4 * Functions used for compression.
8 * Copyright (C) 2012, 2013 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/.
31 #include "wimlib/assert.h"
32 #include "wimlib/compress.h"
33 #include "wimlib/util.h"
39 flush_bits(struct output_bitstream *ostream)
41 *(u16*)ostream->bit_output = cpu_to_le16(ostream->bitbuf);
42 ostream->bit_output = ostream->next_bit_output;
43 ostream->next_bit_output = ostream->output;
45 ostream->num_bytes_remaining -= 2;
48 /* Writes @num_bits bits, given by the @num_bits least significant bits of
49 * @bits, to the output @ostream. */
51 bitstream_put_bits(struct output_bitstream *ostream, output_bitbuf_t bits,
56 wimlib_assert(num_bits <= 16);
57 if (num_bits <= ostream->free_bits) {
58 ostream->bitbuf = (ostream->bitbuf << num_bits) | bits;
59 ostream->free_bits -= num_bits;
62 if (ostream->num_bytes_remaining + (ostream->output -
63 ostream->bit_output) < 2)
66 /* It is tricky to output the bits correctly. The correct way
67 * is to output little-endian 2-byte words, such that the bits
68 * in the SECOND byte logically precede those in the FIRST byte.
69 * While the byte order is little-endian, the bit order is
70 * big-endian; the first bit in a byte is the high-order one.
71 * Any multi-bit numbers are in bit-big-endian form, so the
72 * low-order bit of a multi-bit number is the LAST bit to be
74 rem_bits = num_bits - ostream->free_bits;
75 ostream->bitbuf <<= ostream->free_bits;
76 ostream->bitbuf |= bits >> rem_bits;
78 ostream->free_bits = 16 - rem_bits;
79 ostream->bitbuf = bits;
85 /* Flushes any remaining bits in the output buffer to the output byte stream. */
87 flush_output_bitstream(struct output_bitstream *ostream)
89 if (ostream->num_bytes_remaining + (ostream->output -
90 ostream->bit_output) < 2)
92 if (ostream->free_bits != 16) {
93 ostream->bitbuf <<= ostream->free_bits;
99 /* Initializes an output bit buffer to write its output to the memory location
100 * pointer to by @data. */
102 init_output_bitstream(struct output_bitstream *ostream, void *data,
105 wimlib_assert(num_bytes >= 4);
108 ostream->free_bits = 16;
109 ostream->bit_output = (u8*)data;
110 ostream->next_bit_output = (u8*)data + 2;
111 ostream->output = (u8*)data + 4;
112 ostream->num_bytes_remaining = num_bytes - 4;
115 /* Intermediate (non-leaf) node in a Huffman tree. */
116 typedef struct HuffmanNode {
123 struct HuffmanNode *left_child;
124 struct HuffmanNode *right_child;
127 /* Leaf node in a Huffman tree. The fields are in the same order as the
128 * HuffmanNode, so it can be cast to a HuffmanNode. There are no pointers to
129 * the children in the leaf node. */
139 /* Comparator function for HuffmanLeafNodes. Sorts primarily by symbol
140 * frequency and secondarily by symbol value. */
142 cmp_leaves_by_freq(const void *__leaf1, const void *__leaf2)
144 const HuffmanLeafNode *leaf1 = __leaf1;
145 const HuffmanLeafNode *leaf2 = __leaf2;
147 int freq_diff = (int)leaf1->freq - (int)leaf2->freq;
150 return (int)leaf1->sym - (int)leaf2->sym;
155 /* Comparator function for HuffmanLeafNodes. Sorts primarily by code length and
156 * secondarily by symbol value. */
158 cmp_leaves_by_code_len(const void *__leaf1, const void *__leaf2)
160 const HuffmanLeafNode *leaf1 = __leaf1;
161 const HuffmanLeafNode *leaf2 = __leaf2;
163 int code_len_diff = (int)leaf1->path_len - (int)leaf2->path_len;
165 if (code_len_diff == 0)
166 return (int)leaf1->sym - (int)leaf2->sym;
168 return code_len_diff;
171 /* Recursive function to calculate the depth of the leaves in a Huffman tree.
174 huffman_tree_compute_path_lengths(HuffmanNode *node, u16 cur_len)
176 if (node->sym == (u16)(-1)) {
177 /* Intermediate node. */
178 huffman_tree_compute_path_lengths(node->left_child, cur_len + 1);
179 huffman_tree_compute_path_lengths(node->right_child, cur_len + 1);
182 node->path_len = cur_len;
186 /* make_canonical_huffman_code: - Creates a canonical Huffman code from an array
187 * of symbol frequencies.
189 * The algorithm used is similar to the well-known algorithm that builds a
190 * Huffman tree using a minheap. In that algorithm, the leaf nodes are
191 * initialized and inserted into the minheap with the frequency as the key.
192 * Repeatedly, the top two nodes (nodes with the lowest frequency) are taken out
193 * of the heap and made the children of a new node that has a frequency equal to
194 * the sum of the two frequencies of its children. This new node is inserted
195 * into the heap. When all the nodes have been removed from the heap, what
196 * remains is the Huffman tree. The Huffman code for a symbol is given by the
197 * path to it in the tree, where each left pointer is mapped to a 0 bit and each
198 * right pointer is mapped to a 1 bit.
200 * The algorithm used here uses an optimization that removes the need to
201 * actually use a heap. The leaf nodes are first sorted by frequency, as
202 * opposed to being made into a heap. Note that this sorting step takes O(n log
203 * n) time vs. O(n) time for heapifying the array, where n is the number of
204 * symbols. However, the heapless method is probably faster overall, due to the
205 * time saved later. In the heapless method, whenever an intermediate node is
206 * created, it is not inserted into the sorted array. Instead, the intermediate
207 * nodes are kept in a separate array, which is easily kept sorted because every
208 * time an intermediate node is initialized, it will have a frequency at least
209 * as high as that of the previous intermediate node that was initialized. So
210 * whenever we want the 2 nodes, leaf or intermediate, that have the lowest
211 * frequency, we check the low-frequency ends of both arrays, which is an O(1)
214 * The function builds a canonical Huffman code, not just any Huffman code. A
215 * Huffman code is canonical if the codeword for each symbol numerically
216 * precedes the codeword for all other symbols of the same length that are
217 * numbered higher than the symbol, and additionally, all shorter codewords,
218 * 0-extended, numerically precede longer codewords. A canonical Huffman code
219 * is useful because it can be reconstructed by only knowing the path lengths in
220 * the tree. See the make_huffman_decode_table() function to see how to
221 * reconstruct a canonical Huffman code from only the lengths of the codes.
223 * @num_syms: The number of symbols in the alphabet.
225 * @max_codeword_len: The maximum allowed length of a codeword in the code.
226 * Note that if the code being created runs up against
227 * this restriction, the code ultimately created will be
228 * suboptimal, although there are some advantages for
229 * limiting the length of the codewords.
231 * @freq_tab: An array of length @num_syms that contains the frequencies
232 * of each symbol in the uncompressed data.
234 * @lens: An array of length @num_syms into which the lengths of the
235 * codewords for each symbol will be written.
237 * @codewords: An array of @num_syms short integers into which the
238 * codewords for each symbol will be written. The first
239 * lens[i] bits of codewords[i] will contain the codeword
243 make_canonical_huffman_code(unsigned num_syms, unsigned max_codeword_len,
244 const freq_t freq_tab[], u8 lens[],
247 /* We require at least 2 possible symbols in the alphabet to produce a
248 * valid Huffman decoding table. It is allowed that fewer than 2 symbols
249 * are actually used, though. */
250 wimlib_assert(num_syms >= 2);
252 /* Initialize the lengths and codewords to 0 */
253 memset(lens, 0, num_syms * sizeof(lens[0]));
254 memset(codewords, 0, num_syms * sizeof(codewords[0]));
256 /* Calculate how many symbols have non-zero frequency. These are the
257 * symbols that actually appeared in the input. */
258 unsigned num_used_symbols = 0;
259 for (unsigned i = 0; i < num_syms; i++)
260 if (freq_tab[i] != 0)
264 /* It is impossible to make a code for num_used_symbols symbols if there
265 * aren't enough code bits to uniquely represent all of them. */
266 wimlib_assert((1 << max_codeword_len) > num_used_symbols);
268 /* Initialize the array of leaf nodes with the symbols and their
270 HuffmanLeafNode leaves[num_used_symbols];
271 unsigned leaf_idx = 0;
272 for (unsigned i = 0; i < num_syms; i++) {
273 if (freq_tab[i] != 0) {
274 leaves[leaf_idx].freq = freq_tab[i];
275 leaves[leaf_idx].sym = i;
276 leaves[leaf_idx].height = 0;
281 /* Deal with the special cases where num_used_symbols < 2. */
282 if (num_used_symbols < 2) {
283 if (num_used_symbols == 0) {
284 /* If num_used_symbols is 0, there are no symbols in the
285 * input, so it must be empty. This should be an error,
286 * but the LZX format expects this case to succeed. All
287 * the codeword lengths are simply marked as 0 (which
288 * was already done.) */
290 /* If only one symbol is present, the LZX format
291 * requires that the Huffman code include two codewords.
292 * One is not used. Note that this doesn't make the
293 * encoded data take up more room anyway, since binary
294 * data itself has 2 symbols. */
296 unsigned sym = leaves[0].sym;
301 /* dummy symbol is 1, real symbol is 0 */
305 /* dummy symbol is 0, real symbol is sym */
313 /* Otherwise, there are at least 2 symbols in the input, so we need to
314 * find a real Huffman code. */
317 /* Declare the array of intermediate nodes. An intermediate node is not
318 * associated with a symbol. Instead, it represents some binary code
319 * prefix that is shared between at least 2 codewords. There can be at
320 * most num_used_symbols - 1 intermediate nodes when creating a Huffman
321 * code. This is because if there were at least num_used_symbols nodes,
322 * the code would be suboptimal because there would be at least one
323 * unnecessary intermediate node.
325 * The worst case (greatest number of intermediate nodes) would be if
326 * all the intermediate nodes were chained together. This results in
327 * num_used_symbols - 1 intermediate nodes. If num_used_symbols is at
328 * least 17, this configuration would not be allowed because the LZX
329 * format constrains codes to 16 bits or less each. However, it is
330 * still possible for there to be more than 16 intermediate nodes, as
331 * long as no leaf has a depth of more than 16. */
332 HuffmanNode inodes[num_used_symbols - 1];
335 /* Pointer to the leaf node of lowest frequency that hasn't already been
336 * added as the child of some intermediate note. */
337 HuffmanLeafNode *cur_leaf;
339 /* Pointer past the end of the array of leaves. */
340 HuffmanLeafNode *end_leaf = &leaves[num_used_symbols];
342 /* Pointer to the intermediate node of lowest frequency. */
343 HuffmanNode *cur_inode;
345 /* Pointer to the next unallocated intermediate node. */
346 HuffmanNode *next_inode;
348 /* Only jump back to here if the maximum length of the codewords allowed
349 * by the LZX format (16 bits) is exceeded. */
350 try_building_tree_again:
352 /* Sort the leaves from those that correspond to the least frequent
353 * symbol, to those that correspond to the most frequent symbol. If two
354 * leaves have the same frequency, they are sorted by symbol. */
355 qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_leaves_by_freq);
357 cur_leaf = &leaves[0];
358 cur_inode = &inodes[0];
359 next_inode = &inodes[0];
361 /* The following loop takes the two lowest frequency nodes of those
362 * remaining and makes them the children of the next available
363 * intermediate node. It continues until all the leaf nodes and
364 * intermediate nodes have been used up, or the maximum allowed length
365 * for the codewords is exceeded. For the latter case, we must adjust
366 * the frequencies to be more equal and then execute this loop again. */
369 /* Lowest frequency node. */
372 /* Second lowest frequency node. */
375 /* Get the lowest and second lowest frequency nodes from the
376 * remaining leaves or from the intermediate nodes. */
378 if (cur_leaf != end_leaf && (cur_inode == next_inode ||
379 cur_leaf->freq <= cur_inode->freq)) {
380 f1 = (HuffmanNode*)cur_leaf++;
381 } else if (cur_inode != next_inode) {
385 if (cur_leaf != end_leaf && (cur_inode == next_inode ||
386 cur_leaf->freq <= cur_inode->freq)) {
387 f2 = (HuffmanNode*)cur_leaf++;
388 } else if (cur_inode != next_inode) {
391 /* All nodes used up! */
395 /* next_inode becomes the parent of f1 and f2. */
397 next_inode->freq = f1->freq + f2->freq;
398 next_inode->sym = (u16)(-1); /* Invalid symbol. */
399 next_inode->left_child = f1;
400 next_inode->right_child = f2;
402 /* We need to keep track of the height so that we can detect if
403 * the length of a codeword has execeed max_codeword_len. The
404 * parent node has a height one higher than the maximum height
405 * of its children. */
406 next_inode->height = max(f1->height, f2->height) + 1;
408 /* Check to see if the code length of the leaf farthest away
409 * from next_inode has exceeded the maximum code length. */
410 if (next_inode->height > max_codeword_len) {
411 /* The code lengths can be made more uniform by making
412 * the frequencies more uniform. Divide all the
413 * frequencies by 2, leaving 1 as the minimum frequency.
414 * If this keeps happening, the symbol frequencies will
415 * approach equality, which makes their Huffman
416 * codewords approach the length
417 * log_2(num_used_symbols).
419 for (unsigned i = 0; i < num_used_symbols; i++)
420 if (leaves[i].freq > 1)
421 leaves[i].freq >>= 1;
422 goto try_building_tree_again;
427 /* The Huffman tree is now complete, and its height is no more than
428 * max_codeword_len. */
430 HuffmanNode *root = next_inode - 1;
431 wimlib_assert(root->height <= max_codeword_len);
433 /* Compute the path lengths for the leaf nodes. */
434 huffman_tree_compute_path_lengths(root, 0);
436 /* Sort the leaf nodes primarily by code length and secondarily by
438 qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_leaves_by_code_len);
440 u16 cur_codeword = 0;
441 unsigned cur_codeword_len = 0;
442 for (unsigned i = 0; i < num_used_symbols; i++) {
444 /* Each time a codeword becomes one longer, the current codeword
445 * is left shifted by one place. This is part of the procedure
446 * for enumerating the canonical Huffman code. Additionally,
447 * whenever a codeword is used, 1 is added to the current
450 unsigned len_diff = leaves[i].path_len - cur_codeword_len;
451 cur_codeword <<= len_diff;
452 cur_codeword_len += len_diff;
454 u16 sym = leaves[i].sym;
455 codewords[sym] = cur_codeword;
456 lens[sym] = cur_codeword_len;