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// Copyright 2011 Google Inc. All Rights Reserved.
//
// Use of this source code is governed by a BSD-style license
// that can be found in the COPYING file in the root of the source
// tree. An additional intellectual property rights grant can be found
// in the file PATENTS. All contributing project authors may
// be found in the AUTHORS file in the root of the source tree.
// -----------------------------------------------------------------------------
//
// Author: Jyrki Alakuijala (jyrki@google.com)
//
// Entropy encoding (Huffman) for webp lossless.
#include <assert.h>
#include <stdlib.h>
#include <string.h>
#include "./huffman_encode.h"
#include "./utils.h"
#include "../webp/format_constants.h"
// -----------------------------------------------------------------------------
// Util function to optimize the symbol map for RLE coding
// Heuristics for selecting the stride ranges to collapse.
static int ValuesShouldBeCollapsedToStrideAverage(int a, int b) {
return abs(a - b) < 4;
}
// Change the population counts in a way that the consequent
// Huffman tree compression, especially its RLE-part, give smaller output.
static void OptimizeHuffmanForRle(int length, uint8_t* const good_for_rle,
uint32_t* const counts) {
// 1) Let's make the Huffman code more compatible with rle encoding.
int i;
for (; length >= 0; --length) {
if (length == 0) {
return; // All zeros.
}
if (counts[length - 1] != 0) {
// Now counts[0..length - 1] does not have trailing zeros.
break;
}
}
// 2) Let's mark all population counts that already can be encoded
// with an rle code.
{
// 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.
uint32_t 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.
{
uint32_t stride = 0;
uint32_t limit = counts[0];
uint32_t sum = 0;
for (i = 0; i < length + 1; ++i) {
if (i == length || good_for_rle[i] ||
(i != 0 && good_for_rle[i - 1]) ||
!ValuesShouldBeCollapsedToStrideAverage(counts[i], limit)) {
if (stride >= 4 || (stride >= 3 && sum == 0)) {
uint32_t k;
// The stride must end, collapse what we have, if we have enough (4).
uint32_t 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 - 3) {
// All interesting strides have a count of at least 4,
// at least when non-zeros.
limit = (counts[i] + counts[i + 1] +
counts[i + 2] + counts[i + 3] + 2) / 4;
} else if (i < length) {
limit = counts[i];
} else {
limit = 0;
}
}
++stride;
if (i != length) {
sum += counts[i];
if (stride >= 4) {
limit = (sum + stride / 2) / stride;
}
}
}
}
}
// A comparer function for two Huffman trees: sorts first by 'total count'
// (more comes first), and then by 'value' (more comes first).
static int CompareHuffmanTrees(const void* ptr1, const void* ptr2) {
const HuffmanTree* const t1 = (const HuffmanTree*)ptr1;
const HuffmanTree* const t2 = (const HuffmanTree*)ptr2;
if (t1->total_count_ > t2->total_count_) {
return -1;
} else if (t1->total_count_ < t2->total_count_) {
return 1;
} else {
assert(t1->value_ != t2->value_);
return (t1->value_ < t2->value_) ? -1 : 1;
}
}
static void SetBitDepths(const HuffmanTree* const tree,
const HuffmanTree* const pool,
uint8_t* const bit_depths, int level) {
if (tree->pool_index_left_ >= 0) {
SetBitDepths(&pool[tree->pool_index_left_], pool, bit_depths, level + 1);
SetBitDepths(&pool[tree->pool_index_right_], pool, bit_depths, level + 1);
} else {
bit_depths[tree->value_] = level;
}
}
// Create an optimal Huffman tree.
//
// (data,length): population counts.
// tree_limit: maximum bit depth (inclusive) of the codes.
// bit_depths[]: how many bits are used for the symbol.
//
// Returns 0 when an error has occurred.
//
// The catch here is that the tree cannot be arbitrarily deep
//
// 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
static void GenerateOptimalTree(const uint32_t* const histogram,
int histogram_size,
HuffmanTree* tree, int tree_depth_limit,
uint8_t* const bit_depths) {
uint32_t count_min;
HuffmanTree* tree_pool;
int tree_size_orig = 0;
int i;
for (i = 0; i < histogram_size; ++i) {
if (histogram[i] != 0) {
++tree_size_orig;
}
}
if (tree_size_orig == 0) { // pretty optimal already!
return;
}
tree_pool = tree + tree_size_orig;
// For block sizes with less than 64k symbols we never need to do a
// second iteration of this loop.
// If we actually start running inside this loop a lot, we would perhaps
// be better off with the Katajainen algorithm.
assert(tree_size_orig <= (1 << (tree_depth_limit - 1)));
for (count_min = 1; ; count_min *= 2) {
int tree_size = tree_size_orig;
// We need to pack the Huffman tree in tree_depth_limit bits.
// So, we try by faking histogram entries to be at least 'count_min'.
int idx = 0;
int j;
for (j = 0; j < histogram_size; ++j) {
if (histogram[j] != 0) {
const uint32_t count =
(histogram[j] < count_min) ? count_min : histogram[j];
tree[idx].total_count_ = count;
tree[idx].value_ = j;
tree[idx].pool_index_left_ = -1;
tree[idx].pool_index_right_ = -1;
++idx;
}
}
// Build the Huffman tree.
qsort(tree, tree_size, sizeof(*tree), CompareHuffmanTrees);
if (tree_size > 1) { // Normal case.
int tree_pool_size = 0;
while (tree_size > 1) { // Finish when we have only one root.
uint32_t count;
tree_pool[tree_pool_size++] = tree[tree_size - 1];
tree_pool[tree_pool_size++] = tree[tree_size - 2];
count = tree_pool[tree_pool_size - 1].total_count_ +
tree_pool[tree_pool_size - 2].total_count_;
tree_size -= 2;
{
// Search for the insertion point.
int k;
for (k = 0; k < tree_size; ++k) {
if (tree[k].total_count_ <= count) {
break;
}
}
memmove(tree + (k + 1), tree + k, (tree_size - k) * sizeof(*tree));
tree[k].total_count_ = count;
tree[k].value_ = -1;
tree[k].pool_index_left_ = tree_pool_size - 1;
tree[k].pool_index_right_ = tree_pool_size - 2;
tree_size = tree_size + 1;
}
}
SetBitDepths(&tree[0], tree_pool, bit_depths, 0);
} else if (tree_size == 1) { // Trivial case: only one element.
bit_depths[tree[0].value_] = 1;
}
{
// Test if this Huffman tree satisfies our 'tree_depth_limit' criteria.
int max_depth = bit_depths[0];
for (j = 1; j < histogram_size; ++j) {
if (max_depth < bit_depths[j]) {
max_depth = bit_depths[j];
}
}
if (max_depth <= tree_depth_limit) {
break;
}
}
}
}
// -----------------------------------------------------------------------------
// Coding of the Huffman tree values
static HuffmanTreeToken* CodeRepeatedValues(int repetitions,
HuffmanTreeToken* tokens,
int value, int prev_value) {
assert(value <= MAX_ALLOWED_CODE_LENGTH);
if (value != prev_value) {
tokens->code = value;
tokens->extra_bits = 0;
++tokens;
--repetitions;
}
while (repetitions >= 1) {
if (repetitions < 3) {
int i;
for (i = 0; i < repetitions; ++i) {
tokens->code = value;
tokens->extra_bits = 0;
++tokens;
}
break;
} else if (repetitions < 7) {
tokens->code = 16;
tokens->extra_bits = repetitions - 3;
++tokens;
break;
} else {
tokens->code = 16;
tokens->extra_bits = 3;
++tokens;
repetitions -= 6;
}
}
return tokens;
}
static HuffmanTreeToken* CodeRepeatedZeros(int repetitions,
HuffmanTreeToken* tokens) {
while (repetitions >= 1) {
if (repetitions < 3) {
int i;
for (i = 0; i < repetitions; ++i) {
tokens->code = 0; // 0-value
tokens->extra_bits = 0;
++tokens;
}
break;
} else if (repetitions < 11) {
tokens->code = 17;
tokens->extra_bits = repetitions - 3;
++tokens;
break;
} else if (repetitions < 139) {
tokens->code = 18;
tokens->extra_bits = repetitions - 11;
++tokens;
break;
} else {
tokens->code = 18;
tokens->extra_bits = 0x7f; // 138 repeated 0s
++tokens;
repetitions -= 138;
}
}
return tokens;
}
int VP8LCreateCompressedHuffmanTree(const HuffmanTreeCode* const tree,
HuffmanTreeToken* tokens, int max_tokens) {
HuffmanTreeToken* const starting_token = tokens;
HuffmanTreeToken* const ending_token = tokens + max_tokens;
const int depth_size = tree->num_symbols;
int prev_value = 8; // 8 is the initial value for rle.
int i = 0;
assert(tokens != NULL);
while (i < depth_size) {
const int value = tree->code_lengths[i];
int k = i + 1;
int runs;
while (k < depth_size && tree->code_lengths[k] == value) ++k;
runs = k - i;
if (value == 0) {
tokens = CodeRepeatedZeros(runs, tokens);
} else {
tokens = CodeRepeatedValues(runs, tokens, value, prev_value);
prev_value = value;
}
i += runs;
assert(tokens <= ending_token);
}
(void)ending_token; // suppress 'unused variable' warning
return (int)(tokens - starting_token);
}
// -----------------------------------------------------------------------------
// Pre-reversed 4-bit values.
static const uint8_t kReversedBits[16] = {
0x0, 0x8, 0x4, 0xc, 0x2, 0xa, 0x6, 0xe,
0x1, 0x9, 0x5, 0xd, 0x3, 0xb, 0x7, 0xf
};
static uint32_t ReverseBits(int num_bits, uint32_t bits) {
uint32_t retval = 0;
int i = 0;
while (i < num_bits) {
i += 4;
retval |= kReversedBits[bits & 0xf] << (MAX_ALLOWED_CODE_LENGTH + 1 - i);
bits >>= 4;
}
retval >>= (MAX_ALLOWED_CODE_LENGTH + 1 - num_bits);
return retval;
}
// Get the actual bit values for a tree of bit depths.
static void ConvertBitDepthsToSymbols(HuffmanTreeCode* const tree) {
// 0 bit-depth means that the symbol does not exist.
int i;
int len;
uint32_t next_code[MAX_ALLOWED_CODE_LENGTH + 1];
int depth_count[MAX_ALLOWED_CODE_LENGTH + 1] = { 0 };
assert(tree != NULL);
len = tree->num_symbols;
for (i = 0; i < len; ++i) {
const int code_length = tree->code_lengths[i];
assert(code_length <= MAX_ALLOWED_CODE_LENGTH);
++depth_count[code_length];
}
depth_count[0] = 0; // ignore unused symbol
next_code[0] = 0;
{
uint32_t code = 0;
for (i = 1; i <= MAX_ALLOWED_CODE_LENGTH; ++i) {
code = (code + depth_count[i - 1]) << 1;
next_code[i] = code;
}
}
for (i = 0; i < len; ++i) {
const int code_length = tree->code_lengths[i];
tree->codes[i] = ReverseBits(code_length, next_code[code_length]++);
}
}
// -----------------------------------------------------------------------------
// Main entry point
void VP8LCreateHuffmanTree(uint32_t* const histogram, int tree_depth_limit,
uint8_t* const buf_rle,
HuffmanTree* const huff_tree,
HuffmanTreeCode* const huff_code) {
const int num_symbols = huff_code->num_symbols;
memset(buf_rle, 0, num_symbols * sizeof(*buf_rle));
OptimizeHuffmanForRle(num_symbols, buf_rle, histogram);
GenerateOptimalTree(histogram, num_symbols, huff_tree, tree_depth_limit,
huff_code->code_lengths);
// Create the actual bit codes for the bit lengths.
ConvertBitDepthsToSymbols(huff_code);
}