Adding upstream version 1:115.7.0.upstream/1%115.7.0upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1248 insertions, 0 deletions

diff --git a/media/libwebp/src/enc/histogram_enc.c b/media/libwebp/src/enc/histogram_enc.c
new file mode 100644
index 0000000000..8418def2e1
--- /dev/null
+++ b/media/libwebp/src/enc/histogram_enc.c
@@ -0,0 +1,1248 @@
+// Copyright 2012 Google Inc. All Rights Reserved.
+//
+// Use of this source code is governed by a BSD-style license
+// that can be found in the COPYING file in the root of the source
+// tree. An additional intellectual property rights grant can be found
+// in the file PATENTS. All contributing project authors may
+// be found in the AUTHORS file in the root of the source tree.
+// -----------------------------------------------------------------------------
+//
+// Author: Jyrki Alakuijala (jyrki@google.com)
+//
+#ifdef HAVE_CONFIG_H
+#include "src/webp/config.h"
+#endif
+
+#include <float.h>
+#include <math.h>
+
+#include "src/dsp/lossless.h"
+#include "src/dsp/lossless_common.h"
+#include "src/enc/backward_references_enc.h"
+#include "src/enc/histogram_enc.h"
+#include "src/enc/vp8i_enc.h"
+#include "src/utils/utils.h"
+
+#define MAX_BIT_COST FLT_MAX
+
+// Number of partitions for the three dominant (literal, red and blue) symbol
+// costs.
+#define NUM_PARTITIONS 4
+// The size of the bin-hash corresponding to the three dominant costs.
+#define BIN_SIZE (NUM_PARTITIONS * NUM_PARTITIONS * NUM_PARTITIONS)
+// Maximum number of histograms allowed in greedy combining algorithm.
+#define MAX_HISTO_GREEDY 100
+
+static void HistogramClear(VP8LHistogram* const p) {
+  uint32_t* const literal = p->literal_;
+  const int cache_bits = p->palette_code_bits_;
+  const int histo_size = VP8LGetHistogramSize(cache_bits);
+  memset(p, 0, histo_size);
+  p->palette_code_bits_ = cache_bits;
+  p->literal_ = literal;
+}
+
+// Swap two histogram pointers.
+static void HistogramSwap(VP8LHistogram** const A, VP8LHistogram** const B) {
+  VP8LHistogram* const tmp = *A;
+  *A = *B;
+  *B = tmp;
+}
+
+static void HistogramCopy(const VP8LHistogram* const src,
+                          VP8LHistogram* const dst) {
+  uint32_t* const dst_literal = dst->literal_;
+  const int dst_cache_bits = dst->palette_code_bits_;
+  const int literal_size = VP8LHistogramNumCodes(dst_cache_bits);
+  const int histo_size = VP8LGetHistogramSize(dst_cache_bits);
+  assert(src->palette_code_bits_ == dst_cache_bits);
+  memcpy(dst, src, histo_size);
+  dst->literal_ = dst_literal;
+  memcpy(dst->literal_, src->literal_, literal_size * sizeof(*dst->literal_));
+}
+
+int VP8LGetHistogramSize(int cache_bits) {
+  const int literal_size = VP8LHistogramNumCodes(cache_bits);
+  const size_t total_size = sizeof(VP8LHistogram) + sizeof(int) * literal_size;
+  assert(total_size <= (size_t)0x7fffffff);
+  return (int)total_size;
+}
+
+void VP8LFreeHistogram(VP8LHistogram* const histo) {
+  WebPSafeFree(histo);
+}
+
+void VP8LFreeHistogramSet(VP8LHistogramSet* const histo) {
+  WebPSafeFree(histo);
+}
+
+void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
+                            VP8LHistogram* const histo) {
+  VP8LRefsCursor c = VP8LRefsCursorInit(refs);
+  while (VP8LRefsCursorOk(&c)) {
+    VP8LHistogramAddSinglePixOrCopy(histo, c.cur_pos, NULL, 0);
+    VP8LRefsCursorNext(&c);
+  }
+}
+
+void VP8LHistogramCreate(VP8LHistogram* const p,
+                         const VP8LBackwardRefs* const refs,
+                         int palette_code_bits) {
+  if (palette_code_bits >= 0) {
+    p->palette_code_bits_ = palette_code_bits;
+  }
+  HistogramClear(p);
+  VP8LHistogramStoreRefs(refs, p);
+}
+
+void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits,
+                       int init_arrays) {
+  p->palette_code_bits_ = palette_code_bits;
+  if (init_arrays) {
+    HistogramClear(p);
+  } else {
+    p->trivial_symbol_ = 0;
+    p->bit_cost_ = 0.;
+    p->literal_cost_ = 0.;
+    p->red_cost_ = 0.;
+    p->blue_cost_ = 0.;
+    memset(p->is_used_, 0, sizeof(p->is_used_));
+  }
+}
+
+VP8LHistogram* VP8LAllocateHistogram(int cache_bits) {
+  VP8LHistogram* histo = NULL;
+  const int total_size = VP8LGetHistogramSize(cache_bits);
+  uint8_t* const memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
+  if (memory == NULL) return NULL;
+  histo = (VP8LHistogram*)memory;
+  // literal_ won't necessary be aligned.
+  histo->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
+  VP8LHistogramInit(histo, cache_bits, /*init_arrays=*/ 0);
+  return histo;
+}
+
+// Resets the pointers of the histograms to point to the bit buffer in the set.
+static void HistogramSetResetPointers(VP8LHistogramSet* const set,
+                                      int cache_bits) {
+  int i;
+  const int histo_size = VP8LGetHistogramSize(cache_bits);
+  uint8_t* memory = (uint8_t*) (set->histograms);
+  memory += set->max_size * sizeof(*set->histograms);
+  for (i = 0; i < set->max_size; ++i) {
+    memory = (uint8_t*) WEBP_ALIGN(memory);
+    set->histograms[i] = (VP8LHistogram*) memory;
+    // literal_ won't necessary be aligned.
+    set->histograms[i]->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
+    memory += histo_size;
+  }
+}
+
+// Returns the total size of the VP8LHistogramSet.
+static size_t HistogramSetTotalSize(int size, int cache_bits) {
+  const int histo_size = VP8LGetHistogramSize(cache_bits);
+  return (sizeof(VP8LHistogramSet) + size * (sizeof(VP8LHistogram*) +
+          histo_size + WEBP_ALIGN_CST));
+}
+
+VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
+  int i;
+  VP8LHistogramSet* set;
+  const size_t total_size = HistogramSetTotalSize(size, cache_bits);
+  uint8_t* memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
+  if (memory == NULL) return NULL;
+
+  set = (VP8LHistogramSet*)memory;
+  memory += sizeof(*set);
+  set->histograms = (VP8LHistogram**)memory;
+  set->max_size = size;
+  set->size = size;
+  HistogramSetResetPointers(set, cache_bits);
+  for (i = 0; i < size; ++i) {
+    VP8LHistogramInit(set->histograms[i], cache_bits, /*init_arrays=*/ 0);
+  }
+  return set;
+}
+
+void VP8LHistogramSetClear(VP8LHistogramSet* const set) {
+  int i;
+  const int cache_bits = set->histograms[0]->palette_code_bits_;
+  const int size = set->max_size;
+  const size_t total_size = HistogramSetTotalSize(size, cache_bits);
+  uint8_t* memory = (uint8_t*)set;
+
+  memset(memory, 0, total_size);
+  memory += sizeof(*set);
+  set->histograms = (VP8LHistogram**)memory;
+  set->max_size = size;
+  set->size = size;
+  HistogramSetResetPointers(set, cache_bits);
+  for (i = 0; i < size; ++i) {
+    set->histograms[i]->palette_code_bits_ = cache_bits;
+  }
+}
+
+// Removes the histogram 'i' from 'set' by setting it to NULL.
+static void HistogramSetRemoveHistogram(VP8LHistogramSet* const set, int i,
+                                        int* const num_used) {
+  assert(set->histograms[i] != NULL);
+  set->histograms[i] = NULL;
+  --*num_used;
+  // If we remove the last valid one, shrink until the next valid one.
+  if (i == set->size - 1) {
+    while (set->size >= 1 && set->histograms[set->size - 1] == NULL) {
+      --set->size;
+    }
+  }
+}
+
+// -----------------------------------------------------------------------------
+
+void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo,
+                                     const PixOrCopy* const v,
+                                     int (*const distance_modifier)(int, int),
+                                     int distance_modifier_arg0) {
+  if (PixOrCopyIsLiteral(v)) {
+    ++histo->alpha_[PixOrCopyLiteral(v, 3)];
+    ++histo->red_[PixOrCopyLiteral(v, 2)];
+    ++histo->literal_[PixOrCopyLiteral(v, 1)];
+    ++histo->blue_[PixOrCopyLiteral(v, 0)];
+  } else if (PixOrCopyIsCacheIdx(v)) {
+    const int literal_ix =
+        NUM_LITERAL_CODES + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
+    assert(histo->palette_code_bits_ != 0);
+    ++histo->literal_[literal_ix];
+  } else {
+    int code, extra_bits;
+    VP8LPrefixEncodeBits(PixOrCopyLength(v), &code, &extra_bits);
+    ++histo->literal_[NUM_LITERAL_CODES + code];
+    if (distance_modifier == NULL) {
+      VP8LPrefixEncodeBits(PixOrCopyDistance(v), &code, &extra_bits);
+    } else {
+      VP8LPrefixEncodeBits(
+          distance_modifier(distance_modifier_arg0, PixOrCopyDistance(v)),
+          &code, &extra_bits);
+    }
+    ++histo->distance_[code];
+  }
+}
+
+// -----------------------------------------------------------------------------
+// Entropy-related functions.
+
+static WEBP_INLINE float BitsEntropyRefine(const VP8LBitEntropy* entropy) {
+  float mix;
+  if (entropy->nonzeros < 5) {
+    if (entropy->nonzeros <= 1) {
+      return 0;
+    }
+    // Two symbols, they will be 0 and 1 in a Huffman code.
+    // Let's mix in a bit of entropy to favor good clustering when
+    // distributions of these are combined.
+    if (entropy->nonzeros == 2) {
+      return 0.99f * entropy->sum + 0.01f * entropy->entropy;
+    }
+    // No matter what the entropy says, we cannot be better than min_limit
+    // with Huffman coding. I am mixing a bit of entropy into the
+    // min_limit since it produces much better (~0.5 %) compression results
+    // perhaps because of better entropy clustering.
+    if (entropy->nonzeros == 3) {
+      mix = 0.95f;
+    } else {
+      mix = 0.7f;  // nonzeros == 4.
+    }
+  } else {
+    mix = 0.627f;
+  }
+
+  {
+    float min_limit = 2.f * entropy->sum - entropy->max_val;
+    min_limit = mix * min_limit + (1.f - mix) * entropy->entropy;
+    return (entropy->entropy < min_limit) ? min_limit : entropy->entropy;
+  }
+}
+
+float VP8LBitsEntropy(const uint32_t* const array, int n) {
+  VP8LBitEntropy entropy;
+  VP8LBitsEntropyUnrefined(array, n, &entropy);
+
+  return BitsEntropyRefine(&entropy);
+}
+
+static float InitialHuffmanCost(void) {
+  // Small bias because Huffman code length is typically not stored in
+  // full length.
+  static const int kHuffmanCodeOfHuffmanCodeSize = CODE_LENGTH_CODES * 3;
+  static const float kSmallBias = 9.1f;
+  return kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
+}
+
+// Finalize the Huffman cost based on streak numbers and length type (<3 or >=3)
+static float FinalHuffmanCost(const VP8LStreaks* const stats) {
+  // The constants in this function are experimental and got rounded from
+  // their original values in 1/8 when switched to 1/1024.
+  float retval = InitialHuffmanCost();
+  // Second coefficient: Many zeros in the histogram are covered efficiently
+  // by a run-length encode. Originally 2/8.
+  retval += stats->counts[0] * 1.5625f + 0.234375f * stats->streaks[0][1];
+  // Second coefficient: Constant values are encoded less efficiently, but still
+  // RLE'ed. Originally 6/8.
+  retval += stats->counts[1] * 2.578125f + 0.703125f * stats->streaks[1][1];
+  // 0s are usually encoded more efficiently than non-0s.
+  // Originally 15/8.
+  retval += 1.796875f * stats->streaks[0][0];
+  // Originally 26/8.
+  retval += 3.28125f * stats->streaks[1][0];
+  return retval;
+}
+
+// Get the symbol entropy for the distribution 'population'.
+// Set 'trivial_sym', if there's only one symbol present in the distribution.
+static float PopulationCost(const uint32_t* const population, int length,
+                            uint32_t* const trivial_sym,
+                            uint8_t* const is_used) {
+  VP8LBitEntropy bit_entropy;
+  VP8LStreaks stats;
+  VP8LGetEntropyUnrefined(population, length, &bit_entropy, &stats);
+  if (trivial_sym != NULL) {
+    *trivial_sym = (bit_entropy.nonzeros == 1) ? bit_entropy.nonzero_code
+                                               : VP8L_NON_TRIVIAL_SYM;
+  }
+  // The histogram is used if there is at least one non-zero streak.
+  *is_used = (stats.streaks[1][0] != 0 || stats.streaks[1][1] != 0);
+
+  return BitsEntropyRefine(&bit_entropy) + FinalHuffmanCost(&stats);
+}
+
+// trivial_at_end is 1 if the two histograms only have one element that is
+// non-zero: both the zero-th one, or both the last one.
+static WEBP_INLINE float GetCombinedEntropy(const uint32_t* const X,
+                                            const uint32_t* const Y, int length,
+                                            int is_X_used, int is_Y_used,
+                                            int trivial_at_end) {
+  VP8LStreaks stats;
+  if (trivial_at_end) {
+    // This configuration is due to palettization that transforms an indexed
+    // pixel into 0xff000000 | (pixel << 8) in VP8LBundleColorMap.
+    // BitsEntropyRefine is 0 for histograms with only one non-zero value.
+    // Only FinalHuffmanCost needs to be evaluated.
+    memset(&stats, 0, sizeof(stats));
+    // Deal with the non-zero value at index 0 or length-1.
+    stats.streaks[1][0] = 1;
+    // Deal with the following/previous zero streak.
+    stats.counts[0] = 1;
+    stats.streaks[0][1] = length - 1;
+    return FinalHuffmanCost(&stats);
+  } else {
+    VP8LBitEntropy bit_entropy;
+    if (is_X_used) {
+      if (is_Y_used) {
+        VP8LGetCombinedEntropyUnrefined(X, Y, length, &bit_entropy, &stats);
+      } else {
+        VP8LGetEntropyUnrefined(X, length, &bit_entropy, &stats);
+      }
+    } else {
+      if (is_Y_used) {
+        VP8LGetEntropyUnrefined(Y, length, &bit_entropy, &stats);
+      } else {
+        memset(&stats, 0, sizeof(stats));
+        stats.counts[0] = 1;
+        stats.streaks[0][length > 3] = length;
+        VP8LBitEntropyInit(&bit_entropy);
+      }
+    }
+
+    return BitsEntropyRefine(&bit_entropy) + FinalHuffmanCost(&stats);
+  }
+}
+
+// Estimates the Entropy + Huffman + other block overhead size cost.
+float VP8LHistogramEstimateBits(VP8LHistogram* const p) {
+  return
+      PopulationCost(p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_),
+                     NULL, &p->is_used_[0])
+      + PopulationCost(p->red_, NUM_LITERAL_CODES, NULL, &p->is_used_[1])
+      + PopulationCost(p->blue_, NUM_LITERAL_CODES, NULL, &p->is_used_[2])
+      + PopulationCost(p->alpha_, NUM_LITERAL_CODES, NULL, &p->is_used_[3])
+      + PopulationCost(p->distance_, NUM_DISTANCE_CODES, NULL, &p->is_used_[4])
+      + VP8LExtraCost(p->literal_ + NUM_LITERAL_CODES, NUM_LENGTH_CODES)
+      + VP8LExtraCost(p->distance_, NUM_DISTANCE_CODES);
+}
+
+// -----------------------------------------------------------------------------
+// Various histogram combine/cost-eval functions
+
+static int GetCombinedHistogramEntropy(const VP8LHistogram* const a,
+                                       const VP8LHistogram* const b,
+                                       float cost_threshold, float* cost) {
+  const int palette_code_bits = a->palette_code_bits_;
+  int trivial_at_end = 0;
+  assert(a->palette_code_bits_ == b->palette_code_bits_);
+  *cost += GetCombinedEntropy(a->literal_, b->literal_,
+                              VP8LHistogramNumCodes(palette_code_bits),
+                              a->is_used_[0], b->is_used_[0], 0);
+  *cost += VP8LExtraCostCombined(a->literal_ + NUM_LITERAL_CODES,
+                                 b->literal_ + NUM_LITERAL_CODES,
+                                 NUM_LENGTH_CODES);
+  if (*cost > cost_threshold) return 0;
+
+  if (a->trivial_symbol_ != VP8L_NON_TRIVIAL_SYM &&
+      a->trivial_symbol_ == b->trivial_symbol_) {
+    // A, R and B are all 0 or 0xff.
+    const uint32_t color_a = (a->trivial_symbol_ >> 24) & 0xff;
+    const uint32_t color_r = (a->trivial_symbol_ >> 16) & 0xff;
+    const uint32_t color_b = (a->trivial_symbol_ >> 0) & 0xff;
+    if ((color_a == 0 || color_a == 0xff) &&
+        (color_r == 0 || color_r == 0xff) &&
+        (color_b == 0 || color_b == 0xff)) {
+      trivial_at_end = 1;
+    }
+  }
+
+  *cost +=
+      GetCombinedEntropy(a->red_, b->red_, NUM_LITERAL_CODES, a->is_used_[1],
+                         b->is_used_[1], trivial_at_end);
+  if (*cost > cost_threshold) return 0;
+
+  *cost +=
+      GetCombinedEntropy(a->blue_, b->blue_, NUM_LITERAL_CODES, a->is_used_[2],
+                         b->is_used_[2], trivial_at_end);
+  if (*cost > cost_threshold) return 0;
+
+  *cost +=
+      GetCombinedEntropy(a->alpha_, b->alpha_, NUM_LITERAL_CODES,
+                         a->is_used_[3], b->is_used_[3], trivial_at_end);
+  if (*cost > cost_threshold) return 0;
+
+  *cost +=
+      GetCombinedEntropy(a->distance_, b->distance_, NUM_DISTANCE_CODES,
+                         a->is_used_[4], b->is_used_[4], 0);
+  *cost +=
+      VP8LExtraCostCombined(a->distance_, b->distance_, NUM_DISTANCE_CODES);
+  if (*cost > cost_threshold) return 0;
+
+  return 1;
+}
+
+static WEBP_INLINE void HistogramAdd(const VP8LHistogram* const a,
+                                     const VP8LHistogram* const b,
+                                     VP8LHistogram* const out) {
+  VP8LHistogramAdd(a, b, out);
+  out->trivial_symbol_ = (a->trivial_symbol_ == b->trivial_symbol_)
+                       ? a->trivial_symbol_
+                       : VP8L_NON_TRIVIAL_SYM;
+}
+
+// Performs out = a + b, computing the cost C(a+b) - C(a) - C(b) while comparing
+// to the threshold value 'cost_threshold'. The score returned is
+//  Score = C(a+b) - C(a) - C(b), where C(a) + C(b) is known and fixed.
+// Since the previous score passed is 'cost_threshold', we only need to compare
+// the partial cost against 'cost_threshold + C(a) + C(b)' to possibly bail-out
+// early.
+static float HistogramAddEval(const VP8LHistogram* const a,
+                              const VP8LHistogram* const b,
+                              VP8LHistogram* const out, float cost_threshold) {
+  float cost = 0;
+  const float sum_cost = a->bit_cost_ + b->bit_cost_;
+  cost_threshold += sum_cost;
+
+  if (GetCombinedHistogramEntropy(a, b, cost_threshold, &cost)) {
+    HistogramAdd(a, b, out);
+    out->bit_cost_ = cost;
+    out->palette_code_bits_ = a->palette_code_bits_;
+  }
+
+  return cost - sum_cost;
+}
+
+// Same as HistogramAddEval(), except that the resulting histogram
+// is not stored. Only the cost C(a+b) - C(a) is evaluated. We omit
+// the term C(b) which is constant over all the evaluations.
+static float HistogramAddThresh(const VP8LHistogram* const a,
+                                const VP8LHistogram* const b,
+                                float cost_threshold) {
+  float cost;
+  assert(a != NULL && b != NULL);
+  cost = -a->bit_cost_;
+  GetCombinedHistogramEntropy(a, b, cost_threshold, &cost);
+  return cost;
+}
+
+// -----------------------------------------------------------------------------
+
+// The structure to keep track of cost range for the three dominant entropy
+// symbols.
+typedef struct {
+  float literal_max_;
+  float literal_min_;
+  float red_max_;
+  float red_min_;
+  float blue_max_;
+  float blue_min_;
+} DominantCostRange;
+
+static void DominantCostRangeInit(DominantCostRange* const c) {
+  c->literal_max_ = 0.;
+  c->literal_min_ = MAX_BIT_COST;
+  c->red_max_ = 0.;
+  c->red_min_ = MAX_BIT_COST;
+  c->blue_max_ = 0.;
+  c->blue_min_ = MAX_BIT_COST;
+}
+
+static void UpdateDominantCostRange(
+    const VP8LHistogram* const h, DominantCostRange* const c) {
+  if (c->literal_max_ < h->literal_cost_) c->literal_max_ = h->literal_cost_;
+  if (c->literal_min_ > h->literal_cost_) c->literal_min_ = h->literal_cost_;
+  if (c->red_max_ < h->red_cost_) c->red_max_ = h->red_cost_;
+  if (c->red_min_ > h->red_cost_) c->red_min_ = h->red_cost_;
+  if (c->blue_max_ < h->blue_cost_) c->blue_max_ = h->blue_cost_;
+  if (c->blue_min_ > h->blue_cost_) c->blue_min_ = h->blue_cost_;
+}
+
+static void UpdateHistogramCost(VP8LHistogram* const h) {
+  uint32_t alpha_sym, red_sym, blue_sym;
+  const float alpha_cost =
+      PopulationCost(h->alpha_, NUM_LITERAL_CODES, &alpha_sym, &h->is_used_[3]);
+  const float distance_cost =
+      PopulationCost(h->distance_, NUM_DISTANCE_CODES, NULL, &h->is_used_[4]) +
+      VP8LExtraCost(h->distance_, NUM_DISTANCE_CODES);
+  const int num_codes = VP8LHistogramNumCodes(h->palette_code_bits_);
+  h->literal_cost_ =
+      PopulationCost(h->literal_, num_codes, NULL, &h->is_used_[0]) +
+          VP8LExtraCost(h->literal_ + NUM_LITERAL_CODES, NUM_LENGTH_CODES);
+  h->red_cost_ =
+      PopulationCost(h->red_, NUM_LITERAL_CODES, &red_sym, &h->is_used_[1]);
+  h->blue_cost_ =
+      PopulationCost(h->blue_, NUM_LITERAL_CODES, &blue_sym, &h->is_used_[2]);
+  h->bit_cost_ = h->literal_cost_ + h->red_cost_ + h->blue_cost_ +
+                 alpha_cost + distance_cost;
+  if ((alpha_sym | red_sym | blue_sym) == VP8L_NON_TRIVIAL_SYM) {
+    h->trivial_symbol_ = VP8L_NON_TRIVIAL_SYM;
+  } else {
+    h->trivial_symbol_ =
+        ((uint32_t)alpha_sym << 24) | (red_sym << 16) | (blue_sym << 0);
+  }
+}
+
+static int GetBinIdForEntropy(float min, float max, float val) {
+  const float range = max - min;
+  if (range > 0.) {
+    const float delta = val - min;
+    return (int)((NUM_PARTITIONS - 1e-6) * delta / range);
+  } else {
+    return 0;
+  }
+}
+
+static int GetHistoBinIndex(const VP8LHistogram* const h,
+                            const DominantCostRange* const c, int low_effort) {
+  int bin_id = GetBinIdForEntropy(c->literal_min_, c->literal_max_,
+                                  h->literal_cost_);
+  assert(bin_id < NUM_PARTITIONS);
+  if (!low_effort) {
+    bin_id = bin_id * NUM_PARTITIONS
+           + GetBinIdForEntropy(c->red_min_, c->red_max_, h->red_cost_);
+    bin_id = bin_id * NUM_PARTITIONS
+           + GetBinIdForEntropy(c->blue_min_, c->blue_max_, h->blue_cost_);
+    assert(bin_id < BIN_SIZE);
+  }
+  return bin_id;
+}
+
+// Construct the histograms from backward references.
+static void HistogramBuild(
+    int xsize, int histo_bits, const VP8LBackwardRefs* const backward_refs,
+    VP8LHistogramSet* const image_histo) {
+  int x = 0, y = 0;
+  const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
+  VP8LHistogram** const histograms = image_histo->histograms;
+  VP8LRefsCursor c = VP8LRefsCursorInit(backward_refs);
+  assert(histo_bits > 0);
+  VP8LHistogramSetClear(image_histo);
+  while (VP8LRefsCursorOk(&c)) {
+    const PixOrCopy* const v = c.cur_pos;
+    const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
+    VP8LHistogramAddSinglePixOrCopy(histograms[ix], v, NULL, 0);
+    x += PixOrCopyLength(v);
+    while (x >= xsize) {
+      x -= xsize;
+      ++y;
+    }
+    VP8LRefsCursorNext(&c);
+  }
+}
+
+// Copies the histograms and computes its bit_cost.
+static const uint16_t kInvalidHistogramSymbol = (uint16_t)(-1);
+static void HistogramCopyAndAnalyze(VP8LHistogramSet* const orig_histo,
+                                    VP8LHistogramSet* const image_histo,
+                                    int* const num_used,
+                                    uint16_t* const histogram_symbols) {
+  int i, cluster_id;
+  int num_used_orig = *num_used;
+  VP8LHistogram** const orig_histograms = orig_histo->histograms;
+  VP8LHistogram** const histograms = image_histo->histograms;
+  assert(image_histo->max_size == orig_histo->max_size);
+  for (cluster_id = 0, i = 0; i < orig_histo->max_size; ++i) {
+    VP8LHistogram* const histo = orig_histograms[i];
+    UpdateHistogramCost(histo);
+
+    // Skip the histogram if it is completely empty, which can happen for tiles
+    // with no information (when they are skipped because of LZ77).
+    if (!histo->is_used_[0] && !histo->is_used_[1] && !histo->is_used_[2]
+        && !histo->is_used_[3] && !histo->is_used_[4]) {
+      // The first histogram is always used. If an histogram is empty, we set
+      // its id to be the same as the previous one: this will improve
+      // compressibility for later LZ77.
+      assert(i > 0);
+      HistogramSetRemoveHistogram(image_histo, i, num_used);
+      HistogramSetRemoveHistogram(orig_histo, i, &num_used_orig);
+      histogram_symbols[i] = kInvalidHistogramSymbol;
+    } else {
+      // Copy histograms from orig_histo[] to image_histo[].
+      HistogramCopy(histo, histograms[i]);
+      histogram_symbols[i] = cluster_id++;
+      assert(cluster_id <= image_histo->max_size);
+    }
+  }
+}
+
+// Partition histograms to different entropy bins for three dominant (literal,
+// red and blue) symbol costs and compute the histogram aggregate bit_cost.
+static void HistogramAnalyzeEntropyBin(VP8LHistogramSet* const image_histo,
+                                       uint16_t* const bin_map,
+                                       int low_effort) {
+  int i;
+  VP8LHistogram** const histograms = image_histo->histograms;
+  const int histo_size = image_histo->size;
+  DominantCostRange cost_range;
+  DominantCostRangeInit(&cost_range);
+
+  // Analyze the dominant (literal, red and blue) entropy costs.
+  for (i = 0; i < histo_size; ++i) {
+    if (histograms[i] == NULL) continue;
+    UpdateDominantCostRange(histograms[i], &cost_range);
+  }
+
+  // bin-hash histograms on three of the dominant (literal, red and blue)
+  // symbol costs and store the resulting bin_id for each histogram.
+  for (i = 0; i < histo_size; ++i) {
+    // bin_map[i] is not set to a special value as its use will later be guarded
+    // by another (histograms[i] == NULL).
+    if (histograms[i] == NULL) continue;
+    bin_map[i] = GetHistoBinIndex(histograms[i], &cost_range, low_effort);
+  }
+}
+
+// Merges some histograms with same bin_id together if it's advantageous.
+// Sets the remaining histograms to NULL.
+static void HistogramCombineEntropyBin(
+    VP8LHistogramSet* const image_histo, int* num_used,
+    const uint16_t* const clusters, uint16_t* const cluster_mappings,
+    VP8LHistogram* cur_combo, const uint16_t* const bin_map, int num_bins,
+    float combine_cost_factor, int low_effort) {
+  VP8LHistogram** const histograms = image_histo->histograms;
+  int idx;
+  struct {
+    int16_t first;    // position of the histogram that accumulates all
+                      // histograms with the same bin_id
+    uint16_t num_combine_failures;   // number of combine failures per bin_id
+  } bin_info[BIN_SIZE];
+
+  assert(num_bins <= BIN_SIZE);
+  for (idx = 0; idx < num_bins; ++idx) {
+    bin_info[idx].first = -1;
+    bin_info[idx].num_combine_failures = 0;
+  }
+
+  // By default, a cluster matches itself.
+  for (idx = 0; idx < *num_used; ++idx) cluster_mappings[idx] = idx;
+  for (idx = 0; idx < image_histo->size; ++idx) {
+    int bin_id, first;
+    if (histograms[idx] == NULL) continue;
+    bin_id = bin_map[idx];
+    first = bin_info[bin_id].first;
+    if (first == -1) {
+      bin_info[bin_id].first = idx;
+    } else if (low_effort) {
+      HistogramAdd(histograms[idx], histograms[first], histograms[first]);
+      HistogramSetRemoveHistogram(image_histo, idx, num_used);
+      cluster_mappings[clusters[idx]] = clusters[first];
+    } else {
+      // try to merge #idx into #first (both share the same bin_id)
+      const float bit_cost = histograms[idx]->bit_cost_;
+      const float bit_cost_thresh = -bit_cost * combine_cost_factor;
+      const float curr_cost_diff = HistogramAddEval(
+          histograms[first], histograms[idx], cur_combo, bit_cost_thresh);
+      if (curr_cost_diff < bit_cost_thresh) {
+        // Try to merge two histograms only if the combo is a trivial one or
+        // the two candidate histograms are already non-trivial.
+        // For some images, 'try_combine' turns out to be false for a lot of
+        // histogram pairs. In that case, we fallback to combining
+        // histograms as usual to avoid increasing the header size.
+        const int try_combine =
+            (cur_combo->trivial_symbol_ != VP8L_NON_TRIVIAL_SYM) ||
+            ((histograms[idx]->trivial_symbol_ == VP8L_NON_TRIVIAL_SYM) &&
+             (histograms[first]->trivial_symbol_ == VP8L_NON_TRIVIAL_SYM));
+        const int max_combine_failures = 32;
+        if (try_combine ||
+            bin_info[bin_id].num_combine_failures >= max_combine_failures) {
+          // move the (better) merged histogram to its final slot
+          HistogramSwap(&cur_combo, &histograms[first]);
+          HistogramSetRemoveHistogram(image_histo, idx, num_used);
+          cluster_mappings[clusters[idx]] = clusters[first];
+        } else {
+          ++bin_info[bin_id].num_combine_failures;
+        }
+      }
+    }
+  }
+  if (low_effort) {
+    // for low_effort case, update the final cost when everything is merged
+    for (idx = 0; idx < image_histo->size; ++idx) {
+      if (histograms[idx] == NULL) continue;
+      UpdateHistogramCost(histograms[idx]);
+    }
+  }
+}
+
+// Implement a Lehmer random number generator with a multiplicative constant of
+// 48271 and a modulo constant of 2^31 - 1.
+static uint32_t MyRand(uint32_t* const seed) {
+  *seed = (uint32_t)(((uint64_t)(*seed) * 48271u) % 2147483647u);
+  assert(*seed > 0);
+  return *seed;
+}
+
+// -----------------------------------------------------------------------------
+// Histogram pairs priority queue
+
+// Pair of histograms. Negative idx1 value means that pair is out-of-date.
+typedef struct {
+  int idx1;
+  int idx2;
+  float cost_diff;
+  float cost_combo;
+} HistogramPair;
+
+typedef struct {
+  HistogramPair* queue;
+  int size;
+  int max_size;
+} HistoQueue;
+
+static int HistoQueueInit(HistoQueue* const histo_queue, const int max_size) {
+  histo_queue->size = 0;
+  histo_queue->max_size = max_size;
+  // We allocate max_size + 1 because the last element at index "size" is
+  // used as temporary data (and it could be up to max_size).
+  histo_queue->queue = (HistogramPair*)WebPSafeMalloc(
+      histo_queue->max_size + 1, sizeof(*histo_queue->queue));
+  return histo_queue->queue != NULL;
+}
+
+static void HistoQueueClear(HistoQueue* const histo_queue) {
+  assert(histo_queue != NULL);
+  WebPSafeFree(histo_queue->queue);
+  histo_queue->size = 0;
+  histo_queue->max_size = 0;
+}
+
+// Pop a specific pair in the queue by replacing it with the last one
+// and shrinking the queue.
+static void HistoQueuePopPair(HistoQueue* const histo_queue,
+                              HistogramPair* const pair) {
+  assert(pair >= histo_queue->queue &&
+         pair < (histo_queue->queue + histo_queue->size));
+  assert(histo_queue->size > 0);
+  *pair = histo_queue->queue[histo_queue->size - 1];
+  --histo_queue->size;
+}
+
+// Check whether a pair in the queue should be updated as head or not.
+static void HistoQueueUpdateHead(HistoQueue* const histo_queue,
+                                 HistogramPair* const pair) {
+  assert(pair->cost_diff < 0.);
+  assert(pair >= histo_queue->queue &&
+         pair < (histo_queue->queue + histo_queue->size));
+  assert(histo_queue->size > 0);
+  if (pair->cost_diff < histo_queue->queue[0].cost_diff) {
+    // Replace the best pair.
+    const HistogramPair tmp = histo_queue->queue[0];
+    histo_queue->queue[0] = *pair;
+    *pair = tmp;
+  }
+}
+
+// Update the cost diff and combo of a pair of histograms. This needs to be
+// called when the the histograms have been merged with a third one.
+static void HistoQueueUpdatePair(const VP8LHistogram* const h1,
+                                 const VP8LHistogram* const h2, float threshold,
+                                 HistogramPair* const pair) {
+  const float sum_cost = h1->bit_cost_ + h2->bit_cost_;
+  pair->cost_combo = 0.;
+  GetCombinedHistogramEntropy(h1, h2, sum_cost + threshold, &pair->cost_combo);
+  pair->cost_diff = pair->cost_combo - sum_cost;
+}
+
+// Create a pair from indices "idx1" and "idx2" provided its cost
+// is inferior to "threshold", a negative entropy.
+// It returns the cost of the pair, or 0. if it superior to threshold.
+static float HistoQueuePush(HistoQueue* const histo_queue,
+                            VP8LHistogram** const histograms, int idx1,
+                            int idx2, float threshold) {
+  const VP8LHistogram* h1;
+  const VP8LHistogram* h2;
+  HistogramPair pair;
+
+  // Stop here if the queue is full.
+  if (histo_queue->size == histo_queue->max_size) return 0.;
+  assert(threshold <= 0.);
+  if (idx1 > idx2) {
+    const int tmp = idx2;
+    idx2 = idx1;
+    idx1 = tmp;
+  }
+  pair.idx1 = idx1;
+  pair.idx2 = idx2;
+  h1 = histograms[idx1];
+  h2 = histograms[idx2];
+
+  HistoQueueUpdatePair(h1, h2, threshold, &pair);
+
+  // Do not even consider the pair if it does not improve the entropy.
+  if (pair.cost_diff >= threshold) return 0.;
+
+  histo_queue->queue[histo_queue->size++] = pair;
+  HistoQueueUpdateHead(histo_queue, &histo_queue->queue[histo_queue->size - 1]);
+
+  return pair.cost_diff;
+}
+
+// -----------------------------------------------------------------------------
+
+// Combines histograms by continuously choosing the one with the highest cost
+// reduction.
+static int HistogramCombineGreedy(VP8LHistogramSet* const image_histo,
+                                  int* const num_used) {
+  int ok = 0;
+  const int image_histo_size = image_histo->size;
+  int i, j;
+  VP8LHistogram** const histograms = image_histo->histograms;
+  // Priority queue of histogram pairs.
+  HistoQueue histo_queue;
+
+  // image_histo_size^2 for the queue size is safe. If you look at
+  // HistogramCombineGreedy, and imagine that UpdateQueueFront always pushes
+  // data to the queue, you insert at most:
+  // - image_histo_size*(image_histo_size-1)/2 (the first two for loops)
+  // - image_histo_size - 1 in the last for loop at the first iteration of
+  //   the while loop, image_histo_size - 2 at the second iteration ...
+  //   therefore image_histo_size*(image_histo_size-1)/2 overall too
+  if (!HistoQueueInit(&histo_queue, image_histo_size * image_histo_size)) {
+    goto End;
+  }
+
+  for (i = 0; i < image_histo_size; ++i) {
+    if (image_histo->histograms[i] == NULL) continue;
+    for (j = i + 1; j < image_histo_size; ++j) {
+      // Initialize queue.
+      if (image_histo->histograms[j] == NULL) continue;
+      HistoQueuePush(&histo_queue, histograms, i, j, 0.);
+    }
+  }
+
+  while (histo_queue.size > 0) {
+    const int idx1 = histo_queue.queue[0].idx1;
+    const int idx2 = histo_queue.queue[0].idx2;
+    HistogramAdd(histograms[idx2], histograms[idx1], histograms[idx1]);
+    histograms[idx1]->bit_cost_ = histo_queue.queue[0].cost_combo;
+
+    // Remove merged histogram.
+    HistogramSetRemoveHistogram(image_histo, idx2, num_used);
+
+    // Remove pairs intersecting the just combined best pair.
+    for (i = 0; i < histo_queue.size;) {
+      HistogramPair* const p = histo_queue.queue + i;
+      if (p->idx1 == idx1 || p->idx2 == idx1 ||
+          p->idx1 == idx2 || p->idx2 == idx2) {
+        HistoQueuePopPair(&histo_queue, p);
+      } else {
+        HistoQueueUpdateHead(&histo_queue, p);
+        ++i;
+      }
+    }
+
+    // Push new pairs formed with combined histogram to the queue.
+    for (i = 0; i < image_histo->size; ++i) {
+      if (i == idx1 || image_histo->histograms[i] == NULL) continue;
+      HistoQueuePush(&histo_queue, image_histo->histograms, idx1, i, 0.);
+    }
+  }
+
+  ok = 1;
+
+ End:
+  HistoQueueClear(&histo_queue);
+  return ok;
+}
+
+// Perform histogram aggregation using a stochastic approach.
+// 'do_greedy' is set to 1 if a greedy approach needs to be performed
+// afterwards, 0 otherwise.
+static int PairComparison(const void* idx1, const void* idx2) {
+  // To be used with bsearch: <0 when *idx1<*idx2, >0 if >, 0 when ==.
+  return (*(int*) idx1 - *(int*) idx2);
+}
+static int HistogramCombineStochastic(VP8LHistogramSet* const image_histo,
+                                      int* const num_used, int min_cluster_size,
+                                      int* const do_greedy) {
+  int j, iter;
+  uint32_t seed = 1;
+  int tries_with_no_success = 0;
+  const int outer_iters = *num_used;
+  const int num_tries_no_success = outer_iters / 2;
+  VP8LHistogram** const histograms = image_histo->histograms;
+  // Priority queue of histogram pairs. Its size of 'kHistoQueueSize'
+  // impacts the quality of the compression and the speed: the smaller the
+  // faster but the worse for the compression.
+  HistoQueue histo_queue;
+  const int kHistoQueueSize = 9;
+  int ok = 0;
+  // mapping from an index in image_histo with no NULL histogram to the full
+  // blown image_histo.
+  int* mappings;
+
+  if (*num_used < min_cluster_size) {
+    *do_greedy = 1;
+    return 1;
+  }
+
+  mappings = (int*) WebPSafeMalloc(*num_used, sizeof(*mappings));
+  if (mappings == NULL) return 0;
+  if (!HistoQueueInit(&histo_queue, kHistoQueueSize)) goto End;
+  // Fill the initial mapping.
+  for (j = 0, iter = 0; iter < image_histo->size; ++iter) {
+    if (histograms[iter] == NULL) continue;
+    mappings[j++] = iter;
+  }
+  assert(j == *num_used);
+
+  // Collapse similar histograms in 'image_histo'.
+  for (iter = 0;
+       iter < outer_iters && *num_used >= min_cluster_size &&
+           ++tries_with_no_success < num_tries_no_success;
+       ++iter) {
+    int* mapping_index;
+    float best_cost =
+        (histo_queue.size == 0) ? 0.f : histo_queue.queue[0].cost_diff;
+    int best_idx1 = -1, best_idx2 = 1;
+    const uint32_t rand_range = (*num_used - 1) * (*num_used);
+    // (*num_used) / 2 was chosen empirically. Less means faster but worse
+    // compression.
+    const int num_tries = (*num_used) / 2;
+
+    // Pick random samples.
+    for (j = 0; *num_used >= 2 && j < num_tries; ++j) {
+      float curr_cost;
+      // Choose two different histograms at random and try to combine them.
+      const uint32_t tmp = MyRand(&seed) % rand_range;
+      uint32_t idx1 = tmp / (*num_used - 1);
+      uint32_t idx2 = tmp % (*num_used - 1);
+      if (idx2 >= idx1) ++idx2;
+      idx1 = mappings[idx1];
+      idx2 = mappings[idx2];
+
+      // Calculate cost reduction on combination.
+      curr_cost =
+          HistoQueuePush(&histo_queue, histograms, idx1, idx2, best_cost);
+      if (curr_cost < 0) {  // found a better pair?
+        best_cost = curr_cost;
+        // Empty the queue if we reached full capacity.
+        if (histo_queue.size == histo_queue.max_size) break;
+      }
+    }
+    if (histo_queue.size == 0) continue;
+
+    // Get the best histograms.
+    best_idx1 = histo_queue.queue[0].idx1;
+    best_idx2 = histo_queue.queue[0].idx2;
+    assert(best_idx1 < best_idx2);
+    // Pop best_idx2 from mappings.
+    mapping_index = (int*) bsearch(&best_idx2, mappings, *num_used,
+                                   sizeof(best_idx2), &PairComparison);
+    assert(mapping_index != NULL);
+    memmove(mapping_index, mapping_index + 1, sizeof(*mapping_index) *
+        ((*num_used) - (mapping_index - mappings) - 1));
+    // Merge the histograms and remove best_idx2 from the queue.
+    HistogramAdd(histograms[best_idx2], histograms[best_idx1],
+                 histograms[best_idx1]);
+    histograms[best_idx1]->bit_cost_ = histo_queue.queue[0].cost_combo;
+    HistogramSetRemoveHistogram(image_histo, best_idx2, num_used);
+    // Parse the queue and update each pair that deals with best_idx1,
+    // best_idx2 or image_histo_size.
+    for (j = 0; j < histo_queue.size;) {
+      HistogramPair* const p = histo_queue.queue + j;
+      const int is_idx1_best = p->idx1 == best_idx1 || p->idx1 == best_idx2;
+      const int is_idx2_best = p->idx2 == best_idx1 || p->idx2 == best_idx2;
+      int do_eval = 0;
+      // The front pair could have been duplicated by a random pick so
+      // check for it all the time nevertheless.
+      if (is_idx1_best && is_idx2_best) {
+        HistoQueuePopPair(&histo_queue, p);
+        continue;
+      }
+      // Any pair containing one of the two best indices should only refer to
+      // best_idx1. Its cost should also be updated.
+      if (is_idx1_best) {
+        p->idx1 = best_idx1;
+        do_eval = 1;
+      } else if (is_idx2_best) {
+        p->idx2 = best_idx1;
+        do_eval = 1;
+      }
+      // Make sure the index order is respected.
+      if (p->idx1 > p->idx2) {
+        const int tmp = p->idx2;
+        p->idx2 = p->idx1;
+        p->idx1 = tmp;
+      }
+      if (do_eval) {
+        // Re-evaluate the cost of an updated pair.
+        HistoQueueUpdatePair(histograms[p->idx1], histograms[p->idx2], 0., p);
+        if (p->cost_diff >= 0.) {
+          HistoQueuePopPair(&histo_queue, p);
+          continue;
+        }
+      }
+      HistoQueueUpdateHead(&histo_queue, p);
+      ++j;
+    }
+    tries_with_no_success = 0;
+  }
+  *do_greedy = (*num_used <= min_cluster_size);
+  ok = 1;
+
+ End:
+  HistoQueueClear(&histo_queue);
+  WebPSafeFree(mappings);
+  return ok;
+}
+
+// -----------------------------------------------------------------------------
+// Histogram refinement
+
+// Find the best 'out' histogram for each of the 'in' histograms.
+// At call-time, 'out' contains the histograms of the clusters.
+// Note: we assume that out[]->bit_cost_ is already up-to-date.
+static void HistogramRemap(const VP8LHistogramSet* const in,
+                           VP8LHistogramSet* const out,
+                           uint16_t* const symbols) {
+  int i;
+  VP8LHistogram** const in_histo = in->histograms;
+  VP8LHistogram** const out_histo = out->histograms;
+  const int in_size = out->max_size;
+  const int out_size = out->size;
+  if (out_size > 1) {
+    for (i = 0; i < in_size; ++i) {
+      int best_out = 0;
+      float best_bits = MAX_BIT_COST;
+      int k;
+      if (in_histo[i] == NULL) {
+        // Arbitrarily set to the previous value if unused to help future LZ77.
+        symbols[i] = symbols[i - 1];
+        continue;
+      }
+      for (k = 0; k < out_size; ++k) {
+        float cur_bits;
+        cur_bits = HistogramAddThresh(out_histo[k], in_histo[i], best_bits);
+        if (k == 0 || cur_bits < best_bits) {
+          best_bits = cur_bits;
+          best_out = k;
+        }
+      }
+      symbols[i] = best_out;
+    }
+  } else {
+    assert(out_size == 1);
+    for (i = 0; i < in_size; ++i) {
+      symbols[i] = 0;
+    }
+  }
+
+  // Recompute each out based on raw and symbols.
+  VP8LHistogramSetClear(out);
+  out->size = out_size;
+
+  for (i = 0; i < in_size; ++i) {
+    int idx;
+    if (in_histo[i] == NULL) continue;
+    idx = symbols[i];
+    HistogramAdd(in_histo[i], out_histo[idx], out_histo[idx]);
+  }
+}
+
+static float GetCombineCostFactor(int histo_size, int quality) {
+  float combine_cost_factor = 0.16f;
+  if (quality < 90) {
+    if (histo_size > 256) combine_cost_factor /= 2.f;
+    if (histo_size > 512) combine_cost_factor /= 2.f;
+    if (histo_size > 1024) combine_cost_factor /= 2.f;
+    if (quality <= 50) combine_cost_factor /= 2.f;
+  }
+  return combine_cost_factor;
+}
+
+// Given a HistogramSet 'set', the mapping of clusters 'cluster_mapping' and the
+// current assignment of the cells in 'symbols', merge the clusters and
+// assign the smallest possible clusters values.
+static void OptimizeHistogramSymbols(const VP8LHistogramSet* const set,
+                                     uint16_t* const cluster_mappings,
+                                     int num_clusters,
+                                     uint16_t* const cluster_mappings_tmp,
+                                     uint16_t* const symbols) {
+  int i, cluster_max;
+  int do_continue = 1;
+  // First, assign the lowest cluster to each pixel.
+  while (do_continue) {
+    do_continue = 0;
+    for (i = 0; i < num_clusters; ++i) {
+      int k;
+      k = cluster_mappings[i];
+      while (k != cluster_mappings[k]) {
+        cluster_mappings[k] = cluster_mappings[cluster_mappings[k]];
+        k = cluster_mappings[k];
+      }
+      if (k != cluster_mappings[i]) {
+        do_continue = 1;
+        cluster_mappings[i] = k;
+      }
+    }
+  }
+  // Create a mapping from a cluster id to its minimal version.
+  cluster_max = 0;
+  memset(cluster_mappings_tmp, 0,
+         set->max_size * sizeof(*cluster_mappings_tmp));
+  assert(cluster_mappings[0] == 0);
+  // Re-map the ids.
+  for (i = 0; i < set->max_size; ++i) {
+    int cluster;
+    if (symbols[i] == kInvalidHistogramSymbol) continue;
+    cluster = cluster_mappings[symbols[i]];
+    assert(symbols[i] < num_clusters);
+    if (cluster > 0 && cluster_mappings_tmp[cluster] == 0) {
+      ++cluster_max;
+      cluster_mappings_tmp[cluster] = cluster_max;
+    }
+    symbols[i] = cluster_mappings_tmp[cluster];
+  }
+
+  // Make sure all cluster values are used.
+  cluster_max = 0;
+  for (i = 0; i < set->max_size; ++i) {
+    if (symbols[i] == kInvalidHistogramSymbol) continue;
+    if (symbols[i] <= cluster_max) continue;
+    ++cluster_max;
+    assert(symbols[i] == cluster_max);
+  }
+}
+
+static void RemoveEmptyHistograms(VP8LHistogramSet* const image_histo) {
+  uint32_t size;
+  int i;
+  for (i = 0, size = 0; i < image_histo->size; ++i) {
+    if (image_histo->histograms[i] == NULL) continue;
+    image_histo->histograms[size++] = image_histo->histograms[i];
+  }
+  image_histo->size = size;
+}
+
+int VP8LGetHistoImageSymbols(int xsize, int ysize,
+                             const VP8LBackwardRefs* const refs, int quality,
+                             int low_effort, int histogram_bits, int cache_bits,
+                             VP8LHistogramSet* const image_histo,
+                             VP8LHistogram* const tmp_histo,
+                             uint16_t* const histogram_symbols,
+                             const WebPPicture* const pic, int percent_range,
+                             int* const percent) {
+  const int histo_xsize =
+      histogram_bits ? VP8LSubSampleSize(xsize, histogram_bits) : 1;
+  const int histo_ysize =
+      histogram_bits ? VP8LSubSampleSize(ysize, histogram_bits) : 1;
+  const int image_histo_raw_size = histo_xsize * histo_ysize;
+  VP8LHistogramSet* const orig_histo =
+      VP8LAllocateHistogramSet(image_histo_raw_size, cache_bits);
+  // Don't attempt linear bin-partition heuristic for
+  // histograms of small sizes (as bin_map will be very sparse) and
+  // maximum quality q==100 (to preserve the compression gains at that level).
+  const int entropy_combine_num_bins = low_effort ? NUM_PARTITIONS : BIN_SIZE;
+  int entropy_combine;
+  uint16_t* const map_tmp =
+      WebPSafeMalloc(2 * image_histo_raw_size, sizeof(map_tmp));
+  uint16_t* const cluster_mappings = map_tmp + image_histo_raw_size;
+  int num_used = image_histo_raw_size;
+  if (orig_histo == NULL || map_tmp == NULL) {
+    WebPEncodingSetError(pic, VP8_ENC_ERROR_OUT_OF_MEMORY);
+    goto Error;
+  }
+
+  // Construct the histograms from backward references.
+  HistogramBuild(xsize, histogram_bits, refs, orig_histo);
+  // Copies the histograms and computes its bit_cost.
+  // histogram_symbols is optimized
+  HistogramCopyAndAnalyze(orig_histo, image_histo, &num_used,
+                          histogram_symbols);
+
+  entropy_combine =
+      (num_used > entropy_combine_num_bins * 2) && (quality < 100);
+
+  if (entropy_combine) {
+    uint16_t* const bin_map = map_tmp;
+    const float combine_cost_factor =
+        GetCombineCostFactor(image_histo_raw_size, quality);
+    const uint32_t num_clusters = num_used;
+
+    HistogramAnalyzeEntropyBin(image_histo, bin_map, low_effort);
+    // Collapse histograms with similar entropy.
+    HistogramCombineEntropyBin(
+        image_histo, &num_used, histogram_symbols, cluster_mappings, tmp_histo,
+        bin_map, entropy_combine_num_bins, combine_cost_factor, low_effort);
+    OptimizeHistogramSymbols(image_histo, cluster_mappings, num_clusters,
+                             map_tmp, histogram_symbols);
+  }
+
+  // Don't combine the histograms using stochastic and greedy heuristics for
+  // low-effort compression mode.
+  if (!low_effort || !entropy_combine) {
+    const float x = quality / 100.f;
+    // cubic ramp between 1 and MAX_HISTO_GREEDY:
+    const int threshold_size = (int)(1 + (x * x * x) * (MAX_HISTO_GREEDY - 1));
+    int do_greedy;
+    if (!HistogramCombineStochastic(image_histo, &num_used, threshold_size,
+                                    &do_greedy)) {
+      WebPEncodingSetError(pic, VP8_ENC_ERROR_OUT_OF_MEMORY);
+      goto Error;
+    }
+    if (do_greedy) {
+      RemoveEmptyHistograms(image_histo);
+      if (!HistogramCombineGreedy(image_histo, &num_used)) {
+        WebPEncodingSetError(pic, VP8_ENC_ERROR_OUT_OF_MEMORY);
+        goto Error;
+      }
+    }
+  }
+
+  // Find the optimal map from original histograms to the final ones.
+  RemoveEmptyHistograms(image_histo);
+  HistogramRemap(orig_histo, image_histo, histogram_symbols);
+
+  if (!WebPReportProgress(pic, *percent + percent_range, percent)) {
+    goto Error;
+  }
+
+ Error:
+  VP8LFreeHistogramSet(orig_histo);
+  WebPSafeFree(map_tmp);
+  return (pic->error_code == VP8_ENC_OK);
+}