root/3rdparty/libwebp/enc/backward_references.c

DEFINITIONS

1. DistanceToPlaneCode
2. FindMatchLength
3. VP8LInitBackwardRefs
4. VP8LClearBackwardRefs
5. VP8LBackwardRefsAlloc
6. GetPixPairHash64
7. HashChainInit
8. HashChainDelete
9. HashChainInsert
10. GetParamsForHashChainFindCopy
11. HashChainFindCopy
12. PushBackCopy
13. BackwardReferencesRle
14. BackwardReferencesHashChain
15. ConvertPopulationCountTableToBitEstimates
16. CostModelBuild
17. GetLiteralCost
18. GetCacheCost
19. GetLengthCost
20. GetDistanceCost
21. BackwardReferencesHashChainDistanceOnly
22. TraceBackwards
23. BackwardReferencesHashChainFollowChosenPath
24. BackwardReferencesTraceBackwards
25. BackwardReferences2DLocality
26. VP8LGetBackwardReferences
27. ComputeCacheHistogram
28. VP8LCalculateEstimateForCacheSize

// 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;
}