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/.
30 #include "wimlib/assert.h"
31 #include "wimlib/compiler.h"
32 #include "wimlib/compress.h"
33 #include "wimlib/util.h"
38 /* Writes @num_bits bits, given by the @num_bits least significant bits of
39 * @bits, to the output @ostream. */
41 bitstream_put_bits(struct output_bitstream *ostream, u32 bits,
44 while (num_bits > ostream->free_bits) {
45 /* Buffer variable does not have space for the new bits. It
46 * needs to be flushed as a 16-bit integer. Bits in the second
47 * byte logically precede those in the first byte
48 * (little-endian), but within each byte the bits are ordered
49 * from high to low. This is true for both XPRESS and LZX
52 /* There must be at least 2 bytes of space remaining. */
53 if (unlikely(ostream->bytes_remaining < 2)) {
54 ostream->overrun = true;
58 /* Fill the buffer with as many bits that fit. */
59 unsigned fill_bits = ostream->free_bits;
61 ostream->bitbuf <<= fill_bits;
62 ostream->bitbuf |= bits >> (num_bits - fill_bits);
64 *(le16*)ostream->bit_output = cpu_to_le16(ostream->bitbuf);
65 ostream->bit_output = ostream->next_bit_output;
66 ostream->next_bit_output = ostream->output;
68 ostream->bytes_remaining -= 2;
70 ostream->free_bits = 16;
71 num_bits -= fill_bits;
72 bits &= (1U << num_bits) - 1;
75 /* Buffer variable has space for the new bits. */
76 ostream->bitbuf = (ostream->bitbuf << num_bits) | bits;
77 ostream->free_bits -= num_bits;
81 bitstream_put_byte(struct output_bitstream *ostream, u8 n)
83 if (unlikely(ostream->bytes_remaining < 1)) {
84 ostream->overrun = true;
87 *ostream->output++ = n;
88 ostream->bytes_remaining--;
91 /* Flushes any remaining bits to the output bitstream.
93 * Returns -1 if the stream has overrun; otherwise returns the total number of
94 * bytes in the output. */
96 flush_output_bitstream(struct output_bitstream *ostream)
98 if (unlikely(ostream->overrun))
99 return ~(input_idx_t)0;
101 *(le16*)ostream->bit_output =
102 cpu_to_le16((u16)((u32)ostream->bitbuf << ostream->free_bits));
103 *(le16*)ostream->next_bit_output =
106 return ostream->output - ostream->output_start;
109 /* Initializes an output bit buffer to write its output to the memory location
110 * pointer to by @data. */
112 init_output_bitstream(struct output_bitstream *ostream,
113 void *data, unsigned num_bytes)
115 wimlib_assert(num_bytes >= 4);
118 ostream->free_bits = 16;
119 ostream->output_start = data;
120 ostream->bit_output = data;
121 ostream->next_bit_output = data + 2;
122 ostream->output = data + 4;
123 ostream->bytes_remaining = num_bytes;
124 ostream->overrun = false;
136 typedef struct HuffmanIntermediateNode {
137 HuffmanNode node_base;
138 HuffmanNode *left_child;
139 HuffmanNode *right_child;
140 } HuffmanIntermediateNode;
143 /* Comparator function for HuffmanNodes. Sorts primarily by symbol
144 * frequency and secondarily by symbol value. */
146 cmp_nodes_by_freq(const void *_leaf1, const void *_leaf2)
148 const HuffmanNode *leaf1 = _leaf1;
149 const HuffmanNode *leaf2 = _leaf2;
151 int freq_diff = (int)leaf1->freq - (int)leaf2->freq;
154 return (int)leaf1->sym - (int)leaf2->sym;
159 /* Comparator function for HuffmanNodes. Sorts primarily by code length and
160 * secondarily by symbol value. */
162 cmp_nodes_by_code_len(const void *_leaf1, const void *_leaf2)
164 const HuffmanNode *leaf1 = _leaf1;
165 const HuffmanNode *leaf2 = _leaf2;
167 int code_len_diff = (int)leaf1->path_len - (int)leaf2->path_len;
169 if (code_len_diff == 0)
170 return (int)leaf1->sym - (int)leaf2->sym;
172 return code_len_diff;
175 #define INVALID_SYMBOL 0xffff
177 /* Recursive function to calculate the depth of the leaves in a Huffman tree.
180 huffman_tree_compute_path_lengths(HuffmanNode *base_node, u16 cur_len)
182 if (base_node->sym == INVALID_SYMBOL) {
183 /* Intermediate node. */
184 HuffmanIntermediateNode *node = (HuffmanIntermediateNode*)base_node;
185 huffman_tree_compute_path_lengths(node->left_child, cur_len + 1);
186 huffman_tree_compute_path_lengths(node->right_child, cur_len + 1);
189 base_node->path_len = cur_len;
193 /* make_canonical_huffman_code: - Creates a canonical Huffman code from an array
194 * of symbol frequencies.
196 * The algorithm used is similar to the well-known algorithm that builds a
197 * Huffman tree using a minheap. In that algorithm, the leaf nodes are
198 * initialized and inserted into the minheap with the frequency as the key.
199 * Repeatedly, the top two nodes (nodes with the lowest frequency) are taken out
200 * of the heap and made the children of a new node that has a frequency equal to
201 * the sum of the two frequencies of its children. This new node is inserted
202 * into the heap. When all the nodes have been removed from the heap, what
203 * remains is the Huffman tree. The Huffman code for a symbol is given by the
204 * path to it in the tree, where each left pointer is mapped to a 0 bit and each
205 * right pointer is mapped to a 1 bit.
207 * The algorithm used here uses an optimization that removes the need to
208 * actually use a heap. The leaf nodes are first sorted by frequency, as
209 * opposed to being made into a heap. Note that this sorting step takes O(n log
210 * n) time vs. O(n) time for heapifying the array, where n is the number of
211 * symbols. However, the heapless method is probably faster overall, due to the
212 * time saved later. In the heapless method, whenever an intermediate node is
213 * created, it is not inserted into the sorted array. Instead, the intermediate
214 * nodes are kept in a separate array, which is easily kept sorted because every
215 * time an intermediate node is initialized, it will have a frequency at least
216 * as high as that of the previous intermediate node that was initialized. So
217 * whenever we want the 2 nodes, leaf or intermediate, that have the lowest
218 * frequency, we check the low-frequency ends of both arrays, which is an O(1)
221 * The function builds a canonical Huffman code, not just any Huffman code. A
222 * Huffman code is canonical if the codeword for each symbol numerically
223 * precedes the codeword for all other symbols of the same length that are
224 * numbered higher than the symbol, and additionally, all shorter codewords,
225 * 0-extended, numerically precede longer codewords. A canonical Huffman code
226 * is useful because it can be reconstructed by only knowing the path lengths in
227 * the tree. See the make_huffman_decode_table() function to see how to
228 * reconstruct a canonical Huffman code from only the lengths of the codes.
230 * @num_syms: The number of symbols in the alphabet.
232 * @max_codeword_len: The maximum allowed length of a codeword in the code.
233 * Note that if the code being created runs up against
234 * this restriction, the code ultimately created will be
235 * suboptimal, although there are some advantages for
236 * limiting the length of the codewords.
238 * @freq_tab: An array of length @num_syms that contains the frequencies
239 * of each symbol in the uncompressed data.
241 * @lens: An array of length @num_syms into which the lengths of the
242 * codewords for each symbol will be written.
244 * @codewords: An array of @num_syms short integers into which the
245 * codewords for each symbol will be written. The first
246 * lens[i] bits of codewords[i] will contain the codeword
250 make_canonical_huffman_code(unsigned num_syms,
251 unsigned max_codeword_len,
252 const freq_t freq_tab[restrict],
254 u16 codewords[restrict])
256 /* We require at least 2 possible symbols in the alphabet to produce a
257 * valid Huffman decoding table. It is allowed that fewer than 2 symbols
258 * are actually used, though. */
259 wimlib_assert(num_syms >= 2);
261 /* Initialize the lengths and codewords to 0 */
262 memset(lens, 0, num_syms * sizeof(lens[0]));
263 memset(codewords, 0, num_syms * sizeof(codewords[0]));
265 /* Calculate how many symbols have non-zero frequency. These are the
266 * symbols that actually appeared in the input. */
267 unsigned num_used_symbols = 0;
268 for (unsigned i = 0; i < num_syms; i++)
269 if (freq_tab[i] != 0)
273 /* It is impossible to make a code for num_used_symbols symbols if there
274 * aren't enough code bits to uniquely represent all of them. */
275 wimlib_assert((1 << max_codeword_len) > num_used_symbols);
277 /* Initialize the array of leaf nodes with the symbols and their
279 HuffmanNode leaves[num_used_symbols];
280 unsigned leaf_idx = 0;
281 for (unsigned i = 0; i < num_syms; i++) {
282 if (freq_tab[i] != 0) {
283 leaves[leaf_idx].freq = freq_tab[i];
284 leaves[leaf_idx].sym = i;
285 leaves[leaf_idx].height = 0;
290 /* Deal with the special cases where num_used_symbols < 2. */
291 if (num_used_symbols < 2) {
292 if (num_used_symbols == 0) {
293 /* If num_used_symbols is 0, there are no symbols in the
294 * input, so it must be empty. This should be an error,
295 * but the LZX format expects this case to succeed. All
296 * the codeword lengths are simply marked as 0 (which
297 * was already done.) */
299 /* If only one symbol is present, the LZX format
300 * requires that the Huffman code include two codewords.
301 * One is not used. Note that this doesn't make the
302 * encoded data take up more room anyway, since binary
303 * data itself has 2 symbols. */
305 unsigned sym = leaves[0].sym;
310 /* dummy symbol is 1, real symbol is 0 */
314 /* dummy symbol is 0, real symbol is sym */
322 /* Otherwise, there are at least 2 symbols in the input, so we need to
323 * find a real Huffman code. */
326 /* Declare the array of intermediate nodes. An intermediate node is not
327 * associated with a symbol. Instead, it represents some binary code
328 * prefix that is shared between at least 2 codewords. There can be at
329 * most num_used_symbols - 1 intermediate nodes when creating a Huffman
330 * code. This is because if there were at least num_used_symbols nodes,
331 * the code would be suboptimal because there would be at least one
332 * unnecessary intermediate node.
334 * The worst case (greatest number of intermediate nodes) would be if
335 * all the intermediate nodes were chained together. This results in
336 * num_used_symbols - 1 intermediate nodes. If num_used_symbols is at
337 * least 17, this configuration would not be allowed because the LZX
338 * format constrains codes to 16 bits or less each. However, it is
339 * still possible for there to be more than 16 intermediate nodes, as
340 * long as no leaf has a depth of more than 16. */
341 HuffmanIntermediateNode inodes[num_used_symbols - 1];
344 /* Pointer to the leaf node of lowest frequency that hasn't already been
345 * added as the child of some intermediate note. */
346 HuffmanNode *cur_leaf;
348 /* Pointer past the end of the array of leaves. */
349 HuffmanNode *end_leaf = &leaves[num_used_symbols];
351 /* Pointer to the intermediate node of lowest frequency. */
352 HuffmanIntermediateNode *cur_inode;
354 /* Pointer to the next unallocated intermediate node. */
355 HuffmanIntermediateNode *next_inode;
357 /* Only jump back to here if the maximum length of the codewords allowed
358 * by the LZX format (16 bits) is exceeded. */
359 try_building_tree_again:
361 /* Sort the leaves from those that correspond to the least frequent
362 * symbol, to those that correspond to the most frequent symbol. If two
363 * leaves have the same frequency, they are sorted by symbol. */
364 qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_nodes_by_freq);
366 cur_leaf = &leaves[0];
367 cur_inode = &inodes[0];
368 next_inode = &inodes[0];
370 /* The following loop takes the two lowest frequency nodes of those
371 * remaining and makes them the children of the next available
372 * intermediate node. It continues until all the leaf nodes and
373 * intermediate nodes have been used up, or the maximum allowed length
374 * for the codewords is exceeded. For the latter case, we must adjust
375 * the frequencies to be more equal and then execute this loop again. */
378 /* Lowest frequency node. */
381 /* Second lowest frequency node. */
384 /* Get the lowest and second lowest frequency nodes from the
385 * remaining leaves or from the intermediate nodes. */
387 if (cur_leaf != end_leaf && (cur_inode == next_inode ||
388 cur_leaf->freq <= cur_inode->node_base.freq)) {
390 } else if (cur_inode != next_inode) {
391 f1 = (HuffmanNode*)cur_inode++;
394 if (cur_leaf != end_leaf && (cur_inode == next_inode ||
395 cur_leaf->freq <= cur_inode->node_base.freq)) {
397 } else if (cur_inode != next_inode) {
398 f2 = (HuffmanNode*)cur_inode++;
400 /* All nodes used up! */
404 /* next_inode becomes the parent of f1 and f2. */
406 next_inode->node_base.freq = f1->freq + f2->freq;
407 next_inode->node_base.sym = INVALID_SYMBOL;
408 next_inode->left_child = f1;
409 next_inode->right_child = f2;
411 /* We need to keep track of the height so that we can detect if
412 * the length of a codeword has execeed max_codeword_len. The
413 * parent node has a height one higher than the maximum height
414 * of its children. */
415 next_inode->node_base.height = max(f1->height, f2->height) + 1;
417 /* Check to see if the code length of the leaf farthest away
418 * from next_inode has exceeded the maximum code length. */
419 if (next_inode->node_base.height > max_codeword_len) {
420 /* The code lengths can be made more uniform by making
421 * the frequencies more uniform. Divide all the
422 * frequencies by 2, leaving 1 as the minimum frequency.
423 * If this keeps happening, the symbol frequencies will
424 * approach equality, which makes their Huffman
425 * codewords approach the length
426 * log_2(num_used_symbols).
428 for (unsigned i = 0; i < num_used_symbols; i++)
429 if (leaves[i].freq > 1)
430 leaves[i].freq >>= 1;
431 goto try_building_tree_again;
436 /* The Huffman tree is now complete, and its height is no more than
437 * max_codeword_len. */
439 HuffmanIntermediateNode *root = next_inode - 1;
440 wimlib_assert(root->node_base.height <= max_codeword_len);
442 /* Compute the path lengths for the leaf nodes. */
443 huffman_tree_compute_path_lengths(&root->node_base, 0);
445 /* Sort the leaf nodes primarily by code length and secondarily by
447 qsort(leaves, num_used_symbols, sizeof(leaves[0]), cmp_nodes_by_code_len);
449 u16 cur_codeword = 0;
450 unsigned cur_codeword_len = 0;
451 for (unsigned i = 0; i < num_used_symbols; i++) {
453 /* Each time a codeword becomes one longer, the current codeword
454 * is left shifted by one place. This is part of the procedure
455 * for enumerating the canonical Huffman code. Additionally,
456 * whenever a codeword is used, 1 is added to the current
459 unsigned len_diff = leaves[i].path_len - cur_codeword_len;
460 cur_codeword <<= len_diff;
461 cur_codeword_len += len_diff;
463 u16 sym = leaves[i].sym;
464 codewords[sym] = cur_codeword;
465 lens[sym] = cur_codeword_len;