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// Copyright (c) the JPEG XL Project Authors. All rights reserved.
//
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
#include "lib/jxl/enc_cluster.h"
#include <algorithm>
#include <cmath>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <tuple>
#include "lib/jxl/base/status.h"
#undef HWY_TARGET_INCLUDE
#define HWY_TARGET_INCLUDE "lib/jxl/enc_cluster.cc"
#include <hwy/foreach_target.h>
#include <hwy/highway.h>
#include "lib/jxl/base/fast_math-inl.h"
#include "lib/jxl/enc_ans.h"
HWY_BEFORE_NAMESPACE();
namespace jxl {
namespace HWY_NAMESPACE {
// These templates are not found via ADL.
using hwy::HWY_NAMESPACE::Eq;
using hwy::HWY_NAMESPACE::IfThenZeroElse;
template <class V>
V Entropy(V count, V inv_total, V total) {
const HWY_CAPPED(float, Histogram::kRounding) d;
const auto zero = Set(d, 0.0f);
// TODO(eustas): why (0 - x) instead of Neg(x)?
return IfThenZeroElse(
Eq(count, total),
Sub(zero, Mul(count, FastLog2f(d, Mul(inv_total, count)))));
}
void HistogramEntropy(const Histogram& a) {
a.entropy_ = 0.0f;
if (a.total_count_ == 0) return;
const HWY_CAPPED(float, Histogram::kRounding) df;
const HWY_CAPPED(int32_t, Histogram::kRounding) di;
const auto inv_tot = Set(df, 1.0f / a.total_count_);
auto entropy_lanes = Zero(df);
auto total = Set(df, a.total_count_);
for (size_t i = 0; i < a.data_.size(); i += Lanes(di)) {
const auto counts = LoadU(di, &a.data_[i]);
entropy_lanes =
Add(entropy_lanes, Entropy(ConvertTo(df, counts), inv_tot, total));
}
a.entropy_ += GetLane(SumOfLanes(df, entropy_lanes));
}
float HistogramDistance(const Histogram& a, const Histogram& b) {
if (a.total_count_ == 0 || b.total_count_ == 0) return 0;
const HWY_CAPPED(float, Histogram::kRounding) df;
const HWY_CAPPED(int32_t, Histogram::kRounding) di;
const auto inv_tot = Set(df, 1.0f / (a.total_count_ + b.total_count_));
auto distance_lanes = Zero(df);
auto total = Set(df, a.total_count_ + b.total_count_);
for (size_t i = 0; i < std::max(a.data_.size(), b.data_.size());
i += Lanes(di)) {
const auto a_counts =
a.data_.size() > i ? LoadU(di, &a.data_[i]) : Zero(di);
const auto b_counts =
b.data_.size() > i ? LoadU(di, &b.data_[i]) : Zero(di);
const auto counts = ConvertTo(df, Add(a_counts, b_counts));
distance_lanes = Add(distance_lanes, Entropy(counts, inv_tot, total));
}
const float total_distance = GetLane(SumOfLanes(df, distance_lanes));
return total_distance - a.entropy_ - b.entropy_;
}
constexpr const float kInfinity = std::numeric_limits<float>::infinity();
float HistogramKLDivergence(const Histogram& actual, const Histogram& coding) {
if (actual.total_count_ == 0) return 0;
if (coding.total_count_ == 0) return kInfinity;
const HWY_CAPPED(float, Histogram::kRounding) df;
const HWY_CAPPED(int32_t, Histogram::kRounding) di;
const auto coding_inv = Set(df, 1.0f / coding.total_count_);
auto cost_lanes = Zero(df);
for (size_t i = 0; i < actual.data_.size(); i += Lanes(di)) {
const auto counts = LoadU(di, &actual.data_[i]);
const auto coding_counts =
coding.data_.size() > i ? LoadU(di, &coding.data_[i]) : Zero(di);
const auto coding_probs = Mul(ConvertTo(df, coding_counts), coding_inv);
const auto neg_coding_cost = BitCast(
df,
IfThenZeroElse(Eq(counts, Zero(di)),
IfThenElse(Eq(coding_counts, Zero(di)),
BitCast(di, Set(df, -kInfinity)),
BitCast(di, FastLog2f(df, coding_probs)))));
cost_lanes = NegMulAdd(ConvertTo(df, counts), neg_coding_cost, cost_lanes);
}
const float total_cost = GetLane(SumOfLanes(df, cost_lanes));
return total_cost - actual.entropy_;
}
// First step of a k-means clustering with a fancy distance metric.
Status FastClusterHistograms(const std::vector<Histogram>& in,
size_t max_histograms, std::vector<Histogram>* out,
std::vector<uint32_t>* histogram_symbols) {
const size_t prev_histograms = out->size();
out->reserve(max_histograms);
histogram_symbols->clear();
histogram_symbols->resize(in.size(), max_histograms);
std::vector<float> dists(in.size(), std::numeric_limits<float>::max());
size_t largest_idx = 0;
for (size_t i = 0; i < in.size(); i++) {
if (in[i].total_count_ == 0) {
(*histogram_symbols)[i] = 0;
dists[i] = 0.0f;
continue;
}
HistogramEntropy(in[i]);
if (in[i].total_count_ > in[largest_idx].total_count_) {
largest_idx = i;
}
}
if (prev_histograms > 0) {
for (size_t j = 0; j < prev_histograms; ++j) {
HistogramEntropy((*out)[j]);
}
for (size_t i = 0; i < in.size(); i++) {
if (dists[i] == 0.0f) continue;
for (size_t j = 0; j < prev_histograms; ++j) {
dists[i] = std::min(HistogramKLDivergence(in[i], (*out)[j]), dists[i]);
}
}
auto max_dist = std::max_element(dists.begin(), dists.end());
if (*max_dist > 0.0f) {
largest_idx = max_dist - dists.begin();
}
}
constexpr float kMinDistanceForDistinct = 48.0f;
while (out->size() < max_histograms) {
(*histogram_symbols)[largest_idx] = out->size();
out->push_back(in[largest_idx]);
dists[largest_idx] = 0.0f;
largest_idx = 0;
for (size_t i = 0; i < in.size(); i++) {
if (dists[i] == 0.0f) continue;
dists[i] = std::min(HistogramDistance(in[i], out->back()), dists[i]);
if (dists[i] > dists[largest_idx]) largest_idx = i;
}
if (dists[largest_idx] < kMinDistanceForDistinct) break;
}
for (size_t i = 0; i < in.size(); i++) {
if ((*histogram_symbols)[i] != max_histograms) continue;
size_t best = 0;
float best_dist = std::numeric_limits<float>::max();
for (size_t j = 0; j < out->size(); j++) {
float dist = j < prev_histograms ? HistogramKLDivergence(in[i], (*out)[j])
: HistogramDistance(in[i], (*out)[j]);
if (dist < best_dist) {
best = j;
best_dist = dist;
}
}
JXL_ENSURE(best_dist < std::numeric_limits<float>::max());
if (best >= prev_histograms) {
(*out)[best].AddHistogram(in[i]);
HistogramEntropy((*out)[best]);
}
(*histogram_symbols)[i] = best;
}
return true;
}
// NOLINTNEXTLINE(google-readability-namespace-comments)
} // namespace HWY_NAMESPACE
} // namespace jxl
HWY_AFTER_NAMESPACE();
#if HWY_ONCE
namespace jxl {
HWY_EXPORT(FastClusterHistograms); // Local function
HWY_EXPORT(HistogramEntropy); // Local function
StatusOr<float> Histogram::PopulationCost() const {
return ANSPopulationCost(data_.data(), data_.size());
}
float Histogram::ShannonEntropy() const {
HWY_DYNAMIC_DISPATCH(HistogramEntropy)(*this);
return entropy_;
}
namespace {
// -----------------------------------------------------------------------------
// Histogram refinement
// Reorder histograms in *out so that the new symbols in *symbols come in
// increasing order.
void HistogramReindex(std::vector<Histogram>* out, size_t prev_histograms,
std::vector<uint32_t>* symbols) {
std::vector<Histogram> tmp(*out);
std::map<int, int> new_index;
for (size_t i = 0; i < prev_histograms; ++i) {
new_index[i] = i;
}
int next_index = prev_histograms;
for (uint32_t symbol : *symbols) {
if (new_index.find(symbol) == new_index.end()) {
new_index[symbol] = next_index;
(*out)[next_index] = tmp[symbol];
++next_index;
}
}
out->resize(next_index);
for (uint32_t& symbol : *symbols) {
symbol = new_index[symbol];
}
}
} // namespace
// 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.
Status ClusterHistograms(const HistogramParams& params,
const std::vector<Histogram>& in,
size_t max_histograms, std::vector<Histogram>* out,
std::vector<uint32_t>* histogram_symbols) {
size_t prev_histograms = out->size();
max_histograms = std::min(max_histograms, params.max_histograms);
max_histograms = std::min(max_histograms, in.size());
if (params.clustering == HistogramParams::ClusteringType::kFastest) {
max_histograms = std::min(max_histograms, static_cast<size_t>(4));
}
JXL_RETURN_IF_ERROR(HWY_DYNAMIC_DISPATCH(FastClusterHistograms)(
in, prev_histograms + max_histograms, out, histogram_symbols));
if (prev_histograms == 0 &&
params.clustering == HistogramParams::ClusteringType::kBest) {
for (auto& histo : *out) {
JXL_ASSIGN_OR_RETURN(
histo.entropy_,
ANSPopulationCost(histo.data_.data(), histo.data_.size()));
}
uint32_t next_version = 2;
std::vector<uint32_t> version(out->size(), 1);
std::vector<uint32_t> renumbering(out->size());
std::iota(renumbering.begin(), renumbering.end(), 0);
// Try to pair up clusters if doing so reduces the total cost.
struct HistogramPair {
// validity of a pair: p.version == max(version[i], version[j])
float cost;
uint32_t first;
uint32_t second;
uint32_t version;
// We use > because priority queues sort in *decreasing* order, but we
// want lower cost elements to appear first.
bool operator<(const HistogramPair& other) const {
return std::make_tuple(cost, first, second, version) >
std::make_tuple(other.cost, other.first, other.second,
other.version);
}
};
// Create list of all pairs by increasing merging cost.
std::priority_queue<HistogramPair> pairs_to_merge;
for (uint32_t i = 0; i < out->size(); i++) {
for (uint32_t j = i + 1; j < out->size(); j++) {
Histogram histo;
histo.AddHistogram((*out)[i]);
histo.AddHistogram((*out)[j]);
JXL_ASSIGN_OR_RETURN(float cost, ANSPopulationCost(histo.data_.data(),
histo.data_.size()));
cost -= (*out)[i].entropy_ + (*out)[j].entropy_;
// Avoid enqueueing pairs that are not advantageous to merge.
if (cost >= 0) continue;
pairs_to_merge.push(
HistogramPair{cost, i, j, std::max(version[i], version[j])});
}
}
// Merge the best pair to merge, add new pairs that get formed as a
// consequence.
while (!pairs_to_merge.empty()) {
uint32_t first = pairs_to_merge.top().first;
uint32_t second = pairs_to_merge.top().second;
uint32_t ver = pairs_to_merge.top().version;
pairs_to_merge.pop();
if (ver != std::max(version[first], version[second]) ||
version[first] == 0 || version[second] == 0) {
continue;
}
(*out)[first].AddHistogram((*out)[second]);
JXL_ASSIGN_OR_RETURN(float cost,
ANSPopulationCost((*out)[first].data_.data(),
(*out)[first].data_.size()));
(*out)[first].entropy_ = cost;
for (uint32_t& item : renumbering) {
if (item == second) {
item = first;
}
}
version[second] = 0;
version[first] = next_version++;
for (uint32_t j = 0; j < out->size(); j++) {
if (j == first) continue;
if (version[j] == 0) continue;
Histogram histo;
histo.AddHistogram((*out)[first]);
histo.AddHistogram((*out)[j]);
JXL_ASSIGN_OR_RETURN(float cost, ANSPopulationCost(histo.data_.data(),
histo.data_.size()));
cost -= (*out)[first].entropy_ + (*out)[j].entropy_;
// Avoid enqueueing pairs that are not advantageous to merge.
if (cost >= 0) continue;
pairs_to_merge.push(
HistogramPair{cost, std::min(first, j), std::max(first, j),
std::max(version[first], version[j])});
}
}
std::vector<uint32_t> reverse_renumbering(out->size(), -1);
size_t num_alive = 0;
for (size_t i = 0; i < out->size(); i++) {
if (version[i] == 0) continue;
(*out)[num_alive++] = (*out)[i];
reverse_renumbering[i] = num_alive - 1;
}
out->resize(num_alive);
for (uint32_t& item : *histogram_symbols) {
item = reverse_renumbering[renumbering[item]];
}
}
// Convert the context map to a canonical form.
HistogramReindex(out, prev_histograms, histogram_symbols);
return true;
}
} // namespace jxl
#endif // HWY_ONCE