.c
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gcc -O3 -I/usr/include/jerasure -o mat mat.c -lJerasure
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#include <jerasure/reed_sol.h>
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#include <jerasure.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <assert.h>
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// Generate LRC matrix: (groups*local + global) code rows with (data_drives) columns
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// w should be >= log2(data_drives + groups*local + global), but not necessary 8/16/32
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int* reed_sol_vandermonde_lrc_matrix(int data_drives, int groups, int local, int global, int w)
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{
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if (w < 0 || w > 32 || data_drives + groups*local + global > (1<<w))
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{
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return NULL;
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}
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int *lrc_matrix = (int*)malloc(sizeof(int) * (local*groups+global));
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int *matrix = reed_sol_vandermonde_coding_matrix(data_drives, local+global, w);
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// Enough to transform LRC 8+2+2 GF(8) matrix into MR-LRC
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//for (int i = 0; i < local+global; i++)
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//{
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// int t = matrix[i*data_drives + 3];
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// matrix[i*data_drives + 3] = matrix[i*data_drives + 7];
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// matrix[i*data_drives + 7] = t;
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//}
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for (int gr = 0; gr < groups; gr++)
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{
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for (int l = 0; l < local; l++)
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{
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for (int j = 0; j < data_drives; j++)
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{
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lrc_matrix[(gr*local+l)*data_drives + j] = (j / (data_drives/groups)) == gr ? matrix[l*data_drives + j] : 0;
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}
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}
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}
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for (int i = 0; i < global; i++)
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{
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for (int j = 0; j < data_drives; j++)
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{
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lrc_matrix[(groups*local+i)*data_drives + j] = matrix[(local+i)*data_drives + j];
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}
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}
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free(matrix);
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return lrc_matrix;
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}
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struct lrc_test_result_t
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{
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int success, impossible, failures;
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};
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// Check if the generated LRC with given parameters is Maximally Reconstructible (MR-LRC)
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// Example of a MR-LRC: (8, 2, 1, 2, 6, 8)
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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)
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{
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int n = data_drives;
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int total_rows = n + groups*local + global;
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int impossible = 0, success = 0, failures = 0;
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int *lost_per_group = (int*)malloc(sizeof(int) * groups);
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int *recovered_per_group = (int*)malloc(sizeof(int) * groups);
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int *selected_inverted = (int*)malloc(sizeof(int) * data_drives);
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// global+1 is always recoverable
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for (int lost = global+2; lost <= groups*local+global; lost++)
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{
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int *erased_matrix = (int*)malloc(sizeof(int) * (total_rows-lost)*n);
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int *inverted_matrix = (int*)malloc(sizeof(int) * (total_rows-lost)*n);
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int *p = (int*)malloc(sizeof(int) * (total_rows-lost));
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for (int i = 0; i < n; i++)
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p[i] = i;
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int *p2 = (int*)malloc(sizeof(int) * n);
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if (total_rows-lost > n)
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{
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p[n-1] = n; // skip combinations with all N data disks (0..n-1)
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for (int i = n; i < total_rows-lost; i++)
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p[i] = i+1;
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p[total_rows-lost-1]--; // will be incremented on the first step
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}
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int inc = total_rows-lost-1;
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while (1)
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{
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p[inc]++;
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if (p[inc] >= n+groups*local+global)
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{
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if (inc == 0)
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break;
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inc--;
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}
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else if (inc+1 < total_rows-lost)
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{
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p[inc+1] = p[inc];
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inc++;
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}
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else
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{
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// Check if it should be recoverable
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// Calculate count of data chunks lost in each group
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int nsel = 0;
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for (int gr = 0; gr < groups; gr++)
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{
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lost_per_group[gr] = ((gr+1)*(n/groups) > n ? (n - gr*(n/groups)) : n/groups);
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recovered_per_group[gr] = 0;
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}
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for (int j = 0; j < total_rows-lost; j++)
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{
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if (p[j] < n)
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{
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lost_per_group[(p[j] / (n/groups))]--;
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selected_inverted[nsel++] = j;
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}
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}
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// Every local parity chunk is supposed to restore 1 missing chunk inside its group
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// So, subtract local parity chunk counts from each group lost chunk count
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for (int j = 0; j < total_rows-lost; j++)
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{
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if (p[j] >= n && p[j] < n+groups*local)
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{
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int gr = (p[j]-n)/local;
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if (lost_per_group[gr] > recovered_per_group[gr] && nsel < n)
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{
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selected_inverted[nsel++] = j;
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}
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recovered_per_group[gr]++;
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}
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}
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// Every global parity chunk is supposed to restore 1 chunk of all that are still missing
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int still_missing = 0;
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for (int gr = 0; gr < groups; gr++)
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{
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int non_fixed = lost_per_group[gr] - recovered_per_group[gr];
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still_missing += (non_fixed > 0 ? non_fixed : 0);
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}
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for (int j = 0; j < total_rows-lost; j++)
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{
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if (p[j] >= n+groups*local)
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{
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if (still_missing > 0 && nsel < n)
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{
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selected_inverted[nsel++] = j;
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}
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still_missing--;
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}
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}
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if (still_missing <= 0)
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{
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// We hope it can be recoverable. Try to invert it
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assert(nsel == n);
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for (int i = 0; i < n; i++)
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{
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for (int j = 0; j < n; j++)
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{
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erased_matrix[i*n+j] = lrc_matrix[p[selected_inverted[i]]*n+j];
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}
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}
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int invert_ok = jerasure_invert_matrix(erased_matrix, inverted_matrix, n, w);
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if (invert_ok < 0)
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{
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failures++;
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if (log_level > 0)
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{
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printf("\nFAIL: ");
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for (int i = 0; i < total_rows-lost; i++)
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{
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printf("%d ", p[i]);
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}
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printf("\nDIRECT:\n");
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for (int i = 0; i < total_rows-lost; i++)
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{
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for (int j = 0; j < n; j++)
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printf("%d ", lrc_matrix[p[i]*n+j]);
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printf("\n");
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}
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printf("INVERSE:\n");
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for (int i = 0; i < total_rows-lost; i++)
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{
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for (int j = 0; j < n; j++)
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printf("%d ", inverted_matrix[i*n+j]);
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printf("\n");
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}
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}
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}
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else
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{
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success++;
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if (log_level > 2)
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{
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printf("OK: ");
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for (int i = 0; i < total_rows-lost; i++)
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{
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printf("%d ", p[i]);
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}
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printf("\n");
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}
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}
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}
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else
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{
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impossible++;
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if (log_level > 1)
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{
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printf("IMPOSSIBLE: ");
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for (int i = 0; i < total_rows-lost; i++)
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{
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printf("%d ", p[i]);
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}
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printf("\n");
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}
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}
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}
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}
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free(p2);
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free(p);
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free(inverted_matrix);
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free(erased_matrix);
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}
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free(lost_per_group);
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free(recovered_per_group);
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return (struct lrc_test_result_t){
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.success = success,
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.impossible = impossible,
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.failures = failures,
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};
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}
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int main()
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{
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int W = 8, MATRIX_W = 8;
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int n = 8, groups = 2, local = 1, global = 2;
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//n = 4, groups = 2, local = 1, global = 1;
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int total_rows = n+groups*local+global;
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int *matrix = reed_sol_vandermonde_lrc_matrix(n, groups, local, global, MATRIX_W);
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int *lrc_matrix = (int*)malloc(sizeof(int) * total_rows*n);
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// Fill identity+LRC matrix
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for (int i = 0; i < n; i++)
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for (int j = 0; j < n; j++)
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lrc_matrix[i*n + j] = j == i ? 1 : 0;
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memcpy(lrc_matrix + n*n, matrix, (total_rows-n)*n*sizeof(int));
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free(matrix);
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matrix = NULL;
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// Print LRC matrix
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for (int i = 0; i < total_rows; i++)
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{
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for (int j = 0; j < n; j++)
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{
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printf("%d ", lrc_matrix[i*n+j]);
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}
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printf("\n");
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}
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struct lrc_test_result_t t = check_mr_lrc(lrc_matrix, n, groups, local, global, W, 1);
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printf("\n%d recovered, %d impossible, %d failures\n", t.success, t.impossible, t.failures);
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return 0;
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}
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// 1 1 1 1 0 0 0 0
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// 0 0 0 0 1 1 1 1
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// 1 55 39 73 84 181 225 217
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// 1 172 70 235 143 34 200 101
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//
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// Can't recover
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// 1 2 4 5 8 9 10 11 -1
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// 2 3 4 6 8 9 10 11 -1
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// FULL:
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// 1 0 0 0 0 0 0 0
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// 0 1 0 0 0 0 0 0
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// 0 0 1 0 0 0 0 0
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// 0 0 0 1 0 0 0 0
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// 0 0 0 0 1 0 0 0
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// 0 0 0 0 0 1 0 0
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// 0 0 0 0 0 0 1 0
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// 0 0 0 0 0 0 0 1
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// 1 1 1 1 0 0 0 0
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// 0 0 0 0 1 1 1 1
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// 1 55 39 73 84 181 225 217
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// 1 172 70 235 143 34 200 101
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// FIRST UNRECOVERABLE:
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// 0 1 0 0 0 0 0 0
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// 0 0 1 0 0 0 0 0
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// 0 0 0 0 1 0 0 0
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// 0 0 0 0 0 1 0 0
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// 1 1 1 1 0 0 0 0
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// 0 0 0 0 1 1 1 1
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// 1 55 39 73 84 181 225 217
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// 1 172 70 235 143 34 200 101
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// SECOND UNRECOVERABLE:
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// 0 0 1 0 0 0 0 0
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// 0 0 0 1 0 0 0 0
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// 0 0 0 0 1 0 0 0
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// 0 0 0 0 0 0 1 0
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// 1 1 1 1 0 0 0 0
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// 0 0 0 0 1 1 1 1
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// 1 55 39 73 84 181 225 217
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// 1 172 70 235 143 34 200 101
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// Ho ho ho
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