backward_references.c 29.5 KB
Newer Older
a  
Kai Westerkamp 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
// 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)
//

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

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

#define VALUES_IN_BYTE 256

#define HASH_BITS 18
#define HASH_SIZE (1 << HASH_BITS)
#define HASH_MULTIPLIER (0xc6a4a7935bd1e995ULL)

// 1M window (4M bytes) minus 120 special codes for short distances.
#define WINDOW_SIZE ((1 << 20) - 120)

// Bounds for the match length.
#define MIN_LENGTH 2
#define MAX_LENGTH 4096

typedef struct {
  // Stores the most recently added position with the given hash value.
  int32_t hash_to_first_index_[HASH_SIZE];
  // chain_[pos] stores the previous position with the same hash value
  // for every pixel in the image.
  int32_t* chain_;
} HashChain;

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

static const uint8_t plane_to_code_lut[128] = {
 96,   73,  55,  39,  23,  13,   5,  1,  255, 255, 255, 255, 255, 255, 255, 255,
 101,  78,  58,  42,  26,  16,   8,  2,    0,   3,  9,   17,  27,  43,  59,  79,
 102,  86,  62,  46,  32,  20,  10,  6,    4,   7,  11,  21,  33,  47,  63,  87,
 105,  90,  70,  52,  37,  28,  18,  14,  12,  15,  19,  29,  38,  53,  71,  91,
 110,  99,  82,  66,  48,  35,  30,  24,  22,  25,  31,  36,  49,  67,  83, 100,
 115, 108,  94,  76,  64,  50,  44,  40,  34,  41,  45,  51,  65,  77,  95, 109,
 118, 113, 103,  92,  80,  68,  60,  56,  54,  57,  61,  69,  81,  93, 104, 114,
 119, 116, 111, 106,  97,  88,  84,  74,  72,  75,  85,  89,  98, 107, 112, 117
};

static int DistanceToPlaneCode(int xsize, int dist) {
  const int yoffset = dist / xsize;
  const int xoffset = dist - yoffset * xsize;
  if (xoffset <= 8 && yoffset < 8) {
    return plane_to_code_lut[yoffset * 16 + 8 - xoffset] + 1;
  } else if (xoffset > xsize - 8 && yoffset < 7) {
    return plane_to_code_lut[(yoffset + 1) * 16 + 8 + (xsize - xoffset)] + 1;
  }
  return dist + 120;
}

static WEBP_INLINE int FindMatchLength(const uint32_t* const array1,
                                       const uint32_t* const array2,
                                       const int max_limit) {
  int match_len = 0;
  while (match_len < max_limit && array1[match_len] == array2[match_len]) {
    ++match_len;
  }
  return match_len;
}

// -----------------------------------------------------------------------------
//  VP8LBackwardRefs

void VP8LInitBackwardRefs(VP8LBackwardRefs* const refs) {
  if (refs != NULL) {
    refs->refs = NULL;
    refs->size = 0;
    refs->max_size = 0;
  }
}

void VP8LClearBackwardRefs(VP8LBackwardRefs* const refs) {
  if (refs != NULL) {
    free(refs->refs);
    VP8LInitBackwardRefs(refs);
  }
}

int VP8LBackwardRefsAlloc(VP8LBackwardRefs* const refs, int max_size) {
  assert(refs != NULL);
  refs->size = 0;
  refs->max_size = 0;
  refs->refs = (PixOrCopy*)WebPSafeMalloc((uint64_t)max_size,
                                          sizeof(*refs->refs));
  if (refs->refs == NULL) return 0;
  refs->max_size = max_size;
  return 1;
}

// -----------------------------------------------------------------------------
// Hash chains

static WEBP_INLINE uint64_t GetPixPairHash64(const uint32_t* const argb) {
  uint64_t key = ((uint64_t)(argb[1]) << 32) | argb[0];
  key = (key * HASH_MULTIPLIER) >> (64 - HASH_BITS);
  return key;
}

static int HashChainInit(HashChain* const p, int size) {
  int i;
  p->chain_ = (int*)WebPSafeMalloc((uint64_t)size, sizeof(*p->chain_));
  if (p->chain_ == NULL) {
    return 0;
  }
  for (i = 0; i < size; ++i) {
    p->chain_[i] = -1;
  }
  for (i = 0; i < HASH_SIZE; ++i) {
    p->hash_to_first_index_[i] = -1;
  }
  return 1;
}

static void HashChainDelete(HashChain* const p) {
  if (p != NULL) {
    free(p->chain_);
    free(p);
  }
}

// Insertion of two pixels at a time.
static void HashChainInsert(HashChain* const p,
                            const uint32_t* const argb, int pos) {
  const uint64_t hash_code = GetPixPairHash64(argb);
  p->chain_[pos] = p->hash_to_first_index_[hash_code];
  p->hash_to_first_index_[hash_code] = pos;
}

static void GetParamsForHashChainFindCopy(int quality, int xsize,
                                          int cache_bits, int* window_size,
                                          int* iter_pos, int* iter_limit) {
  const int iter_mult = (quality < 27) ? 1 : 1 + ((quality - 27) >> 4);
  const int iter_neg = -iter_mult * (quality >> 1);
  // Limit the backward-ref window size for lower qualities.
  const int max_window_size = (quality > 50) ? WINDOW_SIZE
                            : (quality > 25) ? (xsize << 8)
                            : (xsize << 4);
  assert(xsize > 0);
  *window_size = (max_window_size > WINDOW_SIZE) ? WINDOW_SIZE
               : max_window_size;
  *iter_pos = 8 + (quality >> 3);
  // For lower entropy images, the rigourous search loop in HashChainFindCopy
  // can be relaxed.
  *iter_limit = (cache_bits > 0) ? iter_neg : iter_neg / 2;
}

static int HashChainFindCopy(const HashChain* const p,
                             int base_position, int xsize_signed,
                             const uint32_t* const argb, int maxlen,
                             int window_size, int iter_pos, int iter_limit,
                             int* const distance_ptr,
                             int* const length_ptr) {
  const uint32_t* const argb_start = argb + base_position;
  uint64_t best_val = 0;
  uint32_t best_length = 1;
  uint32_t best_distance = 0;
  const uint32_t xsize = (uint32_t)xsize_signed;
  const int min_pos =
      (base_position > window_size) ? base_position - window_size : 0;
  int pos;
  assert(xsize > 0);
  for (pos = p->hash_to_first_index_[GetPixPairHash64(argb_start)];
       pos >= min_pos;
       pos = p->chain_[pos]) {
    uint64_t val;
    uint32_t curr_length;
    uint32_t distance;
    if (iter_pos < 0) {
      if (iter_pos < iter_limit || best_val >= 0xff0000) {
        break;
      }
    }
    --iter_pos;
    if (argb[pos + best_length - 1] != argb_start[best_length - 1]) {
      continue;
    }
    curr_length = FindMatchLength(argb + pos, argb_start, maxlen);
    if (curr_length < best_length) {
      continue;
    }
    distance = (uint32_t)(base_position - pos);
    val = curr_length << 16;
    // Favoring 2d locality here gives savings for certain images.
    if (distance < 9 * xsize) {
      const uint32_t y = distance / xsize;
      uint32_t x = distance % xsize;
      if (x > (xsize >> 1)) {
        x = xsize - x;
      }
      if (x <= 7) {
        val += 9 * 9 + 9 * 9;
        val -= y * y + x * x;
      }
    }
    if (best_val < val) {
      best_val = val;
      best_length = curr_length;
      best_distance = distance;
      if (curr_length >= MAX_LENGTH) {
        break;
      }
      if ((best_distance == 1 || distance == xsize) &&
          best_length >= 128) {
        break;
      }
    }
  }
  *distance_ptr = (int)best_distance;
  *length_ptr = best_length;
  return (best_length >= MIN_LENGTH);
}

static WEBP_INLINE void PushBackCopy(VP8LBackwardRefs* const refs, int length) {
  int size = refs->size;
  while (length >= MAX_LENGTH) {
    refs->refs[size++] = PixOrCopyCreateCopy(1, MAX_LENGTH);
    length -= MAX_LENGTH;
  }
  if (length > 0) {
    refs->refs[size++] = PixOrCopyCreateCopy(1, length);
  }
  refs->size = size;
}

static void BackwardReferencesRle(int xsize, int ysize,
                                  const uint32_t* const argb,
                                  VP8LBackwardRefs* const refs) {
  const int pix_count = xsize * ysize;
  int match_len = 0;
  int i;
  refs->size = 0;
  PushBackCopy(refs, match_len);    // i=0 case
  refs->refs[refs->size++] = PixOrCopyCreateLiteral(argb[0]);
  for (i = 1; i < pix_count; ++i) {
    if (argb[i] == argb[i - 1]) {
      ++match_len;
    } else {
      PushBackCopy(refs, match_len);
      match_len = 0;
      refs->refs[refs->size++] = PixOrCopyCreateLiteral(argb[i]);
    }
  }
  PushBackCopy(refs, match_len);
}

static int BackwardReferencesHashChain(int xsize, int ysize,
                                       const uint32_t* const argb,
                                       int cache_bits, int quality,
                                       VP8LBackwardRefs* const refs) {
  int i;
  int ok = 0;
  int cc_init = 0;
  const int use_color_cache = (cache_bits > 0);
  const int pix_count = xsize * ysize;
  HashChain* const hash_chain = (HashChain*)malloc(sizeof(*hash_chain));
  VP8LColorCache hashers;
  int window_size = WINDOW_SIZE;
  int iter_pos = 1;
  int iter_limit = -1;

  if (hash_chain == NULL) return 0;
  if (use_color_cache) {
    cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    if (!cc_init) goto Error;
  }

  if (!HashChainInit(hash_chain, pix_count)) goto Error;

  refs->size = 0;
  GetParamsForHashChainFindCopy(quality, xsize, cache_bits,
                                &window_size, &iter_pos, &iter_limit);
  for (i = 0; i < pix_count; ) {
    // Alternative#1: Code the pixels starting at 'i' using backward reference.
    int offset = 0;
    int len = 0;
    if (i < pix_count - 1) {  // FindCopy(i,..) reads pixels at [i] and [i + 1].
      int maxlen = pix_count - i;
      if (maxlen > MAX_LENGTH) {
        maxlen = MAX_LENGTH;
      }
      HashChainFindCopy(hash_chain, i, xsize, argb, maxlen,
                        window_size, iter_pos, iter_limit,
                        &offset, &len);
    }
    if (len >= MIN_LENGTH) {
      // Alternative#2: Insert the pixel at 'i' as literal, and code the
      // pixels starting at 'i + 1' using backward reference.
      int offset2 = 0;
      int len2 = 0;
      int k;
      HashChainInsert(hash_chain, &argb[i], i);
      if (i < pix_count - 2) {  // FindCopy(i+1,..) reads [i + 1] and [i + 2].
        int maxlen = pix_count - (i + 1);
        if (maxlen > MAX_LENGTH) {
          maxlen = MAX_LENGTH;
        }
        HashChainFindCopy(hash_chain, i + 1, xsize, argb, maxlen,
                          window_size, iter_pos, iter_limit,
                          &offset2, &len2);
        if (len2 > len + 1) {
          const uint32_t pixel = argb[i];
          // Alternative#2 is a better match. So push pixel at 'i' as literal.
          if (use_color_cache && VP8LColorCacheContains(&hashers, pixel)) {
            const int ix = VP8LColorCacheGetIndex(&hashers, pixel);
            refs->refs[refs->size] = PixOrCopyCreateCacheIdx(ix);
          } else {
            refs->refs[refs->size] = PixOrCopyCreateLiteral(pixel);
          }
          ++refs->size;
          if (use_color_cache) VP8LColorCacheInsert(&hashers, pixel);
          i++;  // Backward reference to be done for next pixel.
          len = len2;
          offset = offset2;
        }
      }
      if (len >= MAX_LENGTH) {
        len = MAX_LENGTH - 1;
      }
      refs->refs[refs->size++] = PixOrCopyCreateCopy(offset, len);
      if (use_color_cache) {
        for (k = 0; k < len; ++k) {
          VP8LColorCacheInsert(&hashers, argb[i + k]);
        }
      }
      // Add to the hash_chain (but cannot add the last pixel).
      {
        const int last = (len < pix_count - 1 - i) ? len : pix_count - 1 - i;
        for (k = 1; k < last; ++k) {
          HashChainInsert(hash_chain, &argb[i + k], i + k);
        }
      }
      i += len;
    } else {
      const uint32_t pixel = argb[i];
      if (use_color_cache && VP8LColorCacheContains(&hashers, pixel)) {
        // push pixel as a PixOrCopyCreateCacheIdx pixel
        const int ix = VP8LColorCacheGetIndex(&hashers, pixel);
        refs->refs[refs->size] = PixOrCopyCreateCacheIdx(ix);
      } else {
        refs->refs[refs->size] = PixOrCopyCreateLiteral(pixel);
      }
      ++refs->size;
      if (use_color_cache) VP8LColorCacheInsert(&hashers, pixel);
      if (i + 1 < pix_count) {
        HashChainInsert(hash_chain, &argb[i], i);
      }
      ++i;
    }
  }
  ok = 1;
Error:
  if (cc_init) VP8LColorCacheClear(&hashers);
  HashChainDelete(hash_chain);
  return ok;
}

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

typedef struct {
  double alpha_[VALUES_IN_BYTE];
  double red_[VALUES_IN_BYTE];
  double literal_[PIX_OR_COPY_CODES_MAX];
  double blue_[VALUES_IN_BYTE];
  double distance_[NUM_DISTANCE_CODES];
} CostModel;

static int BackwardReferencesTraceBackwards(
    int xsize, int ysize, int recursive_cost_model,
    const uint32_t* const argb, int quality, int cache_bits,
    VP8LBackwardRefs* const refs);

static void ConvertPopulationCountTableToBitEstimates(
    int num_symbols, const int population_counts[], double output[]) {
  int sum = 0;
  int nonzeros = 0;
  int i;
  for (i = 0; i < num_symbols; ++i) {
    sum += population_counts[i];
    if (population_counts[i] > 0) {
      ++nonzeros;
    }
  }
  if (nonzeros <= 1) {
    memset(output, 0, num_symbols * sizeof(*output));
  } else {
    const double logsum = VP8LFastLog2(sum);
    for (i = 0; i < num_symbols; ++i) {
      output[i] = logsum - VP8LFastLog2(population_counts[i]);
    }
  }
}

static int CostModelBuild(CostModel* const m, int xsize, int ysize,
                          int recursion_level, const uint32_t* const argb,
                          int quality, int cache_bits) {
  int ok = 0;
  VP8LHistogram histo;
  VP8LBackwardRefs refs;

  if (!VP8LBackwardRefsAlloc(&refs, xsize * ysize)) goto Error;

  if (recursion_level > 0) {
    if (!BackwardReferencesTraceBackwards(xsize, ysize, recursion_level - 1,
                                          argb, quality, cache_bits, &refs)) {
      goto Error;
    }
  } else {
    if (!BackwardReferencesHashChain(xsize, ysize, argb, cache_bits, quality,
                                     &refs)) {
      goto Error;
    }
  }
  VP8LHistogramCreate(&histo, &refs, cache_bits);
  ConvertPopulationCountTableToBitEstimates(
      VP8LHistogramNumCodes(&histo), histo.literal_, m->literal_);
  ConvertPopulationCountTableToBitEstimates(
      VALUES_IN_BYTE, histo.red_, m->red_);
  ConvertPopulationCountTableToBitEstimates(
      VALUES_IN_BYTE, histo.blue_, m->blue_);
  ConvertPopulationCountTableToBitEstimates(
      VALUES_IN_BYTE, histo.alpha_, m->alpha_);
  ConvertPopulationCountTableToBitEstimates(
      NUM_DISTANCE_CODES, histo.distance_, m->distance_);
  ok = 1;

 Error:
  VP8LClearBackwardRefs(&refs);
  return ok;
}

static WEBP_INLINE double GetLiteralCost(const CostModel* const m, uint32_t v) {
  return m->alpha_[v >> 24] +
         m->red_[(v >> 16) & 0xff] +
         m->literal_[(v >> 8) & 0xff] +
         m->blue_[v & 0xff];
}

static WEBP_INLINE double GetCacheCost(const CostModel* const m, uint32_t idx) {
  const int literal_idx = VALUES_IN_BYTE + NUM_LENGTH_CODES + idx;
  return m->literal_[literal_idx];
}

static WEBP_INLINE double GetLengthCost(const CostModel* const m,
                                        uint32_t length) {
  int code, extra_bits_count, extra_bits_value;
  PrefixEncode(length, &code, &extra_bits_count, &extra_bits_value);
  return m->literal_[VALUES_IN_BYTE + code] + extra_bits_count;
}

static WEBP_INLINE double GetDistanceCost(const CostModel* const m,
                                          uint32_t distance) {
  int code, extra_bits_count, extra_bits_value;
  PrefixEncode(distance, &code, &extra_bits_count, &extra_bits_value);
  return m->distance_[code] + extra_bits_count;
}

static int BackwardReferencesHashChainDistanceOnly(
    int xsize, int ysize, int recursive_cost_model, const uint32_t* const argb,
    int quality, int cache_bits, uint32_t* const dist_array) {
  int i;
  int ok = 0;
  int cc_init = 0;
  const int pix_count = xsize * ysize;
  const int use_color_cache = (cache_bits > 0);
  float* const cost =
      (float*)WebPSafeMalloc((uint64_t)pix_count, sizeof(*cost));
  CostModel* cost_model = (CostModel*)malloc(sizeof(*cost_model));
  HashChain* hash_chain = (HashChain*)malloc(sizeof(*hash_chain));
  VP8LColorCache hashers;
  const double mul0 = (recursive_cost_model != 0) ? 1.0 : 0.68;
  const double mul1 = (recursive_cost_model != 0) ? 1.0 : 0.82;
  const int min_distance_code = 2;  // TODO(vikasa): tune as function of quality
  int window_size = WINDOW_SIZE;
  int iter_pos = 1;
  int iter_limit = -1;

  if (cost == NULL || cost_model == NULL || hash_chain == NULL) goto Error;

  if (!HashChainInit(hash_chain, pix_count)) goto Error;

  if (use_color_cache) {
    cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    if (!cc_init) goto Error;
  }

  if (!CostModelBuild(cost_model, xsize, ysize, recursive_cost_model, argb,
                      quality, cache_bits)) {
    goto Error;
  }

  for (i = 0; i < pix_count; ++i) cost[i] = 1e38f;

  // We loop one pixel at a time, but store all currently best points to
  // non-processed locations from this point.
  dist_array[0] = 0;
  GetParamsForHashChainFindCopy(quality, xsize, cache_bits,
                                &window_size, &iter_pos, &iter_limit);
  for (i = 0; i < pix_count; ++i) {
    double prev_cost = 0.0;
    int shortmax;
    if (i > 0) {
      prev_cost = cost[i - 1];
    }
    for (shortmax = 0; shortmax < 2; ++shortmax) {
      int offset = 0;
      int len = 0;
      if (i < pix_count - 1) {  // FindCopy reads pixels at [i] and [i + 1].
        int maxlen = shortmax ? 2 : MAX_LENGTH;
        if (maxlen > pix_count - i) {
          maxlen = pix_count - i;
        }
        HashChainFindCopy(hash_chain, i, xsize, argb, maxlen,
                          window_size, iter_pos, iter_limit,
                          &offset, &len);
      }
      if (len >= MIN_LENGTH) {
        const int code = DistanceToPlaneCode(xsize, offset);
        const double distance_cost =
            prev_cost + GetDistanceCost(cost_model, code);
        int k;
        for (k = 1; k < len; ++k) {
          const double cost_val = distance_cost + GetLengthCost(cost_model, k);
          if (cost[i + k] > cost_val) {
            cost[i + k] = (float)cost_val;
            dist_array[i + k] = k + 1;
          }
        }
        // This if is for speedup only. It roughly doubles the speed, and
        // makes compression worse by .1 %.
        if (len >= 128 && code <= min_distance_code) {
          // Long copy for short distances, let's skip the middle
          // lookups for better copies.
          // 1) insert the hashes.
          if (use_color_cache) {
            for (k = 0; k < len; ++k) {
              VP8LColorCacheInsert(&hashers, argb[i + k]);
            }
          }
          // 2) Add to the hash_chain (but cannot add the last pixel)
          {
            const int last = (len + i < pix_count - 1) ? len + i
                                                       : pix_count - 1;
            for (k = i; k < last; ++k) {
              HashChainInsert(hash_chain, &argb[k], k);
            }
          }
          // 3) jump.
          i += len - 1;  // for loop does ++i, thus -1 here.
          goto next_symbol;
        }
      }
    }
    if (i < pix_count - 1) {
      HashChainInsert(hash_chain, &argb[i], i);
    }
    {
      // inserting a literal pixel
      double cost_val = prev_cost;
      if (use_color_cache && VP8LColorCacheContains(&hashers, argb[i])) {
        const int ix = VP8LColorCacheGetIndex(&hashers, argb[i]);
        cost_val += GetCacheCost(cost_model, ix) * mul0;
      } else {
        cost_val += GetLiteralCost(cost_model, argb[i]) * mul1;
      }
      if (cost[i] > cost_val) {
        cost[i] = (float)cost_val;
        dist_array[i] = 1;  // only one is inserted.
      }
      if (use_color_cache) VP8LColorCacheInsert(&hashers, argb[i]);
    }
 next_symbol: ;
  }
  // Last pixel still to do, it can only be a single step if not reached
  // through cheaper means already.
  ok = 1;
Error:
  if (cc_init) VP8LColorCacheClear(&hashers);
  HashChainDelete(hash_chain);
  free(cost_model);
  free(cost);
  return ok;
}

// We pack the path at the end of *dist_array and return
// a pointer to this part of the array. Example:
// dist_array = [1x2xx3x2] => packed [1x2x1232], chosen_path = [1232]
static void TraceBackwards(uint32_t* const dist_array,
                           int dist_array_size,
                           uint32_t** const chosen_path,
                           int* const chosen_path_size) {
  uint32_t* path = dist_array + dist_array_size;
  uint32_t* cur = dist_array + dist_array_size - 1;
  while (cur >= dist_array) {
    const int k = *cur;
    --path;
    *path = k;
    cur -= k;
  }
  *chosen_path = path;
  *chosen_path_size = (int)(dist_array + dist_array_size - path);
}

static int BackwardReferencesHashChainFollowChosenPath(
    int xsize, int ysize, const uint32_t* const argb,
    int quality, int cache_bits,
    const uint32_t* const chosen_path, int chosen_path_size,
    VP8LBackwardRefs* const refs) {
  const int pix_count = xsize * ysize;
  const int use_color_cache = (cache_bits > 0);
  int size = 0;
  int i = 0;
  int k;
  int ix;
  int ok = 0;
  int cc_init = 0;
  int window_size = WINDOW_SIZE;
  int iter_pos = 1;
  int iter_limit = -1;
  HashChain* hash_chain = (HashChain*)malloc(sizeof(*hash_chain));
  VP8LColorCache hashers;

  if (hash_chain == NULL || !HashChainInit(hash_chain, pix_count)) {
    goto Error;
  }
  if (use_color_cache) {
    cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    if (!cc_init) goto Error;
  }

  refs->size = 0;
  GetParamsForHashChainFindCopy(quality, xsize, cache_bits,
                                &window_size, &iter_pos, &iter_limit);
  for (ix = 0; ix < chosen_path_size; ++ix, ++size) {
    int offset = 0;
    int len = 0;
    int maxlen = chosen_path[ix];
    if (maxlen != 1) {
      HashChainFindCopy(hash_chain, i, xsize, argb, maxlen,
                        window_size, iter_pos, iter_limit,
                        &offset, &len);
      assert(len == maxlen);
      refs->refs[size] = PixOrCopyCreateCopy(offset, len);
      if (use_color_cache) {
        for (k = 0; k < len; ++k) {
          VP8LColorCacheInsert(&hashers, argb[i + k]);
        }
      }
      {
        const int last = (len < pix_count - 1 - i) ? len : pix_count - 1 - i;
        for (k = 0; k < last; ++k) {
          HashChainInsert(hash_chain, &argb[i + k], i + k);
        }
      }
      i += len;
    } else {
      if (use_color_cache && VP8LColorCacheContains(&hashers, argb[i])) {
        // push pixel as a color cache index
        const int idx = VP8LColorCacheGetIndex(&hashers, argb[i]);
        refs->refs[size] = PixOrCopyCreateCacheIdx(idx);
      } else {
        refs->refs[size] = PixOrCopyCreateLiteral(argb[i]);
      }
      if (use_color_cache) VP8LColorCacheInsert(&hashers, argb[i]);
      if (i + 1 < pix_count) {
        HashChainInsert(hash_chain, &argb[i], i);
      }
      ++i;
    }
  }
  assert(size <= refs->max_size);
  refs->size = size;
  ok = 1;
Error:
  if (cc_init) VP8LColorCacheClear(&hashers);
  HashChainDelete(hash_chain);
  return ok;
}

// Returns 1 on success.
static int BackwardReferencesTraceBackwards(int xsize, int ysize,
                                            int recursive_cost_model,
                                            const uint32_t* const argb,
                                            int quality, int cache_bits,
                                            VP8LBackwardRefs* const refs) {
  int ok = 0;
  const int dist_array_size = xsize * ysize;
  uint32_t* chosen_path = NULL;
  int chosen_path_size = 0;
  uint32_t* dist_array =
      (uint32_t*)WebPSafeMalloc((uint64_t)dist_array_size, sizeof(*dist_array));

  if (dist_array == NULL) goto Error;

  if (!BackwardReferencesHashChainDistanceOnly(
      xsize, ysize, recursive_cost_model, argb, quality, cache_bits,
      dist_array)) {
    goto Error;
  }
  TraceBackwards(dist_array, dist_array_size, &chosen_path, &chosen_path_size);
  if (!BackwardReferencesHashChainFollowChosenPath(
      xsize, ysize, argb, quality, cache_bits, chosen_path, chosen_path_size,
      refs)) {
    goto Error;
  }
  ok = 1;
 Error:
  free(dist_array);
  return ok;
}

static void BackwardReferences2DLocality(int xsize,
                                         VP8LBackwardRefs* const refs) {
  int i;
  for (i = 0; i < refs->size; ++i) {
    if (PixOrCopyIsCopy(&refs->refs[i])) {
      const int dist = refs->refs[i].argb_or_distance;
      const int transformed_dist = DistanceToPlaneCode(xsize, dist);
      refs->refs[i].argb_or_distance = transformed_dist;
    }
  }
}

int VP8LGetBackwardReferences(int width, int height,
                              const uint32_t* const argb,
                              int quality, int cache_bits, int use_2d_locality,
                              VP8LBackwardRefs* const best) {
  int ok = 0;
  int lz77_is_useful;
  VP8LBackwardRefs refs_rle, refs_lz77;
  const int num_pix = width * height;

  VP8LBackwardRefsAlloc(&refs_rle, num_pix);
  VP8LBackwardRefsAlloc(&refs_lz77, num_pix);
  VP8LInitBackwardRefs(best);
  if (refs_rle.refs == NULL || refs_lz77.refs == NULL) {
 Error1:
    VP8LClearBackwardRefs(&refs_rle);
    VP8LClearBackwardRefs(&refs_lz77);
    goto End;
  }

  if (!BackwardReferencesHashChain(width, height, argb, cache_bits, quality,
                                   &refs_lz77)) {
    goto End;
  }
  // Backward Reference using RLE only.
  BackwardReferencesRle(width, height, argb, &refs_rle);

  {
    double bit_cost_lz77, bit_cost_rle;
    VP8LHistogram* const histo = (VP8LHistogram*)malloc(sizeof(*histo));
    if (histo == NULL) goto Error1;
    // Evaluate lz77 coding
    VP8LHistogramCreate(histo, &refs_lz77, cache_bits);
    bit_cost_lz77 = VP8LHistogramEstimateBits(histo);
    // Evaluate RLE coding
    VP8LHistogramCreate(histo, &refs_rle, cache_bits);
    bit_cost_rle = VP8LHistogramEstimateBits(histo);
    // Decide if LZ77 is useful.
    lz77_is_useful = (bit_cost_lz77 < bit_cost_rle);
    free(histo);
  }

  // Choose appropriate backward reference.
  if (lz77_is_useful) {
    // TraceBackwards is costly. Don't execute it at lower quality (q <= 10).
    const int try_lz77_trace_backwards = (quality > 10);
    *best = refs_lz77;   // default guess: lz77 is better
    VP8LClearBackwardRefs(&refs_rle);
    if (try_lz77_trace_backwards) {
      // Set recursion level for large images using a color cache.
      const int recursion_level =
          (num_pix < 320 * 200) && (cache_bits > 0) ? 1 : 0;
      VP8LBackwardRefs refs_trace;
      if (!VP8LBackwardRefsAlloc(&refs_trace, num_pix)) {
        goto End;
      }
      if (BackwardReferencesTraceBackwards(width, height, recursion_level, argb,
                                           quality, cache_bits, &refs_trace)) {
        VP8LClearBackwardRefs(&refs_lz77);
        *best = refs_trace;
      }
    }
  } else {
    VP8LClearBackwardRefs(&refs_lz77);
    *best = refs_rle;
  }

  if (use_2d_locality) BackwardReferences2DLocality(width, best);

  ok = 1;

 End:
  if (!ok) {
    VP8LClearBackwardRefs(best);
  }
  return ok;
}

// Returns 1 on success.
static int ComputeCacheHistogram(const uint32_t* const argb,
                                 int xsize, int ysize,
                                 const VP8LBackwardRefs* const refs,
                                 int cache_bits,
                                 VP8LHistogram* const histo) {
  int pixel_index = 0;
  int i;
  uint32_t k;
  VP8LColorCache hashers;
  const int use_color_cache = (cache_bits > 0);
  int cc_init = 0;

  if (use_color_cache) {
    cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    if (!cc_init) return 0;
  }

  for (i = 0; i < refs->size; ++i) {
    const PixOrCopy* const v = &refs->refs[i];
    if (PixOrCopyIsLiteral(v)) {
      if (use_color_cache &&
          VP8LColorCacheContains(&hashers, argb[pixel_index])) {
        // push pixel as a cache index
        const int ix = VP8LColorCacheGetIndex(&hashers, argb[pixel_index]);
        const PixOrCopy token = PixOrCopyCreateCacheIdx(ix);
        VP8LHistogramAddSinglePixOrCopy(histo, &token);
      } else {
        VP8LHistogramAddSinglePixOrCopy(histo, v);
      }
    } else {
      VP8LHistogramAddSinglePixOrCopy(histo, v);
    }
    if (use_color_cache) {
      for (k = 0; k < PixOrCopyLength(v); ++k) {
        VP8LColorCacheInsert(&hashers, argb[pixel_index + k]);
      }
    }
    pixel_index += PixOrCopyLength(v);
  }
  assert(pixel_index == xsize * ysize);
  (void)xsize;  // xsize is not used in non-debug compilations otherwise.
  (void)ysize;  // ysize is not used in non-debug compilations otherwise.
  if (cc_init) VP8LColorCacheClear(&hashers);
  return 1;
}

// Returns how many bits are to be used for a color cache.
int VP8LCalculateEstimateForCacheSize(const uint32_t* const argb,
                                      int xsize, int ysize,
                                      int* const best_cache_bits) {
  int ok = 0;
  int cache_bits;
  double lowest_entropy = 1e99;
  VP8LBackwardRefs refs;
  static const double kSmallPenaltyForLargeCache = 4.0;
  static const int quality = 30;
  if (!VP8LBackwardRefsAlloc(&refs, xsize * ysize) ||
      !BackwardReferencesHashChain(xsize, ysize, argb, 0, quality, &refs)) {
    goto Error;
  }
  for (cache_bits = 0; cache_bits <= MAX_COLOR_CACHE_BITS; ++cache_bits) {
    double cur_entropy;
    VP8LHistogram histo;
    VP8LHistogramInit(&histo, cache_bits);
    ComputeCacheHistogram(argb, xsize, ysize, &refs, cache_bits, &histo);
    cur_entropy = VP8LHistogramEstimateBits(&histo) +
        kSmallPenaltyForLargeCache * cache_bits;
    if (cache_bits == 0 || cur_entropy < lowest_entropy) {
      *best_cache_bits = cache_bits;
      lowest_entropy = cur_entropy;
    }
  }
  ok = 1;
 Error:
  VP8LClearBackwardRefs(&refs);
  return ok;
}