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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 #ifdef HAVE_CONFIG_H
     11 #include "config.h"
     12 #endif
     13 
     14 #include <math.h>
     15 #include <stdio.h>
     16 
     17 #include "./backward_references.h"
     18 #include "./histogram.h"
     19 #include "../dsp/lossless.h"
     20 #include "../utils/utils.h"
     21 
     22 static void HistogramClear(VP8LHistogram* const p) {
     23   memset(p->literal_, 0, sizeof(p->literal_));
     24   memset(p->red_, 0, sizeof(p->red_));
     25   memset(p->blue_, 0, sizeof(p->blue_));
     26   memset(p->alpha_, 0, sizeof(p->alpha_));
     27   memset(p->distance_, 0, sizeof(p->distance_));
     28   p->bit_cost_ = 0;
     29 }
     30 
     31 void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
     32                             VP8LHistogram* const histo) {
     33   int i;
     34   for (i = 0; i < refs->size; ++i) {
     35     VP8LHistogramAddSinglePixOrCopy(histo, &refs->refs[i]);
     36   }
     37 }
     38 
     39 void VP8LHistogramCreate(VP8LHistogram* const p,
     40                          const VP8LBackwardRefs* const refs,
     41                          int palette_code_bits) {
     42   if (palette_code_bits >= 0) {
     43     p->palette_code_bits_ = palette_code_bits;
     44   }
     45   HistogramClear(p);
     46   VP8LHistogramStoreRefs(refs, p);
     47 }
     48 
     49 void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits) {
     50   p->palette_code_bits_ = palette_code_bits;
     51   HistogramClear(p);
     52 }
     53 
     54 VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
     55   int i;
     56   VP8LHistogramSet* set;
     57   VP8LHistogram* bulk;
     58   const uint64_t total_size = sizeof(*set)
     59                             + (uint64_t)size * sizeof(*set->histograms)
     60                             + (uint64_t)size * sizeof(**set->histograms);
     61   uint8_t* memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
     62   if (memory == NULL) return NULL;
     63 
     64   set = (VP8LHistogramSet*)memory;
     65   memory += sizeof(*set);
     66   set->histograms = (VP8LHistogram**)memory;
     67   memory += size * sizeof(*set->histograms);
     68   bulk = (VP8LHistogram*)memory;
     69   set->max_size = size;
     70   set->size = size;
     71   for (i = 0; i < size; ++i) {
     72     set->histograms[i] = bulk + i;
     73     VP8LHistogramInit(set->histograms[i], cache_bits);
     74   }
     75   return set;
     76 }
     77 
     78 // -----------------------------------------------------------------------------
     79 
     80 void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo,
     81                                      const PixOrCopy* const v) {
     82   if (PixOrCopyIsLiteral(v)) {
     83     ++histo->alpha_[PixOrCopyLiteral(v, 3)];
     84     ++histo->red_[PixOrCopyLiteral(v, 2)];
     85     ++histo->literal_[PixOrCopyLiteral(v, 1)];
     86     ++histo->blue_[PixOrCopyLiteral(v, 0)];
     87   } else if (PixOrCopyIsCacheIdx(v)) {
     88     int literal_ix = 256 + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
     89     ++histo->literal_[literal_ix];
     90   } else {
     91     int code, extra_bits_count, extra_bits_value;
     92     PrefixEncode(PixOrCopyLength(v),
     93                  &code, &extra_bits_count, &extra_bits_value);
     94     ++histo->literal_[256 + code];
     95     PrefixEncode(PixOrCopyDistance(v),
     96                  &code, &extra_bits_count, &extra_bits_value);
     97     ++histo->distance_[code];
     98   }
     99 }
    100 
    101 
    102 
    103 static double BitsEntropy(const int* const array, int n) {
    104   double retval = 0.;
    105   int sum = 0;
    106   int nonzeros = 0;
    107   int max_val = 0;
    108   int i;
    109   double mix;
    110   for (i = 0; i < n; ++i) {
    111     if (array[i] != 0) {
    112       sum += array[i];
    113       ++nonzeros;
    114       retval -= VP8LFastSLog2(array[i]);
    115       if (max_val < array[i]) {
    116         max_val = array[i];
    117       }
    118     }
    119   }
    120   retval += VP8LFastSLog2(sum);
    121 
    122   if (nonzeros < 5) {
    123     if (nonzeros <= 1) {
    124       return 0;
    125     }
    126     // Two symbols, they will be 0 and 1 in a Huffman code.
    127     // Let's mix in a bit of entropy to favor good clustering when
    128     // distributions of these are combined.
    129     if (nonzeros == 2) {
    130       return 0.99 * sum + 0.01 * retval;
    131     }
    132     // No matter what the entropy says, we cannot be better than min_limit
    133     // with Huffman coding. I am mixing a bit of entropy into the
    134     // min_limit since it produces much better (~0.5 %) compression results
    135     // perhaps because of better entropy clustering.
    136     if (nonzeros == 3) {
    137       mix = 0.95;
    138     } else {
    139       mix = 0.7;  // nonzeros == 4.
    140     }
    141   } else {
    142     mix = 0.627;
    143   }
    144 
    145   {
    146     double min_limit = 2 * sum - max_val;
    147     min_limit = mix * min_limit + (1.0 - mix) * retval;
    148     return (retval < min_limit) ? min_limit : retval;
    149   }
    150 }
    151 
    152 double VP8LHistogramEstimateBitsBulk(const VP8LHistogram* const p) {
    153   double retval = BitsEntropy(&p->literal_[0], VP8LHistogramNumCodes(p))
    154                 + BitsEntropy(&p->red_[0], 256)
    155                 + BitsEntropy(&p->blue_[0], 256)
    156                 + BitsEntropy(&p->alpha_[0], 256)
    157                 + BitsEntropy(&p->distance_[0], NUM_DISTANCE_CODES);
    158   // Compute the extra bits cost.
    159   int i;
    160   for (i = 2; i < NUM_LENGTH_CODES - 2; ++i) {
    161     retval +=
    162         (i >> 1) * p->literal_[256 + i + 2];
    163   }
    164   for (i = 2; i < NUM_DISTANCE_CODES - 2; ++i) {
    165     retval += (i >> 1) * p->distance_[i + 2];
    166   }
    167   return retval;
    168 }
    169 
    170 
    171 // Returns the cost encode the rle-encoded entropy code.
    172 // The constants in this function are experimental.
    173 static double HuffmanCost(const int* const population, int length) {
    174   // Small bias because Huffman code length is typically not stored in
    175   // full length.
    176   static const int kHuffmanCodeOfHuffmanCodeSize = CODE_LENGTH_CODES * 3;
    177   static const double kSmallBias = 9.1;
    178   double retval = kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
    179   int streak = 0;
    180   int i = 0;
    181   for (; i < length - 1; ++i) {
    182     ++streak;
    183     if (population[i] == population[i + 1]) {
    184       continue;
    185     }
    186  last_streak_hack:
    187     // population[i] points now to the symbol in the streak of same values.
    188     if (streak > 3) {
    189       if (population[i] == 0) {
    190         retval += 1.5625 + 0.234375 * streak;
    191       } else {
    192         retval += 2.578125 + 0.703125 * streak;
    193       }
    194     } else {
    195       if (population[i] == 0) {
    196         retval += 1.796875 * streak;
    197       } else {
    198         retval += 3.28125 * streak;
    199       }
    200     }
    201     streak = 0;
    202   }
    203   if (i == length - 1) {
    204     ++streak;
    205     goto last_streak_hack;
    206   }
    207   return retval;
    208 }
    209 
    210 // Estimates the Huffman dictionary + other block overhead size.
    211 static double HistogramEstimateBitsHeader(const VP8LHistogram* const p) {
    212   return HuffmanCost(&p->alpha_[0], 256) +
    213          HuffmanCost(&p->red_[0], 256) +
    214          HuffmanCost(&p->literal_[0], VP8LHistogramNumCodes(p)) +
    215          HuffmanCost(&p->blue_[0], 256) +
    216          HuffmanCost(&p->distance_[0], NUM_DISTANCE_CODES);
    217 }
    218 
    219 double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
    220   return HistogramEstimateBitsHeader(p) + VP8LHistogramEstimateBitsBulk(p);
    221 }
    222 
    223 static void HistogramBuildImage(int xsize, int histo_bits,
    224                                 const VP8LBackwardRefs* const backward_refs,
    225                                 VP8LHistogramSet* const image) {
    226   int i;
    227   int x = 0, y = 0;
    228   const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
    229   VP8LHistogram** const histograms = image->histograms;
    230   assert(histo_bits > 0);
    231   for (i = 0; i < backward_refs->size; ++i) {
    232     const PixOrCopy* const v = &backward_refs->refs[i];
    233     const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
    234     VP8LHistogramAddSinglePixOrCopy(histograms[ix], v);
    235     x += PixOrCopyLength(v);
    236     while (x >= xsize) {
    237       x -= xsize;
    238       ++y;
    239     }
    240   }
    241 }
    242 
    243 static uint32_t MyRand(uint32_t *seed) {
    244   *seed *= 16807U;
    245   if (*seed == 0) {
    246     *seed = 1;
    247   }
    248   return *seed;
    249 }
    250 
    251 static int HistogramCombine(const VP8LHistogramSet* const in,
    252                             VP8LHistogramSet* const out, int iter_mult,
    253                             int num_pairs, int num_tries_no_success) {
    254   int ok = 0;
    255   int i, iter;
    256   uint32_t seed = 0;
    257   int tries_with_no_success = 0;
    258   int out_size = in->size;
    259   const int outer_iters = in->size * iter_mult;
    260   const int min_cluster_size = 2;
    261   VP8LHistogram* const histos = (VP8LHistogram*)malloc(2 * sizeof(*histos));
    262   VP8LHistogram* cur_combo = histos + 0;    // trial merged histogram
    263   VP8LHistogram* best_combo = histos + 1;   // best merged histogram so far
    264   if (histos == NULL) goto End;
    265 
    266   // Copy histograms from in[] to out[].
    267   assert(in->size <= out->size);
    268   for (i = 0; i < in->size; ++i) {
    269     in->histograms[i]->bit_cost_ = VP8LHistogramEstimateBits(in->histograms[i]);
    270     *out->histograms[i] = *in->histograms[i];
    271   }
    272 
    273   // Collapse similar histograms in 'out'.
    274   for (iter = 0; iter < outer_iters && out_size >= min_cluster_size; ++iter) {
    275     double best_cost_diff = 0.;
    276     int best_idx1 = 0, best_idx2 = 1;
    277     int j;
    278     const int num_tries = (num_pairs < out_size) ? num_pairs : out_size;
    279     seed += iter;
    280     for (j = 0; j < num_tries; ++j) {
    281       double curr_cost_diff;
    282       // Choose two histograms at random and try to combine them.
    283       const uint32_t idx1 = MyRand(&seed) % out_size;
    284       const uint32_t tmp = ((j & 7) + 1) % (out_size - 1);
    285       const uint32_t diff = (tmp < 3) ? tmp : MyRand(&seed) % (out_size - 1);
    286       const uint32_t idx2 = (idx1 + diff + 1) % out_size;
    287       if (idx1 == idx2) {
    288         continue;
    289       }
    290       *cur_combo = *out->histograms[idx1];
    291       VP8LHistogramAdd(cur_combo, out->histograms[idx2]);
    292       cur_combo->bit_cost_ = VP8LHistogramEstimateBits(cur_combo);
    293       // Calculate cost reduction on combining.
    294       curr_cost_diff = cur_combo->bit_cost_
    295                      - out->histograms[idx1]->bit_cost_
    296                      - out->histograms[idx2]->bit_cost_;
    297       if (best_cost_diff > curr_cost_diff) {    // found a better pair?
    298         {     // swap cur/best combo histograms
    299           VP8LHistogram* const tmp_histo = cur_combo;
    300           cur_combo = best_combo;
    301           best_combo = tmp_histo;
    302         }
    303         best_cost_diff = curr_cost_diff;
    304         best_idx1 = idx1;
    305         best_idx2 = idx2;
    306       }
    307     }
    308 
    309     if (best_cost_diff < 0.0) {
    310       *out->histograms[best_idx1] = *best_combo;
    311       // swap best_idx2 slot with last one (which is now unused)
    312       --out_size;
    313       if (best_idx2 != out_size) {
    314         out->histograms[best_idx2] = out->histograms[out_size];
    315         out->histograms[out_size] = NULL;   // just for sanity check.
    316       }
    317       tries_with_no_success = 0;
    318     }
    319     if (++tries_with_no_success >= num_tries_no_success) {
    320       break;
    321     }
    322   }
    323   out->size = out_size;
    324   ok = 1;
    325 
    326  End:
    327   free(histos);
    328   return ok;
    329 }
    330 
    331 // -----------------------------------------------------------------------------
    332 // Histogram refinement
    333 
    334 // What is the bit cost of moving square_histogram from
    335 // cur_symbol to candidate_symbol.
    336 // TODO(skal): we don't really need to copy the histogram and Add(). Instead
    337 // we just need VP8LDualHistogramEstimateBits(A, B) estimation function.
    338 static double HistogramDistance(const VP8LHistogram* const square_histogram,
    339                                 const VP8LHistogram* const candidate) {
    340   const double previous_bit_cost = candidate->bit_cost_;
    341   double new_bit_cost;
    342   VP8LHistogram modified_histo;
    343   modified_histo = *candidate;
    344   VP8LHistogramAdd(&modified_histo, square_histogram);
    345   new_bit_cost = VP8LHistogramEstimateBits(&modified_histo);
    346 
    347   return new_bit_cost - previous_bit_cost;
    348 }
    349 
    350 // Find the best 'out' histogram for each of the 'in' histograms.
    351 // Note: we assume that out[]->bit_cost_ is already up-to-date.
    352 static void HistogramRemap(const VP8LHistogramSet* const in,
    353                            const VP8LHistogramSet* const out,
    354                            uint16_t* const symbols) {
    355   int i;
    356   for (i = 0; i < in->size; ++i) {
    357     int best_out = 0;
    358     double best_bits = HistogramDistance(in->histograms[i], out->histograms[0]);
    359     int k;
    360     for (k = 1; k < out->size; ++k) {
    361       const double cur_bits =
    362           HistogramDistance(in->histograms[i], out->histograms[k]);
    363       if (cur_bits < best_bits) {
    364         best_bits = cur_bits;
    365         best_out = k;
    366       }
    367     }
    368     symbols[i] = best_out;
    369   }
    370 
    371   // Recompute each out based on raw and symbols.
    372   for (i = 0; i < out->size; ++i) {
    373     HistogramClear(out->histograms[i]);
    374   }
    375   for (i = 0; i < in->size; ++i) {
    376     VP8LHistogramAdd(out->histograms[symbols[i]], in->histograms[i]);
    377   }
    378 }
    379 
    380 int VP8LGetHistoImageSymbols(int xsize, int ysize,
    381                              const VP8LBackwardRefs* const refs,
    382                              int quality, int histo_bits, int cache_bits,
    383                              VP8LHistogramSet* const image_in,
    384                              uint16_t* const histogram_symbols) {
    385   int ok = 0;
    386   const int histo_xsize = histo_bits ? VP8LSubSampleSize(xsize, histo_bits) : 1;
    387   const int histo_ysize = histo_bits ? VP8LSubSampleSize(ysize, histo_bits) : 1;
    388   const int histo_image_raw_size = histo_xsize * histo_ysize;
    389 
    390   // Heuristic params for HistogramCombine().
    391   const int num_tries_no_success = 8 + (quality >> 1);
    392   const int iter_mult = (quality < 27) ? 1 : 1 + ((quality - 27) >> 4);
    393   const int num_pairs = (quality < 25) ? 10 : (5 * quality) >> 3;
    394 
    395   VP8LHistogramSet* const image_out =
    396       VP8LAllocateHistogramSet(histo_image_raw_size, cache_bits);
    397   if (image_out == NULL) return 0;
    398 
    399   // Build histogram image.
    400   HistogramBuildImage(xsize, histo_bits, refs, image_out);
    401   // Collapse similar histograms.
    402   if (!HistogramCombine(image_out, image_in, iter_mult, num_pairs,
    403                         num_tries_no_success)) {
    404     goto Error;
    405   }
    406   // Find the optimal map from original histograms to the final ones.
    407   HistogramRemap(image_out, image_in, histogram_symbols);
    408   ok = 1;
    409 
    410 Error:
    411   free(image_out);
    412   return ok;
    413 }
    414