enc/entropy_encode.cc

// Copyright 2010 Google Inc. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Entropy encoding (Huffman) utilities.

#include "./entropy_encode.h"

#include <stdint.h>
#include <algorithm>
#include <limits>
#include <vector>
#include <cstdlib>

#include "./histogram.h"

namespace brotli {

namespace {

struct HuffmanTree {
  HuffmanTree();
  HuffmanTree(int count, int16_t left, int16_t right)
      : total_count_(count),
        index_left_(left),
        index_right_or_value_(right) {
  }
  int total_count_;
  int16_t index_left_;
  int16_t index_right_or_value_;
};

HuffmanTree::HuffmanTree() {}

// Sort the root nodes, least popular first.
bool SortHuffmanTree(const HuffmanTree &v0, const HuffmanTree &v1) {
  if (v0.total_count_ == v1.total_count_) {
    return v0.index_right_or_value_ > v1.index_right_or_value_;
  }
  return v0.total_count_ < v1.total_count_;
}

void SetDepth(const HuffmanTree &p,
              HuffmanTree *pool,
              uint8_t *depth,
              int level) {
  if (p.index_left_ >= 0) {
    ++level;
    SetDepth(pool[p.index_left_], pool, depth, level);
    SetDepth(pool[p.index_right_or_value_], pool, depth, level);
  } else {
    depth[p.index_right_or_value_] = level;
  }
}

}  // namespace

// This function will create a Huffman tree.
//
// The catch here is that the tree cannot be arbitrarily deep.
// Brotli specifies a maximum depth of 15 bits for "code trees"
// and 7 bits for "code length code trees."
//
// count_limit is the value that is to be faked as the minimum value
// and this minimum value is raised until the tree matches the
// maximum length requirement.
//
// This algorithm is not of excellent performance for very long data blocks,
// especially when population counts are longer than 2**tree_limit, but
// we are not planning to use this with extremely long blocks.
//
// See http://en.wikipedia.org/wiki/Huffman_coding
void CreateHuffmanTree(const int *data,
                       const int length,
                       const int tree_limit,
                       uint8_t *depth) {
  // For block sizes below 64 kB, we never need to do a second iteration
  // of this loop. Probably all of our block sizes will be smaller than
  // that, so this loop is mostly of academic interest. If we actually
  // would need this, we would be better off with the Katajainen algorithm.
  for (int count_limit = 1; ; count_limit *= 2) {
    std::vector<HuffmanTree> tree;
    tree.reserve(2 * length + 1);

    for (int i = 0; i < length; ++i) {
      if (data[i]) {
        const int count = std::max(data[i], count_limit);
        tree.push_back(HuffmanTree(count, -1, i));
      }
    }

    const int n = tree.size();
    if (n == 1) {
      depth[tree[0].index_right_or_value_] = 1;      // Only one element.
      break;
    }

    std::sort(tree.begin(), tree.end(), SortHuffmanTree);

    // The nodes are:
    // [0, n): the sorted leaf nodes that we start with.
    // [n]: we add a sentinel here.
    // [n + 1, 2n): new parent nodes are added here, starting from
    //              (n+1). These are naturally in ascending order.
    // [2n]: we add a sentinel at the end as well.
    // There will be (2n+1) elements at the end.
    const HuffmanTree sentinel(std::numeric_limits<int>::max(), -1, -1);
    tree.push_back(sentinel);
    tree.push_back(sentinel);

    int i = 0;      // Points to the next leaf node.
    int j = n + 1;  // Points to the next non-leaf node.
    for (int k = n - 1; k > 0; --k) {
      int left, right;
      if (tree[i].total_count_ <= tree[j].total_count_) {
        left = i;
        ++i;
      } else {
        left = j;
        ++j;
      }
      if (tree[i].total_count_ <= tree[j].total_count_) {
        right = i;
        ++i;
      } else {
        right = j;
        ++j;
      }

      // The sentinel node becomes the parent node.
      int j_end = tree.size() - 1;
      tree[j_end].total_count_ =
          tree[left].total_count_ + tree[right].total_count_;
      tree[j_end].index_left_ = left;
      tree[j_end].index_right_or_value_ = right;

      // Add back the last sentinel node.
      tree.push_back(sentinel);
    }
    SetDepth(tree[2 * n - 1], &tree[0], depth, 0);

    // We need to pack the Huffman tree in tree_limit bits.
    // If this was not successful, add fake entities to the lowest values
    // and retry.
    if (*std::max_element(&depth[0], &depth[length]) <= tree_limit) {
      break;
    }
  }
}

void Reverse(uint8_t* v, int start, int end) {
  --end;
  while (start < end) {
    int tmp = v[start];
    v[start] = v[end];
    v[end] = tmp;
    ++start;
    --end;
  }
}

void WriteHuffmanTreeRepetitions(
    const int previous_value,
    const int value,
    int repetitions,
    uint8_t* tree,
    uint8_t* extra_bits,
    int* tree_size) {
  if (previous_value != value) {
    tree[*tree_size] = value;
    extra_bits[*tree_size] = 0;
    ++(*tree_size);
    --repetitions;
  }
  if (repetitions == 7) {
    tree[*tree_size] = value;
    extra_bits[*tree_size] = 0;
    ++(*tree_size);
    --repetitions;
  }
  if (repetitions < 3) {
    for (int i = 0; i < repetitions; ++i) {
      tree[*tree_size] = value;
      extra_bits[*tree_size] = 0;
      ++(*tree_size);
    }
  } else {
    repetitions -= 3;
    int start = *tree_size;
    while (repetitions >= 0) {
      tree[*tree_size] = 16;
      extra_bits[*tree_size] = repetitions & 0x3;
      ++(*tree_size);
      repetitions >>= 2;
      --repetitions;
    }
    Reverse(tree, start, *tree_size);
    Reverse(extra_bits, start, *tree_size);
  }
}

void WriteHuffmanTreeRepetitionsZeros(
    int repetitions,
    uint8_t* tree,
    uint8_t* extra_bits,
    int* tree_size) {
  if (repetitions == 11) {
    tree[*tree_size] = 0;
    extra_bits[*tree_size] = 0;
    ++(*tree_size);
    --repetitions;
  }
  if (repetitions < 3) {
    for (int i = 0; i < repetitions; ++i) {
      tree[*tree_size] = 0;
      extra_bits[*tree_size] = 0;
      ++(*tree_size);
    }
  } else {
    repetitions -= 3;
    int start = *tree_size;
    while (repetitions >= 0) {
      tree[*tree_size] = 17;
      extra_bits[*tree_size] = repetitions & 0x7;
      ++(*tree_size);
      repetitions >>= 3;
      --repetitions;
    }
    Reverse(tree, start, *tree_size);
    Reverse(extra_bits, start, *tree_size);
  }
}


int OptimizeHuffmanCountsForRle(int length, int* counts) {
  int stride;
  int limit;
  int sum;
  uint8_t* good_for_rle;
  // Let's make the Huffman code more compatible with rle encoding.
  int i;
  for (; length >= 0; --length) {
    if (length == 0) {
      return 1;  // All zeros.
    }
    if (counts[length - 1] != 0) {
      // Now counts[0..length - 1] does not have trailing zeros.
      break;
    }
  }
  {
    int nonzeros = 0;
    int smallest_nonzero = 1 << 30;
    for (i = 0; i < length; ++i) {
      if (counts[i] != 0) {
        ++nonzeros;
        if (smallest_nonzero > counts[i]) {
          smallest_nonzero = counts[i];
        }
      }
    }
    if (nonzeros < 5) {
      // Small histogram will model it well.
      return 1;
    }
    int zeros = length - nonzeros;
    if (smallest_nonzero < 4) {
      if (zeros < 6) {
        for (i = 1; i < length - 1; ++i) {
          if (counts[i - 1] != 0 && counts[i] == 0 && counts[i + 1] != 0) {
            counts[i] = 1;
          }
        }
      }
    }
    if (nonzeros < 28) {
      return 1;
    }
  }
  // 2) Let's mark all population counts that already can be encoded
  // with an rle code.
  good_for_rle = (uint8_t*)calloc(length, 1);
  if (good_for_rle == NULL) {
    return 0;
  }
  {
    // Let's not spoil any of the existing good rle codes.
    // Mark any seq of 0's that is longer as 5 as a good_for_rle.
    // Mark any seq of non-0's that is longer as 7 as a good_for_rle.
    int symbol = counts[0];
    int stride = 0;
    for (i = 0; i < length + 1; ++i) {
      if (i == length || counts[i] != symbol) {
        if ((symbol == 0 && stride >= 5) ||
            (symbol != 0 && stride >= 7)) {
          int k;
          for (k = 0; k < stride; ++k) {
            good_for_rle[i - k - 1] = 1;
          }
        }
        stride = 1;
        if (i != length) {
          symbol = counts[i];
        }
      } else {
        ++stride;
      }
    }
  }
  // 3) Let's replace those population counts that lead to more rle codes.
  // Math here is in 24.8 fixed point representation.
  const int streak_limit = 1240;
  stride = 0;
  limit = 256 * (counts[0] + counts[1] + counts[2]) / 3 + 420;
  sum = 0;
  for (i = 0; i < length + 1; ++i) {
    if (i == length || good_for_rle[i] ||
        (i != 0 && good_for_rle[i - 1]) ||
        abs(256 * counts[i] - limit) >= streak_limit) {
      if (stride >= 4 || (stride >= 3 && sum == 0)) {
        int k;
        // The stride must end, collapse what we have, if we have enough (4).
        int count = (sum + stride / 2) / stride;
        if (count < 1) {
          count = 1;
        }
        if (sum == 0) {
          // Don't make an all zeros stride to be upgraded to ones.
          count = 0;
        }
        for (k = 0; k < stride; ++k) {
          // We don't want to change value at counts[i],
          // that is already belonging to the next stride. Thus - 1.
          counts[i - k - 1] = count;
        }
      }
      stride = 0;
      sum = 0;
      if (i < length - 2) {
        // All interesting strides have a count of at least 4,
        // at least when non-zeros.
        limit = 256 * (counts[i] + counts[i + 1] + counts[i + 2]) / 3 + 420;
      } else if (i < length) {
        limit = 256 * counts[i];
      } else {
        limit = 0;
      }
    }
    ++stride;
    if (i != length) {
      sum += counts[i];
      if (stride >= 4) {
        limit = (256 * sum + stride / 2) / stride;
      }
      if (stride == 4) {
        limit += 120;
      }
    }
  }
  free(good_for_rle);
  return 1;
}


static void DecideOverRleUse(const uint8_t* depth, const int length,
                             bool *use_rle_for_non_zero,
                             bool *use_rle_for_zero) {
  int total_reps_zero = 0;
  int total_reps_non_zero = 0;
  int count_reps_zero = 0;
  int count_reps_non_zero = 0;
  int new_length = length;
  for (int i = 0; i < length; ++i) {
    if (depth[length - i - 1] == 0) {
      --new_length;
    } else {
      break;
    }
  }
  for (uint32_t i = 0; i < new_length;) {
    const int value = depth[i];
    int reps = 1;
    // Find rle coding for longer codes.
    // Shorter codes seem not to benefit from rle.
    for (uint32_t k = i + 1; k < new_length && depth[k] == value; ++k) {
      ++reps;
    }
    if (reps >= 3 && value == 0) {
      total_reps_zero += reps;
      ++count_reps_zero;
    }
    if (reps >= 4 && value != 0) {
      total_reps_non_zero += reps;
      ++count_reps_non_zero;
    }
    i += reps;
  }
  total_reps_non_zero -= count_reps_non_zero * 2;
  total_reps_zero -= count_reps_zero * 2;
  *use_rle_for_non_zero = total_reps_non_zero > 2;
  *use_rle_for_zero = total_reps_zero > 2;
}


void WriteHuffmanTree(const uint8_t* depth, const int length,
                      uint8_t* tree,
                      uint8_t* extra_bits_data,
                      int* huffman_tree_size) {
  int previous_value = 8;

  // First gather statistics on if it is a good idea to do rle.
  bool use_rle_for_non_zero;
  bool use_rle_for_zero;
  DecideOverRleUse(depth, length, &use_rle_for_non_zero, &use_rle_for_zero);

  // Actual rle coding.
  for (uint32_t i = 0; i < length;) {
    const int value = depth[i];
    int reps = 1;
    if (length > 50) {
      // Find rle coding for longer codes.
      // Shorter codes seem not to benefit from rle.
      if ((value != 0 && use_rle_for_non_zero) ||
          (value == 0 && use_rle_for_zero)) {
        for (uint32_t k = i + 1; k < length && depth[k] == value; ++k) {
          ++reps;
        }
      }
    }
    if (value == 0) {
      WriteHuffmanTreeRepetitionsZeros(reps, tree, extra_bits_data,
                                       huffman_tree_size);
    } else {
      WriteHuffmanTreeRepetitions(previous_value, value, reps, tree,
                                  extra_bits_data, huffman_tree_size);
      previous_value = value;
    }
    i += reps;
  }
  // Throw away trailing zeros.
  for (; *huffman_tree_size > 0; --(*huffman_tree_size)) {
    if (tree[*huffman_tree_size - 1] > 0 && tree[*huffman_tree_size - 1] < 17) {
      break;
    }
  }
}

namespace {

uint16_t ReverseBits(int num_bits, uint16_t bits) {
  static const size_t kLut[16] = {  // Pre-reversed 4-bit values.
    0x0, 0x8, 0x4, 0xc, 0x2, 0xa, 0x6, 0xe,
    0x1, 0x9, 0x5, 0xd, 0x3, 0xb, 0x7, 0xf
  };
  size_t retval = kLut[bits & 0xf];
  for (int i = 4; i < num_bits; i += 4) {
    retval <<= 4;
    bits >>= 4;
    retval |= kLut[bits & 0xf];
  }
  retval >>= (-num_bits & 0x3);
  return retval;
}

}  // namespace

void ConvertBitDepthsToSymbols(const uint8_t *depth, int len, uint16_t *bits) {
  // In Brotli, all bit depths are [1..15]
  // 0 bit depth means that the symbol does not exist.
  const int kMaxBits = 16;  // 0..15 are values for bits
  uint16_t bl_count[kMaxBits] = { 0 };
  {
    for (int i = 0; i < len; ++i) {
      ++bl_count[depth[i]];
    }
    bl_count[0] = 0;
  }
  uint16_t next_code[kMaxBits];
  next_code[0] = 0;
  {
    int code = 0;
    for (int bits = 1; bits < kMaxBits; ++bits) {
      code = (code + bl_count[bits - 1]) << 1;
      next_code[bits] = code;
    }
  }
  for (int i = 0; i < len; ++i) {
    if (depth[i]) {
      bits[i] = ReverseBits(depth[i], next_code[depth[i]]++);
    }
  }
}

}  // namespace brotli