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      1 // Copyright 2012 Google Inc. All Rights Reserved.
      2 //
      3 // This code is licensed under the same terms as WebM:
      4 //  Software License Agreement:  http://www.webmproject.org/license/software/
      5 //  Additional IP Rights Grant:  http://www.webmproject.org/license/additional/
      6 // -----------------------------------------------------------------------------
      7 //
      8 // Author: Jyrki Alakuijala (jyrki (at) google.com)
      9 //
     10 
     11 #include <assert.h>
     12 #include <math.h>
     13 #include <stdio.h>
     14 
     15 #include "./backward_references.h"
     16 #include "./histogram.h"
     17 #include "../dsp/lossless.h"
     18 #include "../utils/color_cache.h"
     19 #include "../utils/utils.h"
     20 
     21 #define VALUES_IN_BYTE 256
     22 
     23 #define HASH_BITS 18
     24 #define HASH_SIZE (1 << HASH_BITS)
     25 #define HASH_MULTIPLIER (0xc6a4a7935bd1e995ULL)
     26 
     27 // 1M window (4M bytes) minus 120 special codes for short distances.
     28 #define WINDOW_SIZE ((1 << 20) - 120)
     29 
     30 // Bounds for the match length.
     31 #define MIN_LENGTH 2
     32 #define MAX_LENGTH 4096
     33 
     34 typedef struct {
     35   // Stores the most recently added position with the given hash value.
     36   int32_t hash_to_first_index_[HASH_SIZE];
     37   // chain_[pos] stores the previous position with the same hash value
     38   // for every pixel in the image.
     39   int32_t* chain_;
     40 } HashChain;
     41 
     42 // -----------------------------------------------------------------------------
     43 
     44 static const uint8_t plane_to_code_lut[128] = {
     45  96,   73,  55,  39,  23,  13,   5,  1,  255, 255, 255, 255, 255, 255, 255, 255,
     46  101,  78,  58,  42,  26,  16,   8,  2,    0,   3,  9,   17,  27,  43,  59,  79,
     47  102,  86,  62,  46,  32,  20,  10,  6,    4,   7,  11,  21,  33,  47,  63,  87,
     48  105,  90,  70,  52,  37,  28,  18,  14,  12,  15,  19,  29,  38,  53,  71,  91,
     49  110,  99,  82,  66,  48,  35,  30,  24,  22,  25,  31,  36,  49,  67,  83, 100,
     50  115, 108,  94,  76,  64,  50,  44,  40,  34,  41,  45,  51,  65,  77,  95, 109,
     51  118, 113, 103,  92,  80,  68,  60,  56,  54,  57,  61,  69,  81,  93, 104, 114,
     52  119, 116, 111, 106,  97,  88,  84,  74,  72,  75,  85,  89,  98, 107, 112, 117
     53 };
     54 
     55 static int DistanceToPlaneCode(int xsize, int dist) {
     56   const int yoffset = dist / xsize;
     57   const int xoffset = dist - yoffset * xsize;
     58   if (xoffset <= 8 && yoffset < 8) {
     59     return plane_to_code_lut[yoffset * 16 + 8 - xoffset] + 1;
     60   } else if (xoffset > xsize - 8 && yoffset < 7) {
     61     return plane_to_code_lut[(yoffset + 1) * 16 + 8 + (xsize - xoffset)] + 1;
     62   }
     63   return dist + 120;
     64 }
     65 
     66 static WEBP_INLINE int FindMatchLength(const uint32_t* const array1,
     67                                        const uint32_t* const array2,
     68                                        const int max_limit) {
     69   int match_len = 0;
     70   while (match_len < max_limit && array1[match_len] == array2[match_len]) {
     71     ++match_len;
     72   }
     73   return match_len;
     74 }
     75 
     76 // -----------------------------------------------------------------------------
     77 //  VP8LBackwardRefs
     78 
     79 void VP8LInitBackwardRefs(VP8LBackwardRefs* const refs) {
     80   if (refs != NULL) {
     81     refs->refs = NULL;
     82     refs->size = 0;
     83     refs->max_size = 0;
     84   }
     85 }
     86 
     87 void VP8LClearBackwardRefs(VP8LBackwardRefs* const refs) {
     88   if (refs != NULL) {
     89     free(refs->refs);
     90     VP8LInitBackwardRefs(refs);
     91   }
     92 }
     93 
     94 int VP8LBackwardRefsAlloc(VP8LBackwardRefs* const refs, int max_size) {
     95   assert(refs != NULL);
     96   refs->size = 0;
     97   refs->max_size = 0;
     98   refs->refs = (PixOrCopy*)WebPSafeMalloc((uint64_t)max_size,
     99                                           sizeof(*refs->refs));
    100   if (refs->refs == NULL) return 0;
    101   refs->max_size = max_size;
    102   return 1;
    103 }
    104 
    105 // -----------------------------------------------------------------------------
    106 // Hash chains
    107 
    108 static WEBP_INLINE uint64_t GetPixPairHash64(const uint32_t* const argb) {
    109   uint64_t key = ((uint64_t)(argb[1]) << 32) | argb[0];
    110   key = (key * HASH_MULTIPLIER) >> (64 - HASH_BITS);
    111   return key;
    112 }
    113 
    114 static int HashChainInit(HashChain* const p, int size) {
    115   int i;
    116   p->chain_ = (int*)WebPSafeMalloc((uint64_t)size, sizeof(*p->chain_));
    117   if (p->chain_ == NULL) {
    118     return 0;
    119   }
    120   for (i = 0; i < size; ++i) {
    121     p->chain_[i] = -1;
    122   }
    123   for (i = 0; i < HASH_SIZE; ++i) {
    124     p->hash_to_first_index_[i] = -1;
    125   }
    126   return 1;
    127 }
    128 
    129 static void HashChainDelete(HashChain* const p) {
    130   if (p != NULL) {
    131     free(p->chain_);
    132     free(p);
    133   }
    134 }
    135 
    136 // Insertion of two pixels at a time.
    137 static void HashChainInsert(HashChain* const p,
    138                             const uint32_t* const argb, int pos) {
    139   const uint64_t hash_code = GetPixPairHash64(argb);
    140   p->chain_[pos] = p->hash_to_first_index_[hash_code];
    141   p->hash_to_first_index_[hash_code] = pos;
    142 }
    143 
    144 static void GetParamsForHashChainFindCopy(int quality, int xsize,
    145                                           int* window_size, int* iter_pos,
    146                                           int* iter_limit) {
    147   const int iter_mult = (quality < 27) ? 1 : 1 + ((quality - 27) >> 4);
    148   // Limit the backward-ref window size for lower qualities.
    149   const int max_window_size = (quality > 50) ? WINDOW_SIZE
    150                             : (quality > 25) ? (xsize << 8)
    151                             : (xsize << 4);
    152   assert(xsize > 0);
    153   *window_size = (max_window_size > WINDOW_SIZE) ? WINDOW_SIZE
    154                : max_window_size;
    155   *iter_pos = 5 + (quality >> 3);
    156   *iter_limit = -quality * iter_mult;
    157 }
    158 
    159 static int HashChainFindCopy(const HashChain* const p,
    160                              int base_position, int xsize,
    161                              const uint32_t* const argb, int maxlen,
    162                              int window_size, int iter_pos, int iter_limit,
    163                              int* const distance_ptr,
    164                              int* const length_ptr) {
    165   const uint64_t hash_code = GetPixPairHash64(&argb[base_position]);
    166   int prev_length = 0;
    167   int64_t best_val = 0;
    168   int best_length = 0;
    169   int best_distance = 0;
    170   const uint32_t* const argb_start = argb + base_position;
    171   const int min_pos =
    172       (base_position > window_size) ? base_position - window_size : 0;
    173   int pos;
    174 
    175   assert(xsize > 0);
    176   for (pos = p->hash_to_first_index_[hash_code];
    177        pos >= min_pos;
    178        pos = p->chain_[pos]) {
    179     int64_t val;
    180     int curr_length;
    181     if (iter_pos < 0) {
    182       if (iter_pos < iter_limit || best_val >= 0xff0000) {
    183         break;
    184       }
    185     }
    186     --iter_pos;
    187     if (best_length != 0 &&
    188         argb[pos + best_length - 1] != argb_start[best_length - 1]) {
    189       continue;
    190     }
    191     curr_length = FindMatchLength(argb + pos, argb_start, maxlen);
    192     if (curr_length < prev_length) {
    193       continue;
    194     }
    195     val = 65536 * curr_length;
    196     // Favoring 2d locality here gives savings for certain images.
    197     if (base_position - pos < 9 * xsize) {
    198       const int y = (base_position - pos) / xsize;
    199       int x = (base_position - pos) % xsize;
    200       if (x > xsize / 2) {
    201         x = xsize - x;
    202       }
    203       if (x <= 7 && x >= -8) {
    204         val -= y * y + x * x;
    205       } else {
    206         val -= 9 * 9 + 9 * 9;
    207       }
    208     } else {
    209       val -= 9 * 9 + 9 * 9;
    210     }
    211     if (best_val < val) {
    212       prev_length = curr_length;
    213       best_val = val;
    214       best_length = curr_length;
    215       best_distance = base_position - pos;
    216       if (curr_length >= MAX_LENGTH) {
    217         break;
    218       }
    219       if ((best_distance == 1 || best_distance == xsize) &&
    220           best_length >= 128) {
    221         break;
    222       }
    223     }
    224   }
    225   *distance_ptr = best_distance;
    226   *length_ptr = best_length;
    227   return (best_length >= MIN_LENGTH);
    228 }
    229 
    230 static WEBP_INLINE void PushBackCopy(VP8LBackwardRefs* const refs, int length) {
    231   int size = refs->size;
    232   while (length >= MAX_LENGTH) {
    233     refs->refs[size++] = PixOrCopyCreateCopy(1, MAX_LENGTH);
    234     length -= MAX_LENGTH;
    235   }
    236   if (length > 0) {
    237     refs->refs[size++] = PixOrCopyCreateCopy(1, length);
    238   }
    239   refs->size = size;
    240 }
    241 
    242 static void BackwardReferencesRle(int xsize, int ysize,
    243                                   const uint32_t* const argb,
    244                                   VP8LBackwardRefs* const refs) {
    245   const int pix_count = xsize * ysize;
    246   int match_len = 0;
    247   int i;
    248   refs->size = 0;
    249   PushBackCopy(refs, match_len);    // i=0 case
    250   refs->refs[refs->size++] = PixOrCopyCreateLiteral(argb[0]);
    251   for (i = 1; i < pix_count; ++i) {
    252     if (argb[i] == argb[i - 1]) {
    253       ++match_len;
    254     } else {
    255       PushBackCopy(refs, match_len);
    256       match_len = 0;
    257       refs->refs[refs->size++] = PixOrCopyCreateLiteral(argb[i]);
    258     }
    259   }
    260   PushBackCopy(refs, match_len);
    261 }
    262 
    263 static int BackwardReferencesHashChain(int xsize, int ysize,
    264                                        const uint32_t* const argb,
    265                                        int cache_bits, int quality,
    266                                        VP8LBackwardRefs* const refs) {
    267   int i;
    268   int ok = 0;
    269   int cc_init = 0;
    270   const int use_color_cache = (cache_bits > 0);
    271   const int pix_count = xsize * ysize;
    272   HashChain* const hash_chain = (HashChain*)malloc(sizeof(*hash_chain));
    273   VP8LColorCache hashers;
    274   int window_size = WINDOW_SIZE;
    275   int iter_pos = 1;
    276   int iter_limit = -1;
    277 
    278   if (hash_chain == NULL) return 0;
    279   if (use_color_cache) {
    280     cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    281     if (!cc_init) goto Error;
    282   }
    283 
    284   if (!HashChainInit(hash_chain, pix_count)) goto Error;
    285 
    286   refs->size = 0;
    287   GetParamsForHashChainFindCopy(quality, xsize, &window_size, &iter_pos,
    288                                 &iter_limit);
    289   for (i = 0; i < pix_count; ) {
    290     // Alternative#1: Code the pixels starting at 'i' using backward reference.
    291     int offset = 0;
    292     int len = 0;
    293     if (i < pix_count - 1) {  // FindCopy(i,..) reads pixels at [i] and [i + 1].
    294       int maxlen = pix_count - i;
    295       if (maxlen > MAX_LENGTH) {
    296         maxlen = MAX_LENGTH;
    297       }
    298       HashChainFindCopy(hash_chain, i, xsize, argb, maxlen,
    299                         window_size, iter_pos, iter_limit,
    300                         &offset, &len);
    301     }
    302     if (len >= MIN_LENGTH) {
    303       // Alternative#2: Insert the pixel at 'i' as literal, and code the
    304       // pixels starting at 'i + 1' using backward reference.
    305       int offset2 = 0;
    306       int len2 = 0;
    307       int k;
    308       HashChainInsert(hash_chain, &argb[i], i);
    309       if (i < pix_count - 2) {  // FindCopy(i+1,..) reads [i + 1] and [i + 2].
    310         int maxlen = pix_count - (i + 1);
    311         if (maxlen > MAX_LENGTH) {
    312           maxlen = MAX_LENGTH;
    313         }
    314         HashChainFindCopy(hash_chain, i + 1, xsize, argb, maxlen,
    315                           window_size, iter_pos, iter_limit,
    316                           &offset2, &len2);
    317         if (len2 > len + 1) {
    318           const uint32_t pixel = argb[i];
    319           // Alternative#2 is a better match. So push pixel at 'i' as literal.
    320           if (use_color_cache && VP8LColorCacheContains(&hashers, pixel)) {
    321             const int ix = VP8LColorCacheGetIndex(&hashers, pixel);
    322             refs->refs[refs->size] = PixOrCopyCreateCacheIdx(ix);
    323           } else {
    324             refs->refs[refs->size] = PixOrCopyCreateLiteral(pixel);
    325           }
    326           ++refs->size;
    327           if (use_color_cache) VP8LColorCacheInsert(&hashers, pixel);
    328           i++;  // Backward reference to be done for next pixel.
    329           len = len2;
    330           offset = offset2;
    331         }
    332       }
    333       if (len >= MAX_LENGTH) {
    334         len = MAX_LENGTH - 1;
    335       }
    336       refs->refs[refs->size++] = PixOrCopyCreateCopy(offset, len);
    337       if (use_color_cache) {
    338         for (k = 0; k < len; ++k) {
    339           VP8LColorCacheInsert(&hashers, argb[i + k]);
    340         }
    341       }
    342       // Add to the hash_chain (but cannot add the last pixel).
    343       {
    344         const int last = (len < pix_count - 1 - i) ? len : pix_count - 1 - i;
    345         for (k = 1; k < last; ++k) {
    346           HashChainInsert(hash_chain, &argb[i + k], i + k);
    347         }
    348       }
    349       i += len;
    350     } else {
    351       const uint32_t pixel = argb[i];
    352       if (use_color_cache && VP8LColorCacheContains(&hashers, pixel)) {
    353         // push pixel as a PixOrCopyCreateCacheIdx pixel
    354         const int ix = VP8LColorCacheGetIndex(&hashers, pixel);
    355         refs->refs[refs->size] = PixOrCopyCreateCacheIdx(ix);
    356       } else {
    357         refs->refs[refs->size] = PixOrCopyCreateLiteral(pixel);
    358       }
    359       ++refs->size;
    360       if (use_color_cache) VP8LColorCacheInsert(&hashers, pixel);
    361       if (i + 1 < pix_count) {
    362         HashChainInsert(hash_chain, &argb[i], i);
    363       }
    364       ++i;
    365     }
    366   }
    367   ok = 1;
    368 Error:
    369   if (cc_init) VP8LColorCacheClear(&hashers);
    370   HashChainDelete(hash_chain);
    371   return ok;
    372 }
    373 
    374 // -----------------------------------------------------------------------------
    375 
    376 typedef struct {
    377   double alpha_[VALUES_IN_BYTE];
    378   double red_[VALUES_IN_BYTE];
    379   double literal_[PIX_OR_COPY_CODES_MAX];
    380   double blue_[VALUES_IN_BYTE];
    381   double distance_[NUM_DISTANCE_CODES];
    382 } CostModel;
    383 
    384 static int BackwardReferencesTraceBackwards(
    385     int xsize, int ysize, int recursive_cost_model,
    386     const uint32_t* const argb, int quality, int cache_bits,
    387     VP8LBackwardRefs* const refs);
    388 
    389 static void ConvertPopulationCountTableToBitEstimates(
    390     int num_symbols, const int population_counts[], double output[]) {
    391   int sum = 0;
    392   int nonzeros = 0;
    393   int i;
    394   for (i = 0; i < num_symbols; ++i) {
    395     sum += population_counts[i];
    396     if (population_counts[i] > 0) {
    397       ++nonzeros;
    398     }
    399   }
    400   if (nonzeros <= 1) {
    401     memset(output, 0, num_symbols * sizeof(*output));
    402   } else {
    403     const double logsum = VP8LFastLog2(sum);
    404     for (i = 0; i < num_symbols; ++i) {
    405       output[i] = logsum - VP8LFastLog2(population_counts[i]);
    406     }
    407   }
    408 }
    409 
    410 static int CostModelBuild(CostModel* const m, int xsize, int ysize,
    411                           int recursion_level, const uint32_t* const argb,
    412                           int quality, int cache_bits) {
    413   int ok = 0;
    414   VP8LHistogram histo;
    415   VP8LBackwardRefs refs;
    416 
    417   if (!VP8LBackwardRefsAlloc(&refs, xsize * ysize)) goto Error;
    418 
    419   if (recursion_level > 0) {
    420     if (!BackwardReferencesTraceBackwards(xsize, ysize, recursion_level - 1,
    421                                           argb, quality, cache_bits, &refs)) {
    422       goto Error;
    423     }
    424   } else {
    425     if (!BackwardReferencesHashChain(xsize, ysize, argb, cache_bits, quality,
    426                                      &refs)) {
    427       goto Error;
    428     }
    429   }
    430   VP8LHistogramCreate(&histo, &refs, cache_bits);
    431   ConvertPopulationCountTableToBitEstimates(
    432       VP8LHistogramNumCodes(&histo), histo.literal_, m->literal_);
    433   ConvertPopulationCountTableToBitEstimates(
    434       VALUES_IN_BYTE, histo.red_, m->red_);
    435   ConvertPopulationCountTableToBitEstimates(
    436       VALUES_IN_BYTE, histo.blue_, m->blue_);
    437   ConvertPopulationCountTableToBitEstimates(
    438       VALUES_IN_BYTE, histo.alpha_, m->alpha_);
    439   ConvertPopulationCountTableToBitEstimates(
    440       NUM_DISTANCE_CODES, histo.distance_, m->distance_);
    441   ok = 1;
    442 
    443  Error:
    444   VP8LClearBackwardRefs(&refs);
    445   return ok;
    446 }
    447 
    448 static WEBP_INLINE double GetLiteralCost(const CostModel* const m, uint32_t v) {
    449   return m->alpha_[v >> 24] +
    450          m->red_[(v >> 16) & 0xff] +
    451          m->literal_[(v >> 8) & 0xff] +
    452          m->blue_[v & 0xff];
    453 }
    454 
    455 static WEBP_INLINE double GetCacheCost(const CostModel* const m, uint32_t idx) {
    456   const int literal_idx = VALUES_IN_BYTE + NUM_LENGTH_CODES + idx;
    457   return m->literal_[literal_idx];
    458 }
    459 
    460 static WEBP_INLINE double GetLengthCost(const CostModel* const m,
    461                                         uint32_t length) {
    462   int code, extra_bits_count, extra_bits_value;
    463   PrefixEncode(length, &code, &extra_bits_count, &extra_bits_value);
    464   return m->literal_[VALUES_IN_BYTE + code] + extra_bits_count;
    465 }
    466 
    467 static WEBP_INLINE double GetDistanceCost(const CostModel* const m,
    468                                           uint32_t distance) {
    469   int code, extra_bits_count, extra_bits_value;
    470   PrefixEncode(distance, &code, &extra_bits_count, &extra_bits_value);
    471   return m->distance_[code] + extra_bits_count;
    472 }
    473 
    474 static int BackwardReferencesHashChainDistanceOnly(
    475     int xsize, int ysize, int recursive_cost_model, const uint32_t* const argb,
    476     int quality, int cache_bits, uint32_t* const dist_array) {
    477   int i;
    478   int ok = 0;
    479   int cc_init = 0;
    480   const int pix_count = xsize * ysize;
    481   const int use_color_cache = (cache_bits > 0);
    482   float* const cost =
    483       (float*)WebPSafeMalloc((uint64_t)pix_count, sizeof(*cost));
    484   CostModel* cost_model = (CostModel*)malloc(sizeof(*cost_model));
    485   HashChain* hash_chain = (HashChain*)malloc(sizeof(*hash_chain));
    486   VP8LColorCache hashers;
    487   const double mul0 = (recursive_cost_model != 0) ? 1.0 : 0.68;
    488   const double mul1 = (recursive_cost_model != 0) ? 1.0 : 0.82;
    489   const int min_distance_code = 2;  // TODO(vikasa): tune as function of quality
    490   int window_size = WINDOW_SIZE;
    491   int iter_pos = 1;
    492   int iter_limit = -1;
    493 
    494   if (cost == NULL || cost_model == NULL || hash_chain == NULL) goto Error;
    495 
    496   if (!HashChainInit(hash_chain, pix_count)) goto Error;
    497 
    498   if (use_color_cache) {
    499     cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    500     if (!cc_init) goto Error;
    501   }
    502 
    503   if (!CostModelBuild(cost_model, xsize, ysize, recursive_cost_model, argb,
    504                       quality, cache_bits)) {
    505     goto Error;
    506   }
    507 
    508   for (i = 0; i < pix_count; ++i) cost[i] = 1e38f;
    509 
    510   // We loop one pixel at a time, but store all currently best points to
    511   // non-processed locations from this point.
    512   dist_array[0] = 0;
    513   GetParamsForHashChainFindCopy(quality, xsize, &window_size, &iter_pos,
    514                                 &iter_limit);
    515   for (i = 0; i < pix_count; ++i) {
    516     double prev_cost = 0.0;
    517     int shortmax;
    518     if (i > 0) {
    519       prev_cost = cost[i - 1];
    520     }
    521     for (shortmax = 0; shortmax < 2; ++shortmax) {
    522       int offset = 0;
    523       int len = 0;
    524       if (i < pix_count - 1) {  // FindCopy reads pixels at [i] and [i + 1].
    525         int maxlen = shortmax ? 2 : MAX_LENGTH;
    526         if (maxlen > pix_count - i) {
    527           maxlen = pix_count - i;
    528         }
    529         HashChainFindCopy(hash_chain, i, xsize, argb, maxlen,
    530                           window_size, iter_pos, iter_limit,
    531                           &offset, &len);
    532       }
    533       if (len >= MIN_LENGTH) {
    534         const int code = DistanceToPlaneCode(xsize, offset);
    535         const double distance_cost =
    536             prev_cost + GetDistanceCost(cost_model, code);
    537         int k;
    538         for (k = 1; k < len; ++k) {
    539           const double cost_val = distance_cost + GetLengthCost(cost_model, k);
    540           if (cost[i + k] > cost_val) {
    541             cost[i + k] = (float)cost_val;
    542             dist_array[i + k] = k + 1;
    543           }
    544         }
    545         // This if is for speedup only. It roughly doubles the speed, and
    546         // makes compression worse by .1 %.
    547         if (len >= 128 && code <= min_distance_code) {
    548           // Long copy for short distances, let's skip the middle
    549           // lookups for better copies.
    550           // 1) insert the hashes.
    551           if (use_color_cache) {
    552             for (k = 0; k < len; ++k) {
    553               VP8LColorCacheInsert(&hashers, argb[i + k]);
    554             }
    555           }
    556           // 2) Add to the hash_chain (but cannot add the last pixel)
    557           {
    558             const int last = (len + i < pix_count - 1) ? len + i
    559                                                        : pix_count - 1;
    560             for (k = i; k < last; ++k) {
    561               HashChainInsert(hash_chain, &argb[k], k);
    562             }
    563           }
    564           // 3) jump.
    565           i += len - 1;  // for loop does ++i, thus -1 here.
    566           goto next_symbol;
    567         }
    568       }
    569     }
    570     if (i < pix_count - 1) {
    571       HashChainInsert(hash_chain, &argb[i], i);
    572     }
    573     {
    574       // inserting a literal pixel
    575       double cost_val = prev_cost;
    576       if (use_color_cache && VP8LColorCacheContains(&hashers, argb[i])) {
    577         const int ix = VP8LColorCacheGetIndex(&hashers, argb[i]);
    578         cost_val += GetCacheCost(cost_model, ix) * mul0;
    579       } else {
    580         cost_val += GetLiteralCost(cost_model, argb[i]) * mul1;
    581       }
    582       if (cost[i] > cost_val) {
    583         cost[i] = (float)cost_val;
    584         dist_array[i] = 1;  // only one is inserted.
    585       }
    586       if (use_color_cache) VP8LColorCacheInsert(&hashers, argb[i]);
    587     }
    588  next_symbol: ;
    589   }
    590   // Last pixel still to do, it can only be a single step if not reached
    591   // through cheaper means already.
    592   ok = 1;
    593 Error:
    594   if (cc_init) VP8LColorCacheClear(&hashers);
    595   HashChainDelete(hash_chain);
    596   free(cost_model);
    597   free(cost);
    598   return ok;
    599 }
    600 
    601 // We pack the path at the end of *dist_array and return
    602 // a pointer to this part of the array. Example:
    603 // dist_array = [1x2xx3x2] => packed [1x2x1232], chosen_path = [1232]
    604 static void TraceBackwards(uint32_t* const dist_array,
    605                            int dist_array_size,
    606                            uint32_t** const chosen_path,
    607                            int* const chosen_path_size) {
    608   uint32_t* path = dist_array + dist_array_size;
    609   uint32_t* cur = dist_array + dist_array_size - 1;
    610   while (cur >= dist_array) {
    611     const int k = *cur;
    612     --path;
    613     *path = k;
    614     cur -= k;
    615   }
    616   *chosen_path = path;
    617   *chosen_path_size = (int)(dist_array + dist_array_size - path);
    618 }
    619 
    620 static int BackwardReferencesHashChainFollowChosenPath(
    621     int xsize, int ysize, const uint32_t* const argb,
    622     int quality, int cache_bits,
    623     const uint32_t* const chosen_path, int chosen_path_size,
    624     VP8LBackwardRefs* const refs) {
    625   const int pix_count = xsize * ysize;
    626   const int use_color_cache = (cache_bits > 0);
    627   int size = 0;
    628   int i = 0;
    629   int k;
    630   int ix;
    631   int ok = 0;
    632   int cc_init = 0;
    633   int window_size = WINDOW_SIZE;
    634   int iter_pos = 1;
    635   int iter_limit = -1;
    636   HashChain* hash_chain = (HashChain*)malloc(sizeof(*hash_chain));
    637   VP8LColorCache hashers;
    638 
    639   if (hash_chain == NULL || !HashChainInit(hash_chain, pix_count)) {
    640     goto Error;
    641   }
    642   if (use_color_cache) {
    643     cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    644     if (!cc_init) goto Error;
    645   }
    646 
    647   refs->size = 0;
    648   GetParamsForHashChainFindCopy(quality, xsize, &window_size, &iter_pos,
    649                                 &iter_limit);
    650   for (ix = 0; ix < chosen_path_size; ++ix, ++size) {
    651     int offset = 0;
    652     int len = 0;
    653     int maxlen = chosen_path[ix];
    654     if (maxlen != 1) {
    655       HashChainFindCopy(hash_chain, i, xsize, argb, maxlen,
    656                         window_size, iter_pos, iter_limit,
    657                         &offset, &len);
    658       assert(len == maxlen);
    659       refs->refs[size] = PixOrCopyCreateCopy(offset, len);
    660       if (use_color_cache) {
    661         for (k = 0; k < len; ++k) {
    662           VP8LColorCacheInsert(&hashers, argb[i + k]);
    663         }
    664       }
    665       {
    666         const int last = (len < pix_count - 1 - i) ? len : pix_count - 1 - i;
    667         for (k = 0; k < last; ++k) {
    668           HashChainInsert(hash_chain, &argb[i + k], i + k);
    669         }
    670       }
    671       i += len;
    672     } else {
    673       if (use_color_cache && VP8LColorCacheContains(&hashers, argb[i])) {
    674         // push pixel as a color cache index
    675         const int idx = VP8LColorCacheGetIndex(&hashers, argb[i]);
    676         refs->refs[size] = PixOrCopyCreateCacheIdx(idx);
    677       } else {
    678         refs->refs[size] = PixOrCopyCreateLiteral(argb[i]);
    679       }
    680       if (use_color_cache) VP8LColorCacheInsert(&hashers, argb[i]);
    681       if (i + 1 < pix_count) {
    682         HashChainInsert(hash_chain, &argb[i], i);
    683       }
    684       ++i;
    685     }
    686   }
    687   assert(size <= refs->max_size);
    688   refs->size = size;
    689   ok = 1;
    690 Error:
    691   if (cc_init) VP8LColorCacheClear(&hashers);
    692   HashChainDelete(hash_chain);
    693   return ok;
    694 }
    695 
    696 // Returns 1 on success.
    697 static int BackwardReferencesTraceBackwards(int xsize, int ysize,
    698                                             int recursive_cost_model,
    699                                             const uint32_t* const argb,
    700                                             int quality, int cache_bits,
    701                                             VP8LBackwardRefs* const refs) {
    702   int ok = 0;
    703   const int dist_array_size = xsize * ysize;
    704   uint32_t* chosen_path = NULL;
    705   int chosen_path_size = 0;
    706   uint32_t* dist_array =
    707       (uint32_t*)WebPSafeMalloc((uint64_t)dist_array_size, sizeof(*dist_array));
    708 
    709   if (dist_array == NULL) goto Error;
    710 
    711   if (!BackwardReferencesHashChainDistanceOnly(
    712       xsize, ysize, recursive_cost_model, argb, quality, cache_bits,
    713       dist_array)) {
    714     goto Error;
    715   }
    716   TraceBackwards(dist_array, dist_array_size, &chosen_path, &chosen_path_size);
    717   if (!BackwardReferencesHashChainFollowChosenPath(
    718       xsize, ysize, argb, quality, cache_bits, chosen_path, chosen_path_size,
    719       refs)) {
    720     goto Error;
    721   }
    722   ok = 1;
    723  Error:
    724   free(dist_array);
    725   return ok;
    726 }
    727 
    728 static void BackwardReferences2DLocality(int xsize,
    729                                          VP8LBackwardRefs* const refs) {
    730   int i;
    731   for (i = 0; i < refs->size; ++i) {
    732     if (PixOrCopyIsCopy(&refs->refs[i])) {
    733       const int dist = refs->refs[i].argb_or_distance;
    734       const int transformed_dist = DistanceToPlaneCode(xsize, dist);
    735       refs->refs[i].argb_or_distance = transformed_dist;
    736     }
    737   }
    738 }
    739 
    740 int VP8LGetBackwardReferences(int width, int height,
    741                               const uint32_t* const argb,
    742                               int quality, int cache_bits, int use_2d_locality,
    743                               VP8LBackwardRefs* const best) {
    744   int ok = 0;
    745   int lz77_is_useful;
    746   VP8LBackwardRefs refs_rle, refs_lz77;
    747   const int num_pix = width * height;
    748 
    749   VP8LBackwardRefsAlloc(&refs_rle, num_pix);
    750   VP8LBackwardRefsAlloc(&refs_lz77, num_pix);
    751   VP8LInitBackwardRefs(best);
    752   if (refs_rle.refs == NULL || refs_lz77.refs == NULL) {
    753  Error1:
    754     VP8LClearBackwardRefs(&refs_rle);
    755     VP8LClearBackwardRefs(&refs_lz77);
    756     goto End;
    757   }
    758 
    759   if (!BackwardReferencesHashChain(width, height, argb, cache_bits, quality,
    760                                    &refs_lz77)) {
    761     goto End;
    762   }
    763   // Backward Reference using RLE only.
    764   BackwardReferencesRle(width, height, argb, &refs_rle);
    765 
    766   {
    767     double bit_cost_lz77, bit_cost_rle;
    768     VP8LHistogram* const histo = (VP8LHistogram*)malloc(sizeof(*histo));
    769     if (histo == NULL) goto Error1;
    770     // Evaluate lz77 coding
    771     VP8LHistogramCreate(histo, &refs_lz77, cache_bits);
    772     bit_cost_lz77 = VP8LHistogramEstimateBits(histo);
    773     // Evaluate RLE coding
    774     VP8LHistogramCreate(histo, &refs_rle, cache_bits);
    775     bit_cost_rle = VP8LHistogramEstimateBits(histo);
    776     // Decide if LZ77 is useful.
    777     lz77_is_useful = (bit_cost_lz77 < bit_cost_rle);
    778     free(histo);
    779   }
    780 
    781   // Choose appropriate backward reference.
    782   if (lz77_is_useful) {
    783     // TraceBackwards is costly. Don't execute it at lower quality (q <= 10).
    784     const int try_lz77_trace_backwards = (quality > 10);
    785     *best = refs_lz77;   // default guess: lz77 is better
    786     VP8LClearBackwardRefs(&refs_rle);
    787     if (try_lz77_trace_backwards) {
    788       const int recursion_level = (num_pix < 320 * 200) ? 1 : 0;
    789       VP8LBackwardRefs refs_trace;
    790       if (!VP8LBackwardRefsAlloc(&refs_trace, num_pix)) {
    791         goto End;
    792       }
    793       if (BackwardReferencesTraceBackwards(width, height, recursion_level, argb,
    794                                            quality, cache_bits, &refs_trace)) {
    795         VP8LClearBackwardRefs(&refs_lz77);
    796         *best = refs_trace;
    797       }
    798     }
    799   } else {
    800     VP8LClearBackwardRefs(&refs_lz77);
    801     *best = refs_rle;
    802   }
    803 
    804   if (use_2d_locality) BackwardReferences2DLocality(width, best);
    805 
    806   ok = 1;
    807 
    808  End:
    809   if (!ok) {
    810     VP8LClearBackwardRefs(best);
    811   }
    812   return ok;
    813 }
    814 
    815 // Returns 1 on success.
    816 static int ComputeCacheHistogram(const uint32_t* const argb,
    817                                  int xsize, int ysize,
    818                                  const VP8LBackwardRefs* const refs,
    819                                  int cache_bits,
    820                                  VP8LHistogram* const histo) {
    821   int pixel_index = 0;
    822   int i;
    823   uint32_t k;
    824   VP8LColorCache hashers;
    825   const int use_color_cache = (cache_bits > 0);
    826   int cc_init = 0;
    827 
    828   if (use_color_cache) {
    829     cc_init = VP8LColorCacheInit(&hashers, cache_bits);
    830     if (!cc_init) return 0;
    831   }
    832 
    833   for (i = 0; i < refs->size; ++i) {
    834     const PixOrCopy* const v = &refs->refs[i];
    835     if (PixOrCopyIsLiteral(v)) {
    836       if (use_color_cache &&
    837           VP8LColorCacheContains(&hashers, argb[pixel_index])) {
    838         // push pixel as a cache index
    839         const int ix = VP8LColorCacheGetIndex(&hashers, argb[pixel_index]);
    840         const PixOrCopy token = PixOrCopyCreateCacheIdx(ix);
    841         VP8LHistogramAddSinglePixOrCopy(histo, &token);
    842       } else {
    843         VP8LHistogramAddSinglePixOrCopy(histo, v);
    844       }
    845     } else {
    846       VP8LHistogramAddSinglePixOrCopy(histo, v);
    847     }
    848     if (use_color_cache) {
    849       for (k = 0; k < PixOrCopyLength(v); ++k) {
    850         VP8LColorCacheInsert(&hashers, argb[pixel_index + k]);
    851       }
    852     }
    853     pixel_index += PixOrCopyLength(v);
    854   }
    855   assert(pixel_index == xsize * ysize);
    856   (void)xsize;  // xsize is not used in non-debug compilations otherwise.
    857   (void)ysize;  // ysize is not used in non-debug compilations otherwise.
    858   if (cc_init) VP8LColorCacheClear(&hashers);
    859   return 1;
    860 }
    861 
    862 // Returns how many bits are to be used for a color cache.
    863 int VP8LCalculateEstimateForCacheSize(const uint32_t* const argb,
    864                                       int xsize, int ysize,
    865                                       int* const best_cache_bits) {
    866   int ok = 0;
    867   int cache_bits;
    868   double lowest_entropy = 1e99;
    869   VP8LBackwardRefs refs;
    870   static const double kSmallPenaltyForLargeCache = 4.0;
    871   static const int quality = 30;
    872   if (!VP8LBackwardRefsAlloc(&refs, xsize * ysize) ||
    873       !BackwardReferencesHashChain(xsize, ysize, argb, 0, quality, &refs)) {
    874     goto Error;
    875   }
    876   for (cache_bits = 0; cache_bits <= MAX_COLOR_CACHE_BITS; ++cache_bits) {
    877     double cur_entropy;
    878     VP8LHistogram histo;
    879     VP8LHistogramInit(&histo, cache_bits);
    880     ComputeCacheHistogram(argb, xsize, ysize, &refs, cache_bits, &histo);
    881     cur_entropy = VP8LHistogramEstimateBits(&histo) +
    882         kSmallPenaltyForLargeCache * cache_bits;
    883     if (cache_bits == 0 || cur_entropy < lowest_entropy) {
    884       *best_cache_bits = cache_bits;
    885       lowest_entropy = cur_entropy;
    886     }
    887   }
    888   ok = 1;
    889  Error:
    890   VP8LClearBackwardRefs(&refs);
    891   return ok;
    892 }
    893