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+/* Copyright 2013 Google Inc. All Rights Reserved.
+
+ Distributed under MIT license.
+ See file LICENSE for detail or copy at https://opensource.org/licenses/MIT
+*/
+
+// Functions for clustering similar histograms together.
+
+#ifndef BROTLI_ENC_CLUSTER_H_
+#define BROTLI_ENC_CLUSTER_H_
+
+#include <math.h>
+#include <algorithm>
+#include <map>
+#include <utility>
+#include <vector>
+
+#include "./bit_cost.h"
+#include "./entropy_encode.h"
+#include "./fast_log.h"
+#include "./histogram.h"
+#include "./port.h"
+#include "./types.h"
+
+namespace brotli {
+
+struct HistogramPair {
+ uint32_t idx1;
+ uint32_t idx2;
+ double cost_combo;
+ double cost_diff;
+};
+
+inline bool operator<(const HistogramPair& p1, const HistogramPair& p2) {
+ if (p1.cost_diff != p2.cost_diff) {
+ return p1.cost_diff > p2.cost_diff;
+ }
+ return (p1.idx2 - p1.idx1) > (p2.idx2 - p2.idx1);
+}
+
+// Returns entropy reduction of the context map when we combine two clusters.
+inline double ClusterCostDiff(size_t size_a, size_t size_b) {
+ size_t size_c = size_a + size_b;
+ return static_cast<double>(size_a) * FastLog2(size_a) +
+ static_cast<double>(size_b) * FastLog2(size_b) -
+ static_cast<double>(size_c) * FastLog2(size_c);
+}
+
+// Computes the bit cost reduction by combining out[idx1] and out[idx2] and if
+// it is below a threshold, stores the pair (idx1, idx2) in the *pairs queue.
+template<typename HistogramType>
+void CompareAndPushToQueue(const HistogramType* out,
+ const uint32_t* cluster_size,
+ uint32_t idx1, uint32_t idx2,
+ std::vector<HistogramPair>* pairs) {
+ if (idx1 == idx2) {
+ return;
+ }
+ if (idx2 < idx1) {
+ uint32_t t = idx2;
+ idx2 = idx1;
+ idx1 = t;
+ }
+ bool store_pair = false;
+ HistogramPair p;
+ p.idx1 = idx1;
+ p.idx2 = idx2;
+ p.cost_diff = 0.5 * ClusterCostDiff(cluster_size[idx1], cluster_size[idx2]);
+ p.cost_diff -= out[idx1].bit_cost_;
+ p.cost_diff -= out[idx2].bit_cost_;
+
+ if (out[idx1].total_count_ == 0) {
+ p.cost_combo = out[idx2].bit_cost_;
+ store_pair = true;
+ } else if (out[idx2].total_count_ == 0) {
+ p.cost_combo = out[idx1].bit_cost_;
+ store_pair = true;
+ } else {
+ double threshold = pairs->empty() ? 1e99 :
+ std::max(0.0, (*pairs)[0].cost_diff);
+ HistogramType combo = out[idx1];
+ combo.AddHistogram(out[idx2]);
+ double cost_combo = PopulationCost(combo);
+ if (cost_combo < threshold - p.cost_diff) {
+ p.cost_combo = cost_combo;
+ store_pair = true;
+ }
+ }
+ if (store_pair) {
+ p.cost_diff += p.cost_combo;
+ if (!pairs->empty() && (pairs->front() < p)) {
+ // Replace the top of the queue if needed.
+ pairs->push_back(pairs->front());
+ pairs->front() = p;
+ } else {
+ pairs->push_back(p);
+ }
+ }
+}
+
+template<typename HistogramType>
+void HistogramCombine(HistogramType* out,
+ uint32_t* cluster_size,
+ uint32_t* symbols,
+ size_t symbols_size,
+ size_t max_clusters) {
+ double cost_diff_threshold = 0.0;
+ size_t min_cluster_size = 1;
+
+ // Uniquify the list of symbols.
+ std::vector<uint32_t> clusters(symbols, symbols + symbols_size);
+ std::sort(clusters.begin(), clusters.end());
+ std::vector<uint32_t>::iterator last =
+ std::unique(clusters.begin(), clusters.end());
+ clusters.resize(static_cast<size_t>(last - clusters.begin()));
+
+ // We maintain a heap of histogram pairs, ordered by the bit cost reduction.
+ std::vector<HistogramPair> pairs;
+ for (size_t idx1 = 0; idx1 < clusters.size(); ++idx1) {
+ for (size_t idx2 = idx1 + 1; idx2 < clusters.size(); ++idx2) {
+ CompareAndPushToQueue(out, cluster_size, clusters[idx1], clusters[idx2],
+ &pairs);
+ }
+ }
+
+ while (clusters.size() > min_cluster_size) {
+ if (pairs[0].cost_diff >= cost_diff_threshold) {
+ cost_diff_threshold = 1e99;
+ min_cluster_size = max_clusters;
+ continue;
+ }
+ // Take the best pair from the top of heap.
+ uint32_t best_idx1 = pairs[0].idx1;
+ uint32_t best_idx2 = pairs[0].idx2;
+ out[best_idx1].AddHistogram(out[best_idx2]);
+ out[best_idx1].bit_cost_ = pairs[0].cost_combo;
+ cluster_size[best_idx1] += cluster_size[best_idx2];
+ for (size_t i = 0; i < symbols_size; ++i) {
+ if (symbols[i] == best_idx2) {
+ symbols[i] = best_idx1;
+ }
+ }
+ for (std::vector<uint32_t>::iterator cluster = clusters.begin();
+ cluster != clusters.end(); ++cluster) {
+ if (*cluster >= best_idx2) {
+ clusters.erase(cluster);
+ break;
+ }
+ }
+
+ // Remove pairs intersecting the just combined best pair.
+ size_t copy_to_idx = 0;
+ for (size_t i = 0; i < pairs.size(); ++i) {
+ HistogramPair& p = pairs[i];
+ if (p.idx1 == best_idx1 || p.idx2 == best_idx1 ||
+ p.idx1 == best_idx2 || p.idx2 == best_idx2) {
+ // Remove invalid pair from the queue.
+ continue;
+ }
+ if (pairs.front() < p) {
+ // Replace the top of the queue if needed.
+ HistogramPair front = pairs.front();
+ pairs.front() = p;
+ pairs[copy_to_idx] = front;
+ } else {
+ pairs[copy_to_idx] = p;
+ }
+ ++copy_to_idx;
+ }
+ pairs.resize(copy_to_idx);
+
+ // Push new pairs formed with the combined histogram to the heap.
+ for (size_t i = 0; i < clusters.size(); ++i) {
+ CompareAndPushToQueue(out, cluster_size, best_idx1, clusters[i], &pairs);
+ }
+ }
+}
+
+// -----------------------------------------------------------------------------
+// Histogram refinement
+
+// What is the bit cost of moving histogram from cur_symbol to candidate.
+template<typename HistogramType>
+double HistogramBitCostDistance(const HistogramType& histogram,
+ const HistogramType& candidate) {
+ if (histogram.total_count_ == 0) {
+ return 0.0;
+ }
+ HistogramType tmp = histogram;
+ tmp.AddHistogram(candidate);
+ return PopulationCost(tmp) - candidate.bit_cost_;
+}
+
+// Find the best 'out' histogram for each of the 'in' histograms.
+// Note: we assume that out[]->bit_cost_ is already up-to-date.
+template<typename HistogramType>
+void HistogramRemap(const HistogramType* in, size_t in_size,
+ HistogramType* out, uint32_t* symbols) {
+ // Uniquify the list of symbols.
+ std::vector<uint32_t> all_symbols(symbols, symbols + in_size);
+ std::sort(all_symbols.begin(), all_symbols.end());
+ std::vector<uint32_t>::iterator last =
+ std::unique(all_symbols.begin(), all_symbols.end());
+ all_symbols.resize(static_cast<size_t>(last - all_symbols.begin()));
+
+ for (size_t i = 0; i < in_size; ++i) {
+ uint32_t best_out = i == 0 ? symbols[0] : symbols[i - 1];
+ double best_bits = HistogramBitCostDistance(in[i], out[best_out]);
+ for (std::vector<uint32_t>::const_iterator k = all_symbols.begin();
+ k != all_symbols.end(); ++k) {
+ const double cur_bits = HistogramBitCostDistance(in[i], out[*k]);
+ if (cur_bits < best_bits) {
+ best_bits = cur_bits;
+ best_out = *k;
+ }
+ }
+ symbols[i] = best_out;
+ }
+
+
+ // Recompute each out based on raw and symbols.
+ for (std::vector<uint32_t>::const_iterator k = all_symbols.begin();
+ k != all_symbols.end(); ++k) {
+ out[*k].Clear();
+ }
+ for (size_t i = 0; i < in_size; ++i) {
+ out[symbols[i]].AddHistogram(in[i]);
+ }
+}
+
+// Reorder histograms in *out so that the new symbols in *symbols come in
+// increasing order.
+template<typename HistogramType>
+void HistogramReindex(std::vector<HistogramType>* out,
+ std::vector<uint32_t>* symbols) {
+ std::vector<HistogramType> tmp(*out);
+ std::map<uint32_t, uint32_t> new_index;
+ uint32_t next_index = 0;
+ for (size_t i = 0; i < symbols->size(); ++i) {
+ if (new_index.find((*symbols)[i]) == new_index.end()) {
+ new_index[(*symbols)[i]] = next_index;
+ (*out)[next_index] = tmp[(*symbols)[i]];
+ ++next_index;
+ }
+ }
+ out->resize(next_index);
+ for (size_t i = 0; i < symbols->size(); ++i) {
+ (*symbols)[i] = new_index[(*symbols)[i]];
+ }
+}
+
+// Clusters similar histograms in 'in' together, the selected histograms are
+// placed in 'out', and for each index in 'in', *histogram_symbols will
+// indicate which of the 'out' histograms is the best approximation.
+template<typename HistogramType>
+void ClusterHistograms(const std::vector<HistogramType>& in,
+ size_t num_contexts, size_t num_blocks,
+ size_t max_histograms,
+ std::vector<HistogramType>* out,
+ std::vector<uint32_t>* histogram_symbols) {
+ const size_t in_size = num_contexts * num_blocks;
+ assert(in_size == in.size());
+ std::vector<uint32_t> cluster_size(in_size, 1);
+ out->resize(in_size);
+ histogram_symbols->resize(in_size);
+ for (size_t i = 0; i < in_size; ++i) {
+ (*out)[i] = in[i];
+ (*out)[i].bit_cost_ = PopulationCost(in[i]);
+ (*histogram_symbols)[i] = static_cast<uint32_t>(i);
+ }
+
+
+ const size_t max_input_histograms = 64;
+ for (size_t i = 0; i < in_size; i += max_input_histograms) {
+ size_t num_to_combine = std::min(in_size - i, max_input_histograms);
+ HistogramCombine(&(*out)[0], &cluster_size[0],
+ &(*histogram_symbols)[i], num_to_combine,
+ max_histograms);
+ }
+
+ // Collapse similar histograms.
+ HistogramCombine(&(*out)[0], &cluster_size[0],
+ &(*histogram_symbols)[0], in_size,
+ max_histograms);
+
+ // Find the optimal map from original histograms to the final ones.
+ HistogramRemap(&in[0], in_size, &(*out)[0], &(*histogram_symbols)[0]);
+
+ // Convert the context map to a canonical form.
+ HistogramReindex(out, histogram_symbols);
+
+}
+
+
+} // namespace brotli
+
+#endif // BROTLI_ENC_CLUSTER_H_
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