4 * Functions used for compression.
8 * Copyright (C) 2012 Eric Biggers
10 * This file is part of wimlib, a library for working with WIM files.
12 * wimlib is free software; you can redistribute it and/or modify it under the
13 * terms of the GNU General Public License as published by the Free
14 * Software Foundation; either version 3 of the License, or (at your option)
17 * wimlib is distributed in the hope that it will be useful, but WITHOUT ANY
18 * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
19 * A PARTICULAR PURPOSE. See the GNU General Public License for more
22 * You should have received a copy of the GNU General Public License
23 * along with wimlib; if not, see http://www.gnu.org/licenses/.
30 static inline void flush_bits(struct output_bitstream *ostream)
32 *(u16*)ostream->bit_output = to_le16(ostream->bitbuf);
33 ostream->bit_output = ostream->next_bit_output;
34 ostream->next_bit_output = ostream->output;
36 ostream->num_bytes_remaining -= 2;
39 /* Writes @num_bits bits, given by the @num_bits least significant bits of
40 * @bits, to the output @ostream. */
41 int bitstream_put_bits(struct output_bitstream *ostream, output_bitbuf_t bits,
46 wimlib_assert(num_bits <= 16);
47 if (num_bits <= ostream->free_bits) {
48 ostream->bitbuf = (ostream->bitbuf << num_bits) | bits;
49 ostream->free_bits -= num_bits;
52 if (ostream->num_bytes_remaining + (ostream->output -
53 ostream->bit_output) < 2)
56 /* It is tricky to output the bits correctly. The correct way
57 * is to output little-endian 2-byte words, such that the bits
58 * in the SECOND byte logically precede those in the FIRST byte.
59 * While the byte order is little-endian, the bit order is
60 * big-endian; the first bit in a byte is the high-order one.
61 * Any multi-bit numbers are in bit-big-endian form, so the
62 * low-order bit of a multi-bit number is the LAST bit to be
64 rem_bits = num_bits - ostream->free_bits;
65 ostream->bitbuf <<= ostream->free_bits;
66 ostream->bitbuf |= bits >> rem_bits;
68 ostream->free_bits = 16 - rem_bits;
69 ostream->bitbuf = bits;
75 /* Flushes any remaining bits in the output buffer to the output byte stream. */
76 int flush_output_bitstream(struct output_bitstream *ostream)
78 if (ostream->num_bytes_remaining + (ostream->output -
79 ostream->bit_output) < 2)
81 if (ostream->free_bits != 16) {
82 ostream->bitbuf <<= ostream->free_bits;
88 /* Initializes an output bit buffer to write its output to the memory location
89 * pointer to by @data. */
90 void init_output_bitstream(struct output_bitstream *ostream, void *data,
94 ostream->free_bits = 16;
95 ostream->bit_output = (u8*)data;
96 ostream->next_bit_output = (u8*)data + 2;
97 ostream->output = (u8*)data + 4;
98 ostream->num_bytes_remaining = num_bytes - 4;
101 /* Intermediate (non-leaf) node in a Huffman tree. */
102 typedef struct HuffmanNode {
109 struct HuffmanNode *left_child;
110 struct HuffmanNode *right_child;
113 /* Leaf node in a Huffman tree. The fields are in the same order as the
114 * HuffmanNode, so it can be cast to a HuffmanNode. There are no pointers to
115 * the children in the leaf node. */
125 /* Comparator function for HuffmanLeafNodes. Sorts primarily by symbol
126 * frequency and secondarily by symbol value. */
127 static int cmp_leaves_by_freq(const void *__leaf1, const void *__leaf2)
129 const HuffmanLeafNode *leaf1 = __leaf1;
130 const HuffmanLeafNode *leaf2 = __leaf2;
132 int freq_diff = (int)leaf1->freq - (int)leaf2->freq;
135 return (int)leaf1->sym - (int)leaf2->sym;
140 /* Comparator function for HuffmanLeafNodes. Sorts primarily by code length and
141 * secondarily by symbol value. */
142 static int cmp_leaves_by_code_len(const void *__leaf1, const void *__leaf2)
144 const HuffmanLeafNode *leaf1 = __leaf1;
145 const HuffmanLeafNode *leaf2 = __leaf2;
147 int code_len_diff = (int)leaf1->path_len - (int)leaf2->path_len;
149 if (code_len_diff == 0)
150 return (int)leaf1->sym - (int)leaf2->sym;
152 return code_len_diff;
155 /* Recursive function to calculate the depth of the leaves in a Huffman tree.
157 static void huffman_tree_compute_path_lengths(HuffmanNode *node, u16 cur_len)
159 if (node->sym == (u16)(-1)) {
160 /* Intermediate node. */
161 huffman_tree_compute_path_lengths(node->left_child, cur_len + 1);
162 huffman_tree_compute_path_lengths(node->right_child, cur_len + 1);
165 node->path_len = cur_len;
169 /* Creates a canonical Huffman code from an array of symbol frequencies.
171 * The algorithm used is similar to the well-known algorithm that builds a
172 * Huffman tree using a minheap. In that algorithm, the leaf nodes are
173 * initialized and inserted into the minheap with the frequency as the key.
174 * Repeatedly, the top two nodes (nodes with the lowest frequency) are taken out
175 * of the heap and made the children of a new node that has a frequency equal to
176 * the sum of the two frequencies of its children. This new node is inserted
177 * into the heap. When all the nodes have been removed from the heap, what
178 * remains is the Huffman tree. The Huffman code for a symbol is given by the
179 * path to it in the tree, where each left pointer is mapped to a 0 bit and each
180 * right pointer is mapped to a 1 bit.
182 * The algorithm used here uses an optimization that removes the need to
183 * actually use a heap. The leaf nodes are first sorted by frequency, as
184 * opposed to being made into a heap. Note that this sorting step takes O(n log
185 * n) time vs. O(n) time for heapifying the array, where n is the number of
186 * symbols. However, the heapless method is probably faster overall, due to the
187 * time saved later. In the heapless method, whenever an intermediate node is
188 * created, it is not inserted into the sorted array. Instead, the intermediate
189 * nodes are kept in a separate array, which is easily kept sorted because every
190 * time an intermediate node is initialized, it will have a frequency at least
191 * as high as that of the previous intermediate node that was initialized. So
192 * whenever we want the 2 nodes, leaf or intermediate, that have the lowest
193 * frequency, we check the low-frequency ends of both arrays, which is an O(1)
196 * The function builds a canonical Huffman code, not just any Huffman code. A
197 * Huffman code is canonical if the codeword for each symbol numerically
198 * precedes the codeword for all other symbols of the same length that are
199 * numbered higher than the symbol, and additionally, all shorter codewords,
200 * 0-extended, numerically precede longer codewords. A canonical Huffman code
201 * is useful because it can be reconstructed by only knowing the path lengths in
202 * the tree. See the make_huffman_decode_table() function to see how to
203 * reconstruct a canonical Huffman code from only the lengths of the codes.
205 * @num_syms: The number of symbols in the alphabet.
207 * @max_codeword_len: The maximum allowed length of a codeword in the code.
208 * Note that if the code being created runs up against
209 * this restriction, the code ultimately created will be
210 * suboptimal, although there are some advantages for
211 * limiting the length of the codewords.
213 * @freq_tab: An array of length @num_syms that contains the frequencies
214 * of each symbol in the uncompressed data.
216 * @lens: An array of length @num_syms into which the lengths of the
217 * codewords for each symbol will be written.
219 * @codewords: An array of @num_syms short integers into which the
220 * codewords for each symbol will be written. The first
221 * lens[i] bits of codewords[i] will contain the codeword
224 void make_canonical_huffman_code(uint num_syms, uint max_codeword_len,
225 const u32 freq_tab[], u8 lens[],
228 /* We require at least 2 possible symbols in the alphabet to produce a
229 * valid Huffman decoding table. It is allowed that fewer than 2 symbols
230 * are actually used, though. */
231 wimlib_assert(num_syms >= 2);
233 /* Initialize the lengths and codewords to 0 */
234 memset(lens, 0, num_syms * sizeof(lens[0]));
235 memset(codewords, 0, num_syms * sizeof(codewords[0]));
237 /* Calculate how many symbols have non-zero frequency. These are the
238 * symbols that actually appeared in the input. */
239 uint num_used_symbols = 0;
240 for (uint i = 0; i < num_syms; i++)
241 if (freq_tab[i] != 0)
245 /* It is impossible to make a code for num_used_symbols symbols if there
246 * aren't enough code bits to uniquely represent all of them. */
247 wimlib_assert((1 << max_codeword_len) > num_used_symbols);
249 /* Initialize the array of leaf nodes with the symbols and their
251 HuffmanLeafNode leaves[num_used_symbols];
253 for (uint i = 0; i < num_syms; i++) {
254 if (freq_tab[i] != 0) {
255 leaves[leaf_idx].freq = freq_tab[i];
256 leaves[leaf_idx].sym = i;
257 leaves[leaf_idx].height = 0;
262 /* Deal with the special cases where num_used_symbols < 2. */
263 if (num_used_symbols < 2) {
264 if (num_used_symbols == 0) {
265 /* If num_used_symbols is 0, there are no symbols in the
266 * input, so it must be empty. This should be an error,
267 * but the LZX format expects this case to succeed. All
268 * the codeword lengths are simply marked as 0 (which
269 * was already done.) */
271 /* If only one symbol is present, the LZX format
272 * requires that the Huffman code include two codewords.
273 * One is not used. Note that this doesn't make the
274 * encoded data take up more room anyway, since binary
275 * data itself has 2 symbols. */
277 uint sym = leaves[0].sym;
282 /* dummy symbol is 1, real symbol is 0 */
286 /* dummy symbol is 0, real symbol is sym */
294 /* Otherwise, there are at least 2 symbols in the input, so we need to
295 * find a real Huffman code. */
298 /* Declare the array of intermediate nodes. An intermediate node is not
299 * associated with a symbol. Instead, it represents some binary code
300 * prefix that is shared between at least 2 codewords. There can be at
301 * most num_used_symbols - 1 intermediate nodes when creating a Huffman
302 * code. This is because if there were at least num_used_symbols nodes,
303 * the code would be suboptimal because there would be at least one
304 * unnecessary intermediate node.
306 * The worst case (greatest number of intermediate nodes) would be if
307 * all the intermediate nodes were chained together. This results in
308 * num_used_symbols - 1 intermediate nodes. If num_used_symbols is at
309 * least 17, this configuration would not be allowed because the LZX
310 * format constrains codes to 16 bits or less each. However, it is
311 * still possible for there to be more than 16 intermediate nodes, as
312 * long as no leaf has a depth of more than 16. */
313 HuffmanNode inodes[num_used_symbols - 1];
316 /* Pointer to the leaf node of lowest frequency that hasn't already been
317 * added as the child of some intermediate note. */
318 HuffmanLeafNode *cur_leaf = &leaves[0];
320 /* Pointer past the end of the array of leaves. */
321 HuffmanLeafNode *end_leaf = &leaves[num_used_symbols];
323 /* Pointer to the intermediate node of lowest frequency. */
324 HuffmanNode *cur_inode = &inodes[0];
326 /* Pointer to the next unallocated intermediate node. */
327 HuffmanNode *next_inode = &inodes[0];
329 /* Only jump back to here if the maximum length of the codewords allowed
330 * by the LZX format (16 bits) is exceeded. */
331 try_building_tree_again:
333 /* Sort the leaves from those that correspond to the least frequent
334 * symbol, to those that correspond to the most frequent symbol. If two
335 * leaves have the same frequency, they are sorted by symbol. */
336 qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_leaves_by_freq);
338 cur_leaf = &leaves[0];
339 cur_inode = &inodes[0];
340 next_inode = &inodes[0];
342 /* The following loop takes the two lowest frequency nodes of those
343 * remaining and makes them the children of the next available
344 * intermediate node. It continues until all the leaf nodes and
345 * intermediate nodes have been used up, or the maximum allowed length
346 * for the codewords is exceeded. For the latter case, we must adjust
347 * the frequencies to be more equal and then execute this loop again. */
350 /* Lowest frequency node. */
351 HuffmanNode *f1 = NULL;
353 /* Second lowest frequency node. */
354 HuffmanNode *f2 = NULL;
356 /* Get the lowest and second lowest frequency nodes from
357 * the remaining leaves or from the intermediate nodes.
360 if (cur_leaf != end_leaf && (cur_inode == next_inode ||
361 cur_leaf->freq <= cur_inode->freq)) {
362 f1 = (HuffmanNode*)cur_leaf++;
363 } else if (cur_inode != next_inode) {
367 if (cur_leaf != end_leaf && (cur_inode == next_inode ||
368 cur_leaf->freq <= cur_inode->freq)) {
369 f2 = (HuffmanNode*)cur_leaf++;
370 } else if (cur_inode != next_inode) {
374 /* All nodes used up! */
375 if (f1 == NULL || f2 == NULL)
378 /* next_inode becomes the parent of f1 and f2. */
380 next_inode->freq = f1->freq + f2->freq;
381 next_inode->sym = (u16)(-1); /* Invalid symbol. */
382 next_inode->left_child = f1;
383 next_inode->right_child = f2;
385 /* We need to keep track of the height so that we can detect if
386 * the length of a codeword has execeed max_codeword_len. The
387 * parent node has a height one higher than the maximum height
388 * of its children. */
389 next_inode->height = max(f1->height, f2->height) + 1;
391 /* Check to see if the code length of the leaf farthest away
392 * from next_inode has exceeded the maximum code length. */
393 if (next_inode->height > max_codeword_len) {
394 /* The code lengths can be made more uniform by making
395 * the frequencies more uniform. Divide all the
396 * frequencies by 2, leaving 1 as the minimum frequency.
397 * If this keeps happening, the symbol frequencies will
398 * approach equality, which makes their Huffman
399 * codewords approach the length
400 * log_2(num_used_symbols).
402 for (uint i = 0; i < num_used_symbols; i++)
403 if (leaves[i].freq > 1)
404 leaves[i].freq >>= 1;
405 goto try_building_tree_again;
410 /* The Huffman tree is now complete, and its height is no more than
411 * max_codeword_len. */
413 HuffmanNode *root = next_inode - 1;
414 wimlib_assert(root->height <= max_codeword_len);
416 /* Compute the path lengths for the leaf nodes. */
417 huffman_tree_compute_path_lengths(root, 0);
419 /* Sort the leaf nodes primarily by code length and secondarily by
421 qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_leaves_by_code_len);
423 u16 cur_codeword = 0;
424 uint cur_codeword_len = 0;
425 for (uint i = 0; i < num_used_symbols; i++) {
427 /* Each time a codeword becomes one longer, the current codeword
428 * is left shifted by one place. This is part of the procedure
429 * for enumerating the canonical Huffman code. Additionally,
430 * whenever a codeword is used, 1 is added to the current
433 uint len_diff = leaves[i].path_len - cur_codeword_len;
434 cur_codeword <<= len_diff;
435 cur_codeword_len += len_diff;
437 u16 sym = leaves[i].sym;
438 codewords[sym] = cur_codeword;
439 lens[sym] = cur_codeword_len;