4 * A compressor for the LZX compression format, as used in WIM files.
8 * Copyright (C) 2012, 2013, 2014, 2015 Eric Biggers
10 * This file is free software; you can redistribute it and/or modify it under
11 * the terms of the GNU Lesser General Public License as published by the Free
12 * Software Foundation; either version 3 of the License, or (at your option) any
15 * This file is distributed in the hope that it will be useful, but WITHOUT
16 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17 * FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
20 * You should have received a copy of the GNU Lesser General Public License
21 * along with this file; if not, see http://www.gnu.org/licenses/.
26 * This file contains a compressor for the LZX ("Lempel-Ziv eXtended")
27 * compression format, as used in the WIM (Windows IMaging) file format.
29 * Two different parsing algorithms are implemented: "near-optimal" and "lazy".
30 * "Near-optimal" is significantly slower than "lazy", but results in a better
31 * compression ratio. The "near-optimal" algorithm is used at the default
34 * This file may need some slight modifications to be used outside of the WIM
35 * format. In particular, in other situations the LZX block header might be
36 * slightly different, and sliding window support might be required.
38 * Note: LZX is a compression format derived from DEFLATE, the format used by
39 * zlib and gzip. Both LZX and DEFLATE use LZ77 matching and Huffman coding.
40 * Certain details are quite similar, such as the method for storing Huffman
41 * codes. However, the main differences are:
43 * - LZX preprocesses the data to attempt to make x86 machine code slightly more
44 * compressible before attempting to compress it further.
46 * - LZX uses a "main" alphabet which combines literals and matches, with the
47 * match symbols containing a "length header" (giving all or part of the match
48 * length) and an "offset slot" (giving, roughly speaking, the order of
49 * magnitude of the match offset).
51 * - LZX does not have static Huffman blocks (that is, the kind with preset
52 * Huffman codes); however it does have two types of dynamic Huffman blocks
53 * ("verbatim" and "aligned").
55 * - LZX has a minimum match length of 2 rather than 3. Length 2 matches can be
56 * useful, but generally only if the parser is smart about choosing them.
58 * - In LZX, offset slots 0 through 2 actually represent entries in an LRU queue
59 * of match offsets. This is very useful for certain types of files, such as
60 * binary files that have repeating records.
68 * Start a new LZX block (with new Huffman codes) after this many bytes.
70 * Note: actual block sizes may slightly exceed this value.
72 * TODO: recursive splitting and cost evaluation might be good for an extremely
73 * high compression mode, but otherwise it is almost always far too slow for how
74 * much it helps. Perhaps some sort of heuristic would be useful?
76 #define LZX_DIV_BLOCK_SIZE 32768
79 * LZX_CACHE_PER_POS is the number of lz_match structures to reserve in the
80 * match cache for each byte position. This value should be high enough so that
81 * nearly the time, all matches found in a given block can fit in the match
82 * cache. However, fallback behavior (immediately terminating the block) on
83 * cache overflow is still required.
85 #define LZX_CACHE_PER_POS 7
88 * LZX_CACHE_LENGTH is the number of lz_match structures in the match cache,
89 * excluding the extra "overflow" entries. The per-position multiplier is '1 +
90 * LZX_CACHE_PER_POS' instead of 'LZX_CACHE_PER_POS' because there is an
91 * overhead of one lz_match per position, used to hold the match count at that
94 #define LZX_CACHE_LENGTH (LZX_DIV_BLOCK_SIZE * (1 + LZX_CACHE_PER_POS))
97 * LZX_MAX_MATCHES_PER_POS is an upper bound on the number of matches that can
98 * ever be saved in the match cache for a single position. Since each match we
99 * save for a single position has a distinct length, we can use the number of
100 * possible match lengths in LZX as this bound. This bound is guaranteed to be
101 * valid in all cases, although if 'nice_match_length < LZX_MAX_MATCH_LEN', then
102 * it will never actually be reached.
104 #define LZX_MAX_MATCHES_PER_POS LZX_NUM_LENS
107 * LZX_BIT_COST is a scaling factor that represents the cost to output one bit.
108 * This makes it possible to consider fractional bit costs.
110 * Note: this is only useful as a statistical trick for when the true costs are
111 * unknown. In reality, each token in LZX requires a whole number of bits to
114 #define LZX_BIT_COST 16
117 * Consideration of aligned offset costs is disabled for now, due to
118 * insufficient benefit gained from the time spent.
120 #define LZX_CONSIDER_ALIGNED_COSTS 0
123 * LZX_MAX_FAST_LEVEL is the maximum compression level at which we use the
126 #define LZX_MAX_FAST_LEVEL 34
129 * LZX_HASH2_ORDER is the log base 2 of the number of entries in the hash table
130 * for finding length 2 matches. This can be as high as 16 (in which case the
131 * hash function is trivial), but using a smaller hash table speeds up
132 * compression due to reduced cache pressure.
134 #define LZX_HASH2_ORDER 12
135 #define LZX_HASH2_LENGTH (1UL << LZX_HASH2_ORDER)
137 #include "wimlib/lzx_common.h"
140 * The maximum allowed window order for the matchfinder.
142 #define MATCHFINDER_MAX_WINDOW_ORDER LZX_MAX_WINDOW_ORDER
146 #include "wimlib/bt_matchfinder.h"
147 #include "wimlib/compress_common.h"
148 #include "wimlib/compressor_ops.h"
149 #include "wimlib/error.h"
150 #include "wimlib/hc_matchfinder.h"
151 #include "wimlib/lz_extend.h"
152 #include "wimlib/unaligned.h"
153 #include "wimlib/util.h"
155 struct lzx_output_bitstream;
157 /* Codewords for the LZX Huffman codes. */
158 struct lzx_codewords {
159 u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
160 u32 len[LZX_LENCODE_NUM_SYMBOLS];
161 u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
164 /* Codeword lengths (in bits) for the LZX Huffman codes.
165 * A zero length means the corresponding codeword has zero frequency. */
167 u8 main[LZX_MAINCODE_MAX_NUM_SYMBOLS + 1];
168 u8 len[LZX_LENCODE_NUM_SYMBOLS + 1];
169 u8 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
172 /* Cost model for near-optimal parsing */
175 /* 'match_cost[offset_slot][len - LZX_MIN_MATCH_LEN]' is the cost for a
176 * length 'len' match that has an offset belonging to 'offset_slot'. */
177 u32 match_cost[LZX_MAX_OFFSET_SLOTS][LZX_NUM_LENS];
179 /* Cost for each symbol in the main code */
180 u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
182 /* Cost for each symbol in the length code */
183 u32 len[LZX_LENCODE_NUM_SYMBOLS];
185 #if LZX_CONSIDER_ALIGNED_COSTS
186 /* Cost for each symbol in the aligned code */
187 u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
191 /* Codewords and lengths for the LZX Huffman codes. */
193 struct lzx_codewords codewords;
194 struct lzx_lens lens;
197 /* Symbol frequency counters for the LZX Huffman codes. */
199 u32 main[LZX_MAINCODE_MAX_NUM_SYMBOLS];
200 u32 len[LZX_LENCODE_NUM_SYMBOLS];
201 u32 aligned[LZX_ALIGNEDCODE_NUM_SYMBOLS];
204 /* Intermediate LZX match/literal format */
207 /* Bits 0 - 9: Main symbol
208 * Bits 10 - 17: Length symbol
209 * Bits 18 - 22: Number of extra offset bits
210 * Bits 23+ : Extra offset bits */
215 * This structure represents a byte position in the input buffer and a node in
216 * the graph of possible match/literal choices.
218 * Logically, each incoming edge to this node is labeled with a literal or a
219 * match that can be taken to reach this position from an earlier position; and
220 * each outgoing edge from this node is labeled with a literal or a match that
221 * can be taken to advance from this position to a later position.
223 struct lzx_optimum_node {
225 /* The cost, in bits, of the lowest-cost path that has been found to
226 * reach this position. This can change as progressively lower cost
227 * paths are found to reach this position. */
231 * The match or literal that was taken to reach this position. This can
232 * change as progressively lower cost paths are found to reach this
235 * This variable is divided into two bitfields.
238 * Low bits are 1, high bits are the literal.
240 * Explicit offset matches:
241 * Low bits are the match length, high bits are the offset plus 2.
243 * Repeat offset matches:
244 * Low bits are the match length, high bits are the queue index.
247 #define OPTIMUM_OFFSET_SHIFT 9
248 #define OPTIMUM_LEN_MASK ((1 << OPTIMUM_OFFSET_SHIFT) - 1)
249 } _aligned_attribute(8);
252 * Least-recently-used queue for match offsets.
254 * This is represented as a 64-bit integer for efficiency. There are three
255 * offsets of 21 bits each. Bit 64 is garbage.
257 struct lzx_lru_queue {
261 #define LZX_QUEUE64_OFFSET_SHIFT 21
262 #define LZX_QUEUE64_OFFSET_MASK (((u64)1 << LZX_QUEUE64_OFFSET_SHIFT) - 1)
264 #define LZX_QUEUE64_R0_SHIFT (0 * LZX_QUEUE64_OFFSET_SHIFT)
265 #define LZX_QUEUE64_R1_SHIFT (1 * LZX_QUEUE64_OFFSET_SHIFT)
266 #define LZX_QUEUE64_R2_SHIFT (2 * LZX_QUEUE64_OFFSET_SHIFT)
268 #define LZX_QUEUE64_R0_MASK (LZX_QUEUE64_OFFSET_MASK << LZX_QUEUE64_R0_SHIFT)
269 #define LZX_QUEUE64_R1_MASK (LZX_QUEUE64_OFFSET_MASK << LZX_QUEUE64_R1_SHIFT)
270 #define LZX_QUEUE64_R2_MASK (LZX_QUEUE64_OFFSET_MASK << LZX_QUEUE64_R2_SHIFT)
273 lzx_lru_queue_init(struct lzx_lru_queue *queue)
275 queue->R = ((u64)1 << LZX_QUEUE64_R0_SHIFT) |
276 ((u64)1 << LZX_QUEUE64_R1_SHIFT) |
277 ((u64)1 << LZX_QUEUE64_R2_SHIFT);
281 lzx_lru_queue_R0(struct lzx_lru_queue queue)
283 return (queue.R >> LZX_QUEUE64_R0_SHIFT) & LZX_QUEUE64_OFFSET_MASK;
287 lzx_lru_queue_R1(struct lzx_lru_queue queue)
289 return (queue.R >> LZX_QUEUE64_R1_SHIFT) & LZX_QUEUE64_OFFSET_MASK;
293 lzx_lru_queue_R2(struct lzx_lru_queue queue)
295 return (queue.R >> LZX_QUEUE64_R2_SHIFT) & LZX_QUEUE64_OFFSET_MASK;
298 /* Push a match offset onto the front (most recently used) end of the queue. */
299 static inline struct lzx_lru_queue
300 lzx_lru_queue_push(struct lzx_lru_queue queue, u32 offset)
302 return (struct lzx_lru_queue) {
303 .R = (queue.R << LZX_QUEUE64_OFFSET_SHIFT) | offset,
307 /* Pop a match offset off the front (most recently used) end of the queue. */
309 lzx_lru_queue_pop(struct lzx_lru_queue *queue_p)
311 u32 offset = queue_p->R & LZX_QUEUE64_OFFSET_MASK;
312 queue_p->R >>= LZX_QUEUE64_OFFSET_SHIFT;
316 /* Swap a match offset to the front of the queue. */
317 static inline struct lzx_lru_queue
318 lzx_lru_queue_swap(struct lzx_lru_queue queue, unsigned idx)
324 return (struct lzx_lru_queue) {
325 .R = (lzx_lru_queue_R1(queue) << LZX_QUEUE64_R0_SHIFT) |
326 (lzx_lru_queue_R0(queue) << LZX_QUEUE64_R1_SHIFT) |
327 (queue.R & LZX_QUEUE64_R2_MASK),
330 return (struct lzx_lru_queue) {
331 .R = (lzx_lru_queue_R2(queue) << LZX_QUEUE64_R0_SHIFT) |
332 (queue.R & LZX_QUEUE64_R1_MASK) |
333 (lzx_lru_queue_R0(queue) << LZX_QUEUE64_R2_SHIFT),
337 /* The main LZX compressor structure */
338 struct lzx_compressor {
340 /* The "nice" match length: if a match of this length is found, then
341 * choose it immediately without further consideration. */
342 unsigned nice_match_length;
344 /* The maximum search depth: consider at most this many potential
345 * matches at each position. */
346 unsigned max_search_depth;
348 /* The log base 2 of the LZX window size for LZ match offset encoding
349 * purposes. This will be >= LZX_MIN_WINDOW_ORDER and <=
350 * LZX_MAX_WINDOW_ORDER. */
351 unsigned window_order;
353 /* The number of symbols in the main alphabet. This depends on
354 * @window_order, since @window_order determines the maximum possible
356 unsigned num_main_syms;
358 /* Number of optimization passes per block */
359 unsigned num_optim_passes;
361 /* The preprocessed buffer of data being compressed */
364 /* The number of bytes of data to be compressed, which is the number of
365 * bytes of data in @in_buffer that are actually valid. */
368 /* Pointer to the compress() implementation chosen at allocation time */
369 void (*impl)(struct lzx_compressor *, struct lzx_output_bitstream *);
371 /* If true, the compressor need not preserve the input buffer if it
372 * compresses the data successfully. */
375 /* The Huffman symbol frequency counters for the current block. */
376 struct lzx_freqs freqs;
378 /* The Huffman codes for the current and previous blocks. The one with
379 * index 'codes_index' is for the current block, and the other one is
380 * for the previous block. */
381 struct lzx_codes codes[2];
382 unsigned codes_index;
385 * The match/literal sequence the algorithm chose for the current block.
387 * Notes on how large this array actually needs to be:
389 * - In lzx_compress_near_optimal(), the maximum block size is
390 * 'LZX_DIV_BLOCK_SIZE + LZX_MAX_MATCH_LEN - 1' bytes. This occurs if
391 * a match of the maximum length is found on the last byte. Although
392 * it is impossible for this particular case to actually result in a
393 * parse of all literals, we reserve this many spaces anyway.
395 * - The worst case for lzx_compress_lazy() is a block of almost all
396 * literals that ends with a series of matches of increasing scores,
397 * causing a sequence of literals to be chosen before the last match
398 * is finally chosen. The number of items actually chosen in this
399 * scenario is limited by the number of distinct match scores that
400 * exist for matches shorter than 'nice_match_length'. Having
401 * 'LZX_MAX_MATCH_LEN - 1' extra spaces is plenty for now.
403 struct lzx_item chosen_items[LZX_DIV_BLOCK_SIZE + LZX_MAX_MATCH_LEN - 1];
405 /* Table mapping match offset => offset slot for small offsets */
406 #define LZX_NUM_FAST_OFFSETS 32768
407 u8 offset_slot_fast[LZX_NUM_FAST_OFFSETS];
410 /* Data for greedy or lazy parsing */
412 /* Hash chains matchfinder (MUST BE LAST!!!) */
413 struct hc_matchfinder hc_mf;
416 /* Data for near-optimal parsing */
419 * The graph nodes for the current block.
421 * We need at least 'LZX_DIV_BLOCK_SIZE +
422 * LZX_MAX_MATCH_LEN - 1' nodes because that is the
423 * maximum block size that may be used. Add 1 because
424 * we need a node to represent end-of-block.
426 * It is possible that nodes past end-of-block are
427 * accessed during match consideration, but this can
428 * only occur if the block was truncated at
429 * LZX_DIV_BLOCK_SIZE. So the same bound still applies.
430 * Note that since nodes past the end of the block will
431 * never actually have an effect on the items that are
432 * chosen for the block, it makes no difference what
433 * their costs are initialized to (if anything).
435 struct lzx_optimum_node optimum_nodes[LZX_DIV_BLOCK_SIZE +
436 LZX_MAX_MATCH_LEN - 1 + 1];
438 /* The cost model for the current block */
439 struct lzx_costs costs;
442 * Cached matches for the current block. This array
443 * contains the matches that were found at each position
444 * in the block. Specifically, for each position, there
445 * is a special 'struct lz_match' whose 'length' field
446 * contains the number of matches that were found at
447 * that position; this is followed by the matches
448 * themselves, if any, sorted by strictly increasing
451 * Note: in rare cases, there will be a very high number
452 * of matches in the block and this array will overflow.
453 * If this happens, we force the end of the current
454 * block. LZX_CACHE_LENGTH is the length at which we
455 * actually check for overflow. The extra slots beyond
456 * this are enough to absorb the worst case overflow,
457 * which occurs if starting at
458 * &match_cache[LZX_CACHE_LENGTH - 1], we write the
459 * match count header, then write
460 * LZX_MAX_MATCHES_PER_POS matches, then skip searching
461 * for matches at 'LZX_MAX_MATCH_LEN - 1' positions and
462 * write the match count header for each.
464 struct lz_match match_cache[LZX_CACHE_LENGTH +
465 LZX_MAX_MATCHES_PER_POS +
466 LZX_MAX_MATCH_LEN - 1];
468 /* Hash table for finding length 2 matches */
469 pos_t hash2_tab[LZX_HASH2_LENGTH];
471 /* Binary trees matchfinder (MUST BE LAST!!!) */
472 struct bt_matchfinder bt_mf;
478 * Structure to keep track of the current state of sending bits to the
479 * compressed output buffer.
481 * The LZX bitstream is encoded as a sequence of 16-bit coding units.
483 struct lzx_output_bitstream {
485 /* Bits that haven't yet been written to the output buffer. */
488 /* Number of bits currently held in @bitbuf. */
491 /* Pointer to the start of the output buffer. */
494 /* Pointer to the position in the output buffer at which the next coding
495 * unit should be written. */
498 /* Pointer just past the end of the output buffer, rounded down to a
499 * 2-byte boundary. */
504 * Initialize the output bitstream.
507 * The output bitstream structure to initialize.
509 * The buffer being written to.
511 * Size of @buffer, in bytes.
514 lzx_init_output(struct lzx_output_bitstream *os, void *buffer, size_t size)
519 os->next = os->start;
520 os->end = os->start + (size & ~1);
524 * Write some bits to the output bitstream.
526 * The bits are given by the low-order @num_bits bits of @bits. Higher-order
527 * bits in @bits cannot be set. At most 17 bits can be written at once.
529 * @max_num_bits is a compile-time constant that specifies the maximum number of
530 * bits that can ever be written at the call site. It is used to optimize away
531 * the conditional code for writing a second 16-bit coding unit when writing
532 * fewer than 17 bits.
534 * If the output buffer space is exhausted, then the bits will be ignored, and
535 * lzx_flush_output() will return 0 when it gets called.
538 lzx_write_varbits(struct lzx_output_bitstream *os,
539 const u32 bits, const unsigned num_bits,
540 const unsigned max_num_bits)
542 /* This code is optimized for LZX, which never needs to write more than
543 * 17 bits at once. */
544 LZX_ASSERT(num_bits <= 17);
545 LZX_ASSERT(num_bits <= max_num_bits);
546 LZX_ASSERT(os->bitcount <= 15);
548 /* Add the bits to the bit buffer variable. @bitcount will be at most
549 * 15, so there will be just enough space for the maximum possible
550 * @num_bits of 17. */
551 os->bitcount += num_bits;
552 os->bitbuf = (os->bitbuf << num_bits) | bits;
554 /* Check whether any coding units need to be written. */
555 if (os->bitcount >= 16) {
559 /* Write a coding unit, unless it would overflow the buffer. */
560 if (os->next != os->end) {
561 put_unaligned_u16_le(os->bitbuf >> os->bitcount, os->next);
565 /* If writing 17 bits, a second coding unit might need to be
566 * written. But because 'max_num_bits' is a compile-time
567 * constant, the compiler will optimize away this code at most
569 if (max_num_bits == 17 && os->bitcount == 16) {
570 if (os->next != os->end) {
571 put_unaligned_u16_le(os->bitbuf, os->next);
579 /* Use when @num_bits is a compile-time constant. Otherwise use
580 * lzx_write_varbits(). */
582 lzx_write_bits(struct lzx_output_bitstream *os, u32 bits, unsigned num_bits)
584 lzx_write_varbits(os, bits, num_bits, num_bits);
588 * Flush the last coding unit to the output buffer if needed. Return the total
589 * number of bytes written to the output buffer, or 0 if an overflow occurred.
592 lzx_flush_output(struct lzx_output_bitstream *os)
594 if (os->next == os->end)
597 if (os->bitcount != 0) {
598 put_unaligned_u16_le(os->bitbuf << (16 - os->bitcount), os->next);
602 return os->next - os->start;
605 /* Build the main, length, and aligned offset Huffman codes used in LZX.
607 * This takes as input the frequency tables for each code and produces as output
608 * a set of tables that map symbols to codewords and codeword lengths. */
610 lzx_make_huffman_codes(struct lzx_compressor *c)
612 const struct lzx_freqs *freqs = &c->freqs;
613 struct lzx_codes *codes = &c->codes[c->codes_index];
615 make_canonical_huffman_code(c->num_main_syms,
616 LZX_MAX_MAIN_CODEWORD_LEN,
619 codes->codewords.main);
621 make_canonical_huffman_code(LZX_LENCODE_NUM_SYMBOLS,
622 LZX_MAX_LEN_CODEWORD_LEN,
625 codes->codewords.len);
627 make_canonical_huffman_code(LZX_ALIGNEDCODE_NUM_SYMBOLS,
628 LZX_MAX_ALIGNED_CODEWORD_LEN,
631 codes->codewords.aligned);
634 /* Reset the symbol frequencies for the LZX Huffman codes. */
636 lzx_reset_symbol_frequencies(struct lzx_compressor *c)
638 memset(&c->freqs, 0, sizeof(c->freqs));
642 lzx_compute_precode_items(const u8 lens[restrict],
643 const u8 prev_lens[restrict],
644 u32 precode_freqs[restrict],
645 unsigned precode_items[restrict])
654 itemptr = precode_items;
657 while (!((len = lens[run_start]) & 0x80)) {
659 /* len = the length being repeated */
661 /* Find the next run of codeword lengths. */
663 run_end = run_start + 1;
665 /* Fast case for a single length. */
666 if (likely(len != lens[run_end])) {
667 delta = prev_lens[run_start] - len;
670 precode_freqs[delta]++;
676 /* Extend the run. */
679 } while (len == lens[run_end]);
684 /* Symbol 18: RLE 20 to 51 zeroes at a time. */
685 while ((run_end - run_start) >= 20) {
686 extra_bits = min((run_end - run_start) - 20, 0x1f);
688 *itemptr++ = 18 | (extra_bits << 5);
689 run_start += 20 + extra_bits;
692 /* Symbol 17: RLE 4 to 19 zeroes at a time. */
693 if ((run_end - run_start) >= 4) {
694 extra_bits = min((run_end - run_start) - 4, 0xf);
696 *itemptr++ = 17 | (extra_bits << 5);
697 run_start += 4 + extra_bits;
701 /* A run of nonzero lengths. */
703 /* Symbol 19: RLE 4 to 5 of any length at a time. */
704 while ((run_end - run_start) >= 4) {
705 extra_bits = (run_end - run_start) > 4;
706 delta = prev_lens[run_start] - len;
710 precode_freqs[delta]++;
711 *itemptr++ = 19 | (extra_bits << 5) | (delta << 6);
712 run_start += 4 + extra_bits;
716 /* Output any remaining lengths without RLE. */
717 while (run_start != run_end) {
718 delta = prev_lens[run_start] - len;
721 precode_freqs[delta]++;
727 return itemptr - precode_items;
731 * Output a Huffman code in the compressed form used in LZX.
733 * The Huffman code is represented in the output as a logical series of codeword
734 * lengths from which the Huffman code, which must be in canonical form, can be
737 * The codeword lengths are themselves compressed using a separate Huffman code,
738 * the "precode", which contains a symbol for each possible codeword length in
739 * the larger code as well as several special symbols to represent repeated
740 * codeword lengths (a form of run-length encoding). The precode is itself
741 * constructed in canonical form, and its codeword lengths are represented
742 * literally in 20 4-bit fields that immediately precede the compressed codeword
743 * lengths of the larger code.
745 * Furthermore, the codeword lengths of the larger code are actually represented
746 * as deltas from the codeword lengths of the corresponding code in the previous
750 * Bitstream to which to write the compressed Huffman code.
752 * The codeword lengths, indexed by symbol, in the Huffman code.
754 * The codeword lengths, indexed by symbol, in the corresponding Huffman
755 * code in the previous block, or all zeroes if this is the first block.
757 * The number of symbols in the Huffman code.
760 lzx_write_compressed_code(struct lzx_output_bitstream *os,
761 const u8 lens[restrict],
762 const u8 prev_lens[restrict],
765 u32 precode_freqs[LZX_PRECODE_NUM_SYMBOLS];
766 u8 precode_lens[LZX_PRECODE_NUM_SYMBOLS];
767 u32 precode_codewords[LZX_PRECODE_NUM_SYMBOLS];
768 unsigned precode_items[num_lens];
769 unsigned num_precode_items;
770 unsigned precode_item;
771 unsigned precode_sym;
773 u8 saved = lens[num_lens];
774 *(u8 *)(lens + num_lens) = 0x80;
776 for (i = 0; i < LZX_PRECODE_NUM_SYMBOLS; i++)
777 precode_freqs[i] = 0;
779 /* Compute the "items" (RLE / literal tokens and extra bits) with which
780 * the codeword lengths in the larger code will be output. */
781 num_precode_items = lzx_compute_precode_items(lens,
786 /* Build the precode. */
787 make_canonical_huffman_code(LZX_PRECODE_NUM_SYMBOLS,
788 LZX_MAX_PRE_CODEWORD_LEN,
789 precode_freqs, precode_lens,
792 /* Output the lengths of the codewords in the precode. */
793 for (i = 0; i < LZX_PRECODE_NUM_SYMBOLS; i++)
794 lzx_write_bits(os, precode_lens[i], LZX_PRECODE_ELEMENT_SIZE);
796 /* Output the encoded lengths of the codewords in the larger code. */
797 for (i = 0; i < num_precode_items; i++) {
798 precode_item = precode_items[i];
799 precode_sym = precode_item & 0x1F;
800 lzx_write_varbits(os, precode_codewords[precode_sym],
801 precode_lens[precode_sym],
802 LZX_MAX_PRE_CODEWORD_LEN);
803 if (precode_sym >= 17) {
804 if (precode_sym == 17) {
805 lzx_write_bits(os, precode_item >> 5, 4);
806 } else if (precode_sym == 18) {
807 lzx_write_bits(os, precode_item >> 5, 5);
809 lzx_write_bits(os, (precode_item >> 5) & 1, 1);
810 precode_sym = precode_item >> 6;
811 lzx_write_varbits(os, precode_codewords[precode_sym],
812 precode_lens[precode_sym],
813 LZX_MAX_PRE_CODEWORD_LEN);
818 *(u8 *)(lens + num_lens) = saved;
821 /* Output a match or literal. */
823 lzx_write_item(struct lzx_output_bitstream *os, struct lzx_item item,
824 unsigned ones_if_aligned, const struct lzx_codes *codes)
826 u64 data = item.data;
827 unsigned main_symbol;
829 unsigned num_extra_bits;
832 main_symbol = data & 0x3FF;
834 lzx_write_varbits(os, codes->codewords.main[main_symbol],
835 codes->lens.main[main_symbol],
836 LZX_MAX_MAIN_CODEWORD_LEN);
838 if (main_symbol < LZX_NUM_CHARS) /* Literal? */
841 len_symbol = (data >> 10) & 0xFF;
843 if (len_symbol != LZX_LENCODE_NUM_SYMBOLS) {
844 lzx_write_varbits(os, codes->codewords.len[len_symbol],
845 codes->lens.len[len_symbol],
846 LZX_MAX_LEN_CODEWORD_LEN);
849 num_extra_bits = (data >> 18) & 0x1F;
850 if (num_extra_bits == 0) /* Small offset or repeat offset match? */
853 extra_bits = data >> 23;
855 if ((num_extra_bits & ones_if_aligned) >= LZX_NUM_ALIGNED_OFFSET_BITS) {
857 /* Aligned offset blocks: The low 3 bits of the extra offset
858 * bits are Huffman-encoded using the aligned offset code. The
859 * remaining bits are output literally. */
861 lzx_write_varbits(os, extra_bits >> LZX_NUM_ALIGNED_OFFSET_BITS,
862 num_extra_bits - LZX_NUM_ALIGNED_OFFSET_BITS,
863 17 - LZX_NUM_ALIGNED_OFFSET_BITS);
865 lzx_write_varbits(os,
866 codes->codewords.aligned[extra_bits & LZX_ALIGNED_OFFSET_BITMASK],
867 codes->lens.aligned[extra_bits & LZX_ALIGNED_OFFSET_BITMASK],
868 LZX_MAX_ALIGNED_CODEWORD_LEN);
870 /* Verbatim blocks, or fewer than 3 extra bits: All extra
871 * offset bits are output literally. */
872 lzx_write_varbits(os, extra_bits, num_extra_bits, 17);
877 * Write all matches and literal bytes (which were precomputed) in an LZX
878 * compressed block to the output bitstream in the final compressed
882 * The output bitstream.
884 * The chosen type of the LZX compressed block (LZX_BLOCKTYPE_ALIGNED or
885 * LZX_BLOCKTYPE_VERBATIM).
887 * The array of matches/literals to output.
889 * Number of matches/literals to output (length of @items).
891 * The main, length, and aligned offset Huffman codes for the current
892 * LZX compressed block.
895 lzx_write_items(struct lzx_output_bitstream *os, int block_type,
896 const struct lzx_item items[], u32 num_items,
897 const struct lzx_codes *codes)
899 unsigned ones_if_aligned = 0U - (block_type == LZX_BLOCKTYPE_ALIGNED);
901 for (u32 i = 0; i < num_items; i++)
902 lzx_write_item(os, items[i], ones_if_aligned, codes);
906 lzx_write_compressed_block(int block_type,
908 unsigned window_order,
909 unsigned num_main_syms,
910 const struct lzx_item chosen_items[],
911 u32 num_chosen_items,
912 const struct lzx_codes * codes,
913 const struct lzx_lens * prev_lens,
914 struct lzx_output_bitstream * os)
916 LZX_ASSERT(block_type == LZX_BLOCKTYPE_ALIGNED ||
917 block_type == LZX_BLOCKTYPE_VERBATIM);
919 /* The first three bits indicate the type of block and are one of the
920 * LZX_BLOCKTYPE_* constants. */
921 lzx_write_bits(os, block_type, 3);
923 /* Output the block size.
925 * The original LZX format seemed to always encode the block size in 3
926 * bytes. However, the implementation in WIMGAPI, as used in WIM files,
927 * uses the first bit to indicate whether the block is the default size
928 * (32768) or a different size given explicitly by the next 16 bits.
930 * By default, this compressor uses a window size of 32768 and therefore
931 * follows the WIMGAPI behavior. However, this compressor also supports
932 * window sizes greater than 32768 bytes, which do not appear to be
933 * supported by WIMGAPI. In such cases, we retain the default size bit
934 * to mean a size of 32768 bytes but output non-default block size in 24
935 * bits rather than 16. The compatibility of this behavior is unknown
936 * because WIMs created with chunk size greater than 32768 can seemingly
937 * only be opened by wimlib anyway. */
938 if (block_size == LZX_DEFAULT_BLOCK_SIZE) {
939 lzx_write_bits(os, 1, 1);
941 lzx_write_bits(os, 0, 1);
943 if (window_order >= 16)
944 lzx_write_bits(os, block_size >> 16, 8);
946 lzx_write_bits(os, block_size & 0xFFFF, 16);
949 /* If it's an aligned offset block, output the aligned offset code. */
950 if (block_type == LZX_BLOCKTYPE_ALIGNED) {
951 for (int i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
952 lzx_write_bits(os, codes->lens.aligned[i],
953 LZX_ALIGNEDCODE_ELEMENT_SIZE);
957 /* Output the main code (two parts). */
958 lzx_write_compressed_code(os, codes->lens.main,
961 lzx_write_compressed_code(os, codes->lens.main + LZX_NUM_CHARS,
962 prev_lens->main + LZX_NUM_CHARS,
963 num_main_syms - LZX_NUM_CHARS);
965 /* Output the length code. */
966 lzx_write_compressed_code(os, codes->lens.len,
968 LZX_LENCODE_NUM_SYMBOLS);
970 /* Output the compressed matches and literals. */
971 lzx_write_items(os, block_type, chosen_items, num_chosen_items, codes);
974 /* Given the frequencies of symbols in an LZX-compressed block and the
975 * corresponding Huffman codes, return LZX_BLOCKTYPE_ALIGNED or
976 * LZX_BLOCKTYPE_VERBATIM if an aligned offset or verbatim block, respectively,
977 * will take fewer bits to output. */
979 lzx_choose_verbatim_or_aligned(const struct lzx_freqs * freqs,
980 const struct lzx_codes * codes)
982 u32 aligned_cost = 0;
983 u32 verbatim_cost = 0;
985 /* A verbatim block requires 3 bits in each place that an aligned symbol
986 * would be used in an aligned offset block. */
987 for (unsigned i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++) {
988 verbatim_cost += LZX_NUM_ALIGNED_OFFSET_BITS * freqs->aligned[i];
989 aligned_cost += codes->lens.aligned[i] * freqs->aligned[i];
992 /* Account for output of the aligned offset code. */
993 aligned_cost += LZX_ALIGNEDCODE_ELEMENT_SIZE * LZX_ALIGNEDCODE_NUM_SYMBOLS;
995 if (aligned_cost < verbatim_cost)
996 return LZX_BLOCKTYPE_ALIGNED;
998 return LZX_BLOCKTYPE_VERBATIM;
1002 * Finish an LZX block:
1004 * - build the Huffman codes
1005 * - decide whether to output the block as VERBATIM or ALIGNED
1006 * - output the block
1007 * - swap the indices of the current and previous Huffman codes
1010 lzx_finish_block(struct lzx_compressor *c, struct lzx_output_bitstream *os,
1011 u32 block_size, u32 num_chosen_items)
1015 lzx_make_huffman_codes(c);
1017 block_type = lzx_choose_verbatim_or_aligned(&c->freqs,
1018 &c->codes[c->codes_index]);
1019 lzx_write_compressed_block(block_type,
1025 &c->codes[c->codes_index],
1026 &c->codes[c->codes_index ^ 1].lens,
1028 c->codes_index ^= 1;
1031 /* Return the offset slot for the specified offset, which must be
1032 * less than LZX_NUM_FAST_OFFSETS. */
1033 static inline unsigned
1034 lzx_get_offset_slot_fast(struct lzx_compressor *c, u32 offset)
1036 LZX_ASSERT(offset < LZX_NUM_FAST_OFFSETS);
1037 return c->offset_slot_fast[offset];
1040 /* Tally, and optionally record, the specified literal byte. */
1042 lzx_declare_literal(struct lzx_compressor *c, unsigned literal,
1043 struct lzx_item **next_chosen_item)
1045 unsigned main_symbol = lzx_main_symbol_for_literal(literal);
1047 c->freqs.main[main_symbol]++;
1049 if (next_chosen_item) {
1050 *(*next_chosen_item)++ = (struct lzx_item) {
1051 .data = main_symbol,
1056 /* Tally, and optionally record, the specified repeat offset match. */
1058 lzx_declare_repeat_offset_match(struct lzx_compressor *c,
1059 unsigned len, unsigned rep_index,
1060 struct lzx_item **next_chosen_item)
1062 unsigned len_header;
1063 unsigned len_symbol;
1064 unsigned main_symbol;
1066 if (len - LZX_MIN_MATCH_LEN < LZX_NUM_PRIMARY_LENS) {
1067 len_header = len - LZX_MIN_MATCH_LEN;
1068 len_symbol = LZX_LENCODE_NUM_SYMBOLS;
1070 len_header = LZX_NUM_PRIMARY_LENS;
1071 len_symbol = len - LZX_MIN_MATCH_LEN - LZX_NUM_PRIMARY_LENS;
1072 c->freqs.len[len_symbol]++;
1075 main_symbol = lzx_main_symbol_for_match(rep_index, len_header);
1077 c->freqs.main[main_symbol]++;
1079 if (next_chosen_item) {
1080 *(*next_chosen_item)++ = (struct lzx_item) {
1081 .data = (u64)main_symbol | ((u64)len_symbol << 10),
1086 /* Tally, and optionally record, the specified explicit offset match. */
1088 lzx_declare_explicit_offset_match(struct lzx_compressor *c, unsigned len, u32 offset,
1089 struct lzx_item **next_chosen_item)
1091 unsigned len_header;
1092 unsigned len_symbol;
1093 unsigned main_symbol;
1094 unsigned offset_slot;
1095 unsigned num_extra_bits;
1098 if (len - LZX_MIN_MATCH_LEN < LZX_NUM_PRIMARY_LENS) {
1099 len_header = len - LZX_MIN_MATCH_LEN;
1100 len_symbol = LZX_LENCODE_NUM_SYMBOLS;
1102 len_header = LZX_NUM_PRIMARY_LENS;
1103 len_symbol = len - LZX_MIN_MATCH_LEN - LZX_NUM_PRIMARY_LENS;
1104 c->freqs.len[len_symbol]++;
1107 offset_slot = (offset < LZX_NUM_FAST_OFFSETS) ?
1108 lzx_get_offset_slot_fast(c, offset) :
1109 lzx_get_offset_slot(offset);
1111 main_symbol = lzx_main_symbol_for_match(offset_slot, len_header);
1113 c->freqs.main[main_symbol]++;
1115 num_extra_bits = lzx_extra_offset_bits[offset_slot];
1117 if (num_extra_bits >= LZX_NUM_ALIGNED_OFFSET_BITS)
1118 c->freqs.aligned[(offset + LZX_OFFSET_ADJUSTMENT) &
1119 LZX_ALIGNED_OFFSET_BITMASK]++;
1121 if (next_chosen_item) {
1123 extra_bits = (offset + LZX_OFFSET_ADJUSTMENT) -
1124 lzx_offset_slot_base[offset_slot];
1126 STATIC_ASSERT(LZX_MAINCODE_MAX_NUM_SYMBOLS <= (1 << 10));
1127 STATIC_ASSERT(LZX_LENCODE_NUM_SYMBOLS <= (1 << 8));
1128 *(*next_chosen_item)++ = (struct lzx_item) {
1129 .data = (u64)main_symbol |
1130 ((u64)len_symbol << 10) |
1131 ((u64)num_extra_bits << 18) |
1132 ((u64)extra_bits << 23),
1138 /* Tally, and optionally record, the specified match or literal. */
1140 lzx_declare_item(struct lzx_compressor *c, u32 item,
1141 struct lzx_item **next_chosen_item)
1143 u32 len = item & OPTIMUM_LEN_MASK;
1144 u32 offset_data = item >> OPTIMUM_OFFSET_SHIFT;
1147 lzx_declare_literal(c, offset_data, next_chosen_item);
1148 else if (offset_data < LZX_NUM_RECENT_OFFSETS)
1149 lzx_declare_repeat_offset_match(c, len, offset_data,
1152 lzx_declare_explicit_offset_match(c, len,
1153 offset_data - LZX_OFFSET_ADJUSTMENT,
1158 lzx_record_item_list(struct lzx_compressor *c,
1159 struct lzx_optimum_node *cur_node,
1160 struct lzx_item **next_chosen_item)
1162 struct lzx_optimum_node *end_node;
1166 /* The list is currently in reverse order (last item to first item).
1168 end_node = cur_node;
1169 saved_item = cur_node->item;
1172 cur_node -= item & OPTIMUM_LEN_MASK;
1173 saved_item = cur_node->item;
1174 cur_node->item = item;
1175 } while (cur_node != c->optimum_nodes);
1177 /* Walk the list of items from beginning to end, tallying and recording
1180 lzx_declare_item(c, cur_node->item, next_chosen_item);
1181 cur_node += (cur_node->item) & OPTIMUM_LEN_MASK;
1182 } while (cur_node != end_node);
1186 lzx_tally_item_list(struct lzx_compressor *c, struct lzx_optimum_node *cur_node)
1188 /* Since we're just tallying the items, we don't need to reverse the
1189 * list. Processing the items in reverse order is fine. */
1191 lzx_declare_item(c, cur_node->item, NULL);
1192 cur_node -= (cur_node->item & OPTIMUM_LEN_MASK);
1193 } while (cur_node != c->optimum_nodes);
1197 * Find an inexpensive path through the graph of possible match/literal choices
1198 * for the current block. The nodes of the graph are
1199 * c->optimum_nodes[0...block_size]. They correspond directly to the bytes in
1200 * the current block, plus one extra node for end-of-block. The edges of the
1201 * graph are matches and literals. The goal is to find the minimum cost path
1202 * from 'c->optimum_nodes[0]' to 'c->optimum_nodes[block_size]'.
1204 * The algorithm works forwards, starting at 'c->optimum_nodes[0]' and
1205 * proceeding forwards one node at a time. At each node, a selection of matches
1206 * (len >= 2), as well as the literal byte (len = 1), is considered. An item of
1207 * length 'len' provides a new path to reach the node 'len' bytes later. If
1208 * such a path is the lowest cost found so far to reach that later node, then
1209 * that later node is updated with the new path.
1211 * Note that although this algorithm is based on minimum cost path search, due
1212 * to various simplifying assumptions the result is not guaranteed to be the
1213 * true minimum cost, or "optimal", path over the graph of all valid LZX
1214 * representations of this block.
1216 * Also, note that because of the presence of the recent offsets queue (which is
1217 * a type of adaptive state), the algorithm cannot work backwards and compute
1218 * "cost to end" instead of "cost to beginning". Furthermore, the way the
1219 * algorithm handles this adaptive state in the "minimum cost" parse is actually
1220 * only an approximation. It's possible for the globally optimal, minimum cost
1221 * path to contain a prefix, ending at a position, where that path prefix is
1222 * *not* the minimum cost path to that position. This can happen if such a path
1223 * prefix results in a different adaptive state which results in lower costs
1224 * later. The algorithm does not solve this problem; it only considers the
1225 * lowest cost to reach each individual position.
1227 static struct lzx_lru_queue
1228 lzx_find_min_cost_path(struct lzx_compressor * const restrict c,
1229 const u8 * const restrict block_begin,
1230 const u32 block_size,
1231 const struct lzx_lru_queue initial_queue)
1233 struct lzx_optimum_node *cur_node = c->optimum_nodes;
1234 struct lzx_optimum_node * const end_node = &c->optimum_nodes[block_size];
1235 struct lz_match *cache_ptr = c->match_cache;
1236 const u8 *in_next = block_begin;
1237 const u8 * const block_end = block_begin + block_size;
1239 /* Instead of storing the match offset LRU queues in the
1240 * 'lzx_optimum_node' structures, we save memory (and cache lines) by
1241 * storing them in a smaller array. This works because the algorithm
1242 * only requires a limited history of the adaptive state. Once a given
1243 * state is more than LZX_MAX_MATCH_LEN bytes behind the current node,
1244 * it is no longer needed. */
1245 struct lzx_lru_queue queues[512];
1247 STATIC_ASSERT(ARRAY_LEN(queues) >= LZX_MAX_MATCH_LEN + 1);
1248 #define QUEUE(in) (queues[(uintptr_t)(in) % ARRAY_LEN(queues)])
1250 /* Initially, the cost to reach each node is "infinity". */
1251 memset(c->optimum_nodes, 0xFF,
1252 (block_size + 1) * sizeof(c->optimum_nodes[0]));
1254 QUEUE(block_begin) = initial_queue;
1256 /* The following loop runs 'block_size' iterations, one per node. */
1258 unsigned num_matches;
1263 * A selection of matches for the block was already saved in
1264 * memory so that we don't have to run the uncompressed data
1265 * through the matchfinder on every optimization pass. However,
1266 * we still search for repeat offset matches during each
1267 * optimization pass because we cannot predict the state of the
1268 * recent offsets queue. But as a heuristic, we don't bother
1269 * searching for repeat offset matches if the general-purpose
1270 * matchfinder failed to find any matches.
1272 * Note that a match of length n at some offset implies there is
1273 * also a match of length l for LZX_MIN_MATCH_LEN <= l <= n at
1274 * that same offset. In other words, we don't necessarily need
1275 * to use the full length of a match. The key heuristic that
1276 * saves a significicant amount of time is that for each
1277 * distinct length, we only consider the smallest offset for
1278 * which that length is available. This heuristic also applies
1279 * to repeat offsets, which we order specially: R0 < R1 < R2 <
1280 * any explicit offset. Of course, this heuristic may be
1281 * produce suboptimal results because offset slots in LZX are
1282 * subject to entropy encoding, but in practice this is a useful
1286 num_matches = cache_ptr->length;
1290 struct lz_match *end_matches = cache_ptr + num_matches;
1291 unsigned next_len = LZX_MIN_MATCH_LEN;
1292 unsigned max_len = min(block_end - in_next, LZX_MAX_MATCH_LEN);
1295 /* Consider R0 match */
1296 matchptr = in_next - lzx_lru_queue_R0(QUEUE(in_next));
1297 if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
1299 STATIC_ASSERT(LZX_MIN_MATCH_LEN == 2);
1301 u32 cost = cur_node->cost +
1302 c->costs.match_cost[0][
1303 next_len - LZX_MIN_MATCH_LEN];
1304 if (cost <= (cur_node + next_len)->cost) {
1305 (cur_node + next_len)->cost = cost;
1306 (cur_node + next_len)->item =
1307 (0 << OPTIMUM_OFFSET_SHIFT) | next_len;
1309 if (unlikely(++next_len > max_len)) {
1310 cache_ptr = end_matches;
1313 } while (in_next[next_len - 1] == matchptr[next_len - 1]);
1317 /* Consider R1 match */
1318 matchptr = in_next - lzx_lru_queue_R1(QUEUE(in_next));
1319 if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
1321 if (matchptr[next_len - 1] != in_next[next_len - 1])
1323 for (unsigned len = 2; len < next_len - 1; len++)
1324 if (matchptr[len] != in_next[len])
1327 u32 cost = cur_node->cost +
1328 c->costs.match_cost[1][
1329 next_len - LZX_MIN_MATCH_LEN];
1330 if (cost <= (cur_node + next_len)->cost) {
1331 (cur_node + next_len)->cost = cost;
1332 (cur_node + next_len)->item =
1333 (1 << OPTIMUM_OFFSET_SHIFT) | next_len;
1335 if (unlikely(++next_len > max_len)) {
1336 cache_ptr = end_matches;
1339 } while (in_next[next_len - 1] == matchptr[next_len - 1]);
1343 /* Consider R2 match */
1344 matchptr = in_next - lzx_lru_queue_R2(QUEUE(in_next));
1345 if (load_u16_unaligned(matchptr) != load_u16_unaligned(in_next))
1347 if (matchptr[next_len - 1] != in_next[next_len - 1])
1349 for (unsigned len = 2; len < next_len - 1; len++)
1350 if (matchptr[len] != in_next[len])
1353 u32 cost = cur_node->cost +
1354 c->costs.match_cost[2][
1355 next_len - LZX_MIN_MATCH_LEN];
1356 if (cost <= (cur_node + next_len)->cost) {
1357 (cur_node + next_len)->cost = cost;
1358 (cur_node + next_len)->item =
1359 (2 << OPTIMUM_OFFSET_SHIFT) | next_len;
1361 if (unlikely(++next_len > max_len)) {
1362 cache_ptr = end_matches;
1365 } while (in_next[next_len - 1] == matchptr[next_len - 1]);
1369 while (next_len > cache_ptr->length)
1370 if (++cache_ptr == end_matches)
1373 /* Consider explicit offset matches */
1375 u32 offset = cache_ptr->offset;
1376 u32 offset_data = offset + LZX_OFFSET_ADJUSTMENT;
1377 unsigned offset_slot = (offset < LZX_NUM_FAST_OFFSETS) ?
1378 lzx_get_offset_slot_fast(c, offset) :
1379 lzx_get_offset_slot(offset);
1381 u32 cost = cur_node->cost +
1382 c->costs.match_cost[offset_slot][
1383 next_len - LZX_MIN_MATCH_LEN];
1384 #if LZX_CONSIDER_ALIGNED_COSTS
1385 if (lzx_extra_offset_bits[offset_slot] >=
1386 LZX_NUM_ALIGNED_OFFSET_BITS)
1387 cost += c->costs.aligned[offset_data &
1388 LZX_ALIGNED_OFFSET_BITMASK];
1390 if (cost < (cur_node + next_len)->cost) {
1391 (cur_node + next_len)->cost = cost;
1392 (cur_node + next_len)->item =
1393 (offset_data << OPTIMUM_OFFSET_SHIFT) | next_len;
1395 } while (++next_len <= cache_ptr->length);
1396 } while (++cache_ptr != end_matches);
1401 /* Consider coding a literal.
1403 * To avoid an extra branch, actually checking the preferability
1404 * of coding the literal is integrated into the queue update
1406 literal = *in_next++;
1407 cost = cur_node->cost +
1408 c->costs.main[lzx_main_symbol_for_literal(literal)];
1410 /* Advance to the next position. */
1413 /* The lowest-cost path to the current position is now known.
1414 * Finalize the recent offsets queue that results from taking
1415 * this lowest-cost path. */
1417 if (cost <= cur_node->cost) {
1418 /* Literal: queue remains unchanged. */
1419 cur_node->cost = cost;
1420 cur_node->item = (literal << OPTIMUM_OFFSET_SHIFT) | 1;
1421 QUEUE(in_next) = QUEUE(in_next - 1);
1423 /* Match: queue update is needed. */
1424 unsigned len = cur_node->item & OPTIMUM_LEN_MASK;
1425 u32 offset_data = cur_node->item >> OPTIMUM_OFFSET_SHIFT;
1426 if (offset_data >= LZX_NUM_RECENT_OFFSETS) {
1427 /* Explicit offset match: insert offset at front */
1429 lzx_lru_queue_push(QUEUE(in_next - len),
1430 offset_data - LZX_OFFSET_ADJUSTMENT);
1432 /* Repeat offset match: swap offset to front */
1434 lzx_lru_queue_swap(QUEUE(in_next - len),
1438 } while (cur_node != end_node);
1440 /* Return the match offset queue at the end of the minimum cost path. */
1441 return QUEUE(block_end);
1444 /* Given the costs for the main and length codewords, compute 'match_costs'. */
1446 lzx_compute_match_costs(struct lzx_compressor *c)
1448 unsigned num_offset_slots = lzx_get_num_offset_slots(c->window_order);
1449 struct lzx_costs *costs = &c->costs;
1451 for (unsigned offset_slot = 0; offset_slot < num_offset_slots; offset_slot++) {
1453 u32 extra_cost = (u32)lzx_extra_offset_bits[offset_slot] * LZX_BIT_COST;
1454 unsigned main_symbol = lzx_main_symbol_for_match(offset_slot, 0);
1457 #if LZX_CONSIDER_ALIGNED_COSTS
1458 if (lzx_extra_offset_bits[offset_slot] >= LZX_NUM_ALIGNED_OFFSET_BITS)
1459 extra_cost -= LZX_NUM_ALIGNED_OFFSET_BITS * LZX_BIT_COST;
1462 for (i = 0; i < LZX_NUM_PRIMARY_LENS; i++)
1463 costs->match_cost[offset_slot][i] =
1464 costs->main[main_symbol++] + extra_cost;
1466 extra_cost += costs->main[main_symbol];
1468 for (; i < LZX_NUM_LENS; i++)
1469 costs->match_cost[offset_slot][i] =
1470 costs->len[i - LZX_NUM_PRIMARY_LENS] + extra_cost;
1474 /* Set default LZX Huffman symbol costs to bootstrap the iterative optimization
1477 lzx_set_default_costs(struct lzx_compressor *c, const u8 *block, u32 block_size)
1480 bool have_byte[256];
1481 unsigned num_used_bytes;
1483 /* The costs below are hard coded to use a scaling factor of 16. */
1484 STATIC_ASSERT(LZX_BIT_COST == 16);
1489 * - Use smaller initial costs for literal symbols when the input buffer
1490 * contains fewer distinct bytes.
1492 * - Assume that match symbols are more costly than literal symbols.
1494 * - Assume that length symbols for shorter lengths are less costly than
1495 * length symbols for longer lengths.
1498 for (i = 0; i < 256; i++)
1499 have_byte[i] = false;
1501 for (i = 0; i < block_size; i++)
1502 have_byte[block[i]] = true;
1505 for (i = 0; i < 256; i++)
1506 num_used_bytes += have_byte[i];
1508 for (i = 0; i < 256; i++)
1509 c->costs.main[i] = 140 - (256 - num_used_bytes) / 4;
1511 for (; i < c->num_main_syms; i++)
1512 c->costs.main[i] = 170;
1514 for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++)
1515 c->costs.len[i] = 103 + (i / 4);
1517 #if LZX_CONSIDER_ALIGNED_COSTS
1518 for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++)
1519 c->costs.aligned[i] = LZX_NUM_ALIGNED_OFFSET_BITS * LZX_BIT_COST;
1522 lzx_compute_match_costs(c);
1525 /* Update the current cost model to reflect the computed Huffman codes. */
1527 lzx_update_costs(struct lzx_compressor *c)
1530 const struct lzx_lens *lens = &c->codes[c->codes_index].lens;
1532 for (i = 0; i < c->num_main_syms; i++)
1533 c->costs.main[i] = (lens->main[i] ? lens->main[i] : 15) * LZX_BIT_COST;
1535 for (i = 0; i < LZX_LENCODE_NUM_SYMBOLS; i++)
1536 c->costs.len[i] = (lens->len[i] ? lens->len[i] : 15) * LZX_BIT_COST;
1538 #if LZX_CONSIDER_ALIGNED_COSTS
1539 for (i = 0; i < LZX_ALIGNEDCODE_NUM_SYMBOLS; i++)
1540 c->costs.aligned[i] = (lens->aligned[i] ? lens->aligned[i] : 7) * LZX_BIT_COST;
1543 lzx_compute_match_costs(c);
1546 static struct lzx_lru_queue
1547 lzx_optimize_and_write_block(struct lzx_compressor *c,
1548 struct lzx_output_bitstream *os,
1549 const u8 *block_begin, const u32 block_size,
1550 const struct lzx_lru_queue initial_queue)
1552 unsigned num_passes_remaining = c->num_optim_passes;
1553 struct lzx_item *next_chosen_item;
1554 struct lzx_lru_queue new_queue;
1556 /* The first optimization pass uses a default cost model. Each
1557 * additional optimization pass uses a cost model derived from the
1558 * Huffman code computed in the previous pass. */
1560 lzx_set_default_costs(c, block_begin, block_size);
1561 lzx_reset_symbol_frequencies(c);
1563 new_queue = lzx_find_min_cost_path(c, block_begin, block_size,
1565 if (num_passes_remaining > 1) {
1566 lzx_tally_item_list(c, c->optimum_nodes + block_size);
1567 lzx_make_huffman_codes(c);
1568 lzx_update_costs(c);
1569 lzx_reset_symbol_frequencies(c);
1571 } while (--num_passes_remaining);
1573 next_chosen_item = c->chosen_items;
1574 lzx_record_item_list(c, c->optimum_nodes + block_size, &next_chosen_item);
1575 lzx_finish_block(c, os, block_size, next_chosen_item - c->chosen_items);
1580 * This is the "near-optimal" LZX compressor.
1582 * For each block, it performs a relatively thorough graph search to find an
1583 * inexpensive (in terms of compressed size) way to output that block.
1585 * Note: there are actually many things this algorithm leaves on the table in
1586 * terms of compression ratio. So although it may be "near-optimal", it is
1587 * certainly not "optimal". The goal is not to produce the optimal compression
1588 * ratio, which for LZX is probably impossible within any practical amount of
1589 * time, but rather to produce a compression ratio significantly better than a
1590 * simpler "greedy" or "lazy" parse while still being relatively fast.
1593 lzx_compress_near_optimal(struct lzx_compressor *c,
1594 struct lzx_output_bitstream *os)
1596 const u8 * const in_begin = c->in_buffer;
1597 const u8 * in_next = in_begin;
1598 const u8 * const in_end = in_begin + c->in_nbytes;
1599 unsigned max_len = LZX_MAX_MATCH_LEN;
1600 unsigned nice_len = min(c->nice_match_length, max_len);
1602 struct lzx_lru_queue queue;
1604 bt_matchfinder_init(&c->bt_mf);
1605 memset(c->hash2_tab, 0, sizeof(c->hash2_tab));
1606 next_hash = bt_matchfinder_hash_3_bytes(in_next);
1607 lzx_lru_queue_init(&queue);
1610 /* Starting a new block */
1611 const u8 * const in_block_begin = in_next;
1612 const u8 * const in_block_end =
1613 in_next + min(LZX_DIV_BLOCK_SIZE, in_end - in_next);
1615 /* Run the block through the matchfinder and cache the matches. */
1616 struct lz_match *cache_ptr = c->match_cache;
1618 struct lz_match *lz_matchptr;
1623 /* If approaching the end of the input buffer, adjust
1624 * 'max_len' and 'nice_len' accordingly. */
1625 if (unlikely(max_len > in_end - in_next)) {
1626 max_len = in_end - in_next;
1627 nice_len = min(max_len, nice_len);
1629 /* This extra check is needed to ensure that we
1630 * never output a length 2 match of the very
1631 * last two bytes with the very first two bytes,
1632 * since such a match has an offset too large to
1633 * be represented. */
1634 if (unlikely(max_len < 3)) {
1636 cache_ptr->length = 0;
1642 lz_matchptr = cache_ptr + 1;
1644 /* Check for a length 2 match. */
1645 hash2 = lz_hash_2_bytes(in_next, LZX_HASH2_ORDER);
1646 cur_match = c->hash2_tab[hash2];
1647 c->hash2_tab[hash2] = in_next - in_begin;
1648 if (cur_match != 0 &&
1649 (LZX_HASH2_ORDER == 16 ||
1650 load_u16_unaligned(&in_begin[cur_match]) ==
1651 load_u16_unaligned(in_next)))
1653 lz_matchptr->length = 2;
1654 lz_matchptr->offset = in_next - &in_begin[cur_match];
1658 /* Check for matches of length >= 3. */
1659 lz_matchptr = bt_matchfinder_get_matches(&c->bt_mf,
1665 c->max_search_depth,
1670 cache_ptr->length = lz_matchptr - (cache_ptr + 1);
1671 cache_ptr = lz_matchptr;
1674 * If there was a very long match found, then don't
1675 * cache any matches for the bytes covered by that
1676 * match. This avoids degenerate behavior when
1677 * compressing highly redundant data, where the number
1678 * of matches can be very large.
1680 * This heuristic doesn't actually hurt the compression
1681 * ratio very much. If there's a long match, then the
1682 * data must be highly compressible, so it doesn't
1683 * matter as much what we do.
1685 if (best_len >= nice_len) {
1688 if (unlikely(max_len > in_end - in_next)) {
1689 max_len = in_end - in_next;
1690 nice_len = min(max_len, nice_len);
1691 if (unlikely(max_len < 3)) {
1693 cache_ptr->length = 0;
1698 c->hash2_tab[lz_hash_2_bytes(in_next, LZX_HASH2_ORDER)] =
1700 bt_matchfinder_skip_position(&c->bt_mf,
1705 c->max_search_depth,
1708 cache_ptr->length = 0;
1710 } while (--best_len);
1712 } while (in_next < in_block_end &&
1713 likely(cache_ptr < &c->match_cache[LZX_CACHE_LENGTH]));
1715 /* We've finished running the block through the matchfinder.
1716 * Now choose a match/literal sequence and write the block. */
1718 queue = lzx_optimize_and_write_block(c, os, in_block_begin,
1719 in_next - in_block_begin,
1721 } while (in_next != in_end);
1725 * Given a pointer to the current byte sequence and the current list of recent
1726 * match offsets, find the longest repeat offset match.
1728 * If no match of at least 2 bytes is found, then return 0.
1730 * If a match of at least 2 bytes is found, then return its length and set
1731 * *rep_max_idx_ret to the index of its offset in @queue.
1734 lzx_find_longest_repeat_offset_match(const u8 * const in_next,
1735 const u32 bytes_remaining,
1736 struct lzx_lru_queue queue,
1737 unsigned *rep_max_idx_ret)
1739 STATIC_ASSERT(LZX_NUM_RECENT_OFFSETS == 3);
1740 LZX_ASSERT(bytes_remaining >= 2);
1742 const unsigned max_len = min(bytes_remaining, LZX_MAX_MATCH_LEN);
1743 const u16 next_2_bytes = load_u16_unaligned(in_next);
1745 unsigned rep_max_len;
1746 unsigned rep_max_idx;
1749 matchptr = in_next - lzx_lru_queue_pop(&queue);
1750 if (load_u16_unaligned(matchptr) == next_2_bytes)
1751 rep_max_len = lz_extend(in_next, matchptr, 2, max_len);
1756 matchptr = in_next - lzx_lru_queue_pop(&queue);
1757 if (load_u16_unaligned(matchptr) == next_2_bytes) {
1758 rep_len = lz_extend(in_next, matchptr, 2, max_len);
1759 if (rep_len > rep_max_len) {
1760 rep_max_len = rep_len;
1765 matchptr = in_next - lzx_lru_queue_pop(&queue);
1766 if (load_u16_unaligned(matchptr) == next_2_bytes) {
1767 rep_len = lz_extend(in_next, matchptr, 2, max_len);
1768 if (rep_len > rep_max_len) {
1769 rep_max_len = rep_len;
1774 *rep_max_idx_ret = rep_max_idx;
1778 /* Fast heuristic scoring for lazy parsing: how "good" is this match? */
1779 static inline unsigned
1780 lzx_explicit_offset_match_score(unsigned len, u32 adjusted_offset)
1782 unsigned score = len;
1784 if (adjusted_offset < 4096)
1787 if (adjusted_offset < 256)
1793 static inline unsigned
1794 lzx_repeat_offset_match_score(unsigned rep_len, unsigned rep_idx)
1799 /* This is the "lazy" LZX compressor. */
1801 lzx_compress_lazy(struct lzx_compressor *c, struct lzx_output_bitstream *os)
1803 const u8 * const in_begin = c->in_buffer;
1804 const u8 * in_next = in_begin;
1805 const u8 * const in_end = in_begin + c->in_nbytes;
1806 unsigned max_len = LZX_MAX_MATCH_LEN;
1807 unsigned nice_len = min(c->nice_match_length, max_len);
1808 struct lzx_lru_queue queue;
1809 u32 next_hashes[2] = {};
1811 hc_matchfinder_init(&c->hc_mf);
1812 lzx_lru_queue_init(&queue);
1815 /* Starting a new block */
1817 const u8 * const in_block_begin = in_next;
1818 const u8 * const in_block_end =
1819 in_next + min(LZX_DIV_BLOCK_SIZE, in_end - in_next);
1820 struct lzx_item *next_chosen_item = c->chosen_items;
1823 u32 cur_offset_data;
1827 u32 next_offset_data;
1828 unsigned next_score;
1829 unsigned rep_max_len;
1830 unsigned rep_max_idx;
1834 lzx_reset_symbol_frequencies(c);
1837 if (unlikely(max_len > in_end - in_next)) {
1838 max_len = in_end - in_next;
1839 nice_len = min(max_len, nice_len);
1842 /* Find the longest match at the current position. */
1844 cur_len = hc_matchfinder_longest_match(&c->hc_mf,
1850 c->max_search_depth,
1855 cur_offset >= 8192 - LZX_OFFSET_ADJUSTMENT &&
1856 cur_offset != lzx_lru_queue_R0(queue) &&
1857 cur_offset != lzx_lru_queue_R1(queue) &&
1858 cur_offset != lzx_lru_queue_R2(queue)))
1860 /* There was no match found, or the only match found
1861 * was a distant length 3 match. Output a literal. */
1862 lzx_declare_literal(c, *in_next++,
1867 if (cur_offset == lzx_lru_queue_R0(queue)) {
1869 cur_offset_data = 0;
1870 skip_len = cur_len - 1;
1871 goto choose_cur_match;
1874 cur_offset_data = cur_offset + LZX_OFFSET_ADJUSTMENT;
1875 cur_score = lzx_explicit_offset_match_score(cur_len, cur_offset_data);
1877 /* Consider a repeat offset match */
1878 rep_max_len = lzx_find_longest_repeat_offset_match(in_next,
1884 if (rep_max_len >= 3 &&
1885 (rep_score = lzx_repeat_offset_match_score(rep_max_len,
1886 rep_max_idx)) >= cur_score)
1888 cur_len = rep_max_len;
1889 cur_offset_data = rep_max_idx;
1890 skip_len = rep_max_len - 1;
1891 goto choose_cur_match;
1896 /* We have a match at the current position. */
1898 /* If we have a very long match, choose it immediately. */
1899 if (cur_len >= nice_len) {
1900 skip_len = cur_len - 1;
1901 goto choose_cur_match;
1904 /* See if there's a better match at the next position. */
1906 if (unlikely(max_len > in_end - in_next)) {
1907 max_len = in_end - in_next;
1908 nice_len = min(max_len, nice_len);
1911 next_len = hc_matchfinder_longest_match(&c->hc_mf,
1917 c->max_search_depth / 2,
1921 if (next_len <= cur_len - 2) {
1923 skip_len = cur_len - 2;
1924 goto choose_cur_match;
1927 next_offset_data = next_offset + LZX_OFFSET_ADJUSTMENT;
1928 next_score = lzx_explicit_offset_match_score(next_len, next_offset_data);
1930 rep_max_len = lzx_find_longest_repeat_offset_match(in_next,
1936 if (rep_max_len >= 3 &&
1937 (rep_score = lzx_repeat_offset_match_score(rep_max_len,
1938 rep_max_idx)) >= next_score)
1941 if (rep_score > cur_score) {
1942 /* The next match is better, and it's a
1943 * repeat offset match. */
1944 lzx_declare_literal(c, *(in_next - 2),
1946 cur_len = rep_max_len;
1947 cur_offset_data = rep_max_idx;
1948 skip_len = cur_len - 1;
1949 goto choose_cur_match;
1952 if (next_score > cur_score) {
1953 /* The next match is better, and it's an
1954 * explicit offset match. */
1955 lzx_declare_literal(c, *(in_next - 2),
1958 cur_offset_data = next_offset_data;
1959 cur_score = next_score;
1960 goto have_cur_match;
1964 /* The original match was better. */
1965 skip_len = cur_len - 2;
1968 if (cur_offset_data < LZX_NUM_RECENT_OFFSETS) {
1969 lzx_declare_repeat_offset_match(c, cur_len,
1972 queue = lzx_lru_queue_swap(queue, cur_offset_data);
1974 lzx_declare_explicit_offset_match(c, cur_len,
1975 cur_offset_data - LZX_OFFSET_ADJUSTMENT,
1977 queue = lzx_lru_queue_push(queue, cur_offset_data - LZX_OFFSET_ADJUSTMENT);
1980 hc_matchfinder_skip_positions(&c->hc_mf,
1986 in_next += skip_len;
1987 } while (in_next < in_block_end);
1989 lzx_finish_block(c, os, in_next - in_block_begin,
1990 next_chosen_item - c->chosen_items);
1991 } while (in_next != in_end);
1995 lzx_init_offset_slot_fast(struct lzx_compressor *c)
1999 for (u32 offset = 0; offset < LZX_NUM_FAST_OFFSETS; offset++) {
2001 while (offset + LZX_OFFSET_ADJUSTMENT >= lzx_offset_slot_base[slot + 1])
2004 c->offset_slot_fast[offset] = slot;
2009 lzx_get_compressor_size(size_t max_bufsize, unsigned compression_level)
2011 if (compression_level <= LZX_MAX_FAST_LEVEL) {
2012 return offsetof(struct lzx_compressor, hc_mf) +
2013 hc_matchfinder_size(max_bufsize);
2015 return offsetof(struct lzx_compressor, bt_mf) +
2016 bt_matchfinder_size(max_bufsize);
2021 lzx_get_needed_memory(size_t max_bufsize, unsigned compression_level,
2026 if (max_bufsize > LZX_MAX_WINDOW_SIZE)
2029 size += lzx_get_compressor_size(max_bufsize, compression_level);
2031 size += max_bufsize; /* in_buffer */
2036 lzx_create_compressor(size_t max_bufsize, unsigned compression_level,
2037 bool destructive, void **c_ret)
2039 unsigned window_order;
2040 struct lzx_compressor *c;
2042 window_order = lzx_get_window_order(max_bufsize);
2043 if (window_order == 0)
2044 return WIMLIB_ERR_INVALID_PARAM;
2046 c = MALLOC(lzx_get_compressor_size(max_bufsize, compression_level));
2050 c->destructive = destructive;
2052 c->num_main_syms = lzx_get_num_main_syms(window_order);
2053 c->window_order = window_order;
2055 if (!c->destructive) {
2056 c->in_buffer = MALLOC(max_bufsize);
2061 if (compression_level <= LZX_MAX_FAST_LEVEL) {
2063 /* Fast compression: Use lazy parsing. */
2065 c->impl = lzx_compress_lazy;
2066 c->max_search_depth = (36 * compression_level) / 20;
2067 c->nice_match_length = (72 * compression_level) / 20;
2069 /* lzx_compress_lazy() needs max_search_depth >= 2 because it
2070 * halves the max_search_depth when attempting a lazy match, and
2071 * max_search_depth cannot be 0. */
2072 if (c->max_search_depth < 2)
2073 c->max_search_depth = 2;
2076 /* Normal / high compression: Use near-optimal parsing. */
2078 c->impl = lzx_compress_near_optimal;
2080 /* Scale nice_match_length and max_search_depth with the
2081 * compression level. */
2082 c->max_search_depth = (24 * compression_level) / 50;
2083 c->nice_match_length = (32 * compression_level) / 50;
2085 /* Set a number of optimization passes appropriate for the
2086 * compression level. */
2088 c->num_optim_passes = 1;
2090 if (compression_level >= 45)
2091 c->num_optim_passes++;
2093 /* Use more optimization passes for higher compression levels.
2094 * But the more passes there are, the less they help --- so
2095 * don't add them linearly. */
2096 if (compression_level >= 70) {
2097 c->num_optim_passes++;
2098 if (compression_level >= 100)
2099 c->num_optim_passes++;
2100 if (compression_level >= 150)
2101 c->num_optim_passes++;
2102 if (compression_level >= 200)
2103 c->num_optim_passes++;
2104 if (compression_level >= 300)
2105 c->num_optim_passes++;
2109 /* max_search_depth == 0 is invalid. */
2110 if (c->max_search_depth < 1)
2111 c->max_search_depth = 1;
2113 if (c->nice_match_length > LZX_MAX_MATCH_LEN)
2114 c->nice_match_length = LZX_MAX_MATCH_LEN;
2116 lzx_init_offset_slot_fast(c);
2123 return WIMLIB_ERR_NOMEM;
2127 lzx_compress(const void *restrict in, size_t in_nbytes,
2128 void *restrict out, size_t out_nbytes_avail, void *restrict _c)
2130 struct lzx_compressor *c = _c;
2131 struct lzx_output_bitstream os;
2134 /* Don't bother trying to compress very small inputs. */
2135 if (in_nbytes < 100)
2138 /* Copy the input data into the internal buffer and preprocess it. */
2140 c->in_buffer = (void *)in;
2142 memcpy(c->in_buffer, in, in_nbytes);
2143 c->in_nbytes = in_nbytes;
2144 lzx_do_e8_preprocessing(c->in_buffer, in_nbytes);
2146 /* Initially, the previous Huffman codeword lengths are all zeroes. */
2148 memset(&c->codes[1].lens, 0, sizeof(struct lzx_lens));
2150 /* Initialize the output bitstream. */
2151 lzx_init_output(&os, out, out_nbytes_avail);
2153 /* Call the compression level-specific compress() function. */
2156 /* Flush the output bitstream and return the compressed size or 0. */
2157 result = lzx_flush_output(&os);
2158 if (!result && c->destructive)
2159 lzx_undo_e8_preprocessing(c->in_buffer, c->in_nbytes);
2164 lzx_free_compressor(void *_c)
2166 struct lzx_compressor *c = _c;
2168 if (!c->destructive)
2173 const struct compressor_ops lzx_compressor_ops = {
2174 .get_needed_memory = lzx_get_needed_memory,
2175 .create_compressor = lzx_create_compressor,
2176 .compress = lzx_compress,
2177 .free_compressor = lzx_free_compressor,