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1 /* Copyright 2013 Google Inc. All Rights Reserved. | |
2 | |
3 Distributed under MIT license. | |
4 See file LICENSE for detail or copy at https://opensource.org/licenses/MIT | |
5 */ | |
6 | |
7 // Block split point selection utilities. | |
8 | |
9 #include "./block_splitter.h" | |
10 | |
11 #include <assert.h> | |
12 #include <math.h> | |
13 | |
14 #include <algorithm> | |
15 #include <cstring> | |
16 #include <vector> | |
17 | |
18 #include "./cluster.h" | |
19 #include "./command.h" | |
20 #include "./fast_log.h" | |
21 #include "./histogram.h" | |
22 | |
23 namespace brotli { | |
24 | |
25 static const size_t kMaxLiteralHistograms = 100; | |
26 static const size_t kMaxCommandHistograms = 50; | |
27 static const double kLiteralBlockSwitchCost = 28.1; | |
28 static const double kCommandBlockSwitchCost = 13.5; | |
29 static const double kDistanceBlockSwitchCost = 14.6; | |
30 static const size_t kLiteralStrideLength = 70; | |
31 static const size_t kCommandStrideLength = 40; | |
32 static const size_t kSymbolsPerLiteralHistogram = 544; | |
33 static const size_t kSymbolsPerCommandHistogram = 530; | |
34 static const size_t kSymbolsPerDistanceHistogram = 544; | |
35 static const size_t kMinLengthForBlockSplitting = 128; | |
36 static const size_t kIterMulForRefining = 2; | |
37 static const size_t kMinItersForRefining = 100; | |
38 | |
39 void CopyLiteralsToByteArray(const Command* cmds, | |
40 const size_t num_commands, | |
41 const uint8_t* data, | |
42 const size_t offset, | |
43 const size_t mask, | |
44 std::vector<uint8_t>* literals) { | |
45 // Count how many we have. | |
46 size_t total_length = 0; | |
47 for (size_t i = 0; i < num_commands; ++i) { | |
48 total_length += cmds[i].insert_len_; | |
49 } | |
50 if (total_length == 0) { | |
51 return; | |
52 } | |
53 | |
54 // Allocate. | |
55 literals->resize(total_length); | |
56 | |
57 // Loop again, and copy this time. | |
58 size_t pos = 0; | |
59 size_t from_pos = offset & mask; | |
60 for (size_t i = 0; i < num_commands && pos < total_length; ++i) { | |
61 size_t insert_len = cmds[i].insert_len_; | |
62 if (from_pos + insert_len > mask) { | |
63 size_t head_size = mask + 1 - from_pos; | |
64 memcpy(&(*literals)[pos], data + from_pos, head_size); | |
65 from_pos = 0; | |
66 pos += head_size; | |
67 insert_len -= head_size; | |
68 } | |
69 if (insert_len > 0) { | |
70 memcpy(&(*literals)[pos], data + from_pos, insert_len); | |
71 pos += insert_len; | |
72 } | |
73 from_pos = (from_pos + insert_len + cmds[i].copy_len()) & mask; | |
74 } | |
75 } | |
76 | |
77 inline static unsigned int MyRand(unsigned int* seed) { | |
78 *seed *= 16807U; | |
79 if (*seed == 0) { | |
80 *seed = 1; | |
81 } | |
82 return *seed; | |
83 } | |
84 | |
85 template<typename HistogramType, typename DataType> | |
86 void InitialEntropyCodes(const DataType* data, size_t length, | |
87 size_t stride, | |
88 size_t num_histograms, | |
89 HistogramType* histograms) { | |
90 for (size_t i = 0; i < num_histograms; ++i) { | |
91 histograms[i].Clear(); | |
92 } | |
93 unsigned int seed = 7; | |
94 size_t block_length = length / num_histograms; | |
95 for (size_t i = 0; i < num_histograms; ++i) { | |
96 size_t pos = length * i / num_histograms; | |
97 if (i != 0) { | |
98 pos += MyRand(&seed) % block_length; | |
99 } | |
100 if (pos + stride >= length) { | |
101 pos = length - stride - 1; | |
102 } | |
103 histograms[i].Add(data + pos, stride); | |
104 } | |
105 } | |
106 | |
107 template<typename HistogramType, typename DataType> | |
108 void RandomSample(unsigned int* seed, | |
109 const DataType* data, | |
110 size_t length, | |
111 size_t stride, | |
112 HistogramType* sample) { | |
113 size_t pos = 0; | |
114 if (stride >= length) { | |
115 pos = 0; | |
116 stride = length; | |
117 } else { | |
118 pos = MyRand(seed) % (length - stride + 1); | |
119 } | |
120 sample->Add(data + pos, stride); | |
121 } | |
122 | |
123 template<typename HistogramType, typename DataType> | |
124 void RefineEntropyCodes(const DataType* data, size_t length, | |
125 size_t stride, | |
126 size_t num_histograms, | |
127 HistogramType* histograms) { | |
128 size_t iters = | |
129 kIterMulForRefining * length / stride + kMinItersForRefining; | |
130 unsigned int seed = 7; | |
131 iters = ((iters + num_histograms - 1) / num_histograms) * num_histograms; | |
132 for (size_t iter = 0; iter < iters; ++iter) { | |
133 HistogramType sample; | |
134 RandomSample(&seed, data, length, stride, &sample); | |
135 size_t ix = iter % num_histograms; | |
136 histograms[ix].AddHistogram(sample); | |
137 } | |
138 } | |
139 | |
140 inline static double BitCost(size_t count) { | |
141 return count == 0 ? -2.0 : FastLog2(count); | |
142 } | |
143 | |
144 // Assigns a block id from the range [0, vec.size()) to each data element | |
145 // in data[0..length) and fills in block_id[0..length) with the assigned values. | |
146 // Returns the number of blocks, i.e. one plus the number of block switches. | |
147 template<typename DataType, int kSize> | |
148 size_t FindBlocks(const DataType* data, const size_t length, | |
149 const double block_switch_bitcost, | |
150 const size_t num_histograms, | |
151 const Histogram<kSize>* histograms, | |
152 double* insert_cost, | |
153 double* cost, | |
154 uint8_t* switch_signal, | |
155 uint8_t *block_id) { | |
156 if (num_histograms <= 1) { | |
157 for (size_t i = 0; i < length; ++i) { | |
158 block_id[i] = 0; | |
159 } | |
160 return 1; | |
161 } | |
162 const size_t bitmaplen = (num_histograms + 7) >> 3; | |
163 assert(num_histograms <= 256); | |
164 memset(insert_cost, 0, sizeof(insert_cost[0]) * kSize * num_histograms); | |
165 for (size_t j = 0; j < num_histograms; ++j) { | |
166 insert_cost[j] = FastLog2(static_cast<uint32_t>( | |
167 histograms[j].total_count_)); | |
168 } | |
169 for (size_t i = kSize; i != 0;) { | |
170 --i; | |
171 for (size_t j = 0; j < num_histograms; ++j) { | |
172 insert_cost[i * num_histograms + j] = | |
173 insert_cost[j] - BitCost(histograms[j].data_[i]); | |
174 } | |
175 } | |
176 memset(cost, 0, sizeof(cost[0]) * num_histograms); | |
177 memset(switch_signal, 0, sizeof(switch_signal[0]) * length * bitmaplen); | |
178 // After each iteration of this loop, cost[k] will contain the difference | |
179 // between the minimum cost of arriving at the current byte position using | |
180 // entropy code k, and the minimum cost of arriving at the current byte | |
181 // position. This difference is capped at the block switch cost, and if it | |
182 // reaches block switch cost, it means that when we trace back from the last | |
183 // position, we need to switch here. | |
184 for (size_t byte_ix = 0; byte_ix < length; ++byte_ix) { | |
185 size_t ix = byte_ix * bitmaplen; | |
186 size_t insert_cost_ix = data[byte_ix] * num_histograms; | |
187 double min_cost = 1e99; | |
188 for (size_t k = 0; k < num_histograms; ++k) { | |
189 // We are coding the symbol in data[byte_ix] with entropy code k. | |
190 cost[k] += insert_cost[insert_cost_ix + k]; | |
191 if (cost[k] < min_cost) { | |
192 min_cost = cost[k]; | |
193 block_id[byte_ix] = static_cast<uint8_t>(k); | |
194 } | |
195 } | |
196 double block_switch_cost = block_switch_bitcost; | |
197 // More blocks for the beginning. | |
198 if (byte_ix < 2000) { | |
199 block_switch_cost *= 0.77 + 0.07 * static_cast<double>(byte_ix) / 2000; | |
200 } | |
201 for (size_t k = 0; k < num_histograms; ++k) { | |
202 cost[k] -= min_cost; | |
203 if (cost[k] >= block_switch_cost) { | |
204 cost[k] = block_switch_cost; | |
205 const uint8_t mask = static_cast<uint8_t>(1u << (k & 7)); | |
206 assert((k >> 3) < bitmaplen); | |
207 switch_signal[ix + (k >> 3)] |= mask; | |
208 } | |
209 } | |
210 } | |
211 // Now trace back from the last position and switch at the marked places. | |
212 size_t byte_ix = length - 1; | |
213 size_t ix = byte_ix * bitmaplen; | |
214 uint8_t cur_id = block_id[byte_ix]; | |
215 size_t num_blocks = 1; | |
216 while (byte_ix > 0) { | |
217 --byte_ix; | |
218 ix -= bitmaplen; | |
219 const uint8_t mask = static_cast<uint8_t>(1u << (cur_id & 7)); | |
220 assert((static_cast<size_t>(cur_id) >> 3) < bitmaplen); | |
221 if (switch_signal[ix + (cur_id >> 3)] & mask) { | |
222 if (cur_id != block_id[byte_ix]) { | |
223 cur_id = block_id[byte_ix]; | |
224 ++num_blocks; | |
225 } | |
226 } | |
227 block_id[byte_ix] = cur_id; | |
228 } | |
229 return num_blocks; | |
230 } | |
231 | |
232 static size_t RemapBlockIds(uint8_t* block_ids, const size_t length, | |
233 uint16_t* new_id, const size_t num_histograms) { | |
234 static const uint16_t kInvalidId = 256; | |
235 for (size_t i = 0; i < num_histograms; ++i) { | |
236 new_id[i] = kInvalidId; | |
237 } | |
238 uint16_t next_id = 0; | |
239 for (size_t i = 0; i < length; ++i) { | |
240 assert(block_ids[i] < num_histograms); | |
241 if (new_id[block_ids[i]] == kInvalidId) { | |
242 new_id[block_ids[i]] = next_id++; | |
243 } | |
244 } | |
245 for (size_t i = 0; i < length; ++i) { | |
246 block_ids[i] = static_cast<uint8_t>(new_id[block_ids[i]]); | |
247 assert(block_ids[i] < num_histograms); | |
248 } | |
249 assert(next_id <= num_histograms); | |
250 return next_id; | |
251 } | |
252 | |
253 template<typename HistogramType, typename DataType> | |
254 void BuildBlockHistograms(const DataType* data, const size_t length, | |
255 const uint8_t* block_ids, | |
256 const size_t num_histograms, | |
257 HistogramType* histograms) { | |
258 for (size_t i = 0; i < num_histograms; ++i) { | |
259 histograms[i].Clear(); | |
260 } | |
261 for (size_t i = 0; i < length; ++i) { | |
262 histograms[block_ids[i]].Add(data[i]); | |
263 } | |
264 } | |
265 | |
266 template<typename HistogramType, typename DataType> | |
267 void ClusterBlocks(const DataType* data, const size_t length, | |
268 const size_t num_blocks, | |
269 uint8_t* block_ids, | |
270 BlockSplit* split) { | |
271 static const size_t kMaxNumberOfBlockTypes = 256; | |
272 static const size_t kHistogramsPerBatch = 64; | |
273 static const size_t kClustersPerBatch = 16; | |
274 std::vector<uint32_t> histogram_symbols(num_blocks); | |
275 std::vector<uint32_t> block_lengths(num_blocks); | |
276 | |
277 size_t block_idx = 0; | |
278 for (size_t i = 0; i < length; ++i) { | |
279 assert(block_idx < num_blocks); | |
280 ++block_lengths[block_idx]; | |
281 if (i + 1 == length || block_ids[i] != block_ids[i + 1]) { | |
282 ++block_idx; | |
283 } | |
284 } | |
285 assert(block_idx == num_blocks); | |
286 | |
287 const size_t expected_num_clusters = | |
288 kClustersPerBatch * | |
289 (num_blocks + kHistogramsPerBatch - 1) / kHistogramsPerBatch; | |
290 std::vector<HistogramType> all_histograms; | |
291 std::vector<uint32_t> cluster_size; | |
292 all_histograms.reserve(expected_num_clusters); | |
293 cluster_size.reserve(expected_num_clusters); | |
294 size_t num_clusters = 0; | |
295 std::vector<HistogramType> histograms( | |
296 std::min(num_blocks, kHistogramsPerBatch)); | |
297 size_t max_num_pairs = kHistogramsPerBatch * kHistogramsPerBatch / 2; | |
298 std::vector<HistogramPair> pairs(max_num_pairs + 1); | |
299 size_t pos = 0; | |
300 for (size_t i = 0; i < num_blocks; i += kHistogramsPerBatch) { | |
301 const size_t num_to_combine = std::min(num_blocks - i, kHistogramsPerBatch); | |
302 uint32_t sizes[kHistogramsPerBatch]; | |
303 uint32_t clusters[kHistogramsPerBatch]; | |
304 uint32_t symbols[kHistogramsPerBatch]; | |
305 uint32_t remap[kHistogramsPerBatch]; | |
306 for (size_t j = 0; j < num_to_combine; ++j) { | |
307 histograms[j].Clear(); | |
308 for (size_t k = 0; k < block_lengths[i + j]; ++k) { | |
309 histograms[j].Add(data[pos++]); | |
310 } | |
311 histograms[j].bit_cost_ = PopulationCost(histograms[j]); | |
312 symbols[j] = clusters[j] = static_cast<uint32_t>(j); | |
313 sizes[j] = 1; | |
314 } | |
315 size_t num_new_clusters = HistogramCombine( | |
316 &histograms[0], sizes, symbols, clusters, &pairs[0], num_to_combine, | |
317 num_to_combine, kHistogramsPerBatch, max_num_pairs); | |
318 for (size_t j = 0; j < num_new_clusters; ++j) { | |
319 all_histograms.push_back(histograms[clusters[j]]); | |
320 cluster_size.push_back(sizes[clusters[j]]); | |
321 remap[clusters[j]] = static_cast<uint32_t>(j); | |
322 } | |
323 for (size_t j = 0; j < num_to_combine; ++j) { | |
324 histogram_symbols[i + j] = | |
325 static_cast<uint32_t>(num_clusters) + remap[symbols[j]]; | |
326 } | |
327 num_clusters += num_new_clusters; | |
328 assert(num_clusters == cluster_size.size()); | |
329 assert(num_clusters == all_histograms.size()); | |
330 } | |
331 | |
332 max_num_pairs = | |
333 std::min(64 * num_clusters, (num_clusters / 2) * num_clusters); | |
334 pairs.resize(max_num_pairs + 1); | |
335 | |
336 std::vector<uint32_t> clusters(num_clusters); | |
337 for (size_t i = 0; i < num_clusters; ++i) { | |
338 clusters[i] = static_cast<uint32_t>(i); | |
339 } | |
340 size_t num_final_clusters = | |
341 HistogramCombine(&all_histograms[0], &cluster_size[0], | |
342 &histogram_symbols[0], | |
343 &clusters[0], &pairs[0], num_clusters, | |
344 num_blocks, kMaxNumberOfBlockTypes, max_num_pairs); | |
345 | |
346 static const uint32_t kInvalidIndex = std::numeric_limits<uint32_t>::max(); | |
347 std::vector<uint32_t> new_index(num_clusters, kInvalidIndex); | |
348 uint32_t next_index = 0; | |
349 pos = 0; | |
350 for (size_t i = 0; i < num_blocks; ++i) { | |
351 HistogramType histo; | |
352 for (size_t j = 0; j < block_lengths[i]; ++j) { | |
353 histo.Add(data[pos++]); | |
354 } | |
355 uint32_t best_out = | |
356 i == 0 ? histogram_symbols[0] : histogram_symbols[i - 1]; | |
357 double best_bits = HistogramBitCostDistance( | |
358 histo, all_histograms[best_out]); | |
359 for (size_t j = 0; j < num_final_clusters; ++j) { | |
360 const double cur_bits = HistogramBitCostDistance( | |
361 histo, all_histograms[clusters[j]]); | |
362 if (cur_bits < best_bits) { | |
363 best_bits = cur_bits; | |
364 best_out = clusters[j]; | |
365 } | |
366 } | |
367 histogram_symbols[i] = best_out; | |
368 if (new_index[best_out] == kInvalidIndex) { | |
369 new_index[best_out] = next_index++; | |
370 } | |
371 } | |
372 uint8_t max_type = 0; | |
373 uint32_t cur_length = 0; | |
374 block_idx = 0; | |
375 split->types.resize(num_blocks); | |
376 split->lengths.resize(num_blocks); | |
377 for (size_t i = 0; i < num_blocks; ++i) { | |
378 cur_length += block_lengths[i]; | |
379 if (i + 1 == num_blocks || | |
380 histogram_symbols[i] != histogram_symbols[i + 1]) { | |
381 const uint8_t id = static_cast<uint8_t>(new_index[histogram_symbols[i]]); | |
382 split->types[block_idx] = id; | |
383 split->lengths[block_idx] = cur_length; | |
384 max_type = std::max(max_type, id); | |
385 cur_length = 0; | |
386 ++block_idx; | |
387 } | |
388 } | |
389 split->types.resize(block_idx); | |
390 split->lengths.resize(block_idx); | |
391 split->num_types = static_cast<size_t>(max_type) + 1; | |
392 } | |
393 | |
394 template<int kSize, typename DataType> | |
395 void SplitByteVector(const std::vector<DataType>& data, | |
396 const size_t literals_per_histogram, | |
397 const size_t max_histograms, | |
398 const size_t sampling_stride_length, | |
399 const double block_switch_cost, | |
400 BlockSplit* split) { | |
401 if (data.empty()) { | |
402 split->num_types = 1; | |
403 return; | |
404 } else if (data.size() < kMinLengthForBlockSplitting) { | |
405 split->num_types = 1; | |
406 split->types.push_back(0); | |
407 split->lengths.push_back(static_cast<uint32_t>(data.size())); | |
408 return; | |
409 } | |
410 size_t num_histograms = data.size() / literals_per_histogram + 1; | |
411 if (num_histograms > max_histograms) { | |
412 num_histograms = max_histograms; | |
413 } | |
414 Histogram<kSize>* histograms = new Histogram<kSize>[num_histograms]; | |
415 // Find good entropy codes. | |
416 InitialEntropyCodes(&data[0], data.size(), | |
417 sampling_stride_length, | |
418 num_histograms, histograms); | |
419 RefineEntropyCodes(&data[0], data.size(), | |
420 sampling_stride_length, | |
421 num_histograms, histograms); | |
422 // Find a good path through literals with the good entropy codes. | |
423 std::vector<uint8_t> block_ids(data.size()); | |
424 size_t num_blocks; | |
425 const size_t bitmaplen = (num_histograms + 7) >> 3; | |
426 double* insert_cost = new double[kSize * num_histograms]; | |
427 double *cost = new double[num_histograms]; | |
428 uint8_t* switch_signal = new uint8_t[data.size() * bitmaplen]; | |
429 uint16_t* new_id = new uint16_t[num_histograms]; | |
430 for (size_t i = 0; i < 10; ++i) { | |
431 num_blocks = FindBlocks(&data[0], data.size(), | |
432 block_switch_cost, | |
433 num_histograms, histograms, | |
434 insert_cost, cost, switch_signal, | |
435 &block_ids[0]); | |
436 num_histograms = RemapBlockIds(&block_ids[0], data.size(), | |
437 new_id, num_histograms); | |
438 BuildBlockHistograms(&data[0], data.size(), &block_ids[0], | |
439 num_histograms, histograms); | |
440 } | |
441 delete[] insert_cost; | |
442 delete[] cost; | |
443 delete[] switch_signal; | |
444 delete[] new_id; | |
445 delete[] histograms; | |
446 ClusterBlocks<Histogram<kSize> >(&data[0], data.size(), num_blocks, | |
447 &block_ids[0], split); | |
448 } | |
449 | |
450 void SplitBlock(const Command* cmds, | |
451 const size_t num_commands, | |
452 const uint8_t* data, | |
453 const size_t pos, | |
454 const size_t mask, | |
455 BlockSplit* literal_split, | |
456 BlockSplit* insert_and_copy_split, | |
457 BlockSplit* dist_split) { | |
458 { | |
459 // Create a continuous array of literals. | |
460 std::vector<uint8_t> literals; | |
461 CopyLiteralsToByteArray(cmds, num_commands, data, pos, mask, &literals); | |
462 // Create the block split on the array of literals. | |
463 // Literal histograms have alphabet size 256. | |
464 SplitByteVector<256>( | |
465 literals, | |
466 kSymbolsPerLiteralHistogram, kMaxLiteralHistograms, | |
467 kLiteralStrideLength, kLiteralBlockSwitchCost, | |
468 literal_split); | |
469 } | |
470 | |
471 { | |
472 // Compute prefix codes for commands. | |
473 std::vector<uint16_t> insert_and_copy_codes(num_commands); | |
474 for (size_t i = 0; i < num_commands; ++i) { | |
475 insert_and_copy_codes[i] = cmds[i].cmd_prefix_; | |
476 } | |
477 // Create the block split on the array of command prefixes. | |
478 SplitByteVector<kNumCommandPrefixes>( | |
479 insert_and_copy_codes, | |
480 kSymbolsPerCommandHistogram, kMaxCommandHistograms, | |
481 kCommandStrideLength, kCommandBlockSwitchCost, | |
482 insert_and_copy_split); | |
483 } | |
484 | |
485 { | |
486 // Create a continuous array of distance prefixes. | |
487 std::vector<uint16_t> distance_prefixes(num_commands); | |
488 size_t pos = 0; | |
489 for (size_t i = 0; i < num_commands; ++i) { | |
490 const Command& cmd = cmds[i]; | |
491 if (cmd.copy_len() && cmd.cmd_prefix_ >= 128) { | |
492 distance_prefixes[pos++] = cmd.dist_prefix_; | |
493 } | |
494 } | |
495 distance_prefixes.resize(pos); | |
496 // Create the block split on the array of distance prefixes. | |
497 SplitByteVector<kNumDistancePrefixes>( | |
498 distance_prefixes, | |
499 kSymbolsPerDistanceHistogram, kMaxCommandHistograms, | |
500 kCommandStrideLength, kDistanceBlockSwitchCost, | |
501 dist_split); | |
502 } | |
503 } | |
504 | |
505 } // namespace brotli | |
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