go-libwebp

Experimental translation from libwebp to Go source.
Log | Files | Refs | README | LICENSE

backward_references_cost_enc.c (29637B)


      1 // Copyright 2017 Google Inc. All Rights Reserved.
      2 //
      3 // Use of this source code is governed by a BSD-style license
      4 // that can be found in the COPYING file in the root of the source
      5 // tree. An additional intellectual property rights grant can be found
      6 // in the file PATENTS. All contributing project authors may
      7 // be found in the AUTHORS file in the root of the source tree.
      8 // -----------------------------------------------------------------------------
      9 //
     10 // Improves a given set of backward references by analyzing its bit cost.
     11 // The algorithm is similar to the Zopfli compression algorithm but tailored to
     12 // images.
     13 //
     14 // Author: Vincent Rabaud (vrabaud@google.com)
     15 //
     16 
     17 #include <assert.h>
     18 #include <string.h>
     19 
     20 #include "src/dsp/lossless_common.h"
     21 #include "src/enc/backward_references_enc.h"
     22 #include "src/enc/histogram_enc.h"
     23 #include "src/utils/color_cache_utils.h"
     24 #include "src/utils/utils.h"
     25 #include "src/webp/format_constants.h"
     26 #include "src/webp/types.h"
     27 
     28 #define VALUES_IN_BYTE 256
     29 
     30 extern void VP8LClearBackwardRefs(VP8LBackwardRefs* const refs);
     31 extern int VP8LDistanceToPlaneCode(int xsize, int dist);
     32 extern void VP8LBackwardRefsCursorAdd(VP8LBackwardRefs* const refs,
     33                                       const PixOrCopy v);
     34 
     35 typedef struct {
     36   uint32_t alpha[VALUES_IN_BYTE];
     37   uint32_t red[VALUES_IN_BYTE];
     38   uint32_t blue[VALUES_IN_BYTE];
     39   uint32_t distance[NUM_DISTANCE_CODES];
     40   uint32_t* literal;
     41 } CostModel;
     42 
     43 static void ConvertPopulationCountTableToBitEstimates(
     44     int num_symbols, const uint32_t population_counts[], uint32_t output[]) {
     45   uint32_t sum = 0;
     46   int nonzeros = 0;
     47   int i;
     48   for (i = 0; i < num_symbols; ++i) {
     49     sum += population_counts[i];
     50     if (population_counts[i] > 0) {
     51       ++nonzeros;
     52     }
     53   }
     54   if (nonzeros <= 1) {
     55     memset(output, 0, num_symbols * sizeof(*output));
     56   } else {
     57     const uint32_t logsum = VP8LFastLog2(sum);
     58     for (i = 0; i < num_symbols; ++i) {
     59       output[i] = logsum - VP8LFastLog2(population_counts[i]);
     60     }
     61   }
     62 }
     63 
     64 static int CostModelBuild(CostModel* const m, int xsize, int cache_bits,
     65                           const VP8LBackwardRefs* const refs) {
     66   int ok = 0;
     67   VP8LHistogram* const histo = VP8LAllocateHistogram(cache_bits);
     68   if (histo == NULL) goto Error;
     69 
     70   // The following code is similar to VP8LHistogramCreate but converts the
     71   // distance to plane code.
     72   VP8LHistogramInit(histo, cache_bits, /*init_arrays=*/ 1);
     73   VP8LHistogramStoreRefs(refs, VP8LDistanceToPlaneCode, xsize, histo);
     74 
     75   ConvertPopulationCountTableToBitEstimates(
     76       VP8LHistogramNumCodes(histo->palette_code_bits), histo->literal,
     77       m->literal);
     78   ConvertPopulationCountTableToBitEstimates(
     79       VALUES_IN_BYTE, histo->red, m->red);
     80   ConvertPopulationCountTableToBitEstimates(
     81       VALUES_IN_BYTE, histo->blue, m->blue);
     82   ConvertPopulationCountTableToBitEstimates(
     83       VALUES_IN_BYTE, histo->alpha, m->alpha);
     84   ConvertPopulationCountTableToBitEstimates(
     85       NUM_DISTANCE_CODES, histo->distance, m->distance);
     86   ok = 1;
     87 
     88  Error:
     89   VP8LFreeHistogram(histo);
     90   return ok;
     91 }
     92 
     93 static WEBP_INLINE int64_t GetLiteralCost(const CostModel* const m,
     94                                           uint32_t v) {
     95   return (int64_t)m->alpha[v >> 24] + m->red[(v >> 16) & 0xff] +
     96          m->literal[(v >> 8) & 0xff] + m->blue[v & 0xff];
     97 }
     98 
     99 static WEBP_INLINE int64_t GetCacheCost(const CostModel* const m,
    100                                         uint32_t idx) {
    101   const int literal_idx = VALUES_IN_BYTE + NUM_LENGTH_CODES + idx;
    102   return (int64_t)m->literal[literal_idx];
    103 }
    104 
    105 static WEBP_INLINE int64_t GetLengthCost(const CostModel* const m,
    106                                          uint32_t length) {
    107   int code, extra_bits;
    108   VP8LPrefixEncodeBits(length, &code, &extra_bits);
    109   return (int64_t)m->literal[VALUES_IN_BYTE + code] +
    110          ((int64_t)extra_bits << LOG_2_PRECISION_BITS);
    111 }
    112 
    113 static WEBP_INLINE int64_t GetDistanceCost(const CostModel* const m,
    114                                            uint32_t distance) {
    115   int code, extra_bits;
    116   VP8LPrefixEncodeBits(distance, &code, &extra_bits);
    117   return (int64_t)m->distance[code] +
    118          ((int64_t)extra_bits << LOG_2_PRECISION_BITS);
    119 }
    120 
    121 static WEBP_INLINE void AddSingleLiteralWithCostModel(
    122     const uint32_t* const argb, VP8LColorCache* const hashers,
    123     const CostModel* const cost_model, int idx, int use_color_cache,
    124     int64_t prev_cost, int64_t* const cost, uint16_t* const dist_array) {
    125   int64_t cost_val = prev_cost;
    126   const uint32_t color = argb[idx];
    127   const int ix = use_color_cache ? VP8LColorCacheContains(hashers, color) : -1;
    128   if (ix >= 0) {
    129     // use_color_cache is true and hashers contains color
    130     cost_val += DivRound(GetCacheCost(cost_model, ix) * 68, 100);
    131   } else {
    132     if (use_color_cache) VP8LColorCacheInsert(hashers, color);
    133     cost_val += DivRound(GetLiteralCost(cost_model, color) * 82, 100);
    134   }
    135   if (cost[idx] > cost_val) {
    136     cost[idx] = cost_val;
    137     dist_array[idx] = 1;  // only one is inserted.
    138   }
    139 }
    140 
    141 // -----------------------------------------------------------------------------
    142 // CostManager and interval handling
    143 
    144 // Empirical value to avoid high memory consumption but good for performance.
    145 #define COST_CACHE_INTERVAL_SIZE_MAX 500
    146 
    147 // To perform backward reference every pixel at index 'index' is considered and
    148 // the cost for the MAX_LENGTH following pixels computed. Those following pixels
    149 // at index 'index' + k (k from 0 to MAX_LENGTH) have a cost of:
    150 //     cost = distance cost at index + GetLengthCost(cost_model, k)
    151 // and the minimum value is kept. GetLengthCost(cost_model, k) is cached in an
    152 // array of size MAX_LENGTH.
    153 // Instead of performing MAX_LENGTH comparisons per pixel, we keep track of the
    154 // minimal values using intervals of constant cost.
    155 // An interval is defined by the 'index' of the pixel that generated it and
    156 // is only useful in a range of indices from 'start' to 'end' (exclusive), i.e.
    157 // it contains the minimum value for pixels between start and end.
    158 // Intervals are stored in a linked list and ordered by 'start'. When a new
    159 // interval has a better value, old intervals are split or removed. There are
    160 // therefore no overlapping intervals.
    161 typedef struct CostInterval CostInterval;
    162 struct CostInterval {
    163   int64_t cost;
    164   int start;
    165   int end;
    166   int index;
    167   CostInterval* previous;
    168   CostInterval* next;
    169 };
    170 
    171 // The GetLengthCost(cost_model, k) are cached in a CostCacheInterval.
    172 typedef struct {
    173   int64_t cost;
    174   int start;
    175   int end;       // Exclusive.
    176 } CostCacheInterval;
    177 
    178 // This structure is in charge of managing intervals and costs.
    179 // It caches the different CostCacheInterval, caches the different
    180 // GetLengthCost(cost_model, k) in cost_cache and the CostInterval's (whose
    181 // 'count' is limited by COST_CACHE_INTERVAL_SIZE_MAX).
    182 #define COST_MANAGER_MAX_FREE_LIST 10
    183 typedef struct {
    184   CostInterval* head;
    185   int count;  // The number of stored intervals.
    186   CostCacheInterval* cache_intervals;
    187   size_t cache_intervals_size;
    188   // Contains the GetLengthCost(cost_model, k).
    189   int64_t cost_cache[MAX_LENGTH];
    190   int64_t* costs;
    191   uint16_t* dist_array;
    192   // Most of the time, we only need few intervals -> use a free-list, to avoid
    193   // fragmentation with small allocs in most common cases.
    194   CostInterval intervals[COST_MANAGER_MAX_FREE_LIST];
    195   CostInterval* free_intervals;
    196   // These are regularly malloc'd remains. This list can't grow larger than than
    197   // size COST_CACHE_INTERVAL_SIZE_MAX - COST_MANAGER_MAX_FREE_LIST, note.
    198   CostInterval* recycled_intervals;
    199 } CostManager;
    200 
    201 static void CostIntervalAddToFreeList(CostManager* const manager,
    202                                       CostInterval* const interval) {
    203   interval->next = manager->free_intervals;
    204   manager->free_intervals = interval;
    205 }
    206 
    207 static int CostIntervalIsInFreeList(const CostManager* const manager,
    208                                     const CostInterval* const interval) {
    209   return (interval >= &manager->intervals[0] &&
    210           interval <= &manager->intervals[COST_MANAGER_MAX_FREE_LIST - 1]);
    211 }
    212 
    213 static void CostManagerInitFreeList(CostManager* const manager) {
    214   int i;
    215   manager->free_intervals = NULL;
    216   for (i = 0; i < COST_MANAGER_MAX_FREE_LIST; ++i) {
    217     CostIntervalAddToFreeList(manager, &manager->intervals[i]);
    218   }
    219 }
    220 
    221 static void DeleteIntervalList(CostManager* const manager,
    222                                const CostInterval* interval) {
    223   while (interval != NULL) {
    224     const CostInterval* const next = interval->next;
    225     if (!CostIntervalIsInFreeList(manager, interval)) {
    226       WebPSafeFree((void*)interval);
    227     }  // else: do nothing
    228     interval = next;
    229   }
    230 }
    231 
    232 static void CostManagerClear(CostManager* const manager) {
    233   if (manager == NULL) return;
    234 
    235   WebPSafeFree(manager->costs);
    236   WebPSafeFree(manager->cache_intervals);
    237 
    238   // Clear the interval lists.
    239   DeleteIntervalList(manager, manager->head);
    240   manager->head = NULL;
    241   DeleteIntervalList(manager, manager->recycled_intervals);
    242   manager->recycled_intervals = NULL;
    243 
    244   // Reset pointers, 'count' and 'cache_intervals_size'.
    245   memset(manager, 0, sizeof(*manager));
    246   CostManagerInitFreeList(manager);
    247 }
    248 
    249 static int CostManagerInit(CostManager* const manager,
    250                            uint16_t* const dist_array, int pix_count,
    251                            const CostModel* const cost_model) {
    252   int i;
    253   const int cost_cache_size = (pix_count > MAX_LENGTH) ? MAX_LENGTH : pix_count;
    254 
    255   manager->costs = NULL;
    256   manager->cache_intervals = NULL;
    257   manager->head = NULL;
    258   manager->recycled_intervals = NULL;
    259   manager->count = 0;
    260   manager->dist_array = dist_array;
    261   CostManagerInitFreeList(manager);
    262 
    263   // Fill in the 'cost_cache'.
    264   // Has to be done in two passes due to a GCC bug on i686
    265   // related to https://gcc.gnu.org/bugzilla/show_bug.cgi?id=323
    266   for (i = 0; i < cost_cache_size; ++i) {
    267     manager->cost_cache[i] = GetLengthCost(cost_model, i);
    268   }
    269   manager->cache_intervals_size = 1;
    270   for (i = 1; i < cost_cache_size; ++i) {
    271     // Get the number of bound intervals.
    272     if (manager->cost_cache[i] != manager->cost_cache[i - 1]) {
    273       ++manager->cache_intervals_size;
    274     }
    275   }
    276 
    277   // With the current cost model, we usually have below 20 intervals.
    278   // The worst case scenario with a cost model would be if every length has a
    279   // different cost, hence MAX_LENGTH but that is impossible with the current
    280   // implementation that spirals around a pixel.
    281   assert(manager->cache_intervals_size <= MAX_LENGTH);
    282   manager->cache_intervals = (CostCacheInterval*)WebPSafeMalloc(
    283       manager->cache_intervals_size, sizeof(*manager->cache_intervals));
    284   if (manager->cache_intervals == NULL) {
    285     CostManagerClear(manager);
    286     return 0;
    287   }
    288 
    289   // Fill in the 'cache_intervals'.
    290   {
    291     CostCacheInterval* cur = manager->cache_intervals;
    292 
    293     // Consecutive values in 'cost_cache' are compared and if a big enough
    294     // difference is found, a new interval is created and bounded.
    295     cur->start = 0;
    296     cur->end = 1;
    297     cur->cost = manager->cost_cache[0];
    298     for (i = 1; i < cost_cache_size; ++i) {
    299       const int64_t cost_val = manager->cost_cache[i];
    300       if (cost_val != cur->cost) {
    301         ++cur;
    302         // Initialize an interval.
    303         cur->start = i;
    304         cur->cost = cost_val;
    305       }
    306       cur->end = i + 1;
    307     }
    308     assert((size_t)(cur - manager->cache_intervals) + 1 ==
    309            manager->cache_intervals_size);
    310   }
    311 
    312   manager->costs =
    313       (int64_t*)WebPSafeMalloc(pix_count, sizeof(*manager->costs));
    314   if (manager->costs == NULL) {
    315     CostManagerClear(manager);
    316     return 0;
    317   }
    318   // Set the initial 'costs' to INT64_MAX for every pixel as we will keep the
    319   // minimum.
    320   for (i = 0; i < pix_count; ++i) manager->costs[i] = WEBP_INT64_MAX;
    321 
    322   return 1;
    323 }
    324 
    325 // Given the cost and the position that define an interval, update the cost at
    326 // pixel 'i' if it is smaller than the previously computed value.
    327 static WEBP_INLINE void UpdateCost(CostManager* const manager, int i,
    328                                    int position, int64_t cost) {
    329   const int k = i - position;
    330   assert(k >= 0 && k < MAX_LENGTH);
    331 
    332   if (manager->costs[i] > cost) {
    333     manager->costs[i] = cost;
    334     manager->dist_array[i] = k + 1;
    335   }
    336 }
    337 
    338 // Given the cost and the position that define an interval, update the cost for
    339 // all the pixels between 'start' and 'end' excluded.
    340 static WEBP_INLINE void UpdateCostPerInterval(CostManager* const manager,
    341                                               int start, int end, int position,
    342                                               int64_t cost) {
    343   int i;
    344   for (i = start; i < end; ++i) UpdateCost(manager, i, position, cost);
    345 }
    346 
    347 // Given two intervals, make 'prev' be the previous one of 'next' in 'manager'.
    348 static WEBP_INLINE void ConnectIntervals(CostManager* const manager,
    349                                          CostInterval* const prev,
    350                                          CostInterval* const next) {
    351   if (prev != NULL) {
    352     prev->next = next;
    353   } else {
    354     manager->head = next;
    355   }
    356 
    357   if (next != NULL) next->previous = prev;
    358 }
    359 
    360 // Pop an interval in the manager.
    361 static WEBP_INLINE void PopInterval(CostManager* const manager,
    362                                     CostInterval* const interval) {
    363   if (interval == NULL) return;
    364 
    365   ConnectIntervals(manager, interval->previous, interval->next);
    366   if (CostIntervalIsInFreeList(manager, interval)) {
    367     CostIntervalAddToFreeList(manager, interval);
    368   } else {  // recycle regularly malloc'd intervals too
    369     interval->next = manager->recycled_intervals;
    370     manager->recycled_intervals = interval;
    371   }
    372   --manager->count;
    373   assert(manager->count >= 0);
    374 }
    375 
    376 // Update the cost at index i by going over all the stored intervals that
    377 // overlap with i.
    378 // If 'do_clean_intervals' is set to something different than 0, intervals that
    379 // end before 'i' will be popped.
    380 static WEBP_INLINE void UpdateCostAtIndex(CostManager* const manager, int i,
    381                                           int do_clean_intervals) {
    382   CostInterval* current = manager->head;
    383 
    384   while (current != NULL && current->start <= i) {
    385     CostInterval* const next = current->next;
    386     if (current->end <= i) {
    387       if (do_clean_intervals) {
    388         // We have an outdated interval, remove it.
    389         PopInterval(manager, current);
    390       }
    391     } else {
    392       UpdateCost(manager, i, current->index, current->cost);
    393     }
    394     current = next;
    395   }
    396 }
    397 
    398 // Given a current orphan interval and its previous interval, before
    399 // it was orphaned (which can be NULL), set it at the right place in the list
    400 // of intervals using the 'start' ordering and the previous interval as a hint.
    401 static WEBP_INLINE void PositionOrphanInterval(CostManager* const manager,
    402                                                CostInterval* const current,
    403                                                CostInterval* previous) {
    404   assert(current != NULL);
    405 
    406   if (previous == NULL) previous = manager->head;
    407   while (previous != NULL && current->start < previous->start) {
    408     previous = previous->previous;
    409   }
    410   while (previous != NULL && previous->next != NULL &&
    411          previous->next->start < current->start) {
    412     previous = previous->next;
    413   }
    414 
    415   if (previous != NULL) {
    416     ConnectIntervals(manager, current, previous->next);
    417   } else {
    418     ConnectIntervals(manager, current, manager->head);
    419   }
    420   ConnectIntervals(manager, previous, current);
    421 }
    422 
    423 // Insert an interval in the list contained in the manager by starting at
    424 // 'interval_in' as a hint. The intervals are sorted by 'start' value.
    425 static WEBP_INLINE void InsertInterval(CostManager* const manager,
    426                                        CostInterval* const interval_in,
    427                                        int64_t cost, int position, int start,
    428                                        int end) {
    429   CostInterval* interval_new;
    430 
    431   if (start >= end) return;
    432   if (manager->count >= COST_CACHE_INTERVAL_SIZE_MAX) {
    433     // Serialize the interval if we cannot store it.
    434     UpdateCostPerInterval(manager, start, end, position, cost);
    435     return;
    436   }
    437   if (manager->free_intervals != NULL) {
    438     interval_new = manager->free_intervals;
    439     manager->free_intervals = interval_new->next;
    440   } else if (manager->recycled_intervals != NULL) {
    441     interval_new = manager->recycled_intervals;
    442     manager->recycled_intervals = interval_new->next;
    443   } else {  // malloc for good
    444     interval_new = (CostInterval*)WebPSafeMalloc(1, sizeof(*interval_new));
    445     if (interval_new == NULL) {
    446       // Write down the interval if we cannot create it.
    447       UpdateCostPerInterval(manager, start, end, position, cost);
    448       return;
    449     }
    450   }
    451 
    452   interval_new->cost = cost;
    453   interval_new->index = position;
    454   interval_new->start = start;
    455   interval_new->end = end;
    456   PositionOrphanInterval(manager, interval_new, interval_in);
    457 
    458   ++manager->count;
    459 }
    460 
    461 // Given a new cost interval defined by its start at position, its length value
    462 // and distance_cost, add its contributions to the previous intervals and costs.
    463 // If handling the interval or one of its subintervals becomes to heavy, its
    464 // contribution is added to the costs right away.
    465 static WEBP_INLINE void PushInterval(CostManager* const manager,
    466                                      int64_t distance_cost, int position,
    467                                      int len) {
    468   size_t i;
    469   CostInterval* interval = manager->head;
    470   CostInterval* interval_next;
    471   const CostCacheInterval* const cost_cache_intervals =
    472       manager->cache_intervals;
    473   // If the interval is small enough, no need to deal with the heavy
    474   // interval logic, just serialize it right away. This constant is empirical.
    475   const int kSkipDistance = 10;
    476 
    477   if (len < kSkipDistance) {
    478     int j;
    479     for (j = position; j < position + len; ++j) {
    480       const int k = j - position;
    481       int64_t cost_tmp;
    482       assert(k >= 0 && k < MAX_LENGTH);
    483       cost_tmp = distance_cost + manager->cost_cache[k];
    484 
    485       if (manager->costs[j] > cost_tmp) {
    486         manager->costs[j] = cost_tmp;
    487         manager->dist_array[j] = k + 1;
    488       }
    489     }
    490     return;
    491   }
    492 
    493   for (i = 0; i < manager->cache_intervals_size &&
    494               cost_cache_intervals[i].start < len;
    495        ++i) {
    496     // Define the intersection of the ith interval with the new one.
    497     int start = position + cost_cache_intervals[i].start;
    498     const int end = position + (cost_cache_intervals[i].end > len
    499                                  ? len
    500                                  : cost_cache_intervals[i].end);
    501     const int64_t cost = distance_cost + cost_cache_intervals[i].cost;
    502 
    503     for (; interval != NULL && interval->start < end;
    504          interval = interval_next) {
    505       interval_next = interval->next;
    506 
    507       // Make sure we have some overlap
    508       if (start >= interval->end) continue;
    509 
    510       if (cost >= interval->cost) {
    511         // When intervals are represented, the lower, the better.
    512         // [**********************************************************[
    513         // start                                                    end
    514         //                   [----------------------------------[
    515         //                   interval->start        interval->end
    516         // If we are worse than what we already have, add whatever we have so
    517         // far up to interval.
    518         const int start_new = interval->end;
    519         InsertInterval(manager, interval, cost, position, start,
    520                        interval->start);
    521         start = start_new;
    522         if (start >= end) break;
    523         continue;
    524       }
    525 
    526       if (start <= interval->start) {
    527         if (interval->end <= end) {
    528           //                   [----------------------------------[
    529           //                   interval->start        interval->end
    530           // [**************************************************************[
    531           // start                                                        end
    532           // We can safely remove the old interval as it is fully included.
    533           PopInterval(manager, interval);
    534         } else {
    535           //              [------------------------------------[
    536           //              interval->start          interval->end
    537           // [*****************************[
    538           // start                       end
    539           interval->start = end;
    540           break;
    541         }
    542       } else {
    543         if (end < interval->end) {
    544           // [--------------------------------------------------------------[
    545           // interval->start                                    interval->end
    546           //                     [*****************************[
    547           //                     start                       end
    548           // We have to split the old interval as it fully contains the new one.
    549           const int end_original = interval->end;
    550           interval->end = start;
    551           InsertInterval(manager, interval, interval->cost, interval->index,
    552                          end, end_original);
    553           interval = interval->next;
    554           break;
    555         } else {
    556           // [------------------------------------[
    557           // interval->start          interval->end
    558           //                     [*****************************[
    559           //                     start                       end
    560           interval->end = start;
    561         }
    562       }
    563     }
    564     // Insert the remaining interval from start to end.
    565     InsertInterval(manager, interval, cost, position, start, end);
    566   }
    567 }
    568 
    569 static int BackwardReferencesHashChainDistanceOnly(
    570     int xsize, int ysize, const uint32_t* const argb, int cache_bits,
    571     const VP8LHashChain* const hash_chain, const VP8LBackwardRefs* const refs,
    572     uint16_t* const dist_array) {
    573   int i;
    574   int ok = 0;
    575   int cc_init = 0;
    576   const int pix_count = xsize * ysize;
    577   const int use_color_cache = (cache_bits > 0);
    578   const size_t literal_array_size =
    579       sizeof(*((CostModel*)NULL)->literal) * VP8LHistogramNumCodes(cache_bits);
    580   const size_t cost_model_size = sizeof(CostModel) + literal_array_size;
    581   CostModel* const cost_model =
    582       (CostModel*)WebPSafeCalloc(1ULL, cost_model_size);
    583   VP8LColorCache hashers;
    584   CostManager* cost_manager =
    585       (CostManager*)WebPSafeCalloc(1ULL, sizeof(*cost_manager));
    586   int offset_prev = -1, len_prev = -1;
    587   int64_t offset_cost = -1;
    588   int first_offset_is_constant = -1;  // initialized with 'impossible' value
    589   int reach = 0;
    590 
    591   if (cost_model == NULL || cost_manager == NULL) goto Error;
    592 
    593   cost_model->literal = (uint32_t*)(cost_model + 1);
    594   if (use_color_cache) {
    595     cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    596     if (!cc_init) goto Error;
    597   }
    598 
    599   if (!CostModelBuild(cost_model, xsize, cache_bits, refs)) {
    600     goto Error;
    601   }
    602 
    603   if (!CostManagerInit(cost_manager, dist_array, pix_count, cost_model)) {
    604     goto Error;
    605   }
    606 
    607   // We loop one pixel at a time, but store all currently best points to
    608   // non-processed locations from this point.
    609   dist_array[0] = 0;
    610   // Add first pixel as literal.
    611   AddSingleLiteralWithCostModel(argb, &hashers, cost_model, /*idx=*/0,
    612                                 use_color_cache, /*prev_cost=*/0,
    613                                 cost_manager->costs, dist_array);
    614 
    615   for (i = 1; i < pix_count; ++i) {
    616     const int64_t prev_cost = cost_manager->costs[i - 1];
    617     int offset, len;
    618     VP8LHashChainFindCopy(hash_chain, i, &offset, &len);
    619 
    620     // Try adding the pixel as a literal.
    621     AddSingleLiteralWithCostModel(argb, &hashers, cost_model, i,
    622                                   use_color_cache, prev_cost,
    623                                   cost_manager->costs, dist_array);
    624 
    625     // If we are dealing with a non-literal.
    626     if (len >= 2) {
    627       if (offset != offset_prev) {
    628         const int code = VP8LDistanceToPlaneCode(xsize, offset);
    629         offset_cost = GetDistanceCost(cost_model, code);
    630         first_offset_is_constant = 1;
    631         PushInterval(cost_manager, prev_cost + offset_cost, i, len);
    632       } else {
    633         assert(offset_cost >= 0);
    634         assert(len_prev >= 0);
    635         assert(first_offset_is_constant == 0 || first_offset_is_constant == 1);
    636         // Instead of considering all contributions from a pixel i by calling:
    637         //         PushInterval(cost_manager, prev_cost + offset_cost, i, len);
    638         // we optimize these contributions in case offset_cost stays the same
    639         // for consecutive pixels. This describes a set of pixels similar to a
    640         // previous set (e.g. constant color regions).
    641         if (first_offset_is_constant) {
    642           reach = i - 1 + len_prev - 1;
    643           first_offset_is_constant = 0;
    644         }
    645 
    646         if (i + len - 1 > reach) {
    647           // We can only be go further with the same offset if the previous
    648           // length was maxed, hence len_prev == len == MAX_LENGTH.
    649           // TODO(vrabaud), bump i to the end right away (insert cache and
    650           // update cost).
    651           // TODO(vrabaud), check if one of the points in between does not have
    652           // a lower cost.
    653           // Already consider the pixel at "reach" to add intervals that are
    654           // better than whatever we add.
    655           int offset_j, len_j = 0;
    656           int j;
    657           assert(len == MAX_LENGTH || len == pix_count - i);
    658           // Figure out the last consecutive pixel within [i, reach + 1] with
    659           // the same offset.
    660           for (j = i; j <= reach; ++j) {
    661             VP8LHashChainFindCopy(hash_chain, j + 1, &offset_j, &len_j);
    662             if (offset_j != offset) {
    663               VP8LHashChainFindCopy(hash_chain, j, &offset_j, &len_j);
    664               break;
    665             }
    666           }
    667           // Update the cost at j - 1 and j.
    668           UpdateCostAtIndex(cost_manager, j - 1, 0);
    669           UpdateCostAtIndex(cost_manager, j, 0);
    670 
    671           PushInterval(cost_manager, cost_manager->costs[j - 1] + offset_cost,
    672                        j, len_j);
    673           reach = j + len_j - 1;
    674         }
    675       }
    676     }
    677 
    678     UpdateCostAtIndex(cost_manager, i, 1);
    679     offset_prev = offset;
    680     len_prev = len;
    681   }
    682 
    683   ok = !refs->error;
    684  Error:
    685   if (cc_init) VP8LColorCacheClear(&hashers);
    686   CostManagerClear(cost_manager);
    687   WebPSafeFree(cost_model);
    688   WebPSafeFree(cost_manager);
    689   return ok;
    690 }
    691 
    692 // We pack the path at the end of *dist_array and return
    693 // a pointer to this part of the array. Example:
    694 // dist_array = [1x2xx3x2] => packed [1x2x1232], chosen_path = [1232]
    695 static void TraceBackwards(uint16_t* const dist_array,
    696                            int dist_array_size,
    697                            uint16_t** const chosen_path,
    698                            int* const chosen_path_size) {
    699   uint16_t* path = dist_array + dist_array_size;
    700   uint16_t* cur = dist_array + dist_array_size - 1;
    701   while (cur >= dist_array) {
    702     const int k = *cur;
    703     --path;
    704     *path = k;
    705     cur -= k;
    706   }
    707   *chosen_path = path;
    708   *chosen_path_size = (int)(dist_array + dist_array_size - path);
    709 }
    710 
    711 static int BackwardReferencesHashChainFollowChosenPath(
    712     const uint32_t* const argb, int cache_bits,
    713     const uint16_t* const chosen_path, int chosen_path_size,
    714     const VP8LHashChain* const hash_chain, VP8LBackwardRefs* const refs) {
    715   const int use_color_cache = (cache_bits > 0);
    716   int ix;
    717   int i = 0;
    718   int ok = 0;
    719   int cc_init = 0;
    720   VP8LColorCache hashers;
    721 
    722   if (use_color_cache) {
    723     cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    724     if (!cc_init) goto Error;
    725   }
    726 
    727   VP8LClearBackwardRefs(refs);
    728   for (ix = 0; ix < chosen_path_size; ++ix) {
    729     const int len = chosen_path[ix];
    730     if (len != 1) {
    731       int k;
    732       const int offset = VP8LHashChainFindOffset(hash_chain, i);
    733       VP8LBackwardRefsCursorAdd(refs, PixOrCopyCreateCopy(offset, len));
    734       if (use_color_cache) {
    735         for (k = 0; k < len; ++k) {
    736           VP8LColorCacheInsert(&hashers, argb[i + k]);
    737         }
    738       }
    739       i += len;
    740     } else {
    741       PixOrCopy v;
    742       const int idx =
    743           use_color_cache ? VP8LColorCacheContains(&hashers, argb[i]) : -1;
    744       if (idx >= 0) {
    745         // use_color_cache is true and hashers contains argb[i]
    746         // push pixel as a color cache index
    747         v = PixOrCopyCreateCacheIdx(idx);
    748       } else {
    749         if (use_color_cache) VP8LColorCacheInsert(&hashers, argb[i]);
    750         v = PixOrCopyCreateLiteral(argb[i]);
    751       }
    752       VP8LBackwardRefsCursorAdd(refs, v);
    753       ++i;
    754     }
    755   }
    756   ok = !refs->error;
    757  Error:
    758   if (cc_init) VP8LColorCacheClear(&hashers);
    759   return ok;
    760 }
    761 
    762 // Returns 1 on success.
    763 extern int VP8LBackwardReferencesTraceBackwards(
    764     int xsize, int ysize, const uint32_t* const argb, int cache_bits,
    765     const VP8LHashChain* const hash_chain,
    766     const VP8LBackwardRefs* const refs_src, VP8LBackwardRefs* const refs_dst);
    767 int VP8LBackwardReferencesTraceBackwards(int xsize, int ysize,
    768                                          const uint32_t* const argb,
    769                                          int cache_bits,
    770                                          const VP8LHashChain* const hash_chain,
    771                                          const VP8LBackwardRefs* const refs_src,
    772                                          VP8LBackwardRefs* const refs_dst) {
    773   int ok = 0;
    774   const int dist_array_size = xsize * ysize;
    775   uint16_t* chosen_path = NULL;
    776   int chosen_path_size = 0;
    777   uint16_t* dist_array =
    778       (uint16_t*)WebPSafeMalloc(dist_array_size, sizeof(*dist_array));
    779 
    780   if (dist_array == NULL) goto Error;
    781 
    782   if (!BackwardReferencesHashChainDistanceOnly(
    783           xsize, ysize, argb, cache_bits, hash_chain, refs_src, dist_array)) {
    784     goto Error;
    785   }
    786   TraceBackwards(dist_array, dist_array_size, &chosen_path, &chosen_path_size);
    787   if (!BackwardReferencesHashChainFollowChosenPath(
    788           argb, cache_bits, chosen_path, chosen_path_size, hash_chain,
    789           refs_dst)) {
    790     goto Error;
    791   }
    792   ok = 1;
    793  Error:
    794   WebPSafeFree(dist_array);
    795   return ok;
    796 }