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+// Copyright 2011 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)
+//
+// Entropy encoding (Huffman) for webp lossless.
+
+#include <assert.h>
+#include <stdlib.h>
+#include <string.h>
+#include "./huffman_encode.h"
+#include "../utils/utils.h"
+#include "../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
+// Hufmann tree compression, especially its RLE-part, give smaller output.
+static int OptimizeHuffmanForRle(int length, int* const counts) {
+ uint8_t* good_for_rle;
+ // 1) 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;
+ }
+ }
+ // 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.
+ {
+ int stride = 0;
+ int limit = counts[0];
+ int 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)) {
+ 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 - 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;
+ }
+ }
+ }
+ }
+ free(good_for_rle);
+ return 1;
+}
+
+typedef struct {
+ int total_count_;
+ int value_;
+ int pool_index_left_;
+ int pool_index_right_;
+} HuffmanTree;
+
+// 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 {
+ if (t1->value_ < t2->value_) {
+ return -1;
+ }
+ if (t1->value_ > t2->value_) {
+ return 1;
+ }
+ return 0;
+ }
+}
+
+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 int GenerateOptimalTree(const int* const histogram, int histogram_size,
+ int tree_depth_limit,
+ uint8_t* const bit_depths) {
+ int count_min;
+ HuffmanTree* tree_pool;
+ HuffmanTree* tree;
+ int tree_size_orig = 0;
+ int i;
+
+ for (i = 0; i < histogram_size; ++i) {
+ if (histogram[i] != 0) {
+ ++tree_size_orig;
+ }
+ }
+
+ // 3 * tree_size is enough to cover all the nodes representing a
+ // population and all the inserted nodes combining two existing nodes.
+ // The tree pool needs 2 * (tree_size_orig - 1) entities, and the
+ // tree needs exactly tree_size_orig entities.
+ tree = (HuffmanTree*)WebPSafeMalloc(3ULL * tree_size_orig, sizeof(*tree));
+ if (tree == NULL) return 0;
+ 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 int 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.
+ int 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;
+ }
+ }
+ }
+ free(tree);
+ return 1;
+}
+
+// -----------------------------------------------------------------------------
+// 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
+
+int VP8LCreateHuffmanTree(int* const histogram, int tree_depth_limit,
+ HuffmanTreeCode* const tree) {
+ const int num_symbols = tree->num_symbols;
+ if (!OptimizeHuffmanForRle(num_symbols, histogram)) {
+ return 0;
+ }
+ if (!GenerateOptimalTree(histogram, num_symbols,
+ tree_depth_limit, tree->code_lengths)) {
+ return 0;
+ }
+ // Create the actual bit codes for the bit lengths.
+ ConvertBitDepthsToSymbols(tree);
+ return 1;
+}