4 * Code for decompression shared among multiple compression formats.
8 * Copyright (C) 2012, 2013, 2014 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/decompress_common.h"
31 #include "wimlib/error.h"
37 # define USE_SSE2_FILL
38 # include <emmintrin.h>
40 # define USE_LONG_FILL
44 /* Construct a direct mapping entry in the lookup table. */
45 #define MAKE_DIRECT_ENTRY(symbol, length) ((symbol) | ((length) << 11))
48 * make_huffman_decode_table() -
50 * Build a decoding table for a canonical prefix code, or "Huffman code".
52 * This takes as input the length of the codeword for each symbol in the
53 * alphabet and produces as output a table that can be used for fast
54 * decoding of prefix-encoded symbols using read_huffsym().
56 * Strictly speaking, a canonical prefix code might not be a Huffman
57 * code. But this algorithm will work either way; and in fact, since
58 * Huffman codes are defined in terms of symbol frequencies, there is no
59 * way for the decompressor to know whether the code is a true Huffman
60 * code or not until all symbols have been decoded.
62 * Because the prefix code is assumed to be "canonical", it can be
63 * reconstructed directly from the codeword lengths. A prefix code is
64 * canonical if and only if a longer codeword never lexicographically
65 * precedes a shorter codeword, and the lexicographic ordering of
66 * codewords of the same length is the same as the lexicographic ordering
67 * of the corresponding symbols. Consequently, we can sort the symbols
68 * primarily by codeword length and secondarily by symbol value, then
69 * reconstruct the prefix code by generating codewords lexicographically
72 * This function does not, however, generate the prefix code explicitly.
73 * Instead, it directly builds a table for decoding symbols using the
74 * code. The basic idea is this: given the next 'max_codeword_len' bits
75 * in the input, we can look up the decoded symbol by indexing a table
76 * containing 2**max_codeword_len entries. A codeword with length
77 * 'max_codeword_len' will have exactly one entry in this table, whereas
78 * a codeword shorter than 'max_codeword_len' will have multiple entries
79 * in this table. Precisely, a codeword of length n will be represented
80 * by 2**(max_codeword_len - n) entries in this table. The 0-based index
81 * of each such entry will contain the corresponding codeword as a prefix
82 * when zero-padded on the left to 'max_codeword_len' binary digits.
84 * That's the basic idea, but we implement two optimizations regarding
85 * the format of the decode table itself:
87 * - For many compression formats, the maximum codeword length is too
88 * long for it to be efficient to build the full decoding table
89 * whenever a new prefix code is used. Instead, we can build the table
90 * using only 2**table_bits entries, where 'table_bits' is some number
91 * less than or equal to 'max_codeword_len'. Then, only codewords of
92 * length 'table_bits' and shorter can be directly looked up. For
93 * longer codewords, the direct lookup instead produces the root of a
94 * binary tree. Using this tree, the decoder can do traditional
95 * bit-by-bit decoding of the remainder of the codeword. Child nodes
96 * are allocated in extra entries at the end of the table; leaf nodes
97 * contain symbols. Note that the long-codeword case is, in general,
98 * not performance critical, since in Huffman codes the most frequently
99 * used symbols are assigned the shortest codeword lengths.
101 * - When we decode a symbol using a direct lookup of the table, we still
102 * need to know its length so that the bitstream can be advanced by the
103 * appropriate number of bits. The simple solution is to simply retain
104 * the 'lens' array and use the decoded symbol as an index into it.
105 * However, this requires two separate array accesses in the fast path.
106 * The optimization is to store the length directly in the decode
107 * table. We use the bottom 11 bits for the symbol and the top 5 bits
108 * for the length. In addition, to combine this optimization with the
109 * previous one, we introduce a special case where the top 2 bits of
110 * the length are both set if the entry is actually the root of a
114 * The array in which to create the decoding table.
115 * This must be 16-byte aligned and must have a length of at least
116 * ((2**table_bits) + 2 * num_syms) entries.
119 * The number of symbols in the alphabet; also, the length of the
120 * 'lens' array. Must be less than or equal to
121 * DECODE_TABLE_MAX_SYMBOLS.
124 * The order of the decode table size, as explained above. Must be
125 * less than or equal to DECODE_TABLE_MAX_TABLE_BITS.
128 * An array of length @num_syms, indexable by symbol, that gives the
129 * length of the codeword, in bits, for that symbol. The length can
130 * be 0, which means that the symbol does not have a codeword
134 * The longest codeword length allowed in the compression format.
135 * All entries in 'lens' must be less than or equal to this value.
136 * This must be less than or equal to DECODE_TABLE_MAX_CODEWORD_LEN.
138 * Returns 0 on success, or -1 if the lengths do not form a valid prefix
142 make_huffman_decode_table(u16 decode_table[const restrict],
143 const unsigned num_syms,
144 const unsigned table_bits,
145 const u8 lens[const restrict],
146 const unsigned max_codeword_len)
148 const unsigned table_num_entries = 1 << table_bits;
149 unsigned len_counts[max_codeword_len + 1];
150 u16 sorted_syms[num_syms];
152 void *decode_table_ptr;
154 unsigned codeword_len;
155 unsigned stores_per_loop;
156 unsigned decode_table_pos;
159 const unsigned entries_per_long = sizeof(unsigned long) / sizeof(decode_table[0]);
163 const unsigned entries_per_xmm = sizeof(__m128i) / sizeof(decode_table[0]);
166 /* Check parameters if assertions are enabled. */
167 wimlib_assert2((uintptr_t)decode_table % DECODE_TABLE_ALIGNMENT == 0);
168 wimlib_assert2(num_syms <= DECODE_TABLE_MAX_SYMBOLS);
169 wimlib_assert2(table_bits <= DECODE_TABLE_MAX_TABLE_BITS);
170 wimlib_assert2(max_codeword_len <= DECODE_TABLE_MAX_CODEWORD_LEN);
171 for (unsigned sym = 0; sym < num_syms; sym++)
172 wimlib_assert2(lens[sym] <= max_codeword_len);
174 /* Count how many symbols have each possible codeword length.
175 * Note that a length of 0 indicates the corresponding symbol is not
176 * used in the code and therefore does not have a codeword. */
177 for (unsigned len = 0; len <= max_codeword_len; len++)
179 for (unsigned sym = 0; sym < num_syms; sym++)
180 len_counts[lens[sym]]++;
182 /* We can assume all lengths are <= max_codeword_len, but we
183 * cannot assume they form a valid prefix code. A codeword of
184 * length n should require a proportion of the codespace equaling
185 * (1/2)^n. The code is valid if and only if the codespace is
186 * exactly filled by the lengths, by this measure. */
188 for (unsigned len = 1; len <= max_codeword_len; len++) {
190 left -= len_counts[len];
191 if (unlikely(left < 0)) {
192 /* The lengths overflow the codespace; that is, the code
193 * is over-subscribed. */
194 DEBUG("Invalid prefix code (over-subscribed)");
199 if (unlikely(left != 0)) {
200 /* The lengths do not fill the codespace; that is, they form an
202 if (left == (1 << max_codeword_len)) {
203 /* The code is completely empty. This is arguably
204 * invalid, but in fact it is valid in LZX and XPRESS,
205 * so we must allow it. By definition, no symbols can
206 * be decoded with an empty code. Consequently, we
207 * technically don't even need to fill in the decode
208 * table. However, to avoid accessing uninitialized
209 * memory if the algorithm nevertheless attempts to
210 * decode symbols using such a code, we zero out the
212 memset(decode_table, 0,
213 table_num_entries * sizeof(decode_table[0]));
216 DEBUG("Invalid prefix code (incomplete set)");
220 /* Sort the symbols primarily by length and secondarily by symbol order.
223 unsigned offsets[max_codeword_len + 1];
225 /* Initialize 'offsets' so that offsets[len] for 1 <= len <=
226 * max_codeword_len is the number of codewords shorter than
229 for (unsigned len = 1; len < max_codeword_len; len++)
230 offsets[len + 1] = offsets[len] + len_counts[len];
232 /* Use the 'offsets' array to sort the symbols.
233 * Note that we do not include symbols that are not used in the
234 * code. Consequently, fewer than 'num_syms' entries in
235 * 'sorted_syms' may be filled. */
236 for (unsigned sym = 0; sym < num_syms; sym++)
238 sorted_syms[offsets[lens[sym]]++] = sym;
241 /* Fill entries for codewords with length <= table_bits
242 * --- that is, those short enough for a direct mapping.
244 * The table will start with entries for the shortest codeword(s), which
245 * have the most entries. From there, the number of entries per
246 * codeword will decrease. As an optimization, we may begin filling
247 * entries with SSE2 vector accesses (8 entries/store), then change to
248 * 'unsigned long' accesses (2 or 4 entries/store), then change to
249 * 16-bit accesses (1 entry/store). */
250 decode_table_ptr = decode_table;
254 /* Fill the entries one 128-bit vector at a time.
255 * This is 8 entries per store. */
256 stores_per_loop = (1 << (table_bits - codeword_len)) / entries_per_xmm;
257 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
258 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
259 for (; sym_idx < end_sym_idx; sym_idx++) {
260 /* Note: unlike in the 'long' version below, the __m128i
261 * type already has __attribute__((may_alias)), so using
262 * it to access the decode table, which is an array of
263 * unsigned shorts, will not violate strict aliasing.
270 entry = MAKE_DIRECT_ENTRY(sorted_syms[sym_idx], codeword_len);
272 v = _mm_set1_epi16(entry);
273 p = (__m128i*)decode_table_ptr;
278 decode_table_ptr = p;
281 #endif /* USE_SSE2_FILL */
284 /* Fill the entries one 'unsigned long' at a time.
285 * On 32-bit systems this is 2 entries per store, while on 64-bit
286 * systems this is 4 entries per store. */
287 stores_per_loop = (1 << (table_bits - codeword_len)) / entries_per_long;
288 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
289 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
290 for (; sym_idx < end_sym_idx; sym_idx++) {
292 /* Accessing the array of unsigned shorts as unsigned
293 * longs would violate strict aliasing and would require
294 * compiling the code with -fno-strict-aliasing to
295 * guarantee correctness. To work around this problem,
296 * use the gcc 'may_alias' extension to define a special
297 * unsigned long type that may alias any other in-memory
299 typedef unsigned long __attribute__((may_alias)) aliased_long_t;
305 BUILD_BUG_ON(sizeof(unsigned long) != 4 &&
306 sizeof(unsigned long) != 8);
308 v = MAKE_DIRECT_ENTRY(sorted_syms[sym_idx], codeword_len);
310 if (sizeof(unsigned long) == 8) {
311 /* This may produce a compiler warning if an
312 * 'unsigned long' is 32 bits, but this won't be
313 * executed unless an 'unsigned long' is at
314 * least 64 bits anyway. */
318 p = (aliased_long_t *)decode_table_ptr;
324 decode_table_ptr = p;
327 #endif /* USE_LONG_FILL */
329 /* Fill the entries one 16-bit integer at a time. */
330 stores_per_loop = (1 << (table_bits - codeword_len));
331 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
332 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
333 for (; sym_idx < end_sym_idx; sym_idx++) {
338 entry = MAKE_DIRECT_ENTRY(sorted_syms[sym_idx], codeword_len);
340 p = (u16*)decode_table_ptr;
347 decode_table_ptr = p;
351 /* If we've filled in the entire table, we are done. Otherwise,
352 * there are codewords longer than table_bits for which we must
353 * generate binary trees. */
355 decode_table_pos = (u16*)decode_table_ptr - decode_table;
356 if (decode_table_pos != table_num_entries) {
358 unsigned next_free_tree_slot;
359 unsigned cur_codeword;
361 /* First, zero out the remaining entries. This is
362 * necessary so that these entries appear as
363 * "unallocated" in the next part. Each of these entries
364 * will eventually be filled with the representation of
365 * the root node of a binary tree. */
366 j = decode_table_pos;
369 } while (++j != table_num_entries);
371 /* We allocate child nodes starting at the end of the
372 * direct lookup table. Note that there should be
373 * 2*num_syms extra entries for this purpose, although
374 * fewer than this may actually be needed. */
375 next_free_tree_slot = table_num_entries;
377 /* Iterate through each codeword with length greater than
378 * 'table_bits', primarily in order of codeword length
379 * and secondarily in order of symbol. */
380 for (cur_codeword = decode_table_pos << 1;
381 codeword_len <= max_codeword_len;
382 codeword_len++, cur_codeword <<= 1)
384 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
385 for (; sym_idx < end_sym_idx; sym_idx++, cur_codeword++)
387 /* 'sym' is the symbol represented by the
389 unsigned sym = sorted_syms[sym_idx];
391 unsigned extra_bits = codeword_len - table_bits;
393 unsigned node_idx = cur_codeword >> extra_bits;
395 /* Go through each bit of the current codeword
396 * beyond the prefix of length @table_bits and
397 * walk the appropriate binary tree, allocating
398 * any slots that have not yet been allocated.
400 * Note that the 'pointer' entry to the binary
401 * tree, which is stored in the direct lookup
402 * portion of the table, is represented
403 * identically to other internal (non-leaf)
404 * nodes of the binary tree; it can be thought
405 * of as simply the root of the tree. The
406 * representation of these internal nodes is
407 * simply the index of the left child combined
408 * with the special bits 0xC000 to distingush
409 * the entry from direct mapping and leaf node
413 /* At least one bit remains in the
414 * codeword, but the current node is an
415 * unallocated leaf. Change it to an
417 if (decode_table[node_idx] == 0) {
418 decode_table[node_idx] =
419 next_free_tree_slot | 0xC000;
420 decode_table[next_free_tree_slot++] = 0;
421 decode_table[next_free_tree_slot++] = 0;
424 /* Go to the left child if the next bit
425 * in the codeword is 0; otherwise go to
426 * the right child. */
427 node_idx = decode_table[node_idx] & 0x3FFF;
429 node_idx += (cur_codeword >> extra_bits) & 1;
430 } while (extra_bits != 0);
432 /* We've traversed the tree using the entire
433 * codeword, and we're now at the entry where
434 * the actual symbol will be stored. This is
435 * distinguished from internal nodes by not
436 * having its high two bits set. */
437 decode_table[node_idx] = sym;