Use the upstream version of libwebp, v0.4.3.

third_party/libwebp/enc/backward_references.c

+// 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 "./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_MULTIPLIER (0xc6a4a7935bd1e995ULL)
+
+#define MIN_BLOCK_SIZE 256  // minimum block size for backward references
+
+#define MAX_ENTROPY    (1e30f)
+
+// 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
+
+// -----------------------------------------------------------------------------
+
+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
+
+struct PixOrCopyBlock {
+  PixOrCopyBlock* next_;   // next block (or NULL)
+  PixOrCopy* start_;       // data start
+  int size_;               // currently used size
+};
+
+static void ClearBackwardRefs(VP8LBackwardRefs* const refs) {
+  assert(refs != NULL);
+  if (refs->tail_ != NULL) {
+    *refs->tail_ = refs->free_blocks_;  // recycle all blocks at once
+  }
+  refs->free_blocks_ = refs->refs_;
+  refs->tail_ = &refs->refs_;
+  refs->last_block_ = NULL;
+  refs->refs_ = NULL;
+}
+
+void VP8LBackwardRefsClear(VP8LBackwardRefs* const refs) {
+  assert(refs != NULL);
+  ClearBackwardRefs(refs);
+  while (refs->free_blocks_ != NULL) {
+    PixOrCopyBlock* const next = refs->free_blocks_->next_;
+    WebPSafeFree(refs->free_blocks_);
+    refs->free_blocks_ = next;
+  }
+}
+
+void VP8LBackwardRefsInit(VP8LBackwardRefs* const refs, int block_size) {
+  assert(refs != NULL);
+  memset(refs, 0, sizeof(*refs));
+  refs->tail_ = &refs->refs_;
+  refs->block_size_ =
+      (block_size < MIN_BLOCK_SIZE) ? MIN_BLOCK_SIZE : block_size;
+}
+
+VP8LRefsCursor VP8LRefsCursorInit(const VP8LBackwardRefs* const refs) {
+  VP8LRefsCursor c;
+  c.cur_block_ = refs->refs_;
+  if (refs->refs_ != NULL) {
+    c.cur_pos = c.cur_block_->start_;
+    c.last_pos_ = c.cur_pos + c.cur_block_->size_;
+  } else {
+    c.cur_pos = NULL;
+    c.last_pos_ = NULL;
+  }
+  return c;
+}
+
+void VP8LRefsCursorNextBlock(VP8LRefsCursor* const c) {
+  PixOrCopyBlock* const b = c->cur_block_->next_;
+  c->cur_pos = (b == NULL) ? NULL : b->start_;
+  c->last_pos_ = (b == NULL) ? NULL : b->start_ + b->size_;
+  c->cur_block_ = b;
+}
+
+// Create a new block, either from the free list or allocated
+static PixOrCopyBlock* BackwardRefsNewBlock(VP8LBackwardRefs* const refs) {
+  PixOrCopyBlock* b = refs->free_blocks_;
+  if (b == NULL) {   // allocate new memory chunk
+    const size_t total_size =
+        sizeof(*b) + refs->block_size_ * sizeof(*b->start_);
+    b = (PixOrCopyBlock*)WebPSafeMalloc(1ULL, total_size);
+    if (b == NULL) {
+      refs->error_ |= 1;
+      return NULL;
+    }
+    b->start_ = (PixOrCopy*)((uint8_t*)b + sizeof(*b));  // not always aligned
+  } else {  // recycle from free-list
+    refs->free_blocks_ = b->next_;
+  }
+  *refs->tail_ = b;
+  refs->tail_ = &b->next_;
+  refs->last_block_ = b;
+  b->next_ = NULL;
+  b->size_ = 0;
+  return b;
+}
+
+static WEBP_INLINE void BackwardRefsCursorAdd(VP8LBackwardRefs* const refs,
+                                              const PixOrCopy v) {
+  PixOrCopyBlock* b = refs->last_block_;
+  if (b == NULL || b->size_ == refs->block_size_) {
+    b = BackwardRefsNewBlock(refs);
+    if (b == NULL) return;   // refs->error_ is set
+  }
+  b->start_[b->size_++] = v;
+}
+
+int VP8LBackwardRefsCopy(const VP8LBackwardRefs* const src,
+                         VP8LBackwardRefs* const dst) {
+  const PixOrCopyBlock* b = src->refs_;
+  ClearBackwardRefs(dst);
+  assert(src->block_size_ == dst->block_size_);
+  while (b != NULL) {
+    PixOrCopyBlock* const new_b = BackwardRefsNewBlock(dst);
+    if (new_b == NULL) return 0;   // dst->error_ is set
+    memcpy(new_b->start_, b->start_, b->size_ * sizeof(*b->start_));
+    new_b->size_ = b->size_;
+    b = b->next_;
+  }
+  return 1;
+}
+
+// -----------------------------------------------------------------------------
+// Hash chains
+
+// initialize as empty
+static void HashChainInit(VP8LHashChain* const p) {
+  int i;
+  assert(p != NULL);
+  for (i = 0; i < p->size_; ++i) {
+    p->chain_[i] = -1;
+  }
+  for (i = 0; i < HASH_SIZE; ++i) {
+    p->hash_to_first_index_[i] = -1;
+  }
+}
+
+int VP8LHashChainInit(VP8LHashChain* const p, int size) {
+  assert(p->size_ == 0);
+  assert(p->chain_ == NULL);
+  assert(size > 0);
+  p->chain_ = (int*)WebPSafeMalloc(size, sizeof(*p->chain_));
+  if (p->chain_ == NULL) return 0;
+  p->size_ = size;
+  HashChainInit(p);
+  return 1;
+}
+
+void VP8LHashChainClear(VP8LHashChain* const p) {
+  assert(p != NULL);
+  WebPSafeFree(p->chain_);
+  p->size_ = 0;
+  p->chain_ = NULL;
+}
+
+// -----------------------------------------------------------------------------
+
+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;
+}
+
+// Insertion of two pixels at a time.
+static void HashChainInsert(VP8LHashChain* 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 rigorous search loop in HashChainFindCopy
+  // can be relaxed.
+  *iter_limit = (cache_bits > 0) ? iter_neg : iter_neg / 2;
+}
+
+static int HashChainFindCopy(const VP8LHashChain* const p,
+                             int base_position, int xsize_signed,
+                             const uint32_t* const argb, int max_len,
+                             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);
+  if (max_len > MAX_LENGTH) {
+    max_len = MAX_LENGTH;
+  }
+  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;
+    const uint32_t* const ptr1 = (argb + pos + best_length - 1);
+    const uint32_t* const ptr2 = (argb_start + best_length - 1);
+
+    if (iter_pos < 0) {
+      if (iter_pos < iter_limit || best_val >= 0xff0000) {
+        break;
+      }
+    }
+    --iter_pos;
+
+    // Before 'expensive' linear match, check if the two arrays match at the
+    // current best length index and also for the succeeding elements.
+    if (ptr1[0] != ptr2[0] || ptr1[1] != ptr2[1]) continue;
+
+    curr_length = FindMatchLength(argb + pos, argb_start, max_len);
+    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 >= (uint32_t)max_len) {
+        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) {
+  while (length >= MAX_LENGTH) {
+    BackwardRefsCursorAdd(refs, PixOrCopyCreateCopy(1, MAX_LENGTH));
+    length -= MAX_LENGTH;
+  }
+  if (length > 0) {
+    BackwardRefsCursorAdd(refs, PixOrCopyCreateCopy(1, length));
+  }
+}
+
+static int 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;
+  ClearBackwardRefs(refs);
+  PushBackCopy(refs, match_len);    // i=0 case
+  BackwardRefsCursorAdd(refs, 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;
+      BackwardRefsCursorAdd(refs, PixOrCopyCreateLiteral(argb[i]));
+    }
+  }
+  PushBackCopy(refs, match_len);
+  return !refs->error_;
+}
+
+static int BackwardReferencesHashChain(int xsize, int ysize,
+                                       const uint32_t* const argb,
+                                       int cache_bits, int quality,
+                                       VP8LHashChain* const hash_chain,
+                                       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;
+  VP8LColorCache hashers;
+  int window_size = WINDOW_SIZE;
+  int iter_pos = 1;
+  int iter_limit = -1;
+
+  if (use_color_cache) {
+    cc_init = VP8LColorCacheInit(&hashers, cache_bits);
+    if (!cc_init) goto Error;
+  }
+
+  ClearBackwardRefs(refs);
+  GetParamsForHashChainFindCopy(quality, xsize, cache_bits,
+                                &window_size, &iter_pos, &iter_limit);
+  HashChainInit(hash_chain);
+  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 max_len = pix_count - i;
+      HashChainFindCopy(hash_chain, i, xsize, argb, max_len,
+                        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 max_len = pix_count - (i + 1);
+        HashChainFindCopy(hash_chain, i + 1, xsize, argb, max_len,
+                          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.
+          PixOrCopy v;
+          if (use_color_cache && VP8LColorCacheContains(&hashers, pixel)) {
+            const int ix = VP8LColorCacheGetIndex(&hashers, pixel);
+            v = PixOrCopyCreateCacheIdx(ix);
+          } else {
+            if (use_color_cache) VP8LColorCacheInsert(&hashers, pixel);
+            v = PixOrCopyCreateLiteral(pixel);
+          }
+          BackwardRefsCursorAdd(refs, v);
+          i++;  // Backward reference to be done for next pixel.
+          len = len2;
+          offset = offset2;
+        }
+      }
+      if (len >= MAX_LENGTH) {
+        len = MAX_LENGTH - 1;
+      }
+      BackwardRefsCursorAdd(refs, 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];
+      PixOrCopy v;
+      if (use_color_cache && VP8LColorCacheContains(&hashers, pixel)) {
+        // push pixel as a PixOrCopyCreateCacheIdx pixel
+        const int ix = VP8LColorCacheGetIndex(&hashers, pixel);
+        v = PixOrCopyCreateCacheIdx(ix);
+      } else {
+        if (use_color_cache) VP8LColorCacheInsert(&hashers, pixel);
+        v = PixOrCopyCreateLiteral(pixel);
+      }
+      BackwardRefsCursorAdd(refs, v);
+      if (i + 1 < pix_count) {
+        HashChainInsert(hash_chain, &argb[i], i);
+      }
+      ++i;
+    }
+  }
+  ok = !refs->error_;
+Error:
+  if (cc_init) VP8LColorCacheClear(&hashers);
+  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,
+    VP8LHashChain* const hash_chain,
+    VP8LBackwardRefs* const refs);
+
+static void ConvertPopulationCountTableToBitEstimates(
+    int num_symbols, const uint32_t population_counts[], double output[]) {
+  uint32_t 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,
+                          VP8LHashChain* const hash_chain,
+                          VP8LBackwardRefs* const refs) {
+  int ok = 0;
+  VP8LHistogram* histo = NULL;
+
+  ClearBackwardRefs(refs);
+  if (recursion_level > 0) {
+    if (!BackwardReferencesTraceBackwards(xsize, ysize, recursion_level - 1,
+                                          argb, quality, cache_bits, hash_chain,
+                                          refs)) {
+      goto Error;
+    }
+  } else {
+    if (!BackwardReferencesHashChain(xsize, ysize, argb, cache_bits, quality,
+                                     hash_chain, refs)) {
+      goto Error;
+    }
+  }
+  histo = VP8LAllocateHistogram(cache_bits);
+  if (histo == NULL) goto Error;
+
+  VP8LHistogramCreate(histo, refs, cache_bits);
+
+  ConvertPopulationCountTableToBitEstimates(
+      VP8LHistogramNumCodes(histo->palette_code_bits_),
+      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:
+  VP8LFreeHistogram(histo);
+  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;
+  VP8LPrefixEncodeBits(length, &code, &extra_bits);
+  return m->literal_[VALUES_IN_BYTE + code] + extra_bits;
+}
+
+static WEBP_INLINE double GetDistanceCost(const CostModel* const m,
+                                          uint32_t distance) {
+  int code, extra_bits;
+  VP8LPrefixEncodeBits(distance, &code, &extra_bits);
+  return m->distance_[code] + extra_bits;
+}
+
+static int BackwardReferencesHashChainDistanceOnly(
+    int xsize, int ysize, int recursive_cost_model, const uint32_t* const argb,
+    int quality, int cache_bits, VP8LHashChain* const hash_chain,
+    VP8LBackwardRefs* const refs, 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(pix_count, sizeof(*cost));
+  CostModel* cost_model = (CostModel*)WebPSafeMalloc(1ULL, sizeof(*cost_model));
+  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) 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, hash_chain, refs)) {
+    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);
+  HashChainInit(hash_chain);
+  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 max_len = shortmax ? 2 : pix_count - i;
+        HashChainFindCopy(hash_chain, i, xsize, argb, max_len,
+                          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 {
+        if (use_color_cache) VP8LColorCacheInsert(&hashers, argb[i]);
+        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.
+      }
+    }
+ next_symbol: ;
+  }
+  // Last pixel still to do, it can only be a single step if not reached
+  // through cheaper means already.
+  ok = !refs->error_;
+Error:
+  if (cc_init) VP8LColorCacheClear(&hashers);
+  WebPSafeFree(cost_model);
+  WebPSafeFree(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,
+    VP8LHashChain* const hash_chain,
+    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;
+  VP8LColorCache hashers;
+
+  if (use_color_cache) {
+    cc_init = VP8LColorCacheInit(&hashers, cache_bits);
+    if (!cc_init) goto Error;
+  }
+
+  ClearBackwardRefs(refs);
+  GetParamsForHashChainFindCopy(quality, xsize, cache_bits,
+                                &window_size, &iter_pos, &iter_limit);
+  HashChainInit(hash_chain);
+  for (ix = 0; ix < chosen_path_size; ++ix, ++size) {
+    int offset = 0;
+    int len = 0;
+    int max_len = chosen_path[ix];
+    if (max_len != 1) {
+      HashChainFindCopy(hash_chain, i, xsize, argb, max_len,
+                        window_size, iter_pos, iter_limit,
+                        &offset, &len);
+      assert(len == max_len);
+      BackwardRefsCursorAdd(refs, 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 {
+      PixOrCopy v;
+      if (use_color_cache && VP8LColorCacheContains(&hashers, argb[i])) {
+        // push pixel as a color cache index
+        const int idx = VP8LColorCacheGetIndex(&hashers, argb[i]);
+        v = PixOrCopyCreateCacheIdx(idx);
+      } else {
+        if (use_color_cache) VP8LColorCacheInsert(&hashers, argb[i]);
+        v = PixOrCopyCreateLiteral(argb[i]);
+      }
+      BackwardRefsCursorAdd(refs, v);
+      if (i + 1 < pix_count) {
+        HashChainInsert(hash_chain, &argb[i], i);
+      }
+      ++i;
+    }
+  }
+  ok = !refs->error_;
+Error:
+  if (cc_init) VP8LColorCacheClear(&hashers);
+  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,
+                                            VP8LHashChain* const hash_chain,
+                                            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(dist_array_size, sizeof(*dist_array));
+
+  if (dist_array == NULL) goto Error;
+
+  if (!BackwardReferencesHashChainDistanceOnly(
+      xsize, ysize, recursive_cost_model, argb, quality, cache_bits, hash_chain,
+      refs, 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,
+      hash_chain, refs)) {
+    goto Error;
+  }
+  ok = 1;
+ Error:
+  WebPSafeFree(dist_array);
+  return ok;
+}
+
+static void BackwardReferences2DLocality(int xsize,
+                                         const VP8LBackwardRefs* const refs) {
+  VP8LRefsCursor c = VP8LRefsCursorInit(refs);
+  while (VP8LRefsCursorOk(&c)) {
+    if (PixOrCopyIsCopy(c.cur_pos)) {
+      const int dist = c.cur_pos->argb_or_distance;
+      const int transformed_dist = DistanceToPlaneCode(xsize, dist);
+      c.cur_pos->argb_or_distance = transformed_dist;
+    }
+    VP8LRefsCursorNext(&c);
+  }
+}
+
+VP8LBackwardRefs* VP8LGetBackwardReferences(
+    int width, int height, const uint32_t* const argb, int quality,
+    int cache_bits, int use_2d_locality, VP8LHashChain* const hash_chain,
+    VP8LBackwardRefs refs_array[2]) {
+  int lz77_is_useful;
+  const int num_pix = width * height;
+  VP8LBackwardRefs* best = NULL;
+  VP8LBackwardRefs* const refs_lz77 = &refs_array[0];
+  VP8LBackwardRefs* const refs_rle = &refs_array[1];
+
+  if (!BackwardReferencesHashChain(width, height, argb, cache_bits, quality,
+                                   hash_chain, refs_lz77)) {
+    return NULL;
+  }
+  if (!BackwardReferencesRle(width, height, argb, refs_rle)) {
+    return NULL;
+  }
+
+  {
+    double bit_cost_lz77, bit_cost_rle;
+    VP8LHistogram* const histo = VP8LAllocateHistogram(cache_bits);
+    if (histo == NULL) return NULL;
+    // 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);
+    VP8LFreeHistogram(histo);
+  }
+
+  // Choose appropriate backward reference.
+  if (lz77_is_useful) {
+    // TraceBackwards is costly. Don't execute it at lower quality.
+    const int try_lz77_trace_backwards = (quality >= 25);
+    best = refs_lz77;   // default guess: lz77 is better
+    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* const refs_trace = &refs_array[1];
+      ClearBackwardRefs(refs_trace);
+      if (BackwardReferencesTraceBackwards(width, height, recursion_level, argb,
+                                           quality, cache_bits, hash_chain,
+                                           refs_trace)) {
+        best = refs_trace;
+      }
+    }
+  } else {
+    best = refs_rle;
+  }
+
+  if (use_2d_locality) BackwardReferences2DLocality(width, best);
+
+  return best;
+}
+
+// Returns entropy for the given cache bits.
+static double ComputeCacheEntropy(const uint32_t* const argb,
+                                  int xsize, int ysize,
+                                  const VP8LBackwardRefs* const refs,
+                                  int cache_bits) {
+  int pixel_index = 0;
+  uint32_t k;
+  const int use_color_cache = (cache_bits > 0);
+  int cc_init = 0;
+  double entropy = MAX_ENTROPY;
+  const double kSmallPenaltyForLargeCache = 4.0;
+  VP8LColorCache hashers;
+  VP8LRefsCursor c = VP8LRefsCursorInit(refs);
+  VP8LHistogram* histo = VP8LAllocateHistogram(cache_bits);
+  if (histo == NULL) goto Error;
+
+  if (use_color_cache) {
+    cc_init = VP8LColorCacheInit(&hashers, cache_bits);
+    if (!cc_init) goto Error;
+  }
+
+  while (VP8LRefsCursorOk(&c)) {
+    const PixOrCopy* const v = c.cur_pos;
+    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);
+    VP8LRefsCursorNext(&c);
+  }
+  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.
+  entropy = VP8LHistogramEstimateBits(histo) +
+      kSmallPenaltyForLargeCache * cache_bits;
+ Error:
+  if (cc_init) VP8LColorCacheClear(&hashers);
+  VP8LFreeHistogram(histo);
+  return entropy;
+}
+
+// *best_cache_bits will contain how many bits are to be used for a color cache.
+// Returns 0 in case of memory error.
+int VP8LCalculateEstimateForCacheSize(const uint32_t* const argb,
+                                      int xsize, int ysize, int quality,
+                                      VP8LHashChain* const hash_chain,
+                                      VP8LBackwardRefs* const refs,
+                                      int* const best_cache_bits) {
+  int eval_low = 1;
+  int eval_high = 1;
+  double entropy_low = MAX_ENTROPY;
+  double entropy_high = MAX_ENTROPY;
+  int cache_bits_low = 0;
+  int cache_bits_high = MAX_COLOR_CACHE_BITS;
+
+  if (!BackwardReferencesHashChain(xsize, ysize, argb, 0, quality, hash_chain,
+                                   refs)) {
+    return 0;
+  }
+  // Do a binary search to find the optimal entropy for cache_bits.
+  while (cache_bits_high - cache_bits_low > 1) {
+    if (eval_low) {
+      entropy_low =
+          ComputeCacheEntropy(argb, xsize, ysize, refs, cache_bits_low);
+      eval_low = 0;
+    }
+    if (eval_high) {
+      entropy_high =
+          ComputeCacheEntropy(argb, xsize, ysize, refs, cache_bits_high);
+      eval_high = 0;
+    }
+    if (entropy_high < entropy_low) {
+      *best_cache_bits = cache_bits_high;
+      cache_bits_low = (cache_bits_low + cache_bits_high) / 2;
+      eval_low = 1;
+    } else {
+      *best_cache_bits = cache_bits_low;
+      cache_bits_high = (cache_bits_low + cache_bits_high) / 2;
+      eval_high = 1;
+    }
+  }
+  return 1;
+}