histogram_enc.c 36.1 KB
Newer Older
wester committed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990
// 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_enc.h"
#include "./histogram_enc.h"
#include "../dsp/lossless.h"
#include "../dsp/lossless_common.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)
// 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 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 int histo_size = VP8LGetHistogramSize(cache_bits);
  const size_t total_size =
      sizeof(*set) + size * (sizeof(*set->histograms) +
      histo_size + WEBP_ALIGN_CST);
  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) {
    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));
    VP8LHistogramInit(set->histograms[i], cache_bits);
    memory += histo_size;
  }
  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];
  }
}

// -----------------------------------------------------------------------------
// Entropy-related functions.

static WEBP_INLINE double BitsEntropyRefine(const VP8LBitEntropy* entropy) {
  double 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 0.99 * entropy->sum + 0.01 * 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 = 0.95;
    } else {
      mix = 0.7;  // nonzeros == 4.
    }
  } else {
    mix = 0.627;
  }

  {
    double min_limit = 2 * entropy->sum - entropy->max_val;
    min_limit = mix * min_limit + (1.0 - mix) * entropy->entropy;
    return (entropy->entropy < min_limit) ? min_limit : entropy->entropy;
  }
}

double VP8LBitsEntropy(const uint32_t* const array, int n,
                       uint32_t* const trivial_symbol) {
  VP8LBitEntropy entropy;
  VP8LBitsEntropyUnrefined(array, n, &entropy);
  if (trivial_symbol != NULL) {
    *trivial_symbol =
        (entropy.nonzeros == 1) ? entropy.nonzero_code : VP8L_NON_TRIVIAL_SYM;
  }

  return BitsEntropyRefine(&entropy);
}

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) {
  // The constants in this function are experimental and got rounded from
  // their original values in 1/8 when switched to 1/1024.
  double retval = InitialHuffmanCost();
  // Second coefficient: Many zeros in the histogram are covered efficiently
  // by a run-length encode. Originally 2/8.
  retval += stats->counts[0] * 1.5625 + 0.234375 * stats->streaks[0][1];
  // Second coefficient: Constant values are encoded less efficiently, but still
  // RLE'ed. Originally 6/8.
  retval += stats->counts[1] * 2.578125 + 0.703125 * stats->streaks[1][1];
  // 0s are usually encoded more efficiently than non-0s.
  // Originally 15/8.
  retval += 1.796875 * stats->streaks[0][0];
  // Originally 26/8.
  retval += 3.28125 * 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 double PopulationCost(const uint32_t* const population, int length,
                             uint32_t* const trivial_sym) {
  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;
  }

  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 double GetCombinedEntropy(const uint32_t* const X,
                                             const uint32_t* const Y,
                                             int length, 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;
    VP8LGetCombinedEntropyUnrefined(X, Y, length, &bit_entropy, &stats);

    return BitsEntropyRefine(&bit_entropy) + FinalHuffmanCost(&stats);
  }
}

// Estimates the Entropy + Huffman + other block overhead size cost.
double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
  return
      PopulationCost(
          p->literal_, VP8LHistogramNumCodes(p->palette_code_bits_), NULL)
      + PopulationCost(p->red_, NUM_LITERAL_CODES, NULL)
      + PopulationCost(p->blue_, NUM_LITERAL_CODES, NULL)
      + PopulationCost(p->alpha_, NUM_LITERAL_CODES, NULL)
      + PopulationCost(p->distance_, NUM_DISTANCE_CODES, NULL)
      + 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_;
  int trivial_at_end = 0;
  assert(a->palette_code_bits_ == b->palette_code_bits_);
  *cost += GetCombinedEntropy(a->literal_, b->literal_,
                              VP8LHistogramNumCodes(palette_code_bits), 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, trivial_at_end);
  if (*cost > cost_threshold) return 0;

  *cost +=
      GetCombinedEntropy(a->blue_, b->blue_, NUM_LITERAL_CODES, trivial_at_end);
  if (*cost > cost_threshold) return 0;

  *cost += GetCombinedEntropy(a->alpha_, b->alpha_, NUM_LITERAL_CODES,
                              trivial_at_end);
  if (*cost > cost_threshold) return 0;

  *cost +=
      GetCombinedEntropy(a->distance_, b->distance_, NUM_DISTANCE_CODES, 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 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)) {
    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 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) {
  uint32_t alpha_sym, red_sym, blue_sym;
  const double alpha_cost =
      PopulationCost(h->alpha_, NUM_LITERAL_CODES, &alpha_sym);
  const double distance_cost =
      PopulationCost(h->distance_, NUM_DISTANCE_CODES, NULL) +
      VP8LExtraCost(h->distance_, NUM_DISTANCE_CODES);
  const int num_codes = VP8LHistogramNumCodes(h->palette_code_bits_);
  h->literal_cost_ = PopulationCost(h->literal_, num_codes, NULL) +
                     VP8LExtraCost(h->literal_ + NUM_LITERAL_CODES,
                                   NUM_LENGTH_CODES);
  h->red_cost_ = PopulationCost(h->red_, NUM_LITERAL_CODES, &red_sym);
  h->blue_cost_ = PopulationCost(h->blue_, NUM_LITERAL_CODES, &blue_sym);
  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(double min, double max, double val) {
  const double range = max - min;
  if (range > 0.) {
    const double 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);
  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,
                                       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) {
    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] = GetHistoBinIndex(histograms[i], &cost_range, low_effort);
  }
}

// Compact image_histo[] by merging some histograms with same bin_id together if
// it's advantageous.
static VP8LHistogram* HistogramCombineEntropyBin(
    VP8LHistogramSet* const image_histo,
    VP8LHistogram* cur_combo,
    const uint16_t* const bin_map, int bin_map_size, int num_bins,
    double combine_cost_factor, int low_effort) {
  VP8LHistogram** const histograms = image_histo->histograms;
  int idx;
  // Work in-place: processed histograms are put at the beginning of
  // image_histo[]. At the end, we just have to truncate the array.
  int size = 0;
  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;
  }

  for (idx = 0; idx < bin_map_size; ++idx) {
    const int bin_id = bin_map[idx];
    const int first = bin_info[bin_id].first;
    assert(size <= idx);
    if (first == -1) {
      // just move histogram #idx to its final position
      histograms[size] = histograms[idx];
      bin_info[bin_id].first = size++;
    } else if (low_effort) {
      HistogramAdd(histograms[idx], histograms[first], histograms[first]);
    } else {
      // try to merge #idx into #first (both share the same bin_id)
      const double bit_cost = histograms[idx]->bit_cost_;
      const double bit_cost_thresh = -bit_cost * combine_cost_factor;
      const double 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]);
        } else {
          histograms[size++] = histograms[idx];
          ++bin_info[bin_id].num_combine_failures;
        }
      } else {
        histograms[size++] = histograms[idx];
      }
    }
  }
  image_histo->size = size;
  if (low_effort) {
    // for low_effort case, update the final cost when everything is merged
    for (idx = 0; idx < size; ++idx) {
      UpdateHistogramCost(histograms[idx]);
    }
  }
  return cur_combo;
}

static uint32_t MyRand(uint32_t* const seed) {
  *seed = (*seed * 16807ull) & 0xffffffffu;
  if (*seed == 0) {
    *seed = 1;
  }
  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;
  double cost_diff;
  double cost_combo;
} HistogramPair;

typedef struct {
  HistogramPair* queue;
  int size;
  int max_size;
} HistoQueue;

static int HistoQueueInit(HistoQueue* const histo_queue, const int max_index) {
  histo_queue->size = 0;
  // max_index^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:
  // - max_index*(max_index-1)/2 (the first two for loops)
  // - max_index - 1 in the last for loop at the first iteration of the while
  //   loop, max_index - 2 at the second iteration ... therefore
  //   max_index*(max_index-1)/2 overall too
  histo_queue->max_size = max_index * max_index;
  // 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);
}

static void SwapHistogramPairs(HistogramPair *p1,
                               HistogramPair *p2) {
  const HistogramPair tmp = *p1;
  *p1 = *p2;
  *p2 = tmp;
}

// Given a valid priority queue in range [0, queue_size) this function checks
// whether histo_queue[queue_size] should be accepted and swaps it with the
// front if it is smaller. Otherwise, it leaves it as is.
static void UpdateQueueFront(HistoQueue* const histo_queue) {
  if (histo_queue->queue[histo_queue->size].cost_diff >= 0) return;

  if (histo_queue->queue[histo_queue->size].cost_diff <
      histo_queue->queue[0].cost_diff) {
    SwapHistogramPairs(histo_queue->queue,
                       histo_queue->queue + histo_queue->size);
  }
  ++histo_queue->size;

  // We cannot add more elements than the capacity.
  // The allocation adds an extra element to the official capacity so that
  // histo_queue->queue[histo_queue->max_size] is read/written within bound.
  assert(histo_queue->size <= histo_queue->max_size);
}

// -----------------------------------------------------------------------------

static void PreparePair(VP8LHistogram** histograms, int idx1, int idx2,
                        HistogramPair* const pair) {
  VP8LHistogram* h1;
  VP8LHistogram* h2;
  double sum_cost;

  if (idx1 > idx2) {
    const int tmp = idx2;
    idx2 = idx1;
    idx1 = tmp;
  }
  pair->idx1 = idx1;
  pair->idx2 = idx2;
  h1 = histograms[idx1];
  h2 = histograms[idx2];
  sum_cost = h1->bit_cost_ + h2->bit_cost_;
  pair->cost_combo = 0.;
  GetCombinedHistogramEntropy(h1, h2, sum_cost, &pair->cost_combo);
  pair->cost_diff = pair->cost_combo - sum_cost;
}

// Combines histograms by continuously choosing the one with the highest cost
// reduction.
static int HistogramCombineGreedy(VP8LHistogramSet* const image_histo) {
  int ok = 0;
  int image_histo_size = image_histo->size;
  int i, j;
  VP8LHistogram** const histograms = image_histo->histograms;
  // Indexes of remaining histograms.
  int* const clusters =
      (int*)WebPSafeMalloc(image_histo_size, sizeof(*clusters));
  // Priority queue of histogram pairs.
  HistoQueue histo_queue;

  if (!HistoQueueInit(&histo_queue, image_histo_size) || clusters == NULL) {
    goto End;
  }

  for (i = 0; i < image_histo_size; ++i) {
    // Initialize clusters indexes.
    clusters[i] = i;
    for (j = i + 1; j < image_histo_size; ++j) {
      // Initialize positions array.
      PreparePair(histograms, i, j, &histo_queue.queue[histo_queue.size]);
      UpdateQueueFront(&histo_queue);
    }
  }

  while (image_histo_size > 1 && histo_queue.size > 0) {
    HistogramPair* copy_to;
    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.
    for (i = 0; i + 1 < image_histo_size; ++i) {
      if (clusters[i] >= idx2) {
        clusters[i] = clusters[i + 1];
      }
    }
    --image_histo_size;

    // Remove pairs intersecting the just combined best pair. This will
    // therefore pop the head of the queue.
    copy_to = histo_queue.queue;
    for (i = 0; i < histo_queue.size; ++i) {
      HistogramPair* const p = histo_queue.queue + i;
      if (p->idx1 == idx1 || p->idx2 == idx1 ||
          p->idx1 == idx2 || p->idx2 == idx2) {
        // Do not copy the invalid pair.
        continue;
      }
      if (p->cost_diff < histo_queue.queue[0].cost_diff) {
        // Replace the top of the queue if we found better.
        SwapHistogramPairs(histo_queue.queue, p);
      }
      SwapHistogramPairs(copy_to, p);
      ++copy_to;
    }
    histo_queue.size = (int)(copy_to - histo_queue.queue);

    // Push new pairs formed with combined histogram to the queue.
    for (i = 0; i < image_histo_size; ++i) {
      if (clusters[i] != idx1) {
        PreparePair(histograms, idx1, clusters[i],
                    &histo_queue.queue[histo_queue.size]);
        UpdateQueueFront(&histo_queue);
      }
    }
  }
  // Move remaining histograms to the beginning of the array.
  for (i = 0; i < image_histo_size; ++i) {
    if (i != clusters[i]) {  // swap the two histograms
      HistogramSwap(&histograms[i], &histograms[clusters[i]]);
    }
  }

  image_histo->size = image_histo_size;
  ok = 1;

 End:
  WebPSafeFree(clusters);
  HistoQueueClear(&histo_queue);
  return ok;
}

static void HistogramCombineStochastic(VP8LHistogramSet* const image_histo,
                                       VP8LHistogram* tmp_histo,
                                       VP8LHistogram* best_combo,
                                       int quality, int min_cluster_size) {
  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;
  int idx2_max = image_histo_size - 1;
  int do_brute_dorce = 0;
  VP8LHistogram** const histograms = image_histo->histograms;

  // Collapse similar histograms in 'image_histo'.
  ++min_cluster_size;
  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;
    int num_tries =
        (num_pairs < image_histo_size) ? num_pairs : image_histo_size;
    // Use a brute force approach if:
    // - stochastic has not worked for a while and
    // - if the number of iterations for brute force is less than the number of
    // iterations if we never find a match ever again stochastically (hence
    // num_tries times the number of remaining outer iterations).
    do_brute_dorce =
        (tries_with_no_success > 10) &&
        (idx2_max * (idx2_max + 1) < 2 * num_tries * (outer_iters - iter));
    if (do_brute_dorce) num_tries = idx2_max;

    seed += iter;
    for (j = 0; j < num_tries; ++j) {
      double curr_cost_diff;
      // Choose two histograms at random and try to combine them.
      uint32_t idx1, idx2;
      if (do_brute_dorce) {
        // Use a brute force approach.
        idx1 = (uint32_t)j;
        idx2 = (uint32_t)idx2_max;
      } else {
        const uint32_t tmp = (j & 7) + 1;
        const uint32_t diff =
            (tmp < 3) ? tmp : MyRand(&seed) % (image_histo_size - 1);
        idx1 = MyRand(&seed) % image_histo_size;
        idx2 = (idx1 + diff + 1) % image_histo_size;
        if (idx1 == idx2) {
          continue;
        }
      }

      // Calculate cost reduction on combining.
      curr_cost_diff = HistogramAddEval(histograms[idx1], histograms[idx2],
                                        tmp_histo, best_cost_diff);
      if (curr_cost_diff < best_cost_diff) {  // found a better pair?
        HistogramSwap(&best_combo, &tmp_histo);
        best_cost_diff = curr_cost_diff;
        best_idx1 = idx1;
        best_idx2 = idx2;
      }
    }
    if (do_brute_dorce) --idx2_max;

    if (best_idx1 >= 0) {
      HistogramSwap(&best_combo, &histograms[best_idx1]);
      // swap best_idx2 slot with last one (which is now unused)
      --image_histo_size;
      if (idx2_max >= image_histo_size) idx2_max = image_histo_size - 1;
      if (best_idx2 != image_histo_size) {
        HistogramSwap(&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 || idx2_max == 0) {
      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 in,
                           const 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 = in->size;
  const int out_size = out->size;
  if (out_size > 1) {
    for (i = 0; i < in_size; ++i) {
      int best_out = 0;
      double best_bits = MAX_COST;
      int k;
      for (k = 0; k < out_size; ++k) {
        const double 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.
  for (i = 0; i < out_size; ++i) {
    HistogramClear(out_histo[i]);
  }

  for (i = 0; i < in_size; ++i) {
    const int idx = symbols[i];
    HistogramAdd(in_histo[i], out_histo[idx], out_histo[idx]);
  }
}

static double GetCombineCostFactor(int histo_size, int quality) {
  double combine_cost_factor = 0.16;
  if (quality < 90) {
    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 low_effort,
                             int histo_bits, int cache_bits,
                             VP8LHistogramSet* const image_histo,
                             VP8LHistogramSet* const tmp_histos,
                             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;
  VP8LHistogramSet* const orig_histo =
      VP8LAllocateHistogramSet(image_histo_raw_size, cache_bits);
  VP8LHistogram* cur_combo;
  // 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;
  const int entropy_combine =
      (orig_histo->size > entropy_combine_num_bins * 2) && (quality < 100);

  if (orig_histo == 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);

  cur_combo = tmp_histos->histograms[1];  // pick up working slot
  if (entropy_combine) {
    const int bin_map_size = orig_histo->size;
    // Reuse histogram_symbols storage. By definition, it's guaranteed to be ok.
    uint16_t* const bin_map = histogram_symbols;
    const double combine_cost_factor =
        GetCombineCostFactor(image_histo_raw_size, quality);

    HistogramAnalyzeEntropyBin(orig_histo, bin_map, low_effort);
    // Collapse histograms with similar entropy.
    cur_combo = HistogramCombineEntropyBin(image_histo, cur_combo,
                                           bin_map, bin_map_size,
                                           entropy_combine_num_bins,
                                           combine_cost_factor, low_effort);
  }

  // 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));
    HistogramCombineStochastic(image_histo, tmp_histos->histograms[0],
                               cur_combo, quality, threshold_size);
    if ((image_histo->size <= threshold_size) &&
        !HistogramCombineGreedy(image_histo)) {
      goto Error;
    }
  }

  // TODO(vikasa): Optimize HistogramRemap for low-effort compression mode also.
  // Find the optimal map from original histograms to the final ones.
  HistogramRemap(orig_histo, image_histo, histogram_symbols);

  ok = 1;

 Error:
  VP8LFreeHistogramSet(orig_histo);
  return ok;
}