third_party/libwebp/enc/histogram.c

   1 // Copyright 2012 Google Inc. All Rights Reserved.
   2 //
   3 // Use of this source code is governed by a BSD-style license
   4 // that can be found in the COPYING file in the root of the source
   5 // tree. An additional intellectual property rights grant can be found
   6 // in the file PATENTS. All contributing project authors may
   7 // be found in the AUTHORS file in the root of the source tree.
   8 // -----------------------------------------------------------------------------
   9 //
  10 // Author: Jyrki Alakuijala (jyrki@google.com)
  11 //
  12 #ifdef HAVE_CONFIG_H
  13 #include "../webp/config.h"
  14 #endif
  15
  16 #include <math.h>
  17
  18 #include "./backward_references.h"
  19 #include "./histogram.h"
  20 #include "../dsp/lossless.h"
  21 #include "../utils/utils.h"
  22
  23 #define MAX_COST 1.e38
  24
  25 // Number of partitions for the three dominant (literal, red and blue) symbol
  26 // costs.
  27 #define NUM_PARTITIONS 4
  28 // The size of the bin-hash corresponding to the three dominant costs.
  29 #define BIN_SIZE (NUM_PARTITIONS * NUM_PARTITIONS * NUM_PARTITIONS)
  30
  31 static void HistogramClear(VP8LHistogram* const p) {
  32   uint32_t* const literal = p->literal_;
  33   const int cache_bits = p->palette_code_bits_;
  34   const int histo_size = VP8LGetHistogramSize(cache_bits);
  35   memset(p, 0, histo_size);
  36   p->palette_code_bits_ = cache_bits;
  37   p->literal_ = literal;
  38 }
  39
  40 static void HistogramCopy(const VP8LHistogram* const src,
  41                           VP8LHistogram* const dst) {
  42   uint32_t* const dst_literal = dst->literal_;
  43   const int dst_cache_bits = dst->palette_code_bits_;
  44   const int histo_size = VP8LGetHistogramSize(dst_cache_bits);
  45   assert(src->palette_code_bits_ == dst_cache_bits);
  46   memcpy(dst, src, histo_size);
  47   dst->literal_ = dst_literal;
  48 }
  49
  50 int VP8LGetHistogramSize(int cache_bits) {
  51   const int literal_size = VP8LHistogramNumCodes(cache_bits);
  52   const size_t total_size = sizeof(VP8LHistogram) + sizeof(int) * literal_size;
  53   assert(total_size <= (size_t)0x7fffffff);
  54   return (int)total_size;
  55 }
  56
  57 void VP8LFreeHistogram(VP8LHistogram* const histo) {
  58   WebPSafeFree(histo);
  59 }
  60
  61 void VP8LFreeHistogramSet(VP8LHistogramSet* const histo) {
  62   WebPSafeFree(histo);
  63 }
  64
  65 void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
  66                             VP8LHistogram* const histo) {
  67   VP8LRefsCursor c = VP8LRefsCursorInit(refs);
  68   while (VP8LRefsCursorOk(&c)) {
  69     VP8LHistogramAddSinglePixOrCopy(histo, c.cur_pos);
  70     VP8LRefsCursorNext(&c);
  71   }
  72 }
  73
  74 void VP8LHistogramCreate(VP8LHistogram* const p,
  75                          const VP8LBackwardRefs* const refs,
  76                          int palette_code_bits) {
  77   if (palette_code_bits >= 0) {
  78     p->palette_code_bits_ = palette_code_bits;
  79   }
  80   HistogramClear(p);
  81   VP8LHistogramStoreRefs(refs, p);
  82 }
  83
  84 void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits) {
  85   p->palette_code_bits_ = palette_code_bits;
  86   HistogramClear(p);
  87 }
  88
  89 VP8LHistogram* VP8LAllocateHistogram(int cache_bits) {
  90   VP8LHistogram* histo = NULL;
  91   const int total_size = VP8LGetHistogramSize(cache_bits);
  92   uint8_t* const memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
  93   if (memory == NULL) return NULL;
  94   histo = (VP8LHistogram*)memory;
  95   // literal_ won't necessary be aligned.
  96   histo->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
  97   VP8LHistogramInit(histo, cache_bits);
  98   return histo;
  99 }
 100
 101 VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
 102   int i;
 103   VP8LHistogramSet* set;
 104   const size_t total_size = sizeof(*set)
 105                             + sizeof(*set->histograms) * size
 106                             + (size_t)VP8LGetHistogramSize(cache_bits) * size;
 107   uint8_t* memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
 108   if (memory == NULL) return NULL;
 109
 110   set = (VP8LHistogramSet*)memory;
 111   memory += sizeof(*set);
 112   set->histograms = (VP8LHistogram**)memory;
 113   memory += size * sizeof(*set->histograms);
 114   set->max_size = size;
 115   set->size = size;
 116   for (i = 0; i < size; ++i) {
 117     set->histograms[i] = (VP8LHistogram*)memory;
 118     // literal_ won't necessary be aligned.
 119     set->histograms[i]->literal_ = (uint32_t*)(memory + sizeof(VP8LHistogram));
 120     VP8LHistogramInit(set->histograms[i], cache_bits);
 121     // There's no padding/alignment between successive histograms.
 122     memory += VP8LGetHistogramSize(cache_bits);
 123   }
 124   return set;
 125 }
 126
 127 // -----------------------------------------------------------------------------
 128
 129 void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo,
 130                                      const PixOrCopy* const v) {
 131   if (PixOrCopyIsLiteral(v)) {
 132     ++histo->alpha_[PixOrCopyLiteral(v, 3)];
 133     ++histo->red_[PixOrCopyLiteral(v, 2)];
 134     ++histo->literal_[PixOrCopyLiteral(v, 1)];
 135     ++histo->blue_[PixOrCopyLiteral(v, 0)];
 136   } else if (PixOrCopyIsCacheIdx(v)) {
 137     const int literal_ix =
 138         NUM_LITERAL_CODES + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
 139     ++histo->literal_[literal_ix];
 140   } else {
 141     int code, extra_bits;
 142     VP8LPrefixEncodeBits(PixOrCopyLength(v), &code, &extra_bits);
 143     ++histo->literal_[NUM_LITERAL_CODES + code];
 144     VP8LPrefixEncodeBits(PixOrCopyDistance(v), &code, &extra_bits);
 145     ++histo->distance_[code];
 146   }
 147 }
 148
 149 static WEBP_INLINE double BitsEntropyRefine(int nonzeros, int sum, int max_val,
 150                                             double retval) {
 151   double mix;
 152   if (nonzeros < 5) {
 153     if (nonzeros <= 1) {
 154       return 0;
 155     }
 156     // Two symbols, they will be 0 and 1 in a Huffman code.
 157     // Let's mix in a bit of entropy to favor good clustering when
 158     // distributions of these are combined.
 159     if (nonzeros == 2) {
 160       return 0.99 * sum + 0.01 * retval;
 161     }
 162     // No matter what the entropy says, we cannot be better than min_limit
 163     // with Huffman coding. I am mixing a bit of entropy into the
 164     // min_limit since it produces much better (~0.5 %) compression results
 165     // perhaps because of better entropy clustering.
 166     if (nonzeros == 3) {
 167       mix = 0.95;
 168     } else {
 169       mix = 0.7;  // nonzeros == 4.
 170     }
 171   } else {
 172     mix = 0.627;
 173   }
 174
 175   {
 176     double min_limit = 2 * sum - max_val;
 177     min_limit = mix * min_limit + (1.0 - mix) * retval;
 178     return (retval < min_limit) ? min_limit : retval;
 179   }
 180 }
 181
 182 static double BitsEntropy(const uint32_t* const array, int n) {
 183   double retval = 0.;
 184   uint32_t sum = 0;
 185   int nonzeros = 0;
 186   uint32_t max_val = 0;
 187   int i;
 188   for (i = 0; i < n; ++i) {
 189     if (array[i] != 0) {
 190       sum += array[i];
 191       ++nonzeros;
 192       retval -= VP8LFastSLog2(array[i]);
 193       if (max_val < array[i]) {
 194         max_val = array[i];
 195       }
 196     }
 197   }
 198   retval += VP8LFastSLog2(sum);
 199   return BitsEntropyRefine(nonzeros, sum, max_val, retval);
 200 }
 201
 202 static double BitsEntropyCombined(const uint32_t* const X,
 203                                   const uint32_t* const Y, int n) {
 204   double retval = 0.;
 205   int sum = 0;
 206   int nonzeros = 0;
 207   int max_val = 0;
 208   int i;
 209   for (i = 0; i < n; ++i) {
 210     const int xy = X[i] + Y[i];
 211     if (xy != 0) {
 212       sum += xy;
 213       ++nonzeros;
 214       retval -= VP8LFastSLog2(xy);
 215       if (max_val < xy) {
 216         max_val = xy;
 217       }
 218     }
 219   }
 220   retval += VP8LFastSLog2(sum);
 221   return BitsEntropyRefine(nonzeros, sum, max_val, retval);
 222 }
 223
 224 static double InitialHuffmanCost(void) {
 225   // Small bias because Huffman code length is typically not stored in
 226   // full length.
 227   static const int kHuffmanCodeOfHuffmanCodeSize = CODE_LENGTH_CODES * 3;
 228   static const double kSmallBias = 9.1;
 229   return kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
 230 }
 231
 232 // Finalize the Huffman cost based on streak numbers and length type (<3 or >=3)
 233 static double FinalHuffmanCost(const VP8LStreaks* const stats) {
 234   double retval = InitialHuffmanCost();
 235   retval += stats->counts[0] * 1.5625 + 0.234375 * stats->streaks[0][1];
 236   retval += stats->counts[1] * 2.578125 + 0.703125 * stats->streaks[1][1];
 237   retval += 1.796875 * stats->streaks[0][0];
 238   retval += 3.28125 * stats->streaks[1][0];
 239   return retval;
 240 }
 241
 242 // Trampolines
 243 static double HuffmanCost(const uint32_t* const population, int length) {
 244   const VP8LStreaks stats = VP8LHuffmanCostCount(population, length);
 245   return FinalHuffmanCost(&stats);
 246 }
 247
 248 static double HuffmanCostCombined(const uint32_t* const X,
 249                                   const uint32_t* const Y, int length) {
 250   const VP8LStreaks stats = VP8LHuffmanCostCombinedCount(X, Y, length);
 251   return FinalHuffmanCost(&stats);
 252 }
 253
 254 // Aggregated costs
 255 static double PopulationCost(const uint32_t* const population, int length) {
 256   return BitsEntropy(population, length) + HuffmanCost(population, length);
 257 }
 258
 259 static double GetCombinedEntropy(const uint32_t* const X,
 260                                  const uint32_t* const Y, int length) {
 261   return BitsEntropyCombined(X, Y, length) + HuffmanCostCombined(X, Y, length);
 262 }
 263
 264 // Estimates the Entropy + Huffman + other block overhead size cost.
 265 double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
 266   return
 267       PopulationCost(p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_))
 268       + PopulationCost(p->red_, NUM_LITERAL_CODES)
 269       + PopulationCost(p->blue_, NUM_LITERAL_CODES)
 270       + PopulationCost(p->alpha_, NUM_LITERAL_CODES)
 271       + PopulationCost(p->distance_, NUM_DISTANCE_CODES)
 272       + VP8LExtraCost(p->literal_ + NUM_LITERAL_CODES, NUM_LENGTH_CODES)
 273       + VP8LExtraCost(p->distance_, NUM_DISTANCE_CODES);
 274 }
 275
 276 double VP8LHistogramEstimateBitsBulk(const VP8LHistogram* const p) {
 277   return
 278       BitsEntropy(p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_))
 279       + BitsEntropy(p->red_, NUM_LITERAL_CODES)
 280       + BitsEntropy(p->blue_, NUM_LITERAL_CODES)
 281       + BitsEntropy(p->alpha_, NUM_LITERAL_CODES)
 282       + BitsEntropy(p->distance_, NUM_DISTANCE_CODES)
 283       + VP8LExtraCost(p->literal_ + NUM_LITERAL_CODES, NUM_LENGTH_CODES)
 284       + VP8LExtraCost(p->distance_, NUM_DISTANCE_CODES);
 285 }
 286
 287 // -----------------------------------------------------------------------------
 288 // Various histogram combine/cost-eval functions
 289
 290 static int GetCombinedHistogramEntropy(const VP8LHistogram* const a,
 291                                        const VP8LHistogram* const b,
 292                                        double cost_threshold,
 293                                        double* cost) {
 294   const int palette_code_bits = a->palette_code_bits_;
 295   assert(a->palette_code_bits_ == b->palette_code_bits_);
 296   *cost += GetCombinedEntropy(a->literal_, b->literal_,
 297                               VP8LHistogramNumCodes(palette_code_bits));
 298   *cost += VP8LExtraCostCombined(a->literal_ + NUM_LITERAL_CODES,
 299                                  b->literal_ + NUM_LITERAL_CODES,
 300                                  NUM_LENGTH_CODES);
 301   if (*cost > cost_threshold) return 0;
 302
 303   *cost += GetCombinedEntropy(a->red_, b->red_, NUM_LITERAL_CODES);
 304   if (*cost > cost_threshold) return 0;
 305
 306   *cost += GetCombinedEntropy(a->blue_, b->blue_, NUM_LITERAL_CODES);
 307   if (*cost > cost_threshold) return 0;
 308
 309   *cost += GetCombinedEntropy(a->alpha_, b->alpha_, NUM_LITERAL_CODES);
 310   if (*cost > cost_threshold) return 0;
 311
 312   *cost += GetCombinedEntropy(a->distance_, b->distance_, NUM_DISTANCE_CODES);
 313   *cost += VP8LExtraCostCombined(a->distance_, b->distance_,
 314                                  NUM_DISTANCE_CODES);
 315   if (*cost > cost_threshold) return 0;
 316
 317   return 1;
 318 }
 319
 320 // Performs out = a + b, computing the cost C(a+b) - C(a) - C(b) while comparing
 321 // to the threshold value 'cost_threshold'. The score returned is
 322 //  Score = C(a+b) - C(a) - C(b), where C(a) + C(b) is known and fixed.
 323 // Since the previous score passed is 'cost_threshold', we only need to compare
 324 // the partial cost against 'cost_threshold + C(a) + C(b)' to possibly bail-out
 325 // early.
 326 static double HistogramAddEval(const VP8LHistogram* const a,
 327                                const VP8LHistogram* const b,
 328                                VP8LHistogram* const out,
 329                                double cost_threshold) {
 330   double cost = 0;
 331   const double sum_cost = a->bit_cost_ + b->bit_cost_;
 332   cost_threshold += sum_cost;
 333
 334   if (GetCombinedHistogramEntropy(a, b, cost_threshold, &cost)) {
 335     VP8LHistogramAdd(a, b, out);
 336     out->bit_cost_ = cost;
 337     out->palette_code_bits_ = a->palette_code_bits_;
 338   }
 339
 340   return cost - sum_cost;
 341 }
 342
 343 // Same as HistogramAddEval(), except that the resulting histogram
 344 // is not stored. Only the cost C(a+b) - C(a) is evaluated. We omit
 345 // the term C(b) which is constant over all the evaluations.
 346 static double HistogramAddThresh(const VP8LHistogram* const a,
 347                                  const VP8LHistogram* const b,
 348                                  double cost_threshold) {
 349   double cost = -a->bit_cost_;
 350   GetCombinedHistogramEntropy(a, b, cost_threshold, &cost);
 351   return cost;
 352 }
 353
 354 // -----------------------------------------------------------------------------
 355
 356 // The structure to keep track of cost range for the three dominant entropy
 357 // symbols.
 358 // TODO(skal): Evaluate if float can be used here instead of double for
 359 // representing the entropy costs.
 360 typedef struct {
 361   double literal_max_;
 362   double literal_min_;
 363   double red_max_;
 364   double red_min_;
 365   double blue_max_;
 366   double blue_min_;
 367 } DominantCostRange;
 368
 369 static void DominantCostRangeInit(DominantCostRange* const c) {
 370   c->literal_max_ = 0.;
 371   c->literal_min_ = MAX_COST;
 372   c->red_max_ = 0.;
 373   c->red_min_ = MAX_COST;
 374   c->blue_max_ = 0.;
 375   c->blue_min_ = MAX_COST;
 376 }
 377
 378 static void UpdateDominantCostRange(
 379     const VP8LHistogram* const h, DominantCostRange* const c) {
 380   if (c->literal_max_ < h->literal_cost_) c->literal_max_ = h->literal_cost_;
 381   if (c->literal_min_ > h->literal_cost_) c->literal_min_ = h->literal_cost_;
 382   if (c->red_max_ < h->red_cost_) c->red_max_ = h->red_cost_;
 383   if (c->red_min_ > h->red_cost_) c->red_min_ = h->red_cost_;
 384   if (c->blue_max_ < h->blue_cost_) c->blue_max_ = h->blue_cost_;
 385   if (c->blue_min_ > h->blue_cost_) c->blue_min_ = h->blue_cost_;
 386 }
 387
 388 static void UpdateHistogramCost(VP8LHistogram* const h) {
 389   const double alpha_cost = PopulationCost(h->alpha_, NUM_LITERAL_CODES);
 390   const double distance_cost =
 391       PopulationCost(h->distance_, NUM_DISTANCE_CODES) +
 392       VP8LExtraCost(h->distance_, NUM_DISTANCE_CODES);
 393   const int num_codes = VP8LHistogramNumCodes(h->palette_code_bits_);
 394   h->literal_cost_ = PopulationCost(h->literal_, num_codes) +
 395                      VP8LExtraCost(h->literal_ + NUM_LITERAL_CODES,
 396                                    NUM_LENGTH_CODES);
 397   h->red_cost_ = PopulationCost(h->red_, NUM_LITERAL_CODES);
 398   h->blue_cost_ = PopulationCost(h->blue_, NUM_LITERAL_CODES);
 399   h->bit_cost_ = h->literal_cost_ + h->red_cost_ + h->blue_cost_ +
 400                  alpha_cost + distance_cost;
 401 }
 402
 403 static int GetBinIdForEntropy(double min, double max, double val) {
 404   const double range = max - min + 1e-6;
 405   const double delta = val - min;
 406   return (int)(NUM_PARTITIONS * delta / range);
 407 }
 408
 409 // TODO(vikasa): Evaluate, if there's any correlation between red & blue.
 410 static int GetHistoBinIndex(
 411     const VP8LHistogram* const h, const DominantCostRange* const c) {
 412   const int bin_id =
 413       GetBinIdForEntropy(c->blue_min_, c->blue_max_, h->blue_cost_) +
 414       NUM_PARTITIONS * GetBinIdForEntropy(c->red_min_, c->red_max_,
 415                                           h->red_cost_) +
 416       NUM_PARTITIONS * NUM_PARTITIONS * GetBinIdForEntropy(c->literal_min_,
 417                                                            c->literal_max_,
 418                                                            h->literal_cost_);
 419   assert(bin_id < BIN_SIZE);
 420   return bin_id;
 421 }
 422
 423 // Construct the histograms from backward references.
 424 static void HistogramBuild(
 425     int xsize, int histo_bits, const VP8LBackwardRefs* const backward_refs,
 426     VP8LHistogramSet* const image_histo) {
 427   int x = 0, y = 0;
 428   const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
 429   VP8LHistogram** const histograms = image_histo->histograms;
 430   VP8LRefsCursor c = VP8LRefsCursorInit(backward_refs);
 431   assert(histo_bits > 0);
 432   // Construct the Histo from a given backward references.
 433   while (VP8LRefsCursorOk(&c)) {
 434     const PixOrCopy* const v = c.cur_pos;
 435     const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
 436     VP8LHistogramAddSinglePixOrCopy(histograms[ix], v);
 437     x += PixOrCopyLength(v);
 438     while (x >= xsize) {
 439       x -= xsize;
 440       ++y;
 441     }
 442     VP8LRefsCursorNext(&c);
 443   }
 444 }
 445
 446 // Copies the histograms and computes its bit_cost.
 447 static void HistogramCopyAndAnalyze(
 448     VP8LHistogramSet* const orig_histo, VP8LHistogramSet* const image_histo) {
 449   int i;
 450   const int histo_size = orig_histo->size;
 451   VP8LHistogram** const orig_histograms = orig_histo->histograms;
 452   VP8LHistogram** const histograms = image_histo->histograms;
 453   for (i = 0; i < histo_size; ++i) {
 454     VP8LHistogram* const histo = orig_histograms[i];
 455     UpdateHistogramCost(histo);
 456     // Copy histograms from orig_histo[] to image_histo[].
 457     HistogramCopy(histo, histograms[i]);
 458   }
 459 }
 460
 461 // Partition histograms to different entropy bins for three dominant (literal,
 462 // red and blue) symbol costs and compute the histogram aggregate bit_cost.
 463 static void HistogramAnalyzeEntropyBin(
 464     VP8LHistogramSet* const image_histo, int16_t* const bin_map) {
 465   int i;
 466   VP8LHistogram** const histograms = image_histo->histograms;
 467   const int histo_size = image_histo->size;
 468   const int bin_depth = histo_size + 1;
 469   DominantCostRange cost_range;
 470   DominantCostRangeInit(&cost_range);
 471
 472   // Analyze the dominant (literal, red and blue) entropy costs.
 473   for (i = 0; i < histo_size; ++i) {
 474     VP8LHistogram* const histo = histograms[i];
 475     UpdateDominantCostRange(histo, &cost_range);
 476   }
 477
 478   // bin-hash histograms on three of the dominant (literal, red and blue)
 479   // symbol costs.
 480   for (i = 0; i < histo_size; ++i) {
 481     int num_histos;
 482     VP8LHistogram* const histo = histograms[i];
 483     const int16_t bin_id = (int16_t)GetHistoBinIndex(histo, &cost_range);
 484     const int bin_offset = bin_id * bin_depth;
 485     // bin_map[n][0] for every bin 'n' maintains the counter for the number of
 486     // histograms in that bin.
 487     // Get and increment the num_histos in that bin.
 488     num_histos = ++bin_map[bin_offset];
 489     assert(bin_offset + num_histos < bin_depth * BIN_SIZE);
 490     // Add histogram i'th index at num_histos (last) position in the bin_map.
 491     bin_map[bin_offset + num_histos] = i;
 492   }
 493 }
 494
 495 // Compact the histogram set by moving the valid one left in the set to the
 496 // head and moving the ones that have been merged to other histograms towards
 497 // the end.
 498 // TODO(vikasa): Evaluate if this method can be avoided by altering the code
 499 // logic of HistogramCombineEntropyBin main loop.
 500 static void HistogramCompactBins(VP8LHistogramSet* const image_histo) {
 501   int start = 0;
 502   int end = image_histo->size - 1;
 503   VP8LHistogram** const histograms = image_histo->histograms;
 504   while (start < end) {
 505     while (start <= end && histograms[start] != NULL &&
 506            histograms[start]->bit_cost_ != 0.) {
 507       ++start;
 508     }
 509     while (start <= end && histograms[end]->bit_cost_ == 0.) {
 510       histograms[end] = NULL;
 511       --end;
 512     }
 513     if (start < end) {
 514       assert(histograms[start] != NULL);
 515       assert(histograms[end] != NULL);
 516       HistogramCopy(histograms[end], histograms[start]);
 517       histograms[end] = NULL;
 518       --end;
 519     }
 520   }
 521   image_histo->size = end + 1;
 522 }
 523
 524 static void HistogramCombineEntropyBin(VP8LHistogramSet* const image_histo,
 525                                        VP8LHistogram* const histos,
 526                                        int16_t* const bin_map, int bin_depth,
 527                                        double combine_cost_factor) {
 528   int bin_id;
 529   VP8LHistogram* cur_combo = histos;
 530   VP8LHistogram** const histograms = image_histo->histograms;
 531
 532   for (bin_id = 0; bin_id < BIN_SIZE; ++bin_id) {
 533     const int bin_offset = bin_id * bin_depth;
 534     const int num_histos = bin_map[bin_offset];
 535     const int idx1 = bin_map[bin_offset + 1];
 536     int n;
 537     for (n = 2; n <= num_histos; ++n) {
 538       const int idx2 = bin_map[bin_offset + n];
 539       const double bit_cost_idx2 = histograms[idx2]->bit_cost_;
 540       if (bit_cost_idx2 > 0.) {
 541         const double bit_cost_thresh = -bit_cost_idx2 * combine_cost_factor;
 542         const double curr_cost_diff =
 543             HistogramAddEval(histograms[idx1], histograms[idx2],
 544                              cur_combo, bit_cost_thresh);
 545         if (curr_cost_diff < bit_cost_thresh) {
 546           HistogramCopy(cur_combo, histograms[idx1]);
 547           histograms[idx2]->bit_cost_ = 0.;
 548         }
 549       }
 550     }
 551   }
 552   HistogramCompactBins(image_histo);
 553 }
 554
 555 static uint32_t MyRand(uint32_t *seed) {
 556   *seed *= 16807U;
 557   if (*seed == 0) {
 558     *seed = 1;
 559   }
 560   return *seed;
 561 }
 562
 563 static void HistogramCombine(VP8LHistogramSet* const image_histo,
 564                              VP8LHistogramSet* const histos, int quality) {
 565   int iter;
 566   uint32_t seed = 0;
 567   int tries_with_no_success = 0;
 568   int image_histo_size = image_histo->size;
 569   const int iter_mult = (quality < 25) ? 2 : 2 + (quality - 25) / 8;
 570   const int outer_iters = image_histo_size * iter_mult;
 571   const int num_pairs = image_histo_size / 2;
 572   const int num_tries_no_success = outer_iters / 2;
 573   const int min_cluster_size = 2;
 574   VP8LHistogram** const histograms = image_histo->histograms;
 575   VP8LHistogram* cur_combo = histos->histograms[0];   // trial histogram
 576   VP8LHistogram* best_combo = histos->histograms[1];  // best histogram so far
 577
 578   // Collapse similar histograms in 'image_histo'.
 579   for (iter = 0;
 580        iter < outer_iters && image_histo_size >= min_cluster_size;
 581        ++iter) {
 582     double best_cost_diff = 0.;
 583     int best_idx1 = -1, best_idx2 = 1;
 584     int j;
 585     const int num_tries =
 586         (num_pairs < image_histo_size) ? num_pairs : image_histo_size;
 587     seed += iter;
 588     for (j = 0; j < num_tries; ++j) {
 589       double curr_cost_diff;
 590       // Choose two histograms at random and try to combine them.
 591       const uint32_t idx1 = MyRand(&seed) % image_histo_size;
 592       const uint32_t tmp = (j & 7) + 1;
 593       const uint32_t diff =
 594           (tmp < 3) ? tmp : MyRand(&seed) % (image_histo_size - 1);
 595       const uint32_t idx2 = (idx1 + diff + 1) % image_histo_size;
 596       if (idx1 == idx2) {
 597         continue;
 598       }
 599
 600       // Calculate cost reduction on combining.
 601       curr_cost_diff = HistogramAddEval(histograms[idx1], histograms[idx2],
 602                                         cur_combo, best_cost_diff);
 603       if (curr_cost_diff < best_cost_diff) {    // found a better pair?
 604         {     // swap cur/best combo histograms
 605           VP8LHistogram* const tmp_histo = cur_combo;
 606           cur_combo = best_combo;
 607           best_combo = tmp_histo;
 608         }
 609         best_cost_diff = curr_cost_diff;
 610         best_idx1 = idx1;
 611         best_idx2 = idx2;
 612       }
 613     }
 614
 615     if (best_idx1 >= 0) {
 616       HistogramCopy(best_combo, histograms[best_idx1]);
 617       // swap best_idx2 slot with last one (which is now unused)
 618       --image_histo_size;
 619       if (best_idx2 != image_histo_size) {
 620         HistogramCopy(histograms[image_histo_size], histograms[best_idx2]);
 621         histograms[image_histo_size] = NULL;
 622       }
 623       tries_with_no_success = 0;
 624     }
 625     if (++tries_with_no_success >= num_tries_no_success) {
 626       break;
 627     }
 628   }
 629   image_histo->size = image_histo_size;
 630 }
 631
 632 // -----------------------------------------------------------------------------
 633 // Histogram refinement
 634
 635 // Find the best 'out' histogram for each of the 'in' histograms.
 636 // Note: we assume that out[]->bit_cost_ is already up-to-date.
 637 static void HistogramRemap(const VP8LHistogramSet* const orig_histo,
 638                            const VP8LHistogramSet* const image_histo,
 639                            uint16_t* const symbols) {
 640   int i;
 641   VP8LHistogram** const orig_histograms = orig_histo->histograms;
 642   VP8LHistogram** const histograms = image_histo->histograms;
 643   for (i = 0; i < orig_histo->size; ++i) {
 644     int best_out = 0;
 645     double best_bits =
 646         HistogramAddThresh(histograms[0], orig_histograms[i], MAX_COST);
 647     int k;
 648     for (k = 1; k < image_histo->size; ++k) {
 649       const double cur_bits =
 650           HistogramAddThresh(histograms[k], orig_histograms[i], best_bits);
 651       if (cur_bits < best_bits) {
 652         best_bits = cur_bits;
 653         best_out = k;
 654       }
 655     }
 656     symbols[i] = best_out;
 657   }
 658
 659   // Recompute each out based on raw and symbols.
 660   for (i = 0; i < image_histo->size; ++i) {
 661     HistogramClear(histograms[i]);
 662   }
 663
 664   for (i = 0; i < orig_histo->size; ++i) {
 665     const int idx = symbols[i];
 666     VP8LHistogramAdd(orig_histograms[i], histograms[idx], histograms[idx]);
 667   }
 668 }
 669
 670 static double GetCombineCostFactor(int histo_size, int quality) {
 671   double combine_cost_factor = 0.16;
 672   if (histo_size > 256) combine_cost_factor /= 2.;
 673   if (histo_size > 512) combine_cost_factor /= 2.;
 674   if (histo_size > 1024) combine_cost_factor /= 2.;
 675   if (quality <= 50) combine_cost_factor /= 2.;
 676   return combine_cost_factor;
 677 }
 678
 679 int VP8LGetHistoImageSymbols(int xsize, int ysize,
 680                              const VP8LBackwardRefs* const refs,
 681                              int quality, int histo_bits, int cache_bits,
 682                              VP8LHistogramSet* const image_histo,
 683                              uint16_t* const histogram_symbols) {
 684   int ok = 0;
 685   const int histo_xsize = histo_bits ? VP8LSubSampleSize(xsize, histo_bits) : 1;
 686   const int histo_ysize = histo_bits ? VP8LSubSampleSize(ysize, histo_bits) : 1;
 687   const int image_histo_raw_size = histo_xsize * histo_ysize;
 688
 689   // The bin_map for every bin follows following semantics:
 690   // bin_map[n][0] = num_histo; // The number of histograms in that bin.
 691   // bin_map[n][1] = index of first histogram in that bin;
 692   // bin_map[n][num_histo] = index of last histogram in that bin;
 693   // bin_map[n][num_histo + 1] ... bin_map[n][bin_depth - 1] = un-used indices.
 694   const int bin_depth = image_histo_raw_size + 1;
 695   int16_t* bin_map = NULL;
 696   VP8LHistogramSet* const histos = VP8LAllocateHistogramSet(2, cache_bits);
 697   VP8LHistogramSet* const orig_histo =
 698       VP8LAllocateHistogramSet(image_histo_raw_size, cache_bits);
 699
 700   if (orig_histo == NULL || histos == NULL) {
 701     goto Error;
 702   }
 703
 704   // Don't attempt linear bin-partition heuristic for:
 705   // histograms of small sizes, as bin_map will be very sparse and;
 706   // Higher qualities (> 90), to preserve the compression gains at those
 707   // quality settings.
 708   if (orig_histo->size > 2 * BIN_SIZE && quality < 90) {
 709     const int bin_map_size = bin_depth * BIN_SIZE;
 710     bin_map = (int16_t*)WebPSafeCalloc(bin_map_size, sizeof(*bin_map));
 711     if (bin_map == NULL) goto Error;
 712   }
 713
 714   // Construct the histograms from backward references.
 715   HistogramBuild(xsize, histo_bits, refs, orig_histo);
 716   // Copies the histograms and computes its bit_cost.
 717   HistogramCopyAndAnalyze(orig_histo, image_histo);
 718
 719   if (bin_map != NULL) {
 720     const double combine_cost_factor =
 721         GetCombineCostFactor(image_histo_raw_size, quality);
 722     HistogramAnalyzeEntropyBin(orig_histo, bin_map);
 723     // Collapse histograms with similar entropy.
 724     HistogramCombineEntropyBin(image_histo, histos->histograms[0],
 725                                bin_map, bin_depth, combine_cost_factor);
 726   }
 727
 728   // Collapse similar histograms by random histogram-pair compares.
 729   HistogramCombine(image_histo, histos, quality);
 730
 731   // Find the optimal map from original histograms to the final ones.
 732   HistogramRemap(orig_histo, image_histo, histogram_symbols);
 733
 734   ok = 1;
 735
 736  Error:
 737   WebPSafeFree(bin_map);
 738   VP8LFreeHistogramSet(orig_histo);
 739   VP8LFreeHistogramSet(histos);
 740   return ok;
 741 }