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/decompress_common.h"
18 #include "wimlib/error.h"
19 #include "wimlib/util.h" /* for BUILD_BUG_ON() */
25 # define USE_SSE2_FILL
26 # include <emmintrin.h>
28 # define USE_LONG_FILL
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_long = sizeof(unsigned long) / sizeof(decode_table[0]);
151 const unsigned entries_per_xmm = sizeof(__m128i) / sizeof(decode_table[0]);
154 /* Check parameters if assertions are enabled. */
155 wimlib_assert2((uintptr_t)decode_table % DECODE_TABLE_ALIGNMENT == 0);
156 wimlib_assert2(num_syms <= DECODE_TABLE_MAX_SYMBOLS);
157 wimlib_assert2(table_bits <= DECODE_TABLE_MAX_TABLE_BITS);
158 wimlib_assert2(max_codeword_len <= DECODE_TABLE_MAX_CODEWORD_LEN);
159 for (unsigned sym = 0; sym < num_syms; sym++)
160 wimlib_assert2(lens[sym] <= max_codeword_len);
162 /* Count how many symbols have each possible codeword length.
163 * Note that a length of 0 indicates the corresponding symbol is not
164 * used in the code and therefore does not have a codeword. */
165 for (unsigned len = 0; len <= max_codeword_len; len++)
167 for (unsigned sym = 0; sym < num_syms; sym++)
168 len_counts[lens[sym]]++;
170 /* We can assume all lengths are <= max_codeword_len, but we
171 * cannot assume they form a valid prefix code. A codeword of
172 * length n should require a proportion of the codespace equaling
173 * (1/2)^n. The code is valid if and only if the codespace is
174 * exactly filled by the lengths, by this measure. */
176 for (unsigned len = 1; len <= max_codeword_len; len++) {
178 left -= len_counts[len];
179 if (unlikely(left < 0)) {
180 /* The lengths overflow the codespace; that is, the code
181 * is over-subscribed. */
182 DEBUG("Invalid prefix code (over-subscribed)");
187 if (unlikely(left != 0)) {
188 /* The lengths do not fill the codespace; that is, they form an
190 if (left == (1 << max_codeword_len)) {
191 /* The code is completely empty. This is arguably
192 * invalid, but in fact it is valid in LZX and XPRESS,
193 * so we must allow it. By definition, no symbols can
194 * be decoded with an empty code. Consequently, we
195 * technically don't even need to fill in the decode
196 * table. However, to avoid accessing uninitialized
197 * memory if the algorithm nevertheless attempts to
198 * decode symbols using such a code, we zero out the
200 memset(decode_table, 0,
201 table_num_entries * sizeof(decode_table[0]));
204 DEBUG("Invalid prefix code (incomplete set)");
208 /* Sort the symbols primarily by length and secondarily by symbol order.
211 unsigned offsets[max_codeword_len + 1];
213 /* Initialize 'offsets' so that offsets[len] for 1 <= len <=
214 * max_codeword_len is the number of codewords shorter than
217 for (unsigned len = 1; len < max_codeword_len; len++)
218 offsets[len + 1] = offsets[len] + len_counts[len];
220 /* Use the 'offsets' array to sort the symbols.
221 * Note that we do not include symbols that are not used in the
222 * code. Consequently, fewer than 'num_syms' entries in
223 * 'sorted_syms' may be filled. */
224 for (unsigned sym = 0; sym < num_syms; sym++)
226 sorted_syms[offsets[lens[sym]]++] = sym;
229 /* Fill entries for codewords with length <= table_bits
230 * --- that is, those short enough for a direct mapping.
232 * The table will start with entries for the shortest codeword(s), which
233 * have the most entries. From there, the number of entries per
234 * codeword will decrease. As an optimization, we may begin filling
235 * entries with SSE2 vector accesses (8 entries/store), then change to
236 * 'unsigned long' accesses (2 or 4 entries/store), then change to
237 * 16-bit accesses (1 entry/store). */
238 decode_table_ptr = decode_table;
242 /* Fill the entries one 128-bit vector at a time.
243 * This is 8 entries per store. */
244 stores_per_loop = (1 << (table_bits - codeword_len)) / entries_per_xmm;
245 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
246 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
247 for (; sym_idx < end_sym_idx; sym_idx++) {
248 /* Note: unlike in the 'long' version below, the __m128i
249 * type already has __attribute__((may_alias)), so using
250 * it to access the decode table, which is an array of
251 * unsigned shorts, will not violate strict aliasing.
258 entry = MAKE_DIRECT_ENTRY(sorted_syms[sym_idx], codeword_len);
260 v = _mm_set1_epi16(entry);
261 p = (__m128i*)decode_table_ptr;
266 decode_table_ptr = p;
269 #endif /* USE_SSE2_FILL */
272 /* Fill the entries one 'unsigned long' at a time.
273 * On 32-bit systems this is 2 entries per store, while on 64-bit
274 * systems this is 4 entries per store. */
275 stores_per_loop = (1 << (table_bits - codeword_len)) / entries_per_long;
276 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
277 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
278 for (; sym_idx < end_sym_idx; sym_idx++) {
280 /* Accessing the array of unsigned shorts as unsigned
281 * longs would violate strict aliasing and would require
282 * compiling the code with -fno-strict-aliasing to
283 * guarantee correctness. To work around this problem,
284 * use the gcc 'may_alias' extension to define a special
285 * unsigned long type that may alias any other in-memory
287 typedef unsigned long __attribute__((may_alias)) aliased_long_t;
293 BUILD_BUG_ON(sizeof(unsigned long) != 4 &&
294 sizeof(unsigned long) != 8);
296 v = MAKE_DIRECT_ENTRY(sorted_syms[sym_idx], codeword_len);
298 if (sizeof(unsigned long) == 8) {
299 /* This may produce a compiler warning if an
300 * 'unsigned long' is 32 bits, but this won't be
301 * executed unless an 'unsigned long' is at
302 * least 64 bits anyway. */
306 p = (aliased_long_t *)decode_table_ptr;
312 decode_table_ptr = p;
315 #endif /* USE_LONG_FILL */
317 /* Fill the entries one 16-bit integer at a time. */
318 stores_per_loop = (1 << (table_bits - codeword_len));
319 for (; stores_per_loop != 0; codeword_len++, stores_per_loop >>= 1) {
320 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
321 for (; sym_idx < end_sym_idx; sym_idx++) {
326 entry = MAKE_DIRECT_ENTRY(sorted_syms[sym_idx], codeword_len);
328 p = (u16*)decode_table_ptr;
335 decode_table_ptr = p;
339 /* If we've filled in the entire table, we are done. Otherwise,
340 * there are codewords longer than table_bits for which we must
341 * generate binary trees. */
343 decode_table_pos = (u16*)decode_table_ptr - decode_table;
344 if (decode_table_pos != table_num_entries) {
346 unsigned next_free_tree_slot;
347 unsigned cur_codeword;
349 /* First, zero out the remaining entries. This is
350 * necessary so that these entries appear as
351 * "unallocated" in the next part. Each of these entries
352 * will eventually be filled with the representation of
353 * the root node of a binary tree. */
354 j = decode_table_pos;
357 } while (++j != table_num_entries);
359 /* We allocate child nodes starting at the end of the
360 * direct lookup table. Note that there should be
361 * 2*num_syms extra entries for this purpose, although
362 * fewer than this may actually be needed. */
363 next_free_tree_slot = table_num_entries;
365 /* Iterate through each codeword with length greater than
366 * 'table_bits', primarily in order of codeword length
367 * and secondarily in order of symbol. */
368 for (cur_codeword = decode_table_pos << 1;
369 codeword_len <= max_codeword_len;
370 codeword_len++, cur_codeword <<= 1)
372 unsigned end_sym_idx = sym_idx + len_counts[codeword_len];
373 for (; sym_idx < end_sym_idx; sym_idx++, cur_codeword++)
375 /* 'sym' is the symbol represented by the
377 unsigned sym = sorted_syms[sym_idx];
379 unsigned extra_bits = codeword_len - table_bits;
381 unsigned node_idx = cur_codeword >> extra_bits;
383 /* Go through each bit of the current codeword
384 * beyond the prefix of length @table_bits and
385 * walk the appropriate binary tree, allocating
386 * any slots that have not yet been allocated.
388 * Note that the 'pointer' entry to the binary
389 * tree, which is stored in the direct lookup
390 * portion of the table, is represented
391 * identically to other internal (non-leaf)
392 * nodes of the binary tree; it can be thought
393 * of as simply the root of the tree. The
394 * representation of these internal nodes is
395 * simply the index of the left child combined
396 * with the special bits 0xC000 to distingush
397 * the entry from direct mapping and leaf node
401 /* At least one bit remains in the
402 * codeword, but the current node is an
403 * unallocated leaf. Change it to an
405 if (decode_table[node_idx] == 0) {
406 decode_table[node_idx] =
407 next_free_tree_slot | 0xC000;
408 decode_table[next_free_tree_slot++] = 0;
409 decode_table[next_free_tree_slot++] = 0;
412 /* Go to the left child if the next bit
413 * in the codeword is 0; otherwise go to
414 * the right child. */
415 node_idx = decode_table[node_idx] & 0x3FFF;
417 node_idx += (cur_codeword >> extra_bits) & 1;
418 } while (extra_bits != 0);
420 /* We've traversed the tree using the entire
421 * codeword, and we're now at the entry where
422 * the actual symbol will be stored. This is
423 * distinguished from internal nodes by not
424 * having its high two bits set. */
425 decode_table[node_idx] = sym;