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34 #include "erasure_code.h" // use <isa-l.h> instead when linking against installed
40 typedef unsigned char u8
;
46 "Usage: ec_piggyback_example [options]\n"
48 " -k <val> Number of source fragments\n"
49 " -p <val> Number of parity fragments\n"
50 " -l <val> Length of fragments\n"
51 " -e <val> Simulate erasure on frag index val. Zero based. Can be repeated.\n"
53 " -b Run timed benchmark\n"
54 " -s Toggle use of sparse matrix opt\n"
55 " -r <seed> Pick random (k, p) with seed\n");
59 // Cauchy-based matrix
60 void gf_gen_full_pb_cauchy_matrix(u8
* a
, int m
, int k
)
64 // Identity matrix in top k x k to indicate a symetric code
66 for (i
= 0; i
< k
; i
++)
69 for (i
= k
; i
< (k
+ p
/ 2); i
++) {
70 for (j
= 0; j
< k
/ 2; j
++)
71 a
[k
* i
+ j
] = gf_inv(i
^ j
);
76 for (j
= 0; j
< k
/ 2; j
++)
79 a
[k
* i
+ j
] = gf_inv((i
- p
/ 2) ^ (j
- k
/ 2));
82 // Fill in mixture of B parity depending on a few localized A sources
84 int repeat_len
= k
/ (p
- 2);
85 int parity_rows
= p
/ 2;
87 for (i
= 1 + k
+ parity_rows
; i
< m
; i
++, r
++) {
88 if (r
== (parity_rows
- 1) - ((k
/ 2 % (parity_rows
- 1))))
91 for (j
= 0; j
< repeat_len
; j
++, c
++)
92 a
[k
* i
+ c
] = gf_inv((k
+ 1) ^ c
);
96 // Vandermonde based matrix - not recommended due to limits when invertable
97 void gf_gen_full_pb_vand_matrix(u8
* a
, int m
, int k
)
100 unsigned char q
, gen
= 1;
102 // Identity matrix in top k x k to indicate a symetric code
104 for (i
= 0; i
< k
; i
++)
107 for (i
= k
; i
< (k
+ (p
/ 2)); i
++) {
109 for (j
= 0; j
< k
/ 2; j
++) {
115 gen
= gf_mul(gen
, 2);
120 for (j
= 0; j
< k
/ 2; j
++) {
127 gen
= gf_mul(gen
, 2);
130 // Fill in mixture of B parity depending on a few localized A sources
132 int repeat_len
= k
/ (p
- 2);
133 int parity_rows
= p
/ 2;
135 for (i
= 1 + k
+ parity_rows
; i
< m
; i
++, r
++) {
136 if (r
== (parity_rows
- 1) - ((k
/ 2 % (parity_rows
- 1))))
139 for (j
= 0; j
< repeat_len
; j
++)
144 void print_matrix(int m
, int k
, unsigned char *s
, const char *msg
)
148 printf("%s:\n", msg
);
149 for (i
= 0; i
< m
; i
++) {
151 for (j
= 0; j
< k
; j
++) {
152 printf(" %2x", 0xff & s
[j
+ (i
* k
)]);
159 void print_list(int n
, unsigned char *s
, const char *msg
)
166 for (i
= 0; i
< n
; i
++)
171 static int gf_gen_decode_matrix(u8
* encode_matrix
,
176 u8
* frag_err_list
, int nerrs
, int k
, int m
);
178 int main(int argc
, char *argv
[])
180 int i
, j
, m
, c
, e
, ret
;
181 int k
= 10, p
= 4, len
= 8 * 1024; // Default params
184 int sparse_matrix_opt
= 1;
186 // Fragment buffer pointers
188 u8
*parity_ptrs
[KMAX
];
189 u8
*recover_srcs
[KMAX
];
190 u8
*recover_outp
[KMAX
];
191 u8 frag_err_list
[MMAX
];
193 // Coefficient matrices
194 u8
*encode_matrix
, *decode_matrix
;
195 u8
*invert_matrix
, *temp_matrix
;
197 u8 decode_index
[MMAX
];
200 for (i
= 0; i
< p
; i
++)
201 frag_err_list
[nerrs
++] = rand() % (k
+ p
);
203 while ((c
= getopt(argc
, argv
, "k:p:l:e:r:hvbs")) != -1) {
218 frag_err_list
[nerrs
++] = e
;
222 k
= (rand() % MMAX
) / 4;
224 p
= (rand() % (MMAX
- k
)) / 4;
226 for (i
= 0; i
< k
&& nerrs
< p
; i
++)
228 frag_err_list
[nerrs
++] = i
;
237 sparse_matrix_opt
= !sparse_matrix_opt
;
247 // Check for valid parameters
248 if (m
> (MMAX
/ 2) || k
> (KMAX
/ 2) || m
< 0 || p
< 2 || k
< 1) {
249 printf(" Input test parameter error m=%d, k=%d, p=%d, erasures=%d\n",
254 printf(" Number of erasures chosen exceeds power of code erasures=%d p=%d\n",
257 for (i
= 0; i
< nerrs
; i
++) {
258 if (frag_err_list
[i
] >= m
)
259 printf(" fragment %d not in range\n", frag_err_list
[i
]);
262 printf("ec_piggyback_example:\n");
265 * One simple way to implement piggyback codes is to keep a 2x wide matrix
266 * that covers the how each parity is related to both A and B sources. This
267 * keeps it easy to generalize in parameters m,k and the resulting sparse
268 * matrix multiplication can be optimized by pre-removal of zero items.
276 encode_matrix
= malloc(m2
* k2
);
277 decode_matrix
= malloc(m2
* k2
);
278 invert_matrix
= malloc(m2
* k2
);
279 temp_matrix
= malloc(m2
* k2
);
280 g_tbls
= malloc(k2
* p2
* 32);
282 if (encode_matrix
== NULL
|| decode_matrix
== NULL
283 || invert_matrix
== NULL
|| temp_matrix
== NULL
|| g_tbls
== NULL
) {
284 printf("Test failure! Error with malloc\n");
287 // Allocate the src fragments
288 for (i
= 0; i
< k
; i
++) {
289 if (NULL
== (frag_ptrs
[i
] = malloc(len
))) {
290 printf("alloc error: Fail\n");
294 // Allocate the parity fragments
295 for (i
= 0; i
< p2
; i
++) {
296 if (NULL
== (parity_ptrs
[i
] = malloc(len
/ 2))) {
297 printf("alloc error: Fail\n");
302 // Allocate buffers for recovered data
303 for (i
= 0; i
< p2
; i
++) {
304 if (NULL
== (recover_outp
[i
] = malloc(len
/ 2))) {
305 printf("alloc error: Fail\n");
310 // Fill sources with random data
311 for (i
= 0; i
< k
; i
++)
312 for (j
= 0; j
< len
; j
++)
313 frag_ptrs
[i
][j
] = rand();
315 printf(" encode (m,k,p)=(%d,%d,%d) len=%d\n", m
, k
, p
, len
);
317 // Pick an encode matrix.
318 gf_gen_full_pb_cauchy_matrix(encode_matrix
, m2
, k2
);
321 print_matrix(m2
, k2
, encode_matrix
, "encode matrix");
323 // Initialize g_tbls from encode matrix
324 ec_init_tables(k2
, p2
, &encode_matrix
[k2
* k2
], g_tbls
);
326 // Fold A and B into single list of fragments
327 for (i
= 0; i
< k
; i
++)
328 frag_ptrs
[i
+ k
] = &frag_ptrs
[i
][len
/ 2];
330 if (!sparse_matrix_opt
) {
331 // Standard encode using no assumptions on the encode matrix
333 // Generate EC parity blocks from sources
334 ec_encode_data(len
/ 2, k2
, p2
, g_tbls
, frag_ptrs
, parity_ptrs
);
338 BENCHMARK(&start
, BENCHMARK_TIME
,
339 ec_encode_data(len
/ 2, k2
, p2
, g_tbls
, frag_ptrs
,
341 printf("ec_piggyback_encode_std: ");
342 perf_print(start
, m2
* len
/ 2);
345 // Sparse matrix optimization - use fact that input matrix is sparse
347 // Keep an encode matrix with some zero elements removed
348 u8
*encode_matrix_faster
, *g_tbls_faster
;
349 encode_matrix_faster
= malloc(m
* k
);
350 g_tbls_faster
= malloc(k
* p
* 32);
351 if (encode_matrix_faster
== NULL
|| g_tbls_faster
== NULL
) {
352 printf("Test failure! Error with malloc\n");
357 * Pack with only the part that we know are non-zero. Alternatively
358 * we could search and keep track of non-zero elements but for
359 * simplicity we just skip the lower quadrant.
361 for (i
= k
, j
= k2
; i
< m
; i
++, j
++)
362 memcpy(&encode_matrix_faster
[k
* i
], &encode_matrix
[k2
* j
], k
);
365 print_matrix(p
, k
, &encode_matrix_faster
[k
* k
],
366 "encode via sparse-opt");
367 print_matrix(p2
/ 2, k2
, &encode_matrix
[(k2
+ p2
/ 2) * k2
],
368 "encode via sparse-opt");
370 // Initialize g_tbls from encode matrix
371 ec_init_tables(k
, p
, &encode_matrix_faster
[k
* k
], g_tbls_faster
);
373 // Generate EC parity blocks from sources
374 ec_encode_data(len
/ 2, k
, p
, g_tbls_faster
, frag_ptrs
, parity_ptrs
);
375 ec_encode_data(len
/ 2, k2
, p
, &g_tbls
[k2
* p
* 32], frag_ptrs
,
380 BENCHMARK(&start
, BENCHMARK_TIME
,
381 ec_encode_data(len
/ 2, k
, p
, g_tbls_faster
, frag_ptrs
,
383 ec_encode_data(len
/ 2, k2
, p
, &g_tbls
[k2
* p
* 32],
384 frag_ptrs
, &parity_ptrs
[p
]));
385 printf("ec_piggyback_encode_sparse: ");
386 perf_print(start
, m2
* len
/ 2);
393 printf(" recover %d fragments\n", nerrs
);
395 // Set frag pointers to correspond to parity
396 for (i
= k2
; i
< m2
; i
++)
397 frag_ptrs
[i
] = parity_ptrs
[i
- k2
];
399 print_list(nerrs2
, frag_err_list
, " frag err list");
401 // Find a decode matrix to regenerate all erasures from remaining frags
402 ret
= gf_gen_decode_matrix(encode_matrix
, decode_matrix
,
403 invert_matrix
, temp_matrix
, decode_index
, frag_err_list
,
407 printf("Fail on generate decode matrix\n");
410 // Pack recovery array pointers as list of valid fragments
411 for (i
= 0; i
< k2
; i
++)
412 if (decode_index
[i
] < k2
)
413 recover_srcs
[i
] = frag_ptrs
[decode_index
[i
]];
415 recover_srcs
[i
] = parity_ptrs
[decode_index
[i
] - k2
];
417 print_list(k2
, decode_index
, " decode index");
420 ec_init_tables(k2
, nerrs2
, decode_matrix
, g_tbls
);
421 ec_encode_data(len
/ 2, k2
, nerrs2
, g_tbls
, recover_srcs
, recover_outp
);
425 BENCHMARK(&start
, BENCHMARK_TIME
,
426 ec_encode_data(len
/ 2, k2
, nerrs2
, g_tbls
, recover_srcs
,
428 printf("ec_piggyback_decode: ");
429 perf_print(start
, (k2
+ nerrs2
) * len
/ 2);
431 // Check that recovered buffers are the same as original
432 printf(" check recovery of block {");
433 for (i
= 0; i
< nerrs2
; i
++) {
434 printf(" %d", frag_err_list
[i
]);
435 if (memcmp(recover_outp
[i
], frag_ptrs
[frag_err_list
[i
]], len
/ 2)) {
436 printf(" Fail erasure recovery %d, frag %d\n", i
, frag_err_list
[i
]);
440 printf(" } done all: Pass\n");
445 // Generate decode matrix from encode matrix and erasure list
447 static int gf_gen_decode_matrix(u8
* encode_matrix
,
451 u8
* decode_index
, u8
* frag_err_list
, int nerrs
, int k
, int m
)
455 u8 s
, *b
= temp_matrix
;
456 u8 frag_in_err
[MMAX
];
458 memset(frag_in_err
, 0, sizeof(frag_in_err
));
460 // Order the fragments in erasure for easier sorting
461 for (i
= 0; i
< nerrs
; i
++) {
462 if (frag_err_list
[i
] < k
)
464 frag_in_err
[frag_err_list
[i
]] = 1;
467 // Construct b (matrix that encoded remaining frags) by removing erased rows
468 for (i
= 0, r
= 0; i
< k
; i
++, r
++) {
469 while (frag_in_err
[r
])
471 for (j
= 0; j
< k
; j
++)
472 b
[k
* i
+ j
] = encode_matrix
[k
* r
+ j
];
476 print_matrix(k
, k
, b
, "matrix to invert");
478 // Invert matrix to get recovery matrix
479 if (gf_invert_matrix(b
, invert_matrix
, k
) < 0)
483 print_matrix(k
, k
, invert_matrix
, "matrix inverted");
485 // Get decode matrix with only wanted recovery rows
486 for (i
= 0; i
< nsrcerrs
; i
++) {
487 for (j
= 0; j
< k
; j
++) {
488 decode_matrix
[k
* i
+ j
] = invert_matrix
[k
* frag_err_list
[i
] + j
];
492 // For non-src (parity) erasures need to multiply encode matrix * invert
493 for (p
= nsrcerrs
; p
< nerrs
; p
++) {
494 for (i
= 0; i
< k
; i
++) {
496 for (j
= 0; j
< k
; j
++)
497 s
^= gf_mul(invert_matrix
[j
* k
+ i
],
498 encode_matrix
[k
* frag_err_list
[p
] + j
]);
500 decode_matrix
[k
* p
+ i
] = s
;
504 print_matrix(nerrs
, k
, decode_matrix
, "decode matrix");