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1 /* Copyright 2013 Google Inc. All Rights Reserved. | 1 /* Copyright 2013 Google Inc. All Rights Reserved. |
2 | 2 |
3 Distributed under MIT license. | 3 Distributed under MIT license. |
4 See file LICENSE for detail or copy at https://opensource.org/licenses/MIT | 4 See file LICENSE for detail or copy at https://opensource.org/licenses/MIT |
5 */ | 5 */ |
6 | 6 |
7 // Functions for clustering similar histograms together. | 7 /* Functions for clustering similar histograms together. */ |
8 | 8 |
9 #ifndef BROTLI_ENC_CLUSTER_H_ | 9 #ifndef BROTLI_ENC_CLUSTER_H_ |
10 #define BROTLI_ENC_CLUSTER_H_ | 10 #define BROTLI_ENC_CLUSTER_H_ |
11 | 11 |
12 #include <math.h> | 12 #include <brotli/types.h> |
13 #include <algorithm> | 13 #include "./histogram.h" |
14 #include <utility> | 14 #include "./memory.h" |
15 #include <vector> | 15 #include "./port.h" |
16 | 16 |
17 #include "./bit_cost.h" | 17 #if defined(__cplusplus) || defined(c_plusplus) |
18 #include "./entropy_encode.h" | 18 extern "C" { |
19 #include "./fast_log.h" | 19 #endif |
20 #include "./histogram.h" | |
21 #include "./port.h" | |
22 #include "./types.h" | |
23 | 20 |
24 namespace brotli { | 21 typedef struct HistogramPair { |
25 | |
26 struct HistogramPair { | |
27 uint32_t idx1; | 22 uint32_t idx1; |
28 uint32_t idx2; | 23 uint32_t idx2; |
29 double cost_combo; | 24 double cost_combo; |
30 double cost_diff; | 25 double cost_diff; |
31 }; | 26 } HistogramPair; |
32 | 27 |
33 inline bool operator<(const HistogramPair& p1, const HistogramPair& p2) { | 28 #define CODE(X) /* Declaration */; |
34 if (p1.cost_diff != p2.cost_diff) { | |
35 return p1.cost_diff > p2.cost_diff; | |
36 } | |
37 return (p1.idx2 - p1.idx1) > (p2.idx2 - p2.idx1); | |
38 } | |
39 | 29 |
40 // Returns entropy reduction of the context map when we combine two clusters. | 30 #define FN(X) X ## Literal |
41 inline double ClusterCostDiff(size_t size_a, size_t size_b) { | 31 #include "./cluster_inc.h" /* NOLINT(build/include) */ |
42 size_t size_c = size_a + size_b; | 32 #undef FN |
43 return static_cast<double>(size_a) * FastLog2(size_a) + | |
44 static_cast<double>(size_b) * FastLog2(size_b) - | |
45 static_cast<double>(size_c) * FastLog2(size_c); | |
46 } | |
47 | 33 |
48 // Computes the bit cost reduction by combining out[idx1] and out[idx2] and if | 34 #define FN(X) X ## Command |
49 // it is below a threshold, stores the pair (idx1, idx2) in the *pairs queue. | 35 #include "./cluster_inc.h" /* NOLINT(build/include) */ |
50 template<typename HistogramType> | 36 #undef FN |
51 void CompareAndPushToQueue(const HistogramType* out, | |
52 const uint32_t* cluster_size, | |
53 uint32_t idx1, uint32_t idx2, | |
54 size_t max_num_pairs, | |
55 HistogramPair* pairs, | |
56 size_t* num_pairs) { | |
57 if (idx1 == idx2) { | |
58 return; | |
59 } | |
60 if (idx2 < idx1) { | |
61 uint32_t t = idx2; | |
62 idx2 = idx1; | |
63 idx1 = t; | |
64 } | |
65 bool store_pair = false; | |
66 HistogramPair p = {}; | |
67 p.idx1 = idx1; | |
68 p.idx2 = idx2; | |
69 p.cost_diff = 0.5 * ClusterCostDiff(cluster_size[idx1], cluster_size[idx2]); | |
70 p.cost_diff -= out[idx1].bit_cost_; | |
71 p.cost_diff -= out[idx2].bit_cost_; | |
72 | 37 |
73 if (out[idx1].total_count_ == 0) { | 38 #define FN(X) X ## Distance |
74 p.cost_combo = out[idx2].bit_cost_; | 39 #include "./cluster_inc.h" /* NOLINT(build/include) */ |
75 store_pair = true; | 40 #undef FN |
76 } else if (out[idx2].total_count_ == 0) { | |
77 p.cost_combo = out[idx1].bit_cost_; | |
78 store_pair = true; | |
79 } else { | |
80 double threshold = *num_pairs == 0 ? 1e99 : | |
81 std::max(0.0, pairs[0].cost_diff); | |
82 HistogramType combo = out[idx1]; | |
83 combo.AddHistogram(out[idx2]); | |
84 double cost_combo = PopulationCost(combo); | |
85 if (cost_combo < threshold - p.cost_diff) { | |
86 p.cost_combo = cost_combo; | |
87 store_pair = true; | |
88 } | |
89 } | |
90 if (store_pair) { | |
91 p.cost_diff += p.cost_combo; | |
92 if (*num_pairs > 0 && pairs[0] < p) { | |
93 // Replace the top of the queue if needed. | |
94 if (*num_pairs < max_num_pairs) { | |
95 pairs[*num_pairs] = pairs[0]; | |
96 ++(*num_pairs); | |
97 } | |
98 pairs[0] = p; | |
99 } else if (*num_pairs < max_num_pairs) { | |
100 pairs[*num_pairs] = p; | |
101 ++(*num_pairs); | |
102 } | |
103 } | |
104 } | |
105 | 41 |
106 template<typename HistogramType> | 42 #undef CODE |
107 size_t HistogramCombine(HistogramType* out, | |
108 uint32_t* cluster_size, | |
109 uint32_t* symbols, | |
110 uint32_t* clusters, | |
111 HistogramPair* pairs, | |
112 size_t num_clusters, | |
113 size_t symbols_size, | |
114 size_t max_clusters, | |
115 size_t max_num_pairs) { | |
116 double cost_diff_threshold = 0.0; | |
117 size_t min_cluster_size = 1; | |
118 | 43 |
119 // We maintain a vector of histogram pairs, with the property that the pair | 44 #if defined(__cplusplus) || defined(c_plusplus) |
120 // with the maximum bit cost reduction is the first. | 45 } /* extern "C" */ |
121 size_t num_pairs = 0; | 46 #endif |
122 for (size_t idx1 = 0; idx1 < num_clusters; ++idx1) { | |
123 for (size_t idx2 = idx1 + 1; idx2 < num_clusters; ++idx2) { | |
124 CompareAndPushToQueue(out, cluster_size, clusters[idx1], clusters[idx2], | |
125 max_num_pairs, &pairs[0], &num_pairs); | |
126 } | |
127 } | |
128 | 47 |
129 while (num_clusters > min_cluster_size) { | 48 #endif /* BROTLI_ENC_CLUSTER_H_ */ |
130 if (pairs[0].cost_diff >= cost_diff_threshold) { | |
131 cost_diff_threshold = 1e99; | |
132 min_cluster_size = max_clusters; | |
133 continue; | |
134 } | |
135 // Take the best pair from the top of heap. | |
136 uint32_t best_idx1 = pairs[0].idx1; | |
137 uint32_t best_idx2 = pairs[0].idx2; | |
138 out[best_idx1].AddHistogram(out[best_idx2]); | |
139 out[best_idx1].bit_cost_ = pairs[0].cost_combo; | |
140 cluster_size[best_idx1] += cluster_size[best_idx2]; | |
141 for (size_t i = 0; i < symbols_size; ++i) { | |
142 if (symbols[i] == best_idx2) { | |
143 symbols[i] = best_idx1; | |
144 } | |
145 } | |
146 for (size_t i = 0; i < num_clusters; ++i) { | |
147 if (clusters[i] == best_idx2) { | |
148 memmove(&clusters[i], &clusters[i + 1], | |
149 (num_clusters - i - 1) * sizeof(clusters[0])); | |
150 break; | |
151 } | |
152 } | |
153 --num_clusters; | |
154 // Remove pairs intersecting the just combined best pair. | |
155 size_t copy_to_idx = 0; | |
156 for (size_t i = 0; i < num_pairs; ++i) { | |
157 HistogramPair& p = pairs[i]; | |
158 if (p.idx1 == best_idx1 || p.idx2 == best_idx1 || | |
159 p.idx1 == best_idx2 || p.idx2 == best_idx2) { | |
160 // Remove invalid pair from the queue. | |
161 continue; | |
162 } | |
163 if (pairs[0] < p) { | |
164 // Replace the top of the queue if needed. | |
165 HistogramPair front = pairs[0]; | |
166 pairs[0] = p; | |
167 pairs[copy_to_idx] = front; | |
168 } else { | |
169 pairs[copy_to_idx] = p; | |
170 } | |
171 ++copy_to_idx; | |
172 } | |
173 num_pairs = copy_to_idx; | |
174 | |
175 // Push new pairs formed with the combined histogram to the heap. | |
176 for (size_t i = 0; i < num_clusters; ++i) { | |
177 CompareAndPushToQueue(out, cluster_size, best_idx1, clusters[i], | |
178 max_num_pairs, &pairs[0], &num_pairs); | |
179 } | |
180 } | |
181 return num_clusters; | |
182 } | |
183 | |
184 // ----------------------------------------------------------------------------- | |
185 // Histogram refinement | |
186 | |
187 // What is the bit cost of moving histogram from cur_symbol to candidate. | |
188 template<typename HistogramType> | |
189 double HistogramBitCostDistance(const HistogramType& histogram, | |
190 const HistogramType& candidate) { | |
191 if (histogram.total_count_ == 0) { | |
192 return 0.0; | |
193 } | |
194 HistogramType tmp = histogram; | |
195 tmp.AddHistogram(candidate); | |
196 return PopulationCost(tmp) - candidate.bit_cost_; | |
197 } | |
198 | |
199 // Find the best 'out' histogram for each of the 'in' histograms. | |
200 // When called, clusters[0..num_clusters) contains the unique values from | |
201 // symbols[0..in_size), but this property is not preserved in this function. | |
202 // Note: we assume that out[]->bit_cost_ is already up-to-date. | |
203 template<typename HistogramType> | |
204 void HistogramRemap(const HistogramType* in, size_t in_size, | |
205 const uint32_t* clusters, size_t num_clusters, | |
206 HistogramType* out, uint32_t* symbols) { | |
207 for (size_t i = 0; i < in_size; ++i) { | |
208 uint32_t best_out = i == 0 ? symbols[0] : symbols[i - 1]; | |
209 double best_bits = HistogramBitCostDistance(in[i], out[best_out]); | |
210 for (size_t j = 0; j < num_clusters; ++j) { | |
211 const double cur_bits = HistogramBitCostDistance(in[i], out[clusters[j]]); | |
212 if (cur_bits < best_bits) { | |
213 best_bits = cur_bits; | |
214 best_out = clusters[j]; | |
215 } | |
216 } | |
217 symbols[i] = best_out; | |
218 } | |
219 | |
220 // Recompute each out based on raw and symbols. | |
221 for (size_t j = 0; j < num_clusters; ++j) { | |
222 out[clusters[j]].Clear(); | |
223 } | |
224 for (size_t i = 0; i < in_size; ++i) { | |
225 out[symbols[i]].AddHistogram(in[i]); | |
226 } | |
227 } | |
228 | |
229 // Reorders elements of the out[0..length) array and changes values in | |
230 // symbols[0..length) array in the following way: | |
231 // * when called, symbols[] contains indexes into out[], and has N unique | |
232 // values (possibly N < length) | |
233 // * on return, symbols'[i] = f(symbols[i]) and | |
234 // out'[symbols'[i]] = out[symbols[i]], for each 0 <= i < length, | |
235 // where f is a bijection between the range of symbols[] and [0..N), and | |
236 // the first occurrences of values in symbols'[i] come in consecutive | |
237 // increasing order. | |
238 // Returns N, the number of unique values in symbols[]. | |
239 template<typename HistogramType> | |
240 size_t HistogramReindex(HistogramType* out, uint32_t* symbols, size_t length) { | |
241 static const uint32_t kInvalidIndex = std::numeric_limits<uint32_t>::max(); | |
242 std::vector<uint32_t> new_index(length, kInvalidIndex); | |
243 uint32_t next_index = 0; | |
244 for (size_t i = 0; i < length; ++i) { | |
245 if (new_index[symbols[i]] == kInvalidIndex) { | |
246 new_index[symbols[i]] = next_index; | |
247 ++next_index; | |
248 } | |
249 } | |
250 std::vector<HistogramType> tmp(next_index); | |
251 next_index = 0; | |
252 for (size_t i = 0; i < length; ++i) { | |
253 if (new_index[symbols[i]] == next_index) { | |
254 tmp[next_index] = out[symbols[i]]; | |
255 ++next_index; | |
256 } | |
257 symbols[i] = new_index[symbols[i]]; | |
258 } | |
259 for (size_t i = 0; i < next_index; ++i) { | |
260 out[i] = tmp[i]; | |
261 } | |
262 return next_index; | |
263 } | |
264 | |
265 // Clusters similar histograms in 'in' together, the selected histograms are | |
266 // placed in 'out', and for each index in 'in', *histogram_symbols will | |
267 // indicate which of the 'out' histograms is the best approximation. | |
268 template<typename HistogramType> | |
269 void ClusterHistograms(const std::vector<HistogramType>& in, | |
270 size_t num_contexts, size_t num_blocks, | |
271 size_t max_histograms, | |
272 std::vector<HistogramType>* out, | |
273 std::vector<uint32_t>* histogram_symbols) { | |
274 const size_t in_size = num_contexts * num_blocks; | |
275 assert(in_size == in.size()); | |
276 std::vector<uint32_t> cluster_size(in_size, 1); | |
277 std::vector<uint32_t> clusters(in_size); | |
278 size_t num_clusters = 0; | |
279 out->resize(in_size); | |
280 histogram_symbols->resize(in_size); | |
281 for (size_t i = 0; i < in_size; ++i) { | |
282 (*out)[i] = in[i]; | |
283 (*out)[i].bit_cost_ = PopulationCost(in[i]); | |
284 (*histogram_symbols)[i] = static_cast<uint32_t>(i); | |
285 } | |
286 | |
287 const size_t max_input_histograms = 64; | |
288 // For the first pass of clustering, we allow all pairs. | |
289 size_t max_num_pairs = max_input_histograms * max_input_histograms / 2; | |
290 std::vector<HistogramPair> pairs(max_num_pairs + 1); | |
291 | |
292 for (size_t i = 0; i < in_size; i += max_input_histograms) { | |
293 size_t num_to_combine = std::min(in_size - i, max_input_histograms); | |
294 for (size_t j = 0; j < num_to_combine; ++j) { | |
295 clusters[num_clusters + j] = static_cast<uint32_t>(i + j); | |
296 } | |
297 size_t num_new_clusters = | |
298 HistogramCombine(&(*out)[0], &cluster_size[0], | |
299 &(*histogram_symbols)[i], | |
300 &clusters[num_clusters], &pairs[0], | |
301 num_to_combine, num_to_combine, | |
302 max_histograms, max_num_pairs); | |
303 num_clusters += num_new_clusters; | |
304 } | |
305 | |
306 // For the second pass, we limit the total number of histogram pairs. | |
307 // After this limit is reached, we only keep searching for the best pair. | |
308 max_num_pairs = | |
309 std::min(64 * num_clusters, (num_clusters / 2) * num_clusters); | |
310 pairs.resize(max_num_pairs + 1); | |
311 | |
312 // Collapse similar histograms. | |
313 num_clusters = HistogramCombine(&(*out)[0], &cluster_size[0], | |
314 &(*histogram_symbols)[0], &clusters[0], | |
315 &pairs[0], num_clusters, in_size, | |
316 max_histograms, max_num_pairs); | |
317 | |
318 // Find the optimal map from original histograms to the final ones. | |
319 HistogramRemap(&in[0], in_size, &clusters[0], num_clusters, | |
320 &(*out)[0], &(*histogram_symbols)[0]); | |
321 | |
322 // Convert the context map to a canonical form. | |
323 size_t num_histograms = | |
324 HistogramReindex(&(*out)[0], &(*histogram_symbols)[0], in_size); | |
325 out->resize(num_histograms); | |
326 } | |
327 | |
328 } // namespace brotli | |
329 | |
330 #endif // BROTLI_ENC_CLUSTER_H_ | |
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