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 symetric 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 symetric 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;
}