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// 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, break ties by value.
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_;
}
// Sort the root nodes, least popular first.
bool SortHuffmanTreeFast(const HuffmanTree &v0, const HuffmanTree &v1) {
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,
const int quality,
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;
}
if (quality > 1) {
std::sort(tree.begin(), tree.end(), SortHuffmanTree);
} else {
std::sort(tree.begin(), tree.end(), SortHuffmanTreeFast);
}
// 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(std::vector<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,
std::vector<uint8_t> *tree,
std::vector<uint8_t> *extra_bits_data) {
if (previous_value != value) {
tree->push_back(value);
extra_bits_data->push_back(0);
--repetitions;
}
if (repetitions == 7) {
tree->push_back(value);
extra_bits_data->push_back(0);
--repetitions;
}
if (repetitions < 3) {
for (int i = 0; i < repetitions; ++i) {
tree->push_back(value);
extra_bits_data->push_back(0);
}
} else {
repetitions -= 3;
int start = tree->size();
while (repetitions >= 0) {
tree->push_back(16);
extra_bits_data->push_back(repetitions & 0x3);
repetitions >>= 2;
--repetitions;
}
Reverse(tree, start, tree->size());
Reverse(extra_bits_data, start, tree->size());
}
}
void WriteHuffmanTreeRepetitionsZeros(
int repetitions,
std::vector<uint8_t> *tree,
std::vector<uint8_t> *extra_bits_data) {
if (repetitions == 11) {
tree->push_back(0);
extra_bits_data->push_back(0);
--repetitions;
}
if (repetitions < 3) {
for (int i = 0; i < repetitions; ++i) {
tree->push_back(0);
extra_bits_data->push_back(0);
}
} else {
repetitions -= 3;
int start = tree->size();
while (repetitions >= 0) {
tree->push_back(17);
extra_bits_data->push_back(repetitions & 0x7);
repetitions >>= 3;
--repetitions;
}
Reverse(tree, start, tree->size());
Reverse(extra_bits_data, 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;
for (uint32_t i = 0; i < length;) {
const int value = depth[i];
int reps = 1;
for (uint32_t k = i + 1; k < 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,
uint32_t length,
std::vector<uint8_t> *tree,
std::vector<uint8_t> *extra_bits_data) {
int previous_value = 8;
// Throw away trailing zeros.
int new_length = length;
for (int i = 0; i < length; ++i) {
if (depth[length - i - 1] == 0) {
--new_length;
} else {
break;
}
}
// First gather statistics on if it is a good idea to do rle.
bool use_rle_for_non_zero = false;
bool use_rle_for_zero = false;
if (length > 50) {
// Find rle coding for longer codes.
// Shorter codes seem not to benefit from rle.
DecideOverRleUse(depth, new_length,
&use_rle_for_non_zero, &use_rle_for_zero);
}
// Actual rle coding.
for (uint32_t i = 0; i < new_length;) {
const int value = depth[i];
int reps = 1;
if ((value != 0 && use_rle_for_non_zero) ||
(value == 0 && use_rle_for_zero)) {
for (uint32_t k = i + 1; k < new_length && depth[k] == value; ++k) {
++reps;
}
}
if (value == 0) {
WriteHuffmanTreeRepetitionsZeros(reps, tree, extra_bits_data);
} else {
WriteHuffmanTreeRepetitions(previous_value,
value, reps, tree, extra_bits_data);
previous_value = value;
}
i += reps;
}
}
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
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