isa-l/examples/ec/ec_piggyback_example.c

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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <getopt.h>
#include "erasure_code.h" // use <isa-l.h> instead when linking against installed
#include "test.h"

#define MMAX 255
#define KMAX 255

typedef unsigned char u8;
int verbose = 0;

int
usage(void)
{
        fprintf(stderr,
                "Usage: ec_piggyback_example [options]\n"
                "  -h        Help\n"
                "  -k <val>  Number of source fragments\n"
                "  -p <val>  Number of parity fragments\n"
                "  -l <val>  Length of fragments\n"
                "  -e <val>  Simulate erasure on frag index val. Zero based. Can be repeated.\n"
                "  -v        Verbose\n"
                "  -b        Run timed benchmark\n"
                "  -s        Toggle use of sparse matrix opt\n"
                "  -r <seed> Pick random (k, p) with seed\n");
        exit(0);
}

// Cauchy-based matrix
void
gf_gen_full_pb_cauchy_matrix(u8 *a, int m, int k)
{
        int i, j, p = m - k;

        // Identity matrix in top k x k to indicate a symmetric code
        memset(a, 0, k * m);
        for (i = 0; i < k; i++)
                a[k * i + i] = 1;

        for (i = k; i < (k + p / 2); i++) {
                for (j = 0; j < k / 2; j++)
                        a[k * i + j] = gf_inv(i ^ j);
                for (; j < k; j++)
                        a[k * i + j] = 0;
        }
        for (; i < m; i++) {
                for (j = 0; j < k / 2; j++)
                        a[k * i + j] = 0;
                for (; j < k; j++)
                        a[k * i + j] = gf_inv((i - p / 2) ^ (j - k / 2));
        }

        // Fill in mixture of B parity depending on a few localized A sources
        int r = 0, c = 0;
        int repeat_len = k / (p - 2);
        int parity_rows = p / 2;

        for (i = 1 + k + parity_rows; i < m; i++, r++) {
                if (r == (parity_rows - 1) - ((k / 2 % (parity_rows - 1))))
                        repeat_len++;

                for (j = 0; j < repeat_len; j++, c++)
                        a[k * i + c] = gf_inv((k + 1) ^ c);
        }
}

// Vandermonde based matrix - not recommended due to limits when invertable
void
gf_gen_full_pb_vand_matrix(u8 *a, int m, int k)
{
        int i, j, p = m - k;
        unsigned char q, gen = 1;

        // Identity matrix in top k x k to indicate a symmetric code
        memset(a, 0, k * m);
        for (i = 0; i < k; i++)
                a[k * i + i] = 1;

        for (i = k; i < (k + (p / 2)); i++) {
                q = 1;
                for (j = 0; j < k / 2; j++) {
                        a[k * i + j] = q;
                        q = gf_mul(q, gen);
                }
                for (; j < k; j++)
                        a[k * i + j] = 0;
                gen = gf_mul(gen, 2);
        }
        gen = 1;
        for (; i < m; i++) {
                q = 1;
                for (j = 0; j < k / 2; j++) {
                        a[k * i + j] = 0;
                }
                for (; j < k; j++) {
                        a[k * i + j] = q;
                        q = gf_mul(q, gen);
                }
                gen = gf_mul(gen, 2);
        }

        // Fill in mixture of B parity depending on a few localized A sources
        int r = 0, c = 0;
        int repeat_len = k / (p - 2);
        int parity_rows = p / 2;

        for (i = 1 + k + parity_rows; i < m; i++, r++) {
                if (r == (parity_rows - 1) - ((k / 2 % (parity_rows - 1))))
                        repeat_len++;

                for (j = 0; j < repeat_len; j++)
                        a[k * i + c++] = 1;
        }
}

void
print_matrix(int m, int k, unsigned char *s, const char *msg)
{
        int i, j;

        printf("%s:\n", msg);
        for (i = 0; i < m; i++) {
                printf("%3d- ", i);
                for (j = 0; j < k; j++) {
                        printf(" %2x", 0xff & s[j + (i * k)]);
                }
                printf("\n");
        }
        printf("\n");
}

void
print_list(int n, unsigned char *s, const char *msg)
{
        int i;
        if (!verbose)
                return;

        printf("%s: ", msg);
        for (i = 0; i < n; i++)
                printf(" %d", s[i]);
        printf("\n");
}

static int
gf_gen_decode_matrix(u8 *encode_matrix, u8 *decode_matrix, u8 *invert_matrix, u8 *temp_matrix,
                     u8 *decode_index, u8 *frag_err_list, int nerrs, int k, int m);

int
main(int argc, char *argv[])
{
        int i, j, m, c, e, ret;
        int k = 10, p = 4, len = 8 * 1024; // Default params
        int nerrs = 0;
        int benchmark = 0;
        int sparse_matrix_opt = 1;

        // Fragment buffer pointers
        u8 *frag_ptrs[MMAX];
        u8 *parity_ptrs[KMAX];
        u8 *recover_srcs[KMAX];
        u8 *recover_outp[KMAX];
        u8 frag_err_list[MMAX];

        // Coefficient matrices
        u8 *encode_matrix, *decode_matrix;
        u8 *invert_matrix, *temp_matrix;
        u8 *g_tbls;
        u8 decode_index[MMAX];

        if (argc == 1)
                for (i = 0; i < p; i++)
                        frag_err_list[nerrs++] = rand() % (k + p);

        while ((c = getopt(argc, argv, "k:p:l:e:r:hvbs")) != -1) {
                switch (c) {
                case 'k':
                        k = atoi(optarg);
                        break;
                case 'p':
                        p = atoi(optarg);
                        break;
                case 'l':
                        len = atoi(optarg);
                        if (len < 0)
                                usage();
                        break;
                case 'e':
                        e = atoi(optarg);
                        frag_err_list[nerrs++] = e;
                        break;
                case 'r':
                        srand(atoi(optarg));
                        k = (rand() % MMAX) / 4;
                        k = (k < 2) ? 2 : k;
                        p = (rand() % (MMAX - k)) / 4;
                        p = (p < 2) ? 2 : p;
                        for (i = 0; i < k && nerrs < p; i++)
                                if (rand() & 1)
                                        frag_err_list[nerrs++] = i;
                        break;
                case 'v':
                        verbose++;
                        break;
                case 'b':
                        benchmark = 1;
                        break;
                case 's':
                        sparse_matrix_opt = !sparse_matrix_opt;
                        break;
                case 'h':
                default:
                        usage();
                        break;
                }
        }
        m = k + p;

        // Check for valid parameters
        if (m > (MMAX / 2) || k > (KMAX / 2) || m < 0 || p < 2 || k < 1) {
                printf(" Input test parameter error m=%d, k=%d, p=%d, erasures=%d\n", m, k, p,
                       nerrs);
                usage();
        }
        if (nerrs > p) {
                printf(" Number of erasures chosen exceeds power of code erasures=%d p=%d\n", nerrs,
                       p);
        }
        for (i = 0; i < nerrs; i++) {
                if (frag_err_list[i] >= m)
                        printf(" fragment %d not in range\n", frag_err_list[i]);
        }

        printf("ec_piggyback_example:\n");

        /*
         * One simple way to implement piggyback codes is to keep a 2x wide matrix
         * that covers the how each parity is related to both A and B sources.  This
         * keeps it easy to generalize in parameters m,k and the resulting sparse
         * matrix multiplication can be optimized by pre-removal of zero items.
         */

        int k2 = 2 * k;
        int p2 = 2 * p;
        int m2 = k2 + p2;
        int nerrs2 = nerrs;

        encode_matrix = malloc(m2 * k2);
        decode_matrix = malloc(m2 * k2);
        invert_matrix = malloc(m2 * k2);
        temp_matrix = malloc(m2 * k2);
        g_tbls = malloc(k2 * p2 * 32);

        if (encode_matrix == NULL || decode_matrix == NULL || invert_matrix == NULL ||
            temp_matrix == NULL || g_tbls == NULL) {
                printf("Test failure! Error with malloc\n");
                return -1;
        }
        // Allocate the src fragments
        for (i = 0; i < k; i++) {
                if (NULL == (frag_ptrs[i] = malloc(len))) {
                        printf("alloc error: Fail\n");
                        return -1;
                }
        }
        // Allocate the parity fragments
        for (i = 0; i < p2; i++) {
                if (NULL == (parity_ptrs[i] = malloc(len / 2))) {
                        printf("alloc error: Fail\n");
                        return -1;
                }
        }

        // Allocate buffers for recovered data
        for (i = 0; i < p2; i++) {
                if (NULL == (recover_outp[i] = malloc(len / 2))) {
                        printf("alloc error: Fail\n");
                        return -1;
                }
        }

        // Fill sources with random data
        for (i = 0; i < k; i++)
                for (j = 0; j < len; j++)
                        frag_ptrs[i][j] = rand();

        printf(" encode (m,k,p)=(%d,%d,%d) len=%d\n", m, k, p, len);

        // Pick an encode matrix.
        gf_gen_full_pb_cauchy_matrix(encode_matrix, m2, k2);

        if (verbose)
                print_matrix(m2, k2, encode_matrix, "encode matrix");

        // Initialize g_tbls from encode matrix
        ec_init_tables(k2, p2, &encode_matrix[k2 * k2], g_tbls);

        // Fold A and B into single list of fragments
        for (i = 0; i < k; i++)
                frag_ptrs[i + k] = &frag_ptrs[i][len / 2];

        if (!sparse_matrix_opt) {
                // Standard encode using no assumptions on the encode matrix

                // Generate EC parity blocks from sources
                ec_encode_data(len / 2, k2, p2, g_tbls, frag_ptrs, parity_ptrs);

                if (benchmark) {
                        struct perf start;
                        BENCHMARK(&start, BENCHMARK_TIME,
                                  ec_encode_data(len / 2, k2, p2, g_tbls, frag_ptrs, parity_ptrs));
                        printf("ec_piggyback_encode_std: ");
                        perf_print(start, m2 * len / 2);
                }
        } else {
                // Sparse matrix optimization - use fact that input matrix is sparse

                // Keep an encode matrix with some zero elements removed
                u8 *encode_matrix_faster, *g_tbls_faster;
                encode_matrix_faster = malloc(m * k);
                g_tbls_faster = malloc(k * p * 32);
                if (encode_matrix_faster == NULL || g_tbls_faster == NULL) {
                        printf("Test failure! Error with malloc\n");
                        return -1;
                }

                /*
                 * Pack with only the part that we know are non-zero.  Alternatively
                 * we could search and keep track of non-zero elements but for
                 * simplicity we just skip the lower quadrant.
                 */
                for (i = k, j = k2; i < m; i++, j++)
                        memcpy(&encode_matrix_faster[k * i], &encode_matrix[k2 * j], k);

                if (verbose) {
                        print_matrix(p, k, &encode_matrix_faster[k * k], "encode via sparse-opt");
                        print_matrix(p2 / 2, k2, &encode_matrix[(k2 + p2 / 2) * k2],
                                     "encode via sparse-opt");
                }
                // Initialize g_tbls from encode matrix
                ec_init_tables(k, p, &encode_matrix_faster[k * k], g_tbls_faster);

                // Generate EC parity blocks from sources
                ec_encode_data(len / 2, k, p, g_tbls_faster, frag_ptrs, parity_ptrs);
                ec_encode_data(len / 2, k2, p, &g_tbls[k2 * p * 32], frag_ptrs, &parity_ptrs[p]);

                if (benchmark) {
                        struct perf start;
                        BENCHMARK(&start, BENCHMARK_TIME,
                                  ec_encode_data(len / 2, k, p, g_tbls_faster, frag_ptrs,
                                                 parity_ptrs);
                                  ec_encode_data(len / 2, k2, p, &g_tbls[k2 * p * 32], frag_ptrs,
                                                 &parity_ptrs[p]));
                        printf("ec_piggyback_encode_sparse: ");
                        perf_print(start, m2 * len / 2);
                }
        }

        if (nerrs <= 0)
                return 0;

        printf(" recover %d fragments\n", nerrs);

        // Set frag pointers to correspond to parity
        for (i = k2; i < m2; i++)
                frag_ptrs[i] = parity_ptrs[i - k2];

        print_list(nerrs2, frag_err_list, " frag err list");

        // Find a decode matrix to regenerate all erasures from remaining frags
        ret = gf_gen_decode_matrix(encode_matrix, decode_matrix, invert_matrix, temp_matrix,
                                   decode_index, frag_err_list, nerrs2, k2, m2);

        if (ret != 0) {
                printf("Fail on generate decode matrix\n");
                return -1;
        }
        // Pack recovery array pointers as list of valid fragments
        for (i = 0; i < k2; i++)
                if (decode_index[i] < k2)
                        recover_srcs[i] = frag_ptrs[decode_index[i]];
                else
                        recover_srcs[i] = parity_ptrs[decode_index[i] - k2];

        print_list(k2, decode_index, " decode index");

        // Recover data
        ec_init_tables(k2, nerrs2, decode_matrix, g_tbls);
        ec_encode_data(len / 2, k2, nerrs2, g_tbls, recover_srcs, recover_outp);

        if (benchmark) {
                struct perf start;
                BENCHMARK(&start, BENCHMARK_TIME,
                          ec_encode_data(len / 2, k2, nerrs2, g_tbls, recover_srcs, recover_outp));
                printf("ec_piggyback_decode: ");
                perf_print(start, (k2 + nerrs2) * len / 2);
        }
        // Check that recovered buffers are the same as original
        printf(" check recovery of block {");
        for (i = 0; i < nerrs2; i++) {
                printf(" %d", frag_err_list[i]);
                if (memcmp(recover_outp[i], frag_ptrs[frag_err_list[i]], len / 2)) {
                        printf(" Fail erasure recovery %d, frag %d\n", i, frag_err_list[i]);
                        return -1;
                }
        }
        printf(" } done all: Pass\n");

        return 0;
}

// Generate decode matrix from encode matrix and erasure list

static int
gf_gen_decode_matrix(u8 *encode_matrix, u8 *decode_matrix, u8 *invert_matrix, u8 *temp_matrix,
                     u8 *decode_index, u8 *frag_err_list, int nerrs, int k, int m)
{
        int i, j, p, r;
        int nsrcerrs = 0;
        u8 s, *b = temp_matrix;
        u8 frag_in_err[MMAX];

        memset(frag_in_err, 0, sizeof(frag_in_err));

        // Order the fragments in erasure for easier sorting
        for (i = 0; i < nerrs; i++) {
                if (frag_err_list[i] < k)
                        nsrcerrs++;
                frag_in_err[frag_err_list[i]] = 1;
        }

        // Construct b (matrix that encoded remaining frags) by removing erased rows
        for (i = 0, r = 0; i < k; i++, r++) {
                while (frag_in_err[r])
                        r++;
                for (j = 0; j < k; j++)
                        b[k * i + j] = encode_matrix[k * r + j];
                decode_index[i] = r;
        }
        if (verbose > 1)
                print_matrix(k, k, b, "matrix to invert");

        // Invert matrix to get recovery matrix
        if (gf_invert_matrix(b, invert_matrix, k) < 0)
                return -1;

        if (verbose > 2)
                print_matrix(k, k, invert_matrix, "matrix inverted");

        // Get decode matrix with only wanted recovery rows
        for (i = 0; i < nsrcerrs; i++) {
                for (j = 0; j < k; j++) {
                        decode_matrix[k * i + j] = invert_matrix[k * frag_err_list[i] + j];
                }
        }

        // For non-src (parity) erasures need to multiply encode matrix * invert
        for (p = nsrcerrs; p < nerrs; p++) {
                for (i = 0; i < k; i++) {
                        s = 0;
                        for (j = 0; j < k; j++)
                                s ^= gf_mul(invert_matrix[j * k + i],
                                            encode_matrix[k * frag_err_list[p] + j]);

                        decode_matrix[k * p + i] = s;
                }
        }
        if (verbose > 1)
                print_matrix(nerrs, k, decode_matrix, "decode matrix");
        return 0;
}