text: // Copyright 2012 Google Inc. All Rights Reserved.
  //
  // This code is licensed under the same terms as WebM:
  //  Software License Agreement:  http://www.webmproject.org/license/software/
  //  Additional IP Rights Grant:  http://www.webmproject.org/license/additional/
  // -----------------------------------------------------------------------------
  //
  // Author: Jyrki Alakuijala (jyrki@google.com)
  //
  #ifdef HAVE_CONFIG_H
  #include "config.h"
  #endif
  
  #include <math.h>
  #include <stdio.h>
  
  #include "./backward_references.h"
  #include "./histogram.h"
  #include "../dsp/lossless.h"
  #include "../utils/utils.h"
  
  static void HistogramClear(VP8LHistogram* const p) {
    memset(p->literal_, 0, sizeof(p->literal_));
    memset(p->red_, 0, sizeof(p->red_));
    memset(p->blue_, 0, sizeof(p->blue_));
    memset(p->alpha_, 0, sizeof(p->alpha_));
    memset(p->distance_, 0, sizeof(p->distance_));
    p->bit_cost_ = 0;
  }
  
  void VP8LHistogramStoreRefs(const VP8LBackwardRefs* const refs,
                              VP8LHistogram* const histo) {
    int i;
    for (i = 0; i < refs->size; ++i) {
      VP8LHistogramAddSinglePixOrCopy(histo, &refs->refs[i]);
    }
  }
  
  void VP8LHistogramCreate(VP8LHistogram* const p,
                           const VP8LBackwardRefs* const refs,
                           int palette_code_bits) {
    if (palette_code_bits >= 0) {
      p->palette_code_bits_ = palette_code_bits;
    }
    HistogramClear(p);
    VP8LHistogramStoreRefs(refs, p);
  }
  
  void VP8LHistogramInit(VP8LHistogram* const p, int palette_code_bits) {
    p->palette_code_bits_ = palette_code_bits;
    HistogramClear(p);
  }
  
  VP8LHistogramSet* VP8LAllocateHistogramSet(int size, int cache_bits) {
    int i;
    VP8LHistogramSet* set;
    VP8LHistogram* bulk;
    const uint64_t total_size = sizeof(*set)
                              + (uint64_t)size * sizeof(*set->histograms)
                              + (uint64_t)size * sizeof(**set->histograms);
    uint8_t* memory = (uint8_t*)WebPSafeMalloc(total_size, sizeof(*memory));
    if (memory == NULL) return NULL;
  
    set = (VP8LHistogramSet*)memory;
    memory += sizeof(*set);
    set->histograms = (VP8LHistogram**)memory;
    memory += size * sizeof(*set->histograms);
    bulk = (VP8LHistogram*)memory;
    set->max_size = size;
    set->size = size;
    for (i = 0; i < size; ++i) {
      set->histograms[i] = bulk + i;
      VP8LHistogramInit(set->histograms[i], cache_bits);
    }
    return set;
  }
  
  // -----------------------------------------------------------------------------
  
  void VP8LHistogramAddSinglePixOrCopy(VP8LHistogram* const histo,
                                       const PixOrCopy* const v) {
    if (PixOrCopyIsLiteral(v)) {
      ++histo->alpha_[PixOrCopyLiteral(v, 3)];
      ++histo->red_[PixOrCopyLiteral(v, 2)];
      ++histo->literal_[PixOrCopyLiteral(v, 1)];
      ++histo->blue_[PixOrCopyLiteral(v, 0)];
    } else if (PixOrCopyIsCacheIdx(v)) {
      int literal_ix = 256 + NUM_LENGTH_CODES + PixOrCopyCacheIdx(v);
      ++histo->literal_[literal_ix];
    } else {
      int code, extra_bits_count, extra_bits_value;
      PrefixEncode(PixOrCopyLength(v),
                   &code, &extra_bits_count, &extra_bits_value);
      ++histo->literal_[256 + code];
      PrefixEncode(PixOrCopyDistance(v),
                   &code, &extra_bits_count, &extra_bits_value);
      ++histo->distance_[code];
    }
  }
  
  
  
  static double BitsEntropy(const int* const array, int n) {
    double retval = 0.;
    int sum = 0;
    int nonzeros = 0;
    int max_val = 0;
    int i;
    double mix;
    for (i = 0; i < n; ++i) {
      if (array[i] != 0) {
        sum += array[i];
        ++nonzeros;
        retval -= VP8LFastSLog2(array[i]);
        if (max_val < array[i]) {
          max_val = array[i];
        }
      }
    }
    retval += VP8LFastSLog2(sum);
  
    if (nonzeros < 5) {
      if (nonzeros <= 1) {
        return 0;
      }
      // Two symbols, they will be 0 and 1 in a Huffman code.
      // Let's mix in a bit of entropy to favor good clustering when
      // distributions of these are combined.
      if (nonzeros == 2) {
        return 0.99 * sum + 0.01 * retval;
      }
      // No matter what the entropy says, we cannot be better than min_limit
      // with Huffman coding. I am mixing a bit of entropy into the
      // min_limit since it produces much better (~0.5 %) compression results
      // perhaps because of better entropy clustering.
      if (nonzeros == 3) {
        mix = 0.95;
      } else {
        mix = 0.7;  // nonzeros == 4.
      }
    } else {
      mix = 0.627;
    }
  
    {
      double min_limit = 2 * sum - max_val;
      min_limit = mix * min_limit + (1.0 - mix) * retval;
      return (retval < min_limit) ? min_limit : retval;
    }
  }
  
  double VP8LHistogramEstimateBitsBulk(const VP8LHistogram* const p) {
    double retval = BitsEntropy(&p->literal_[0], VP8LHistogramNumCodes(p))
                  + BitsEntropy(&p->red_[0], 256)
                  + BitsEntropy(&p->blue_[0], 256)
                  + BitsEntropy(&p->alpha_[0], 256)
                  + BitsEntropy(&p->distance_[0], NUM_DISTANCE_CODES);
    // Compute the extra bits cost.
    int i;
    for (i = 2; i < NUM_LENGTH_CODES - 2; ++i) {
      retval +=
          (i >> 1) * p->literal_[256 + i + 2];
    }
    for (i = 2; i < NUM_DISTANCE_CODES - 2; ++i) {
      retval += (i >> 1) * p->distance_[i + 2];
    }
    return retval;
  }
  
  
  // Returns the cost encode the rle-encoded entropy code.
  // The constants in this function are experimental.
  static double HuffmanCost(const int* const population, int length) {
    // Small bias because Huffman code length is typically not stored in
    // full length.
    static const int kHuffmanCodeOfHuffmanCodeSize = CODE_LENGTH_CODES * 3;
    static const double kSmallBias = 9.1;
    double retval = kHuffmanCodeOfHuffmanCodeSize - kSmallBias;
    int streak = 0;
    int i = 0;
    for (; i < length - 1; ++i) {
      ++streak;
      if (population[i] == population[i + 1]) {
        continue;
      }
   last_streak_hack:
      // population[i] points now to the symbol in the streak of same values.
      if (streak > 3) {
        if (population[i] == 0) {
          retval += 1.5625 + 0.234375 * streak;
        } else {
          retval += 2.578125 + 0.703125 * streak;
        }
      } else {
        if (population[i] == 0) {
          retval += 1.796875 * streak;
        } else {
          retval += 3.28125 * streak;
        }
      }
      streak = 0;
    }
    if (i == length - 1) {
      ++streak;
      goto last_streak_hack;
    }
    return retval;
  }
  
  // Estimates the Huffman dictionary + other block overhead size.
  static double HistogramEstimateBitsHeader(const VP8LHistogram* const p) {
    return HuffmanCost(&p->alpha_[0], 256) +
           HuffmanCost(&p->red_[0], 256) +
           HuffmanCost(&p->literal_[0], VP8LHistogramNumCodes(p)) +
           HuffmanCost(&p->blue_[0], 256) +
           HuffmanCost(&p->distance_[0], NUM_DISTANCE_CODES);
  }
  
  double VP8LHistogramEstimateBits(const VP8LHistogram* const p) {
    return HistogramEstimateBitsHeader(p) + VP8LHistogramEstimateBitsBulk(p);
  }
  
  static void HistogramBuildImage(int xsize, int histo_bits,
                                  const VP8LBackwardRefs* const backward_refs,
                                  VP8LHistogramSet* const image) {
    int i;
    int x = 0, y = 0;
    const int histo_xsize = VP8LSubSampleSize(xsize, histo_bits);
    VP8LHistogram** const histograms = image->histograms;
    assert(histo_bits > 0);
    for (i = 0; i < backward_refs->size; ++i) {
      const PixOrCopy* const v = &backward_refs->refs[i];
      const int ix = (y >> histo_bits) * histo_xsize + (x >> histo_bits);
      VP8LHistogramAddSinglePixOrCopy(histograms[ix], v);
      x += PixOrCopyLength(v);
      while (x >= xsize) {
        x -= xsize;
        ++y;
      }
    }
  }
  
  static uint32_t MyRand(uint32_t *seed) {
    *seed *= 16807U;
    if (*seed == 0) {
      *seed = 1;
    }
    return *seed;
  }
  
  static int HistogramCombine(const VP8LHistogramSet* const in,
                              VP8LHistogramSet* const out, int num_pairs) {
    int ok = 0;
    int i, iter;
    uint32_t seed = 0;
    int tries_with_no_success = 0;
    const int min_cluster_size = 2;
    int out_size = in->size;
    const int outer_iters = in->size * 3;
    VP8LHistogram* const histos = (VP8LHistogram*)malloc(2 * sizeof(*histos));
    VP8LHistogram* cur_combo = histos + 0;    // trial merged histogram
    VP8LHistogram* best_combo = histos + 1;   // best merged histogram so far
    if (histos == NULL) goto End;
  
    // Copy histograms from in[] to out[].
    assert(in->size <= out->size);
    for (i = 0; i < in->size; ++i) {
      in->histograms[i]->bit_cost_ = VP8LHistogramEstimateBits(in->histograms[i]);
      *out->histograms[i] = *in->histograms[i];
    }
  
    // Collapse similar histograms in 'out'.
    for (iter = 0; iter < outer_iters && out_size >= min_cluster_size; ++iter) {
      // We pick the best pair to be combined out of 'inner_iters' pairs.
      double best_cost_diff = 0.;
      int best_idx1 = 0, best_idx2 = 1;
      int j;
      seed += iter;
      for (j = 0; j < num_pairs; ++j) {
        double curr_cost_diff;
        // Choose two histograms at random and try to combine them.
        const uint32_t idx1 = MyRand(&seed) % out_size;
        const uint32_t tmp = ((j & 7) + 1) % (out_size - 1);
        const uint32_t diff = (tmp < 3) ? tmp : MyRand(&seed) % (out_size - 1);
        const uint32_t idx2 = (idx1 + diff + 1) % out_size;
        if (idx1 == idx2) {
          continue;
        }
        *cur_combo = *out->histograms[idx1];
        VP8LHistogramAdd(cur_combo, out->histograms[idx2]);
        cur_combo->bit_cost_ = VP8LHistogramEstimateBits(cur_combo);
        // Calculate cost reduction on combining.
        curr_cost_diff = cur_combo->bit_cost_
                       - out->histograms[idx1]->bit_cost_
                       - out->histograms[idx2]->bit_cost_;
        if (best_cost_diff > curr_cost_diff) {    // found a better pair?
          {     // swap cur/best combo histograms
            VP8LHistogram* const tmp_histo = cur_combo;
            cur_combo = best_combo;
            best_combo = tmp_histo;
          }
          best_cost_diff = curr_cost_diff;
          best_idx1 = idx1;
          best_idx2 = idx2;
        }
      }
  
      if (best_cost_diff < 0.0) {
        *out->histograms[best_idx1] = *best_combo;
        // swap best_idx2 slot with last one (which is now unused)
        --out_size;
        if (best_idx2 != out_size) {
          out->histograms[best_idx2] = out->histograms[out_size];
          out->histograms[out_size] = NULL;   // just for sanity check.
        }
        tries_with_no_success = 0;
      }
      if (++tries_with_no_success >= 50) {
        break;
      }
    }
    out->size = out_size;
    ok = 1;
  
   End:
    free(histos);
    return ok;
  }
  
  // -----------------------------------------------------------------------------
  // Histogram refinement
  
  // What is the bit cost of moving square_histogram from
  // cur_symbol to candidate_symbol.
  // TODO(skal): we don't really need to copy the histogram and Add(). Instead
  // we just need VP8LDualHistogramEstimateBits(A, B) estimation function.
  static double HistogramDistance(const VP8LHistogram* const square_histogram,
                                  const VP8LHistogram* const candidate) {
    const double previous_bit_cost = candidate->bit_cost_;
    double new_bit_cost;
    VP8LHistogram modified_histo;
    modified_histo = *candidate;
    VP8LHistogramAdd(&modified_histo, square_histogram);
    new_bit_cost = VP8LHistogramEstimateBits(&modified_histo);
  
    return new_bit_cost - previous_bit_cost;
  }
  
  // Find the best 'out' histogram for each of the 'in' histograms.
  // Note: we assume that out[]->bit_cost_ is already up-to-date.
  static void HistogramRemap(const VP8LHistogramSet* const in,
                             const VP8LHistogramSet* const out,
                             uint16_t* const symbols) {
    int i;
    for (i = 0; i < in->size; ++i) {
      int best_out = 0;
      double best_bits = HistogramDistance(in->histograms[i], out->histograms[0]);
      int k;
      for (k = 1; k < out->size; ++k) {
        const double cur_bits =
            HistogramDistance(in->histograms[i], out->histograms[k]);
        if (cur_bits < best_bits) {
          best_bits = cur_bits;
          best_out = k;
        }
      }
      symbols[i] = best_out;
    }
  
    // Recompute each out based on raw and symbols.
    for (i = 0; i < out->size; ++i) {
      HistogramClear(out->histograms[i]);
    }
    for (i = 0; i < in->size; ++i) {
      VP8LHistogramAdd(out->histograms[symbols[i]], in->histograms[i]);
    }
  }
  
  int VP8LGetHistoImageSymbols(int xsize, int ysize,
                               const VP8LBackwardRefs* const refs,
                               int quality, int histo_bits, int cache_bits,
                               VP8LHistogramSet* const image_in,
                               uint16_t* const histogram_symbols) {
    int ok = 0;
    const int histo_xsize = histo_bits ? VP8LSubSampleSize(xsize, histo_bits) : 1;
    const int histo_ysize = histo_bits ? VP8LSubSampleSize(ysize, histo_bits) : 1;
    const int num_histo_pairs = 10 + quality / 2;  // For HistogramCombine().
    const int histo_image_raw_size = histo_xsize * histo_ysize;
    VP8LHistogramSet* const image_out =
        VP8LAllocateHistogramSet(histo_image_raw_size, cache_bits);
    if (image_out == NULL) return 0;
  
    // Build histogram image.
    HistogramBuildImage(xsize, histo_bits, refs, image_out);
    // Collapse similar histograms.
    if (!HistogramCombine(image_out, image_in, num_histo_pairs)) {
      goto Error;
    }
    // Find the optimal map from original histograms to the final ones.
    HistogramRemap(image_out, image_in, histogram_symbols);
    ok = 1;
  
  Error:
    free(image_out);
    return ok;
  }
  