src/enc/histogram.c - platform/external/webp - Git at Google

 // Copyright 2012 Google Inc. All Rights Reserved.
 //
 // This code is licensed under the same terms as WebM:
 //  Software License Agreement:  http://www.webmproject.org/license/software/
 //  Additional IP Rights Grant:  http://www.webmproject.org/license/additional/
 // -----------------------------------------------------------------------------
 //
 // Author: Jyrki Alakuijala (jyrki@google.com)
 //
 #ifdef HAVE_CONFIG_H
 #include "config.h"
 #endif

 #include <math.h>
 #include <stdio.h>

 #include "./backward_references.h"
 #include "./histogram.h"
 #include "../dsp/lossless.h"
 #include "../utils/utils.h"

 static void HistogramClear(VP8LHistogram* const p) {
   memset(p->literal_, 0, sizeof(p->literal_));
   memset(p->red_, 0, sizeof(p->red_));
   memset(p->blue_, 0, sizeof(p->blue_));
   memset(p->alpha_, 0, sizeof(p->alpha_));
   memset(p->distance_, 0, sizeof(p->distance_));
   p->bit_cost_ = 0;
 }

 void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
                             VP8LHistogram* const histo) {
   int i;
   for (i = 0; i < refs->size; ++i) {
     VP8LHistogramAddSinglePixOrCopy(histo, &refs->refs[i]);
   }
 }

 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);
 }

 VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
   int i;
   VP8LHistogramSet* set;
   VP8LHistogram* bulk;
   const uint64_t total_size = (uint64_t)sizeof(*set)
                             + size * sizeof(*set->histograms)
                             + size * sizeof(**set->histograms);
   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);
   bulk = (VP8LHistogram*)memory;
   set->max_size = size;
   set->size = size;
   for (i = 0; i < size; ++i) {
     set->histograms[i] = bulk + i;
     VP8LHistogramInit(set->histograms[i], 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)) {
     int literal_ix = 256 + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
     ++histo->literal_[literal_ix];
   } else {
     int code, extra_bits_count, extra_bits_value;
     PrefixEncode(PixOrCopyLength(v),
                  &code, &extra_bits_count, &extra_bits_value);
     ++histo->literal_[256 + code];
     PrefixEncode(PixOrCopyDistance(v),
                  &code, &extra_bits_count, &extra_bits_value);
     ++histo->distance_[code];
   }
 }


 static double BitsEntropy(const int* const array, int n) {
   double retval = 0.;
   int sum = 0;
   int nonzeros = 0;
   int max_val = 0;
   int i;
   double mix;
   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);

   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;
   }
 }

 double VP8LHistogramEstimateBitsBulk(const VP8LHistogram* const p) {
   double retval = BitsEntropy(&p->literal_[0], VP8LHistogramNumCodes(p))
                 + BitsEntropy(&p->red_[0], 256)
                 + BitsEntropy(&p->blue_[0], 256)
                 + BitsEntropy(&p->alpha_[0], 256)
                 + BitsEntropy(&p->distance_[0], NUM_DISTANCE_CODES);
   // Compute the extra bits cost.
   int i;
   for (i = 2; i < NUM_LENGTH_CODES - 2; ++i) {
     retval +=
         (i >> 1) * p->literal_[256 + i + 2];
   }
   for (i = 2; i < NUM_DISTANCE_CODES - 2; ++i) {
     retval += (i >> 1) * p->distance_[i + 2];
   }
   return retval;
 }


 // Returns the cost encode the rle-encoded entropy code.
 // The constants in this function are experimental.
 static double HuffmanCost(const int* const population, int length) {
   // 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;
   double retval = kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
   int streak = 0;
   int i = 0;
   for (; i < length - 1; ++i) {
     ++streak;
     if (population[i] == population[i + 1]) {
       continue;
     }
  last_streak_hack:
     // population[i] points now to the symbol in the streak of same values.
     if (streak > 3) {
       if (population[i] == 0) {
         retval += 1.5625 + 0.234375 * streak;
       } else {
         retval += 2.578125 + 0.703125 * streak;
       }
     } else {
       if (population[i] == 0) {
         retval += 1.796875 * streak;
       } else {
         retval += 3.28125 * streak;
       }
     }
     streak = 0;
   }
   if (i == length - 1) {
     ++streak;
     goto last_streak_hack;
   }
   return retval;
 }

 // Estimates the Huffman dictionary + other block overhead size.
 static double HistogramEstimateBitsHeader(const VP8LHistogram* const p) {
   return HuffmanCost(&p->alpha_[0], 256) +
          HuffmanCost(&p->red_[0], 256) +
          HuffmanCost(&p->literal_[0], VP8LHistogramNumCodes(p)) +
          HuffmanCost(&p->blue_[0], 256) +
          HuffmanCost(&p->distance_[0], NUM_DISTANCE_CODES);
 }

 double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
   return HistogramEstimateBitsHeader(p) + VP8LHistogramEstimateBitsBulk(p);
 }

 static void HistogramBuildImage(int xsize, int histo_bits,
                                 const VP8LBackwardRefs* const backward_refs,
                                 VP8LHistogramSet* const image) {
   int i;
   int x = 0, y = 0;
   const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
   VP8LHistogram** const histograms = image->histograms;
   assert(histo_bits > 0);
   for (i = 0; i < backward_refs->size; ++i) {
     const PixOrCopy* const v = &backward_refs->refs[i];
     const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
     VP8LHistogramAddSinglePixOrCopy(histograms[ix], v);
     x += PixOrCopyLength(v);
     while (x >= xsize) {
       x -= xsize;
       ++y;
     }
   }
 }

 static uint32_t MyRand(uint32_t *seed) {
   *seed *= 16807U;
   if (*seed == 0) {
     *seed = 1;
   }
   return *seed;
 }

 static int HistogramCombine(const VP8LHistogramSet* const in,
                             VP8LHistogramSet* const out, int num_pairs) {
   int ok = 0;
   int i, iter;
   uint32_t seed = 0;
   int tries_with_no_success = 0;
   const int min_cluster_size = 2;
   int out_size = in->size;
   const int outer_iters = in->size * 3;
   VP8LHistogram* const histos = (VP8LHistogram*)malloc(2 * sizeof(*histos));
   VP8LHistogram* cur_combo = histos + 0;    // trial merged histogram
   VP8LHistogram* best_combo = histos + 1;   // best merged histogram so far
   if (histos == NULL) goto End;

   // Copy histograms from in[] to out[].
   assert(in->size <= out->size);
   for (i = 0; i < in->size; ++i) {
     in->histograms[i]->bit_cost_ = VP8LHistogramEstimateBits(in->histograms[i]);
     *out->histograms[i] = *in->histograms[i];
   }

   // Collapse similar histograms in 'out'.
   for (iter = 0; iter < outer_iters && out_size >= min_cluster_size; ++iter) {
     // We pick the best pair to be combined out of 'inner_iters' pairs.
     double best_cost_diff = 0.;
     int best_idx1 = 0, best_idx2 = 1;
     int j;
     seed += iter;
     for (j = 0; j < num_pairs; ++j) {
       double curr_cost_diff;
       // Choose two histograms at random and try to combine them.
       const uint32_t idx1 = MyRand(&seed) % out_size;
       const uint32_t tmp = ((j & 7) + 1) % (out_size - 1);
       const uint32_t diff = (tmp < 3) ? tmp : MyRand(&seed) % (out_size - 1);
       const uint32_t idx2 = (idx1 + diff + 1) % out_size;
       if (idx1 == idx2) {
         continue;
       }
       *cur_combo = *out->histograms[idx1];
       VP8LHistogramAdd(cur_combo, out->histograms[idx2]);
       cur_combo->bit_cost_ = VP8LHistogramEstimateBits(cur_combo);
       // Calculate cost reduction on combining.
       curr_cost_diff = cur_combo->bit_cost_
                      - out->histograms[idx1]->bit_cost_
                      - out->histograms[idx2]->bit_cost_;
       if (best_cost_diff > curr_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_cost_diff < 0.0) {
       *out->histograms[best_idx1] = *best_combo;
       // swap best_idx2 slot with last one (which is now unused)
       --out_size;
       if (best_idx2 != out_size) {
         out->histograms[best_idx2] = out->histograms[out_size];
         out->histograms[out_size] = NULL;   // just for sanity check.
       }
       tries_with_no_success = 0;
     }
     if (++tries_with_no_success >= 50) {
       break;
     }
   }
   out->size = out_size;
   ok = 1;

  End:
   free(histos);
   return ok;
 }

 // -----------------------------------------------------------------------------
 // Histogram refinement

 // What is the bit cost of moving square_histogram from
 // cur_symbol to candidate_symbol.
 // TODO(skal): we don't really need to copy the histogram and Add(). Instead
 // we just need VP8LDualHistogramEstimateBits(A, B) estimation function.
 static double HistogramDistance(const VP8LHistogram* const square_histogram,
                                 const VP8LHistogram* const candidate) {
   const double previous_bit_cost = candidate->bit_cost_;
   double new_bit_cost;
   VP8LHistogram modified_histo;
   modified_histo = *candidate;
   VP8LHistogramAdd(&modified_histo, square_histogram);
   new_bit_cost = VP8LHistogramEstimateBits(&modified_histo);

   return new_bit_cost - previous_bit_cost;
 }

 // Find the best 'out' histogram for each of the 'in' histograms.
 // Note: we assume that out[]->bit_cost_ is already up-to-date.
 static void HistogramRemap(const VP8LHistogramSet* const in,
                            const VP8LHistogramSet* const out,
                            uint16_t* const symbols) {
   int i;
   for (i = 0; i < in->size; ++i) {
     int best_out = 0;
     double best_bits = HistogramDistance(in->histograms[i], out->histograms[0]);
     int k;
     for (k = 1; k < out->size; ++k) {
       const double cur_bits =
           HistogramDistance(in->histograms[i], out->histograms[k]);
       if (cur_bits < best_bits) {
         best_bits = cur_bits;
         best_out = k;
       }
     }
     symbols[i] = best_out;
   }

   // Recompute each out based on raw and symbols.
   for (i = 0; i < out->size; ++i) {
     HistogramClear(out->histograms[i]);
   }
   for (i = 0; i < in->size; ++i) {
     VP8LHistogramAdd(out->histograms[symbols[i]], in->histograms[i]);
   }
 }

 int VP8LGetHistoImageSymbols(int xsize, int ysize,
                              const VP8LBackwardRefs* const refs,
                              int quality, int histo_bits, int cache_bits,
                              VP8LHistogramSet* const image_in,
                              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 num_histo_pairs = 10 + quality / 2;  // For HistogramCombine().
   const int histo_image_raw_size = histo_xsize * histo_ysize;
   VP8LHistogramSet* const image_out =
       VP8LAllocateHistogramSet(histo_image_raw_size, cache_bits);
   if (image_out == NULL) return 0;

   // Build histogram image.
   HistogramBuildImage(xsize, histo_bits, refs, image_out);
   // Collapse similar histograms.
   if (!HistogramCombine(image_out, image_in, num_histo_pairs)) {
     goto Error;
   }
   // Find the optimal map from original histograms to the final ones.
   HistogramRemap(image_out, image_in, histogram_symbols);
   ok = 1;

 Error:
   free(image_out);
   return ok;
 }
	// Copyright 2012 Google Inc. All Rights Reserved.
	//
	// This code is licensed under the same terms as WebM:
	// Software License Agreement: http://www.webmproject.org/license/software/
	// Additional IP Rights Grant: http://www.webmproject.org/license/additional/
	// -----------------------------------------------------------------------------
	//
	// Author: Jyrki Alakuijala (jyrki@google.com)
	//
	#ifdef HAVE_CONFIG_H
	#include "config.h"
	#endif

	#include <math.h>
	#include <stdio.h>

	#include "./backward_references.h"
	#include "./histogram.h"
	#include "../dsp/lossless.h"
	#include "../utils/utils.h"

	static void HistogramClear(VP8LHistogram* const p) {
	memset(p->literal_, 0, sizeof(p->literal_));
	memset(p->red_, 0, sizeof(p->red_));
	memset(p->blue_, 0, sizeof(p->blue_));
	memset(p->alpha_, 0, sizeof(p->alpha_));
	memset(p->distance_, 0, sizeof(p->distance_));
	p->bit_cost_ = 0;
	}

	void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
	VP8LHistogram* const histo) {
	int i;
	for (i = 0; i < refs->size; ++i) {
	VP8LHistogramAddSinglePixOrCopy(histo, &refs->refs[i]);
	}
	}

	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);
	}

	VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
	int i;
	VP8LHistogramSet* set;
	VP8LHistogram* bulk;
	const uint64_t total_size = (uint64_t)sizeof(*set)
	+ size * sizeof(*set->histograms)
	+ size * sizeof(**set->histograms);
	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);
	bulk = (VP8LHistogram*)memory;
	set->max_size = size;
	set->size = size;
	for (i = 0; i < size; ++i) {
	set->histograms[i] = bulk + i;
	VP8LHistogramInit(set->histograms[i], 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)) {
	int literal_ix = 256 + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
	++histo->literal_[literal_ix];
	} else {
	int code, extra_bits_count, extra_bits_value;
	PrefixEncode(PixOrCopyLength(v),
	&code, &extra_bits_count, &extra_bits_value);
	++histo->literal_[256 + code];
	PrefixEncode(PixOrCopyDistance(v),
	&code, &extra_bits_count, &extra_bits_value);
	++histo->distance_[code];
	}
	}



	static double BitsEntropy(const int* const array, int n) {
	double retval = 0.;
	int sum = 0;
	int nonzeros = 0;
	int max_val = 0;
	int i;
	double mix;
	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);

	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;
	}
	}

	double VP8LHistogramEstimateBitsBulk(const VP8LHistogram* const p) {
	double retval = BitsEntropy(&p->literal_[0], VP8LHistogramNumCodes(p))
	+ BitsEntropy(&p->red_[0], 256)
	+ BitsEntropy(&p->blue_[0], 256)
	+ BitsEntropy(&p->alpha_[0], 256)
	+ BitsEntropy(&p->distance_[0], NUM_DISTANCE_CODES);
	// Compute the extra bits cost.
	int i;
	for (i = 2; i < NUM_LENGTH_CODES - 2; ++i) {
	retval +=
	(i >> 1) * p->literal_[256 + i + 2];
	}
	for (i = 2; i < NUM_DISTANCE_CODES - 2; ++i) {
	retval += (i >> 1) * p->distance_[i + 2];
	}
	return retval;
	}


	// Returns the cost encode the rle-encoded entropy code.
	// The constants in this function are experimental.
	static double HuffmanCost(const int* const population, int length) {
	// 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;
	double retval = kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
	int streak = 0;
	int i = 0;
	for (; i < length - 1; ++i) {
	++streak;
	if (population[i] == population[i + 1]) {
	continue;
	}
	last_streak_hack:
	// population[i] points now to the symbol in the streak of same values.
	if (streak > 3) {
	if (population[i] == 0) {
	retval += 1.5625 + 0.234375 * streak;
	} else {
	retval += 2.578125 + 0.703125 * streak;
	}
	} else {
	if (population[i] == 0) {
	retval += 1.796875 * streak;
	} else {
	retval += 3.28125 * streak;
	}
	}
	streak = 0;
	}
	if (i == length - 1) {
	++streak;
	goto last_streak_hack;
	}
	return retval;
	}

	// Estimates the Huffman dictionary + other block overhead size.
	static double HistogramEstimateBitsHeader(const VP8LHistogram* const p) {
	return HuffmanCost(&p->alpha_[0], 256) +
	HuffmanCost(&p->red_[0], 256) +
	HuffmanCost(&p->literal_[0], VP8LHistogramNumCodes(p)) +
	HuffmanCost(&p->blue_[0], 256) +
	HuffmanCost(&p->distance_[0], NUM_DISTANCE_CODES);
	}

	double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
	return HistogramEstimateBitsHeader(p) + VP8LHistogramEstimateBitsBulk(p);
	}

	static void HistogramBuildImage(int xsize, int histo_bits,
	const VP8LBackwardRefs* const backward_refs,
	VP8LHistogramSet* const image) {
	int i;
	int x = 0, y = 0;
	const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
	VP8LHistogram** const histograms = image->histograms;
	assert(histo_bits > 0);
	for (i = 0; i < backward_refs->size; ++i) {
	const PixOrCopy* const v = &backward_refs->refs[i];
	const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
	VP8LHistogramAddSinglePixOrCopy(histograms[ix], v);
	x += PixOrCopyLength(v);
	while (x >= xsize) {
	x -= xsize;
	++y;
	}
	}
	}

	static uint32_t MyRand(uint32_t *seed) {
	seed = 16807U;
	if (*seed == 0) {
	*seed = 1;
	}
	return *seed;
	}

	static int HistogramCombine(const VP8LHistogramSet* const in,
	VP8LHistogramSet* const out, int num_pairs) {
	int ok = 0;
	int i, iter;
	uint32_t seed = 0;
	int tries_with_no_success = 0;
	const int min_cluster_size = 2;
	int out_size = in->size;
	const int outer_iters = in->size * 3;
	VP8LHistogram* const histos = (VP8LHistogram)malloc(2 sizeof(*histos));
	VP8LHistogram* cur_combo = histos + 0; // trial merged histogram
	VP8LHistogram* best_combo = histos + 1; // best merged histogram so far
	if (histos == NULL) goto End;

	// Copy histograms from in[] to out[].
	assert(in->size <= out->size);
	for (i = 0; i < in->size; ++i) {
	in->histograms[i]->bit_cost_ = VP8LHistogramEstimateBits(in->histograms[i]);
	out->histograms[i] = in->histograms[i];
	}

	// Collapse similar histograms in 'out'.
	for (iter = 0; iter < outer_iters && out_size >= min_cluster_size; ++iter) {
	// We pick the best pair to be combined out of 'inner_iters' pairs.
	double best_cost_diff = 0.;
	int best_idx1 = 0, best_idx2 = 1;
	int j;
	seed += iter;
	for (j = 0; j < num_pairs; ++j) {
	double curr_cost_diff;
	// Choose two histograms at random and try to combine them.
	const uint32_t idx1 = MyRand(&seed) % out_size;
	const uint32_t tmp = ((j & 7) + 1) % (out_size - 1);
	const uint32_t diff = (tmp < 3) ? tmp : MyRand(&seed) % (out_size - 1);
	const uint32_t idx2 = (idx1 + diff + 1) % out_size;
	if (idx1 == idx2) {
	continue;
	}
	cur_combo = out->histograms[idx1];
	VP8LHistogramAdd(cur_combo, out->histograms[idx2]);
	cur_combo->bit_cost_ = VP8LHistogramEstimateBits(cur_combo);
	// Calculate cost reduction on combining.
	curr_cost_diff = cur_combo->bit_cost_
	- out->histograms[idx1]->bit_cost_
	- out->histograms[idx2]->bit_cost_;
	if (best_cost_diff > curr_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_cost_diff < 0.0) {
	out->histograms[best_idx1] = best_combo;
	// swap best_idx2 slot with last one (which is now unused)
	--out_size;
	if (best_idx2 != out_size) {
	out->histograms[best_idx2] = out->histograms[out_size];
	out->histograms[out_size] = NULL; // just for sanity check.
	}
	tries_with_no_success = 0;
	}
	if (++tries_with_no_success >= 50) {
	break;
	}
	}
	out->size = out_size;
	ok = 1;

	End:
	free(histos);
	return ok;
	}

	// -----------------------------------------------------------------------------
	// Histogram refinement

	// What is the bit cost of moving square_histogram from
	// cur_symbol to candidate_symbol.
	// TODO(skal): we don't really need to copy the histogram and Add(). Instead
	// we just need VP8LDualHistogramEstimateBits(A, B) estimation function.
	static double HistogramDistance(const VP8LHistogram* const square_histogram,
	const VP8LHistogram* const candidate) {
	const double previous_bit_cost = candidate->bit_cost_;
	double new_bit_cost;
	VP8LHistogram modified_histo;
	modified_histo = *candidate;
	VP8LHistogramAdd(&modified_histo, square_histogram);
	new_bit_cost = VP8LHistogramEstimateBits(&modified_histo);

	return new_bit_cost - previous_bit_cost;
	}

	// Find the best 'out' histogram for each of the 'in' histograms.
	// Note: we assume that out[]->bit_cost_ is already up-to-date.
	static void HistogramRemap(const VP8LHistogramSet* const in,
	const VP8LHistogramSet* const out,
	uint16_t* const symbols) {
	int i;
	for (i = 0; i < in->size; ++i) {
	int best_out = 0;
	double best_bits = HistogramDistance(in->histograms[i], out->histograms[0]);
	int k;
	for (k = 1; k < out->size; ++k) {
	const double cur_bits =
	HistogramDistance(in->histograms[i], out->histograms[k]);
	if (cur_bits < best_bits) {
	best_bits = cur_bits;
	best_out = k;
	}
	}
	symbols[i] = best_out;
	}

	// Recompute each out based on raw and symbols.
	for (i = 0; i < out->size; ++i) {
	HistogramClear(out->histograms[i]);
	}
	for (i = 0; i < in->size; ++i) {
	VP8LHistogramAdd(out->histograms[symbols[i]], in->histograms[i]);
	}
	}

	int VP8LGetHistoImageSymbols(int xsize, int ysize,
	const VP8LBackwardRefs* const refs,
	int quality, int histo_bits, int cache_bits,
	VP8LHistogramSet* const image_in,
	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 num_histo_pairs = 10 + quality / 2; // For HistogramCombine().
	const int histo_image_raw_size = histo_xsize * histo_ysize;
	VP8LHistogramSet* const image_out =
	VP8LAllocateHistogramSet(histo_image_raw_size, cache_bits);
	if (image_out == NULL) return 0;

	// Build histogram image.
	HistogramBuildImage(xsize, histo_bits, refs, image_out);
	// Collapse similar histograms.
	if (!HistogramCombine(image_out, image_in, num_histo_pairs)) {
	goto Error;
	}
	// Find the optimal map from original histograms to the final ones.
	HistogramRemap(image_out, image_in, histogram_symbols);
	ok = 1;

	Error:
	free(image_out);
	return ok;
	}