4 * Code for decompression shared among multiple compression formats.
9 * The author dedicates this file to the public domain.
10 * You can do whatever you want with this file.
17 #include "wimlib/assert.h"
18 #include "wimlib/decompress_common.h"
27 # define USE_SSE2_FILL
28 # include <emmintrin.h>
32 /* Construct a direct mapping entry in the lookup table. */
33 #define MAKE_DIRECT_ENTRY(symbol, length) ((symbol) | ((length) << 11))
36 * make_huffman_decode_table() -
38 * Build a decoding table for a canonical prefix code, or "Huffman code".
40 * This takes as input the length of the codeword for each symbol in the
41 * alphabet and produces as output a table that can be used for fast
42 * decoding of prefix-encoded symbols using read_huffsym().
44 * Strictly speaking, a canonical prefix code might not be a Huffman
45 * code. But this algorithm will work either way; and in fact, since
46 * Huffman codes are defined in terms of symbol frequencies, there is no
47 * way for the decompressor to know whether the code is a true Huffman
48 * code or not until all symbols have been decoded.
50 * Because the prefix code is assumed to be "canonical", it can be
51 * reconstructed directly from the codeword lengths. A prefix code is
52 * canonical if and only if a longer codeword never lexicographically
53 * precedes a shorter codeword, and the lexicographic ordering of
54 * codewords of the same length is the same as the lexicographic ordering
55 * of the corresponding symbols. Consequently, we can sort the symbols
56 * primarily by codeword length and secondarily by symbol value, then
57 * reconstruct the prefix code by generating codewords lexicographically
60 * This function does not, however, generate the prefix code explicitly.
61 * Instead, it directly builds a table for decoding symbols using the
62 * code. The basic idea is this: given the next 'max_codeword_len' bits
63 * in the input, we can look up the decoded symbol by indexing a table
64 * containing 2**max_codeword_len entries. A codeword with length
65 * 'max_codeword_len' will have exactly one entry in this table, whereas
66 * a codeword shorter than 'max_codeword_len' will have multiple entries
67 * in this table. Precisely, a codeword of length n will be represented
68 * by 2**(max_codeword_len - n) entries in this table. The 0-based index
69 * of each such entry will contain the corresponding codeword as a prefix
70 * when zero-padded on the left to 'max_codeword_len' binary digits.
72 * That's the basic idea, but we implement two optimizations regarding
73 * the format of the decode table itself:
75 * - For many compression formats, the maximum codeword length is too
76 * long for it to be efficient to build the full decoding table
77 * whenever a new prefix code is used. Instead, we can build the table
78 * using only 2**table_bits entries, where 'table_bits' is some number
79 * less than or equal to 'max_codeword_len'. Then, only codewords of
80 * length 'table_bits' and shorter can be directly looked up. For
81 * longer codewords, the direct lookup instead produces the root of a
82 * binary tree. Using this tree, the decoder can do traditional
83 * bit-by-bit decoding of the remainder of the codeword. Child nodes
84 * are allocated in extra entries at the end of the table; leaf nodes
85 * contain symbols. Note that the long-codeword case is, in general,
86 * not performance critical, since in Huffman codes the most frequently
87 * used symbols are assigned the shortest codeword lengths.
89 * - When we decode a symbol using a direct lookup of the table, we still
90 * need to know its length so that the bitstream can be advanced by the
91 * appropriate number of bits. The simple solution is to simply retain
92 * the 'lens' array and use the decoded symbol as an index into it.
93 * However, this requires two separate array accesses in the fast path.
94 * The optimization is to store the length directly in the decode
95 * table. We use the bottom 11 bits for the symbol and the top 5 bits
96 * for the length. In addition, to combine this optimization with the
97 * previous one, we introduce a special case where the top 2 bits of
98 * the length are both set if the entry is actually the root of a
102 * The array in which to create the decoding table.
103 * This must be 16-byte aligned and must have a length of at least
104 * ((2**table_bits) + 2 * num_syms) entries.
107 * The number of symbols in the alphabet; also, the length of the
108 * 'lens' array. Must be less than or equal to
109 * DECODE_TABLE_MAX_SYMBOLS.
112 * The order of the decode table size, as explained above. Must be
113 * less than or equal to DECODE_TABLE_MAX_TABLE_BITS.
116 * An array of length @num_syms, indexable by symbol, that gives the
117 * length of the codeword, in bits, for that symbol. The length can
118 * be 0, which means that the symbol does not have a codeword
122 * The longest codeword length allowed in the compression format.
123 * All entries in 'lens' must be less than or equal to this value.
124 * This must be less than or equal to DECODE_TABLE_MAX_CODEWORD_LEN.
126 * Returns 0 on success, or -1 if the lengths do not form a valid prefix
130 make_huffman_decode_table(u16 decode_table[const restrict],
131 const unsigned num_syms,
132 const unsigned table_bits,
133 const u8 lens[const restrict],
134 const unsigned max_codeword_len)
136 const unsigned table_num_entries = 1 << table_bits;
137 unsigned len_counts[max_codeword_len + 1];
138 u16 sorted_syms[num_syms];
140 void *decode_table_ptr;
142 unsigned codeword_len;
143 unsigned stores_per_loop;
144 unsigned decode_table_pos;
147 const unsigned entries_per_word = WORDSIZE / sizeof(decode_table[0]);
151 const unsigned entries_per_xmm = sizeof(__m128i) / sizeof(decode_table[0]);
154 /* Count how many symbols have each possible codeword length.
155 * Note that a length of 0 indicates the corresponding symbol is not
156 * used in the code and therefore does not have a codeword. */
157 for (unsigned len = 0; len <= max_codeword_len; len++)
159 for (unsigned sym = 0; sym < num_syms; sym++)
160 len_counts[lens[sym]]++;
162 /* We can assume all lengths are <= max_codeword_len, but we
163 * cannot assume they form a valid prefix code. A codeword of
164 * length n should require a proportion of the codespace equaling
165 * (1/2)^n. The code is valid if and only if the codespace is
166 * exactly filled by the lengths, by this measure. */
168 for (unsigned len = 1; len <= max_codeword_len; len++) {
170 left -= len_counts[len];
171 if (unlikely(left < 0)) {
172 /* The lengths overflow the codespace; that is, the code
173 * is over-subscribed. */
178 if (unlikely(left != 0)) {
179 /* The lengths do not fill the codespace; that is, they form an
181 if (left == (1 << max_codeword_len)) {
182 /* The code is completely empty. This is arguably
183 * invalid, but in fact it is valid in LZX and XPRESS,
184 * so we must allow it. By definition, no symbols can
185 * be decoded with an empty code. Consequently, we
186 * technically don't even need to fill in the decode
187 * table. However, to avoid accessing uninitialized
188 * memory if the algorithm nevertheless attempts to
189 * decode symbols using such a code, we zero out the
191 memset(decode_table, 0,
192 table_num_entries * sizeof(decode_table[0]));
198 /* Sort the symbols primarily by length and secondarily by symbol order.
201 unsigned offsets[max_codeword_len + 1];
203 /* Initialize 'offsets' so that offsets[len] for 1 <= len <=
204 * max_codeword_len is the number of codewords shorter than
207 for (unsigned len = 1; len < max_codeword_len; len++)
208 offsets[len + 1] = offsets[len] + len_counts[len];
210 /* Use the 'offsets' array to sort the symbols.
211 * Note that we do not include symbols that are not used in the
212 * code. Consequently, fewer than 'num_syms' entries in
213 * 'sorted_syms' may be filled. */
214 for (unsigned sym = 0; sym < num_syms; sym++)
216 sorted_syms[offsets[lens[sym]]++] = sym;
219 /* Fill entries for codewords with length <= table_bits
220 * --- that is, those short enough for a direct mapping.
222 * The table will start with entries for the shortest codeword(s), which
223 * have the most entries. From there, the number of entries per
224 * codeword will decrease. As an optimization, we may begin filling
225 * entries with SSE2 vector accesses (8 entries/store), then change to
226 * 'machine_word_t' accesses (2 or 4 entries/store), then change to
227 * 16-bit accesses (1 entry/store). */
228 decode_table_ptr = decode_table;
232 /* Fill the entries one 128-bit vector at a time.
233 * This is 8 entries per store. */
234 stores_per_loop = (1 << (table_bits - codeword_len)) / entries_per_xmm;
235 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
236 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
237 for (; sym_idx < end_sym_idx; sym_idx++) {
238 /* Note: unlike in the machine_word_t version below, the
239 * __m128i type already has __attribute__((may_alias)),
240 * so using it to access the decode table, which is an
241 * array of unsigned shorts, will not violate strict
248 entry = MAKE_DIRECT_ENTRY(sorted_syms[sym_idx], codeword_len);
250 v = _mm_set1_epi16(entry);
251 p = (__m128i*)decode_table_ptr;
256 decode_table_ptr = p;
259 #endif /* USE_SSE2_FILL */
262 /* Fill the entries one machine word at a time.
263 * On 32-bit systems this is 2 entries per store, while on 64-bit
264 * systems this is 4 entries per store. */
265 stores_per_loop = (1 << (table_bits - codeword_len)) / entries_per_word;
266 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
267 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
268 for (; sym_idx < end_sym_idx; sym_idx++) {
270 /* Accessing the array of u16 as u32 or u64 would
271 * violate strict aliasing and would require compiling
272 * the code with -fno-strict-aliasing to guarantee
273 * correctness. To work around this problem, use the
274 * gcc 'may_alias' extension. */
275 typedef machine_word_t _may_alias_attribute aliased_word_t;
281 BUILD_BUG_ON(WORDSIZE != 4 && WORDSIZE != 8);
283 v = MAKE_DIRECT_ENTRY(sorted_syms[sym_idx], codeword_len);
285 v |= v << (WORDSIZE == 8 ? 32 : 0);
287 p = (aliased_word_t *)decode_table_ptr;
293 decode_table_ptr = p;
296 #endif /* USE_WORD_FILL */
298 /* Fill the entries one 16-bit integer at a time. */
299 stores_per_loop = (1 << (table_bits - codeword_len));
300 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
301 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
302 for (; sym_idx < end_sym_idx; sym_idx++) {
307 entry = MAKE_DIRECT_ENTRY(sorted_syms[sym_idx], codeword_len);
309 p = (u16*)decode_table_ptr;
316 decode_table_ptr = p;
320 /* If we've filled in the entire table, we are done. Otherwise,
321 * there are codewords longer than table_bits for which we must
322 * generate binary trees. */
324 decode_table_pos = (u16*)decode_table_ptr - decode_table;
325 if (decode_table_pos != table_num_entries) {
327 unsigned next_free_tree_slot;
328 unsigned cur_codeword;
330 /* First, zero out the remaining entries. This is
331 * necessary so that these entries appear as
332 * "unallocated" in the next part. Each of these entries
333 * will eventually be filled with the representation of
334 * the root node of a binary tree. */
335 j = decode_table_pos;
338 } while (++j != table_num_entries);
340 /* We allocate child nodes starting at the end of the
341 * direct lookup table. Note that there should be
342 * 2*num_syms extra entries for this purpose, although
343 * fewer than this may actually be needed. */
344 next_free_tree_slot = table_num_entries;
346 /* Iterate through each codeword with length greater than
347 * 'table_bits', primarily in order of codeword length
348 * and secondarily in order of symbol. */
349 for (cur_codeword = decode_table_pos << 1;
350 codeword_len <= max_codeword_len;
351 codeword_len++, cur_codeword <<= 1)
353 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
354 for (; sym_idx < end_sym_idx; sym_idx++, cur_codeword++)
356 /* 'sym' is the symbol represented by the
358 unsigned sym = sorted_syms[sym_idx];
360 unsigned extra_bits = codeword_len - table_bits;
362 unsigned node_idx = cur_codeword >> extra_bits;
364 /* Go through each bit of the current codeword
365 * beyond the prefix of length @table_bits and
366 * walk the appropriate binary tree, allocating
367 * any slots that have not yet been allocated.
369 * Note that the 'pointer' entry to the binary
370 * tree, which is stored in the direct lookup
371 * portion of the table, is represented
372 * identically to other internal (non-leaf)
373 * nodes of the binary tree; it can be thought
374 * of as simply the root of the tree. The
375 * representation of these internal nodes is
376 * simply the index of the left child combined
377 * with the special bits 0xC000 to distingush
378 * the entry from direct mapping and leaf node
382 /* At least one bit remains in the
383 * codeword, but the current node is an
384 * unallocated leaf. Change it to an
386 if (decode_table[node_idx] == 0) {
387 decode_table[node_idx] =
388 next_free_tree_slot | 0xC000;
389 decode_table[next_free_tree_slot++] = 0;
390 decode_table[next_free_tree_slot++] = 0;
393 /* Go to the left child if the next bit
394 * in the codeword is 0; otherwise go to
395 * the right child. */
396 node_idx = decode_table[node_idx] & 0x3FFF;
398 node_idx += (cur_codeword >> extra_bits) & 1;
399 } while (extra_bits != 0);
401 /* We've traversed the tree using the entire
402 * codeword, and we're now at the entry where
403 * the actual symbol will be stored. This is
404 * distinguished from internal nodes by not
405 * having its high two bits set. */
406 decode_table[node_idx] = sym;