// Copyright 2013 Google Inc. All Rights Reserved. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. // // Function to find backward reference copies. #include "./backward_references.h" #include #include #include "./command.h" namespace brotli { static const double kInfinity = 1.0 / 0.0; // Histogram based cost model for zopflification. class ZopfliCostModel { public: void SetFromCommands(size_t num_bytes, size_t position, const uint8_t* ringbuffer, size_t ringbuffer_mask, const Command* commands, int num_commands, int last_insert_len) { std::vector histogram_literal(256, 0); std::vector histogram_cmd(kNumCommandPrefixes, 0); std::vector histogram_dist(kNumDistancePrefixes, 0); size_t pos = position - last_insert_len; for (int i = 0; i < num_commands; i++) { int inslength = commands[i].insert_len_; int copylength = commands[i].copy_len_; int distcode = commands[i].dist_prefix_; int cmdcode = commands[i].cmd_prefix_; histogram_cmd[cmdcode]++; if (cmdcode >= 128) histogram_dist[distcode]++; for (int j = 0; j < inslength; j++) { histogram_literal[ringbuffer[(pos + j) & ringbuffer_mask]]++; } pos += inslength + copylength; } std::vector cost_literal; Set(histogram_literal, &cost_literal); Set(histogram_cmd, &cost_cmd_); Set(histogram_dist, &cost_dist_); min_cost_cmd_ = kInfinity; for (int i = 0; i < kNumCommandPrefixes; ++i) { min_cost_cmd_ = std::min(min_cost_cmd_, cost_cmd_[i]); } literal_costs_.resize(num_bytes + 1); literal_costs_[0] = 0.0; for (int i = 0; i < num_bytes; ++i) { literal_costs_[i + 1] = literal_costs_[i] + cost_literal[ringbuffer[(position + i) & ringbuffer_mask]]; } } void SetFromLiteralCosts(size_t num_bytes, size_t position, const float* literal_cost, size_t literal_cost_mask) { literal_costs_.resize(num_bytes + 1); literal_costs_[0] = 0.0; if (literal_cost) { for (int i = 0; i < num_bytes; ++i) { literal_costs_[i + 1] = literal_costs_[i] + literal_cost[(position + i) & literal_cost_mask]; } } else { for (int i = 1; i <= num_bytes; ++i) { literal_costs_[i] = i * 5.4; } } cost_cmd_.resize(kNumCommandPrefixes); cost_dist_.resize(kNumDistancePrefixes); for (int i = 0; i < kNumCommandPrefixes; ++i) { cost_cmd_[i] = FastLog2(11 + i); } for (int i = 0; i < kNumDistancePrefixes; ++i) { cost_dist_[i] = FastLog2(20 + i); } min_cost_cmd_ = FastLog2(11); } double GetCommandCost( int dist_code, int length_code, int insert_length) const { int inscode = GetInsertLengthCode(insert_length); int copycode = GetCopyLengthCode(length_code); uint16_t cmdcode = CombineLengthCodes(inscode, copycode, dist_code); uint64_t insnumextra = insextra[inscode]; uint64_t copynumextra = copyextra[copycode]; uint16_t dist_symbol; uint32_t distextra; GetDistCode(dist_code, &dist_symbol, &distextra); uint32_t distnumextra = distextra >> 24; double result = insnumextra + copynumextra + distnumextra; result += cost_cmd_[cmdcode]; if (cmdcode >= 128) result += cost_dist_[dist_symbol]; return result; } double GetLiteralCosts(int from, int to) const { return literal_costs_[to] - literal_costs_[from]; } double GetMinCostCmd() const { return min_cost_cmd_; } private: void Set(const std::vector& histogram, std::vector* cost) { cost->resize(histogram.size()); double sum = 0; for (size_t i = 0; i < histogram.size(); i++) { sum += histogram[i]; } for (size_t i = 0; i < histogram.size(); i++) { if (histogram[i] == 0) { (*cost)[i] = -log2(0.25 / sum); continue; } // Shannon bits for this symbol. (*cost)[i] = -log2(histogram[i] / sum); // Cannot be coded with less than 1 bit if ((*cost)[i] < 1) (*cost)[i] = 1; } } std::vector cost_cmd_; // The insert and copy length symbols. std::vector cost_dist_; // Cumulative costs of literals per position in the stream. std::vector literal_costs_; double min_cost_cmd_; }; inline void SetDistanceCache(int distance, int distance_code, int max_distance, const int* dist_cache, int* result_dist_cache) { if (distance <= max_distance && distance_code > 0) { result_dist_cache[0] = distance; memcpy(&result_dist_cache[1], dist_cache, 3 * sizeof(dist_cache[0])); } else { memcpy(result_dist_cache, dist_cache, 4 * sizeof(dist_cache[0])); } } inline int ComputeDistanceCode(int distance, int max_distance, int quality, const int* dist_cache) { if (distance <= max_distance) { if (distance == dist_cache[0]) { return 0; } else if (distance == dist_cache[1]) { return 1; } else if (distance == dist_cache[2]) { return 2; } else if (distance == dist_cache[3]) { return 3; } else if (quality > 3 && distance >= 6) { for (int k = 4; k < kNumDistanceShortCodes; ++k) { int idx = kDistanceCacheIndex[k]; int candidate = dist_cache[idx] + kDistanceCacheOffset[k]; static const int kLimits[16] = { 0, 0, 0, 0, 6, 6, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12 }; if (distance == candidate && distance >= kLimits[k]) { return k; } } } } return distance + 15; } struct ZopfliNode { ZopfliNode() : length(1), distance(0), distance_code(0), length_code(0), insert_length(0), cost(kInfinity) {} // best length to get up to this byte (not including this byte itself) int length; // distance associated with the length int distance; int distance_code; int distance_cache[4]; // length code associated with the length - usually the same as length, // except in case of length-changing dictionary transformation. int length_code; // number of literal inserts before this copy int insert_length; // smallest cost to get to this byte from the beginning, as found so far double cost; }; inline void UpdateZopfliNode(ZopfliNode* nodes, size_t pos, size_t start_pos, int len, int len_code, int dist, int dist_code, int max_dist, const int* dist_cache, double cost) { ZopfliNode& next = nodes[pos + len]; next.length = len; next.length_code = len_code; next.distance = dist; next.distance_code = dist_code; next.insert_length = pos - start_pos; next.cost = cost; SetDistanceCache(dist, dist_code, max_dist, dist_cache, &next.distance_cache[0]); } // Maintains the smallest 2^k cost difference together with their positions class StartPosQueue { public: explicit StartPosQueue(int bits) : mask_((1 << bits) - 1), q_(1 << bits), idx_(0) {} void Clear() { idx_ = 0; } void Push(size_t pos, double costdiff) { q_[idx_ & mask_] = std::make_pair(pos, costdiff); // Restore the sorted order. for (int i = idx_; i > 0 && i > idx_ - mask_; --i) { if (q_[i & mask_].second > q_[(i - 1) & mask_].second) { std::swap(q_[i & mask_], q_[(i - 1) & mask_]); } } ++idx_; } int size() const { return std::min(idx_, mask_ + 1); } size_t GetStartPos(int k) const { return q_[(idx_ - k - 1) & mask_].first; } private: const int mask_; std::vector > q_; int idx_; }; // Returns the minimum possible copy length that can improve the cost of any // future position. int ComputeMinimumCopyLength(const StartPosQueue& queue, const std::vector& nodes, const ZopfliCostModel& model, size_t pos, double min_cost_cmd) { // Compute the minimum possible cost of reaching any future position. const size_t start0 = queue.GetStartPos(0); double min_cost = (nodes[start0].cost + model.GetLiteralCosts(start0, pos) + min_cost_cmd); int len = 2; int next_len_bucket = 4; int next_len_offset = 10; while (pos + len < nodes.size() && nodes[pos + len].cost <= min_cost) { // We already reached (pos + len) with no more cost than the minimum // possible cost of reaching anything from this pos, so there is no point in // looking for lengths <= len. ++len; if (len == next_len_offset) { // We reached the next copy length code bucket, so we add one more // extra bit to the minimum cost. min_cost += 1.0; next_len_offset += next_len_bucket; next_len_bucket *= 2; } } return len; } void ZopfliIterate(size_t num_bytes, size_t position, const uint8_t* ringbuffer, size_t ringbuffer_mask, const size_t max_backward_limit, const ZopfliCostModel& model, const std::vector& num_matches, const std::vector& matches, int* dist_cache, int* last_insert_len, Command* commands, int* num_commands, int* num_literals) { const Command * const orig_commands = commands; std::vector nodes(num_bytes + 1); nodes[0].length = 0; nodes[0].cost = 0; memcpy(nodes[0].distance_cache, dist_cache, 4 * sizeof(dist_cache[0])); StartPosQueue queue(3); const double min_cost_cmd = model.GetMinCostCmd(); size_t cur_match_pos = 0; for (size_t i = 0; i + 3 < num_bytes; i++) { size_t cur_ix = position + i; size_t cur_ix_masked = cur_ix & ringbuffer_mask; size_t max_distance = std::min(cur_ix, max_backward_limit); int max_length = num_bytes - i; queue.Push(i, nodes[i].cost - model.GetLiteralCosts(0, i)); const int min_len = ComputeMinimumCopyLength(queue, nodes, model, i, min_cost_cmd); // Go over the command starting positions in order of increasing cost // difference. for (size_t k = 0; k < 5 && k < queue.size(); ++k) { const size_t start = queue.GetStartPos(k); const double start_costdiff = nodes[start].cost - model.GetLiteralCosts(0, start); const int* dist_cache2 = &nodes[start].distance_cache[0]; // Look for last distance matches using the distance cache from this // starting position. int best_len = min_len - 1; for (int j = 0; j < kNumDistanceShortCodes; ++j) { const int idx = kDistanceCacheIndex[j]; const int backward = dist_cache2[idx] + kDistanceCacheOffset[j]; size_t prev_ix = cur_ix - backward; if (prev_ix >= cur_ix) { continue; } if (PREDICT_FALSE(backward > max_distance)) { continue; } prev_ix &= ringbuffer_mask; if (cur_ix_masked + best_len > ringbuffer_mask || prev_ix + best_len > ringbuffer_mask || ringbuffer[cur_ix_masked + best_len] != ringbuffer[prev_ix + best_len]) { continue; } const size_t len = FindMatchLengthWithLimit(&ringbuffer[prev_ix], &ringbuffer[cur_ix_masked], max_length); for (int l = best_len + 1; l <= len; ++l) { double cmd_cost = model.GetCommandCost(j, l, i - start); double cost = start_costdiff + cmd_cost + model.GetLiteralCosts(0, i); if (cost < nodes[i + l].cost) { UpdateZopfliNode(&nodes[0], i, start, l, l, backward, j, max_distance, dist_cache2, cost); } best_len = l; } } // At higher iterations look only for new last distance matches, since // looking only for new command start positions with the same distances // does not help much. if (k >= 2) continue; // Loop through all possible copy lengths at this position. int len = min_len; for (int j = 0; j < num_matches[i]; ++j) { BackwardMatch match = matches[cur_match_pos + j]; int dist = match.distance; bool is_dictionary_match = dist > max_distance; // We already tried all possible last distance matches, so we can use // normal distance code here. int dist_code = dist + 15; // Try all copy lengths up until the maximum copy length corresponding // to this distance. If the distance refers to the static dictionary, or // the maximum length is long enough, try only one maximum length. int max_len = match.length(); if (len < max_len && (is_dictionary_match || max_len > kMaxZopfliLen)) { len = max_len; } for (; len <= max_len; ++len) { int len_code = is_dictionary_match ? match.length_code() : len; double cmd_cost = model.GetCommandCost(dist_code, len_code, i - start); double cost = start_costdiff + cmd_cost + model.GetLiteralCosts(0, i); if (cost < nodes[i + len].cost) { UpdateZopfliNode(&nodes[0], i, start, len, len_code, dist, dist_code, max_distance, dist_cache2, cost); } } } } cur_match_pos += num_matches[i]; // The zopflification can be too slow in case of very long lengths, so in // such case skip it all, it does not cost a lot of compression ratio. if (num_matches[i] == 1 && matches[cur_match_pos - 1].length() > kMaxZopfliLen) { i += matches[cur_match_pos - 1].length() - 1; queue.Clear(); } } std::vector backwards; size_t index = num_bytes; while (nodes[index].cost == kInfinity) --index; while (index > 0) { int len = nodes[index].length + nodes[index].insert_length; backwards.push_back(len); index -= len; } std::vector path; for (size_t i = backwards.size(); i > 0; i--) { path.push_back(backwards[i - 1]); } size_t pos = 0; for (size_t i = 0; i < path.size(); i++) { const ZopfliNode& next = nodes[pos + path[i]]; int copy_length = next.length; int insert_length = next.insert_length; pos += insert_length; if (i == 0) { insert_length += *last_insert_len; } int distance = next.distance; int len_code = next.length_code; size_t max_distance = std::min(position + pos, max_backward_limit); bool is_dictionary = (distance > max_distance); int dist_code = next.distance_code; Command cmd(insert_length, copy_length, len_code, dist_code); *commands++ = cmd; if (!is_dictionary && dist_code > 0) { dist_cache[3] = dist_cache[2]; dist_cache[2] = dist_cache[1]; dist_cache[1] = dist_cache[0]; dist_cache[0] = distance; } *num_literals += insert_length; insert_length = 0; pos += copy_length; } *last_insert_len = num_bytes - pos; *num_commands += (commands - orig_commands); } template void CreateBackwardReferences(size_t num_bytes, size_t position, const uint8_t* ringbuffer, size_t ringbuffer_mask, const size_t max_backward_limit, const int quality, Hasher* hasher, int* dist_cache, int* last_insert_len, Command* commands, int* num_commands, int* num_literals) { if (num_bytes >= 3 && position >= 3) { // Prepare the hashes for three last bytes of the last write. // These could not be calculated before, since they require knowledge // of both the previous and the current block. hasher->Store(&ringbuffer[(position - 3) & ringbuffer_mask], position - 3); hasher->Store(&ringbuffer[(position - 2) & ringbuffer_mask], position - 2); hasher->Store(&ringbuffer[(position - 1) & ringbuffer_mask], position - 1); } const Command * const orig_commands = commands; int insert_length = *last_insert_len; size_t i = position & ringbuffer_mask; const int i_diff = position - i; const size_t i_end = i + num_bytes; // For speed up heuristics for random data. const int random_heuristics_window_size = quality < 9 ? 64 : 512; int apply_random_heuristics = i + random_heuristics_window_size; // Minimum score to accept a backward reference. const int kMinScore = 4.0; while (i + 3 < i_end) { int max_length = i_end - i; size_t max_distance = std::min(i + i_diff, max_backward_limit); int best_len = 0; int best_len_code = 0; int best_dist = 0; double best_score = kMinScore; bool match_found = hasher->FindLongestMatch( ringbuffer, ringbuffer_mask, dist_cache, i + i_diff, max_length, max_distance, &best_len, &best_len_code, &best_dist, &best_score); if (match_found) { // Found a match. Let's look for something even better ahead. int delayed_backward_references_in_row = 0; for (;;) { --max_length; int best_len_2 = quality < 5 ? std::min(best_len - 1, max_length) : 0; int best_len_code_2 = 0; int best_dist_2 = 0; double best_score_2 = kMinScore; max_distance = std::min(i + i_diff + 1, max_backward_limit); hasher->Store(ringbuffer + i, i + i_diff); match_found = hasher->FindLongestMatch( ringbuffer, ringbuffer_mask, dist_cache, i + i_diff + 1, max_length, max_distance, &best_len_2, &best_len_code_2, &best_dist_2, &best_score_2); double cost_diff_lazy = 7.0; if (match_found && best_score_2 >= best_score + cost_diff_lazy) { // Ok, let's just write one byte for now and start a match from the // next byte. ++i; ++insert_length; best_len = best_len_2; best_len_code = best_len_code_2; best_dist = best_dist_2; best_score = best_score_2; if (++delayed_backward_references_in_row < 4) { continue; } } break; } apply_random_heuristics = i + 2 * best_len + random_heuristics_window_size; max_distance = std::min(i + i_diff, max_backward_limit); // The first 16 codes are special shortcodes, and the minimum offset is 1. int distance_code = ComputeDistanceCode(best_dist, max_distance, quality, dist_cache); if (best_dist <= max_distance && distance_code > 0) { dist_cache[3] = dist_cache[2]; dist_cache[2] = dist_cache[1]; dist_cache[1] = dist_cache[0]; dist_cache[0] = best_dist; } Command cmd(insert_length, best_len, best_len_code, distance_code); *commands++ = cmd; *num_literals += insert_length; insert_length = 0; // Put the hash keys into the table, if there are enough // bytes left. for (int j = 1; j < best_len; ++j) { hasher->Store(&ringbuffer[i + j], i + i_diff + j); } i += best_len; } else { ++insert_length; hasher->Store(ringbuffer + i, i + i_diff); ++i; // If we have not seen matches for a long time, we can skip some // match lookups. Unsuccessful match lookups are very very expensive // and this kind of a heuristic speeds up compression quite // a lot. if (i > apply_random_heuristics) { // Going through uncompressible data, jump. if (i > apply_random_heuristics + 4 * random_heuristics_window_size) { // It is quite a long time since we saw a copy, so we assume // that this data is not compressible, and store hashes less // often. Hashes of non compressible data are less likely to // turn out to be useful in the future, too, so we store less of // them to not to flood out the hash table of good compressible // data. int i_jump = std::min(i + 16, i_end - 4); for (; i < i_jump; i += 4) { hasher->Store(ringbuffer + i, i + i_diff); insert_length += 4; } } else { int i_jump = std::min(i + 8, i_end - 3); for (; i < i_jump; i += 2) { hasher->Store(ringbuffer + i, i + i_diff); insert_length += 2; } } } } } insert_length += (i_end - i); *last_insert_len = insert_length; *num_commands += (commands - orig_commands); } void CreateBackwardReferences(size_t num_bytes, size_t position, const uint8_t* ringbuffer, size_t ringbuffer_mask, const float* literal_cost, size_t literal_cost_mask, const size_t max_backward_limit, const int quality, Hashers* hashers, int hash_type, int* dist_cache, int* last_insert_len, Command* commands, int* num_commands, int* num_literals) { bool zopflify = quality > 9; if (zopflify) { Hashers::H9* hasher = hashers->hash_h9.get(); if (num_bytes >= 3 && position >= 3) { // Prepare the hashes for three last bytes of the last write. // These could not be calculated before, since they require knowledge // of both the previous and the current block. hasher->Store(&ringbuffer[(position - 3) & ringbuffer_mask], position - 3); hasher->Store(&ringbuffer[(position - 2) & ringbuffer_mask], position - 2); hasher->Store(&ringbuffer[(position - 1) & ringbuffer_mask], position - 1); } std::vector num_matches(num_bytes); std::vector matches(3 * num_bytes); size_t cur_match_pos = 0; for (size_t i = 0; i + 3 < num_bytes; ++i) { size_t max_distance = std::min(position + i, max_backward_limit); int max_length = num_bytes - i; // Ensure that we have at least kMaxZopfliLen free slots. if (matches.size() < cur_match_pos + kMaxZopfliLen) { matches.resize(cur_match_pos + kMaxZopfliLen); } hasher->FindAllMatches( ringbuffer, ringbuffer_mask, position + i, max_length, max_distance, &num_matches[i], &matches[cur_match_pos]); hasher->Store(&ringbuffer[(position + i) & ringbuffer_mask], position + i); cur_match_pos += num_matches[i]; if (num_matches[i] == 1) { const int match_len = matches[cur_match_pos - 1].length(); if (match_len > kMaxZopfliLen) { for (int j = 1; j < match_len; ++j) { ++i; hasher->Store( &ringbuffer[(position + i) & ringbuffer_mask], position + i); num_matches[i] = 0; } } } } int orig_num_literals = *num_literals; int orig_last_insert_len = *last_insert_len; int orig_dist_cache[4] = { dist_cache[0], dist_cache[1], dist_cache[2], dist_cache[3] }; int orig_num_commands = *num_commands; static const int kIterations = 2; for (int i = 0; i < kIterations; i++) { ZopfliCostModel model; if (i == 0) { model.SetFromLiteralCosts(num_bytes, position, literal_cost, literal_cost_mask); } else { model.SetFromCommands(num_bytes, position, ringbuffer, ringbuffer_mask, commands, *num_commands - orig_num_commands, orig_last_insert_len); } *num_commands = orig_num_commands; *num_literals = orig_num_literals; *last_insert_len = orig_last_insert_len; memcpy(dist_cache, orig_dist_cache, 4 * sizeof(dist_cache[0])); ZopfliIterate(num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, model, num_matches, matches, dist_cache, last_insert_len, commands, num_commands, num_literals); } return; } switch (hash_type) { case 1: CreateBackwardReferences( num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, quality, hashers->hash_h1.get(), dist_cache, last_insert_len, commands, num_commands, num_literals); break; case 2: CreateBackwardReferences( num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, quality, hashers->hash_h2.get(), dist_cache, last_insert_len, commands, num_commands, num_literals); break; case 3: CreateBackwardReferences( num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, quality, hashers->hash_h3.get(), dist_cache, last_insert_len, commands, num_commands, num_literals); break; case 4: CreateBackwardReferences( num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, quality, hashers->hash_h4.get(), dist_cache, last_insert_len, commands, num_commands, num_literals); break; case 5: CreateBackwardReferences( num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, quality, hashers->hash_h5.get(), dist_cache, last_insert_len, commands, num_commands, num_literals); break; case 6: CreateBackwardReferences( num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, quality, hashers->hash_h6.get(), dist_cache, last_insert_len, commands, num_commands, num_literals); break; case 7: CreateBackwardReferences( num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, quality, hashers->hash_h7.get(), dist_cache, last_insert_len, commands, num_commands, num_literals); break; case 8: CreateBackwardReferences( num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, quality, hashers->hash_h8.get(), dist_cache, last_insert_len, commands, num_commands, num_literals); break; case 9: CreateBackwardReferences( num_bytes, position, ringbuffer, ringbuffer_mask, max_backward_limit, quality, hashers->hash_h9.get(), dist_cache, last_insert_len, commands, num_commands, num_literals); break; default: break; } } } // namespace brotli