Use the upstream version of libwebp, v0.4.3.

third_party/libwebp/enc/histogram.c

+// 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 "../webp/config.h"
+#endif
+
+#include <math.h>
+
+#include "./backward_references.h"
+#include "./histogram.h"
+#include "../dsp/lossless.h"
+#include "../utils/utils.h"
+
+#define MAX_COST 1.e38
+
+// 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)
+
+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;
+}
+
+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 histo_size = VP8LGetHistogramSize(dst_cache_bits);
+  assert(src->palette_code_bits_ == dst_cache_bits);
+  memcpy(dst, src, histo_size);
+  dst->literal_ = 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);
+    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) {
+  p->palette_code_bits_ = palette_code_bits;
+  HistogramClear(p);
+}
+
+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);
+  return histo;
+}
+
+VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
+  int i;
+  VP8LHistogramSet* set;
+  const size_t total_size = sizeof(*set)
+                            + sizeof(*set->histograms) * size
+                            + (size_t)VP8LGetHistogramSize(cache_bits) * size;
+  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;
+  memory += size * sizeof(*set->histograms);
+  set->max_size = size;
+  set->size = size;
+  for (i = 0; i < size; ++i) {
+    set->histograms[i] = (VP8LHistogram*)memory;
+    // literal_ won't necessary be aligned.
+    set->histograms[i]->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
+    VP8LHistogramInit(set->histograms[i], cache_bits);
+    // There's no padding/alignment between successive histograms.
+    memory += VP8LGetHistogramSize(cache_bits);
+  }
+  return set;
+}
+
+// -----------------------------------------------------------------------------
+
+void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo,
+                                     const PixOrCopy* const v) {
+  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);
+    ++histo->literal_[literal_ix];
+  } else {
+    int code, extra_bits;
+    VP8LPrefixEncodeBits(PixOrCopyLength(v), &code, &extra_bits);
+    ++histo->literal_[NUM_LITERAL_CODES + code];
+    VP8LPrefixEncodeBits(PixOrCopyDistance(v), &code, &extra_bits);
+    ++histo->distance_[code];
+  }
+}
+
+static WEBP_INLINE double BitsEntropyRefine(int nonzeros, int sum, int max_val,
+                                            double retval) {
+  double mix;
+  if (nonzeros < 5) {
+    if (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 (nonzeros == 2) {
+      return 0.99 * sum + 0.01 * retval;
+    }
+    // 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 (nonzeros == 3) {
+      mix = 0.95;
+    } else {
+      mix = 0.7;  // nonzeros == 4.
+    }
+  } else {
+    mix = 0.627;
+  }
+
+  {
+    double min_limit = 2 * sum - max_val;
+    min_limit = mix * min_limit + (1.0 - mix) * retval;
+    return (retval < min_limit) ? min_limit : retval;
+  }
+}
+
+static double BitsEntropy(const uint32_t* const array, int n) {
+  double retval = 0.;
+  uint32_t sum = 0;
+  int nonzeros = 0;
+  uint32_t max_val = 0;
+  int i;
+  for (i = 0; i < n; ++i) {
+    if (array[i] != 0) {
+      sum += array[i];
+      ++nonzeros;
+      retval -= VP8LFastSLog2(array[i]);
+      if (max_val < array[i]) {
+        max_val = array[i];
+      }
+    }
+  }
+  retval += VP8LFastSLog2(sum);
+  return BitsEntropyRefine(nonzeros, sum, max_val, retval);
+}
+
+static double BitsEntropyCombined(const uint32_t* const X,
+                                  const uint32_t* const Y, int n) {
+  double retval = 0.;
+  int sum = 0;
+  int nonzeros = 0;
+  int max_val = 0;
+  int i;
+  for (i = 0; i < n; ++i) {
+    const int xy = X[i] + Y[i];
+    if (xy != 0) {
+      sum += xy;
+      ++nonzeros;
+      retval -= VP8LFastSLog2(xy);
+      if (max_val < xy) {
+        max_val = xy;
+      }
+    }
+  }
+  retval += VP8LFastSLog2(sum);
+  return BitsEntropyRefine(nonzeros, sum, max_val, retval);
+}
+
+static double 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 double kSmallBias = 9.1;
+  return kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
+}
+
+// Finalize the Huffman cost based on streak numbers and length type (<3 or >=3)
+static double FinalHuffmanCost(const VP8LStreaks* const stats) {
+  double retval = InitialHuffmanCost();
+  retval += stats->counts[0] * 1.5625 + 0.234375 * stats->streaks[0][1];
+  retval += stats->counts[1] * 2.578125 + 0.703125 * stats->streaks[1][1];
+  retval += 1.796875 * stats->streaks[0][0];
+  retval += 3.28125 * stats->streaks[1][0];
+  return retval;
+}
+
+// Trampolines
+static double HuffmanCost(const uint32_t* const population, int length) {
+  const VP8LStreaks stats = VP8LHuffmanCostCount(population, length);
+  return FinalHuffmanCost(&stats);
+}
+
+static double HuffmanCostCombined(const uint32_t* const X,
+                                  const uint32_t* const Y, int length) {
+  const VP8LStreaks stats = VP8LHuffmanCostCombinedCount(X, Y, length);
+  return FinalHuffmanCost(&stats);
+}
+
+// Aggregated costs
+static double PopulationCost(const uint32_t* const population, int length) {
+  return BitsEntropy(population, length) + HuffmanCost(population, length);
+}
+
+static double GetCombinedEntropy(const uint32_t* const X,
+                                 const uint32_t* const Y, int length) {
+  return BitsEntropyCombined(X, Y, length) + HuffmanCostCombined(X, Y, length);
+}
+
+// Estimates the Entropy + Huffman + other block overhead size cost.
+double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
+  return
+      PopulationCost(p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_))
+      + PopulationCost(p->red_, NUM_LITERAL_CODES)
+      + PopulationCost(p->blue_, NUM_LITERAL_CODES)
+      + PopulationCost(p->alpha_, NUM_LITERAL_CODES)
+      + PopulationCost(p->distance_, NUM_DISTANCE_CODES)
+      + VP8LExtraCost(p->literal_ + NUM_LITERAL_CODES, NUM_LENGTH_CODES)
+      + VP8LExtraCost(p->distance_, NUM_DISTANCE_CODES);
+}
+
+double VP8LHistogramEstimateBitsBulk(const VP8LHistogram* const p) {
+  return
+      BitsEntropy(p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_))
+      + BitsEntropy(p->red_, NUM_LITERAL_CODES)
+      + BitsEntropy(p->blue_, NUM_LITERAL_CODES)
+      + BitsEntropy(p->alpha_, NUM_LITERAL_CODES)
+      + BitsEntropy(p->distance_, NUM_DISTANCE_CODES)
+      + 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,
+                                       double cost_threshold,
+                                       double* cost) {
+  const int palette_code_bits = a->palette_code_bits_;
+  assert(a->palette_code_bits_ == b->palette_code_bits_);
+  *cost += GetCombinedEntropy(a->literal_, b->literal_,
+                              VP8LHistogramNumCodes(palette_code_bits));
+  *cost += VP8LExtraCostCombined(a->literal_ + NUM_LITERAL_CODES,
+                                 b->literal_ + NUM_LITERAL_CODES,
+                                 NUM_LENGTH_CODES);
+  if (*cost > cost_threshold) return 0;
+
+  *cost += GetCombinedEntropy(a->red_, b->red_, NUM_LITERAL_CODES);
+  if (*cost > cost_threshold) return 0;
+
+  *cost += GetCombinedEntropy(a->blue_, b->blue_, NUM_LITERAL_CODES);
+  if (*cost > cost_threshold) return 0;
+
+  *cost += GetCombinedEntropy(a->alpha_, b->alpha_, NUM_LITERAL_CODES);
+  if (*cost > cost_threshold) return 0;
+
+  *cost += GetCombinedEntropy(a->distance_, b->distance_, NUM_DISTANCE_CODES);
+  *cost += VP8LExtraCostCombined(a->distance_, b->distance_,
+                                 NUM_DISTANCE_CODES);
+  if (*cost > cost_threshold) return 0;
+
+  return 1;
+}
+
+// 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 double HistogramAddEval(const VP8LHistogram* const a,
+                               const VP8LHistogram* const b,
+                               VP8LHistogram* const out,
+                               double cost_threshold) {
+  double cost = 0;
+  const double sum_cost = a->bit_cost_ + b->bit_cost_;
+  cost_threshold += sum_cost;
+
+  if (GetCombinedHistogramEntropy(a, b, cost_threshold, &cost)) {
+    VP8LHistogramAdd(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 double HistogramAddThresh(const VP8LHistogram* const a,
+                                 const VP8LHistogram* const b,
+                                 double cost_threshold) {
+  double 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.
+// TODO(skal): Evaluate if float can be used here instead of double for
+// representing the entropy costs.
+typedef struct {
+  double literal_max_;
+  double literal_min_;
+  double red_max_;
+  double red_min_;
+  double blue_max_;
+  double blue_min_;
+} DominantCostRange;
+
+static void DominantCostRangeInit(DominantCostRange* const c) {
+  c->literal_max_ = 0.;
+  c->literal_min_ = MAX_COST;
+  c->red_max_ = 0.;
+  c->red_min_ = MAX_COST;
+  c->blue_max_ = 0.;
+  c->blue_min_ = MAX_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) {
+  const double alpha_cost = PopulationCost(h->alpha_, NUM_LITERAL_CODES);
+  const double distance_cost =
+      PopulationCost(h->distance_, NUM_DISTANCE_CODES) +
+      VP8LExtraCost(h->distance_, NUM_DISTANCE_CODES);
+  const int num_codes = VP8LHistogramNumCodes(h->palette_code_bits_);
+  h->literal_cost_ = PopulationCost(h->literal_, num_codes) +
+                     VP8LExtraCost(h->literal_ + NUM_LITERAL_CODES,
+                                   NUM_LENGTH_CODES);
+  h->red_cost_ = PopulationCost(h->red_, NUM_LITERAL_CODES);
+  h->blue_cost_ = PopulationCost(h->blue_, NUM_LITERAL_CODES);
+  h->bit_cost_ = h->literal_cost_ + h->red_cost_ + h->blue_cost_ +
+                 alpha_cost + distance_cost;
+}
+
+static int GetBinIdForEntropy(double min, double max, double val) {
+  const double range = max - min + 1e-6;
+  const double delta = val - min;
+  return (int)(NUM_PARTITIONS * delta / range);
+}
+
+// TODO(vikasa): Evaluate, if there's any correlation between red & blue.
+static int GetHistoBinIndex(
+    const VP8LHistogram* const h, const DominantCostRange* const c) {
+  const int bin_id =
+      GetBinIdForEntropy(c->blue_min_, c->blue_max_, h->blue_cost_) +
+      NUM_PARTITIONS * GetBinIdForEntropy(c->red_min_, c->red_max_,
+                                          h->red_cost_) +
+      NUM_PARTITIONS * NUM_PARTITIONS * GetBinIdForEntropy(c->literal_min_,
+                                                           c->literal_max_,
+                                                           h->literal_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);
+  // Construct the Histo from a given backward references.
+  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);
+    x += PixOrCopyLength(v);
+    while (x >= xsize) {
+      x -= xsize;
+      ++y;
+    }
+    VP8LRefsCursorNext(&c);
+  }
+}
+
+// Copies the histograms and computes its bit_cost.
+static void HistogramCopyAndAnalyze(
+    VP8LHistogramSet* const orig_histo, VP8LHistogramSet* const image_histo) {
+  int i;
+  const int histo_size = orig_histo->size;
+  VP8LHistogram** const orig_histograms = orig_histo->histograms;
+  VP8LHistogram** const histograms = image_histo->histograms;
+  for (i = 0; i < histo_size; ++i) {
+    VP8LHistogram* const histo = orig_histograms[i];
+    UpdateHistogramCost(histo);
+    // Copy histograms from orig_histo[] to image_histo[].
+    HistogramCopy(histo, histograms[i]);
+  }
+}
+
+// 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, int16_t* const bin_map) {
+  int i;
+  VP8LHistogram** const histograms = image_histo->histograms;
+  const int histo_size = image_histo->size;
+  const int bin_depth = histo_size + 1;
+  DominantCostRange cost_range;
+  DominantCostRangeInit(&cost_range);
+
+  // Analyze the dominant (literal, red and blue) entropy costs.
+  for (i = 0; i < histo_size; ++i) {
+    VP8LHistogram* const histo = histograms[i];
+    UpdateDominantCostRange(histo, &cost_range);
+  }
+
+  // bin-hash histograms on three of the dominant (literal, red and blue)
+  // symbol costs.
+  for (i = 0; i < histo_size; ++i) {
+    int num_histos;
+    VP8LHistogram* const histo = histograms[i];
+    const int16_t bin_id = (int16_t)GetHistoBinIndex(histo, &cost_range);
+    const int bin_offset = bin_id * bin_depth;
+    // bin_map[n][0] for every bin 'n' maintains the counter for the number of
+    // histograms in that bin.
+    // Get and increment the num_histos in that bin.
+    num_histos = ++bin_map[bin_offset];
+    assert(bin_offset + num_histos < bin_depth * BIN_SIZE);
+    // Add histogram i'th index at num_histos (last) position in the bin_map.
+    bin_map[bin_offset + num_histos] = i;
+  }
+}
+
+// Compact the histogram set by moving the valid one left in the set to the
+// head and moving the ones that have been merged to other histograms towards
+// the end.
+// TODO(vikasa): Evaluate if this method can be avoided by altering the code
+// logic of HistogramCombineEntropyBin main loop.
+static void HistogramCompactBins(VP8LHistogramSet* const image_histo) {
+  int start = 0;
+  int end = image_histo->size - 1;
+  VP8LHistogram** const histograms = image_histo->histograms;
+  while (start < end) {
+    while (start <= end && histograms[start] != NULL &&
+           histograms[start]->bit_cost_ != 0.) {
+      ++start;
+    }
+    while (start <= end && histograms[end]->bit_cost_ == 0.) {
+      histograms[end] = NULL;
+      --end;
+    }
+    if (start < end) {
+      assert(histograms[start] != NULL);
+      assert(histograms[end] != NULL);
+      HistogramCopy(histograms[end], histograms[start]);
+      histograms[end] = NULL;
+      --end;
+    }
+  }
+  image_histo->size = end + 1;
+}
+
+static void HistogramCombineEntropyBin(VP8LHistogramSet* const image_histo,
+                                       VP8LHistogram* const histos,
+                                       int16_t* const bin_map, int bin_depth,
+                                       double combine_cost_factor) {
+  int bin_id;
+  VP8LHistogram* cur_combo = histos;
+  VP8LHistogram** const histograms = image_histo->histograms;
+
+  for (bin_id = 0; bin_id < BIN_SIZE; ++bin_id) {
+    const int bin_offset = bin_id * bin_depth;
+    const int num_histos = bin_map[bin_offset];
+    const int idx1 = bin_map[bin_offset + 1];
+    int n;
+    for (n = 2; n <= num_histos; ++n) {
+      const int idx2 = bin_map[bin_offset + n];
+      const double bit_cost_idx2 = histograms[idx2]->bit_cost_;
+      if (bit_cost_idx2 > 0.) {
+        const double bit_cost_thresh = -bit_cost_idx2 * combine_cost_factor;
+        const double curr_cost_diff =
+            HistogramAddEval(histograms[idx1], histograms[idx2],
+                             cur_combo, bit_cost_thresh);
+        if (curr_cost_diff < bit_cost_thresh) {
+          HistogramCopy(cur_combo, histograms[idx1]);
+          histograms[idx2]->bit_cost_ = 0.;
+        }
+      }
+    }
+  }
+  HistogramCompactBins(image_histo);
+}
+
+static uint32_t MyRand(uint32_t *seed) {
+  *seed *= 16807U;
+  if (*seed == 0) {
+    *seed = 1;
+  }
+  return *seed;
+}
+
+static void HistogramCombine(VP8LHistogramSet* const image_histo,
+                             VP8LHistogramSet* const histos, int quality) {
+  int iter;
+  uint32_t seed = 0;
+  int tries_with_no_success = 0;
+  int image_histo_size = image_histo->size;
+  const int iter_mult = (quality < 25) ? 2 : 2 + (quality - 25) / 8;
+  const int outer_iters = image_histo_size * iter_mult;
+  const int num_pairs = image_histo_size / 2;
+  const int num_tries_no_success = outer_iters / 2;
+  const int min_cluster_size = 2;
+  VP8LHistogram** const histograms = image_histo->histograms;
+  VP8LHistogram* cur_combo = histos->histograms[0];   // trial histogram
+  VP8LHistogram* best_combo = histos->histograms[1];  // best histogram so far
+
+  // Collapse similar histograms in 'image_histo'.
+  for (iter = 0;
+       iter < outer_iters && image_histo_size >= min_cluster_size;
+       ++iter) {
+    double best_cost_diff = 0.;
+    int best_idx1 = -1, best_idx2 = 1;
+    int j;
+    const int num_tries =
+        (num_pairs < image_histo_size) ? num_pairs : image_histo_size;
+    seed += iter;
+    for (j = 0; j < num_tries; ++j) {
+      double curr_cost_diff;
+      // Choose two histograms at random and try to combine them.
+      const uint32_t idx1 = MyRand(&seed) % image_histo_size;
+      const uint32_t tmp = (j & 7) + 1;
+      const uint32_t diff =
+          (tmp < 3) ? tmp : MyRand(&seed) % (image_histo_size - 1);
+      const uint32_t idx2 = (idx1 + diff + 1) % image_histo_size;
+      if (idx1 == idx2) {
+        continue;
+      }
+
+      // Calculate cost reduction on combining.
+      curr_cost_diff = HistogramAddEval(histograms[idx1], histograms[idx2],
+                                        cur_combo, best_cost_diff);
+      if (curr_cost_diff < best_cost_diff) {    // found a better pair?
+        {     // swap cur/best combo histograms
+          VP8LHistogram* const tmp_histo = cur_combo;
+          cur_combo = best_combo;
+          best_combo = tmp_histo;
+        }
+        best_cost_diff = curr_cost_diff;
+        best_idx1 = idx1;
+        best_idx2 = idx2;
+      }
+    }
+
+    if (best_idx1 >= 0) {
+      HistogramCopy(best_combo, histograms[best_idx1]);
+      // swap best_idx2 slot with last one (which is now unused)
+      --image_histo_size;
+      if (best_idx2 != image_histo_size) {
+        HistogramCopy(histograms[image_histo_size], histograms[best_idx2]);
+        histograms[image_histo_size] = NULL;
+      }
+      tries_with_no_success = 0;
+    }
+    if (++tries_with_no_success >= num_tries_no_success) {
+      break;
+    }
+  }
+  image_histo->size = image_histo_size;
+}
+
+// -----------------------------------------------------------------------------
+// Histogram refinement
+
+// Find the best 'out' histogram for each of the 'in' histograms.
+// Note: we assume that out[]->bit_cost_ is already up-to-date.
+static void HistogramRemap(const VP8LHistogramSet* const orig_histo,
+                           const VP8LHistogramSet* const image_histo,
+                           uint16_t* const symbols) {
+  int i;
+  VP8LHistogram** const orig_histograms = orig_histo->histograms;
+  VP8LHistogram** const histograms = image_histo->histograms;
+  for (i = 0; i < orig_histo->size; ++i) {
+    int best_out = 0;
+    double best_bits =
+        HistogramAddThresh(histograms[0], orig_histograms[i], MAX_COST);
+    int k;
+    for (k = 1; k < image_histo->size; ++k) {
+      const double cur_bits =
+          HistogramAddThresh(histograms[k], orig_histograms[i], best_bits);
+      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 (i = 0; i < image_histo->size; ++i) {
+    HistogramClear(histograms[i]);
+  }
+
+  for (i = 0; i < orig_histo->size; ++i) {
+    const int idx = symbols[i];
+    VP8LHistogramAdd(orig_histograms[i], histograms[idx], histograms[idx]);
+  }
+}
+
+static double GetCombineCostFactor(int histo_size, int quality) {
+  double combine_cost_factor = 0.16;
+  if (histo_size > 256) combine_cost_factor /= 2.;
+  if (histo_size > 512) combine_cost_factor /= 2.;
+  if (histo_size > 1024) combine_cost_factor /= 2.;
+  if (quality <= 50) combine_cost_factor /= 2.;
+  return combine_cost_factor;
+}
+
+int VP8LGetHistoImageSymbols(int xsize, int ysize,
+                             const VP8LBackwardRefs* const refs,
+                             int quality, int histo_bits, int cache_bits,
+                             VP8LHistogramSet* const image_histo,
+                             uint16_t* const histogram_symbols) {
+  int ok = 0;
+  const int histo_xsize = histo_bits ? VP8LSubSampleSize(xsize, histo_bits) : 1;
+  const int histo_ysize = histo_bits ? VP8LSubSampleSize(ysize, histo_bits) : 1;
+  const int image_histo_raw_size = histo_xsize * histo_ysize;
+
+  // The bin_map for every bin follows following semantics:
+  // bin_map[n][0] = num_histo; // The number of histograms in that bin.
+  // bin_map[n][1] = index of first histogram in that bin;
+  // bin_map[n][num_histo] = index of last histogram in that bin;
+  // bin_map[n][num_histo + 1] ... bin_map[n][bin_depth - 1] = un-used indices.
+  const int bin_depth = image_histo_raw_size + 1;
+  int16_t* bin_map = NULL;
+  VP8LHistogramSet* const histos = VP8LAllocateHistogramSet(2, cache_bits);
+  VP8LHistogramSet* const orig_histo =
+      VP8LAllocateHistogramSet(image_histo_raw_size, cache_bits);
+
+  if (orig_histo == NULL || histos == NULL) {
+    goto Error;
+  }
+
+  // Don't attempt linear bin-partition heuristic for:
+  // histograms of small sizes, as bin_map will be very sparse and;
+  // Higher qualities (> 90), to preserve the compression gains at those
+  // quality settings.
+  if (orig_histo->size > 2 * BIN_SIZE && quality < 90) {
+    const int bin_map_size = bin_depth * BIN_SIZE;
+    bin_map = (int16_t*)WebPSafeCalloc(bin_map_size, sizeof(*bin_map));
+    if (bin_map == NULL) goto Error;
+  }
+
+  // Construct the histograms from backward references.
+  HistogramBuild(xsize, histo_bits, refs, orig_histo);
+  // Copies the histograms and computes its bit_cost.
+  HistogramCopyAndAnalyze(orig_histo, image_histo);
+
+  if (bin_map != NULL) {
+    const double combine_cost_factor =
+        GetCombineCostFactor(image_histo_raw_size, quality);
+    HistogramAnalyzeEntropyBin(orig_histo, bin_map);
+    // Collapse histograms with similar entropy.
+    HistogramCombineEntropyBin(image_histo, histos->histograms[0],
+                               bin_map, bin_depth, combine_cost_factor);
+  }
+
+  // Collapse similar histograms by random histogram-pair compares.
+  HistogramCombine(image_histo, histos, quality);
+
+  // Find the optimal map from original histograms to the final ones.
+  HistogramRemap(orig_histo, image_histo, histogram_symbols);
+
+  ok = 1;
+
+ Error:
+  WebPSafeFree(bin_map);
+  VP8LFreeHistogramSet(orig_histo);
+  VP8LFreeHistogramSet(histos);
+  return ok;
+}