4 * Suffix array match-finder for Lempel-Ziv compression.
8 * Copyright (c) 2013, 2014 Eric Biggers. All rights reserved.
10 * Redistribution and use in source and binary forms, with or without
11 * modification, are permitted provided that the following conditions
14 * 1. Redistributions of source code must retain the above copyright
15 * notice, this list of conditions and the following disclaimer.
17 * 2. Redistributions in binary form must reproduce the above copyright
18 * notice, this list of conditions and the following disclaimer in the
19 * documentation and/or other materials provided with the distribution.
21 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
22 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
23 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
24 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE
25 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
26 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
27 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
28 * BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
29 * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
30 * OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
31 * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
34 #ifndef _WIMLIB_LZ_SARRAY_H
35 #define _WIMLIB_LZ_SARRAY_H
37 #include "wimlib/compiler.h" /* must define '_always_inline_attribute' */
38 #include "wimlib/lz.h" /* must define 'struct raw_match' and LZ_ASSERT() */
39 #include "wimlib/types.h" /* must define 'bool', 'u8', 'u16, and 'u32' */
43 /* Position type --- must be an unsigned type large enough to hold the length of
44 * longest window for which the suffix array match-finder will be used. */
45 typedef u32 lz_sarray_pos_t;
47 /* Length type --- must be an unsigned type large enough to hold the maximum
49 typedef u16 lz_sarray_len_t;
51 /* Cost type, for the user-provided match cost evaluation function. */
52 typedef lz_sarray_pos_t lz_sarray_cost_t;
54 /* Type of distances in suffix array links. A larger type would allow skipping
55 * irrelevant suffixes more quickly, which is especially helpful towards the
56 * start of the window. However, even a single byte allows skipping 255 at a
57 * time, which where it matters is already a big improvement over the
58 * alternative of searching the suffixes consecutively. */
59 typedef u8 lz_sarray_delta_t;
61 #define LZ_SARRAY_LEN_MAX ((lz_sarray_len_t)~0UL)
62 #define LZ_SARRAY_POS_MAX ((lz_sarray_pos_t)~0UL)
63 #define LZ_SARRAY_DELTA_MAX ((lz_sarray_delta_t)~0UL)
64 #define LZ_SARRAY_INFINITE_COST ((lz_sarray_cost_t)~0UL)
66 /* State of the suffix array LZ (Lempel-Ziv) match-finder.
68 * This is defined here for benefit of the inlined code. It's not intended for
69 * code outside the match-finder itself to read or write members from this
72 /* Allocated window size for the match-finder.
74 * Note: this match-finder does not store the window itself, as the
75 * suffix array (@SA) and associated arrays (@ISA, @LCP, @salink) are
76 * sufficient to find matches. This number is the maximum length of
77 * those arrays, or also the maximum window (block) size that can be
78 * passed to lz_sarray_load_window(). */
79 lz_sarray_pos_t max_window_size;
81 /* Minimum length of matches to return. */
82 lz_sarray_len_t min_match_len;
84 /* Maximum length of matches to return. */
85 lz_sarray_len_t max_match_len;
87 /* Maximum matches to consider at each position (max search depth). */
88 u32 max_matches_to_consider;
90 /* Maximum number of matches to return at each position. */
91 u32 max_matches_to_return;
93 /* Current position in the window. */
94 lz_sarray_pos_t cur_pos;
96 /* Current window size. */
97 lz_sarray_pos_t window_size;
99 /* Suffix array for the current window.
100 * This is a mapping from suffix rank to suffix position. */
103 /* Inverse suffix array for the current window.
104 * This is a mapping from suffix position to suffix rank.
105 * If 0 <= r < window_size, then ISA[SA[r]] == r. */
106 lz_sarray_pos_t *ISA;
108 /* Suffix array links.
110 * During a linear scan of the input string to find matches, this array
111 * used to keep track of which rank suffixes in the suffix array appear
112 * before the current position. Instead of searching in the original
113 * suffix array, scans for matches at a given position traverse a linked
114 * list containing (usually) only suffixes that appear before that
116 struct salink *salink;
119 /* Suffix array link. An array of these structures, one per suffix rank, is
120 * used as a replacement for the raw LCP (Longest Common Prefix) array to allow
121 * skipping over suffixes that appear later in the window and hence cannot be
122 * used as LZ77 matches. */
125 /* Temporary fields used while this structure is being
128 * Note: we want the entire `struct salink' to be only 6 bytes,
129 * even though this makes "next_initial" unaligned. */
131 lz_sarray_pos_t next_initial;
132 lz_sarray_len_t lcpnext_initial;
136 /* Intially, the length, in bytes, of the longest common
137 * prefix (LCP) between the suffix having this rank and
138 * the suffix with the the smallest larger rank that
139 * starts earlier in the window than the suffix having
140 * this rank. If no such suffix exists, this will be 0.
142 * Later, during match-finding, after the corresponding
143 * suffix has entered the LZ77 dictionary, this value
144 * may be updated by lz_sarray_update_salink() to refer
145 * instead to a lexicographically closer (but still
146 * larger) suffix that begins at a later position that
147 * has entered the LZ77 dictionary. */
148 lz_sarray_len_t lcpnext;
150 /* Initially, the length, in bytes, of the longest
151 * common prefix (LCP) between the suffix having this
152 * rank and the suffix with the the largest smaller rank
153 * that starts earlier in the window than the suffix
154 * having this rank. If no such suffix exists, this
157 * Later, during match-finding, after the corresponding
158 * suffix has entered the LZ77 dictionary, this value
159 * may be updated by lz_sarray_update_salink() to refer
160 * instead to a lexicographically closer (but still
161 * smaller) suffix that begins at a later position that
162 * has entered the LZ77 dictionary. */
163 lz_sarray_len_t lcpprev;
165 /* Distance to the suffix referred to in the description
166 * of "lcpnext" above, but capped to a maximum value to
167 * save memory; or, 0 if no such suffix exists. If the
168 * true distance was truncated, this will give the
169 * distance to the rank of a suffix that is
170 * lexicographically closer to the current suffix than
171 * the desired suffix, but appears *later* in the window
172 * and hence cannot be used as the basis for a LZ77
174 lz_sarray_delta_t dist_to_next;
176 /* Distance to the suffix referred to in the description
177 * of "lcpprev" above, but capped to a maximum value to
178 * save memory; or, 0 if no such suffix exists. If the
179 * true distance was truncated, this will give the
180 * distance to the rank of a suffix that is
181 * lexicographically closer to the current suffix than
182 * the desired suffix, but appears *later* in the window
183 * and hence cannot be used as the basis for a LZ77
185 lz_sarray_delta_t dist_to_prev;
191 /*-----------------------------------*/
192 /* Functions defined in lz_sarray.c */
193 /*-----------------------------------*/
196 lz_sarray_init(struct lz_sarray *mf,
197 lz_sarray_pos_t max_window_size,
198 lz_sarray_len_t min_match_len,
199 lz_sarray_len_t max_match_len,
200 u32 max_matches_to_consider,
201 u32 max_matches_to_return);
204 lz_sarray_get_needed_memory(lz_sarray_pos_t max_window_size);
207 lz_sarray_destroy(struct lz_sarray *mf);
210 lz_sarray_load_window(struct lz_sarray *mf, const u8 T[], lz_sarray_pos_t n);
212 /*-------------------*/
213 /* Inline functions */
214 /*-------------------*/
216 static _always_inline_attribute lz_sarray_pos_t
217 lz_sarray_get_pos(const struct lz_sarray *mf)
222 /* Advance the suffix array match-finder to the next position. */
223 static _always_inline_attribute void
224 lz_sarray_update_salink(const lz_sarray_pos_t r, struct salink link[])
226 const lz_sarray_pos_t next = r + link[r].dist_to_next;
227 const lz_sarray_pos_t prev = r - link[r].dist_to_prev;
229 if (next != r && link[r].dist_to_next < link[next].dist_to_prev) {
230 link[next].dist_to_prev = link[r].dist_to_next;
231 link[next].lcpprev = link[r].lcpnext;
234 if (prev != r && link[r].dist_to_prev < link[prev].dist_to_next) {
235 link[prev].dist_to_next = link[r].dist_to_prev;
236 link[prev].lcpnext = link[r].lcpprev;
240 /* Skip the current position in the suffix array match-finder. */
241 static _always_inline_attribute void
242 lz_sarray_skip_position(struct lz_sarray *mf)
244 LZ_ASSERT(mf->cur_pos < mf->window_size);
245 lz_sarray_update_salink(mf->ISA[mf->cur_pos++], mf->salink);
249 * Use the suffix array match-finder to retrieve a list of matches at the
252 * Returns the number of matches written into @matches. The matches are
253 * returned in decreasing order by length, and each will be of unique length
254 * between the minimum and maximum match lengths (inclusively) passed to
255 * lz_sarray_init(). Up to @max_matches_to_return (passed to lz_sarray_init())
256 * matches will be returned.
258 * @eval_match_cost is a function for evaluating the cost of a match when
259 * deciding which ones to return. It needs to be fast, and need not be exact;
260 * an implementation might simply rank matches by their offset, for example,
261 * although implementations may choose to take into account additional
262 * information such as repeat offsets.
264 static _always_inline_attribute u32
265 lz_sarray_get_matches(struct lz_sarray *mf,
266 struct raw_match matches[],
267 lz_sarray_cost_t (*eval_match_cost)
268 (lz_sarray_pos_t length,
269 lz_sarray_pos_t offset,
271 const void *eval_match_cost_ctx)
273 LZ_ASSERT(mf->cur_pos < mf->window_size);
274 const lz_sarray_pos_t i = mf->cur_pos++;
276 const lz_sarray_pos_t * const restrict SA = mf->SA;
277 const lz_sarray_pos_t * const restrict ISA = mf->ISA;
278 struct salink * const restrict link = mf->salink;
279 const u32 max_matches_to_consider = mf->max_matches_to_consider;
280 const u32 max_matches_to_return = mf->max_matches_to_return;
282 /* r = Rank of the suffix at the current position. */
283 const lz_sarray_pos_t r = ISA[i];
285 /* Prepare for searching the current position. */
286 lz_sarray_update_salink(r, link);
288 /* L = rank of next suffix to the left;
289 * R = rank of next suffix to the right;
290 * lenL = length of match between current position and the suffix with rank L;
291 * lenR = length of match between current position and the suffix with rank R.
293 * This is left and right relative to the rank of the current suffix.
294 * Since the suffixes in the suffix array are sorted, the longest
295 * matches are immediately to the left and right (using the linked list
296 * to ignore all suffixes that occur later in the window). The match
297 * length decreases the farther left and right we go. We shall keep the
298 * length on both sides in sync in order to choose the lowest-cost match
301 lz_sarray_pos_t L = r - link[r].dist_to_prev;
302 lz_sarray_pos_t R = r + link[r].dist_to_next;
303 lz_sarray_pos_t lenL = link[r].lcpprev;
304 lz_sarray_pos_t lenR = link[r].lcpnext;
306 /* nmatches = number of matches found so far. */
309 /* best_cost = cost of lowest-cost match found so far.
311 * Shorter matches that do not have a lower cost than this are
312 * discarded, since presumably it would be cheaper to output the bytes
313 * from the longer match instead. */
314 lz_sarray_cost_t best_cost = LZ_SARRAY_INFINITE_COST;
316 /* count_remaining = maximum number of possible matches remaining to be
318 u32 count_remaining = max_matches_to_consider;
320 /* pending_offset = offset of lowest-cost match found for the current
321 * length, or 0 if none found yet. */
322 lz_sarray_pos_t pending_offset = 0;
324 /* Note: some 'goto' statements are used in the remainder of this
325 * function to remove unnecessary checks and create branches that the
326 * CPU may predict better. (This function is performance critical.) */
328 if (lenL != 0 && lenL >= lenR)
336 /* Search suffixes on the left until the match length has decreased
337 * below the next match length on the right or to below the minimum
340 lz_sarray_pos_t offset;
341 lz_sarray_cost_t cost;
342 lz_sarray_pos_t old_L;
343 lz_sarray_pos_t old_lenL;
345 /* Check for hard cutoff on amount of work done. */
346 if (count_remaining-- == 0) {
347 if (pending_offset != 0) {
348 /* Save pending match. */
349 matches[nmatches++] = (struct raw_match){
351 .offset = pending_offset,
358 /* Suffix is in LZ77 dictionary. (Check was needed
359 * because the salink array caps distances to save
364 /* Save match offset if it results in lower cost. */
365 cost = (*eval_match_cost)(lenL, offset,
366 eval_match_cost_ctx);
367 if (cost < best_cost) {
369 pending_offset = offset;
373 /* Advance left to previous suffix. */
378 L -= link[L].dist_to_prev;
380 if (link[old_L].lcpprev < old_lenL) {
381 /* Match length decreased. */
383 lenL = link[old_L].lcpprev;
385 if (old_lenL > lenR) {
386 /* Neither the right side nor the left size has
387 * any more matches of length @old_lenL. If a
388 * pending match exists, save it. */
389 if (pending_offset != 0) {
390 matches[nmatches++] = (struct raw_match){
392 .offset = pending_offset,
394 if (nmatches == max_matches_to_return)
401 /* New match length on left is still at
402 * least as large as the next match
403 * length on the right: Keep extending
404 * left, unless the minimum match length
405 * would be underrun. */
412 /* Here we have lenL < lenR. Extend right.
413 * (No check for whether the minimum match length has
414 * been underrun is needed, provided that such lengths
415 * are marked as 0.) */
421 /* Search suffixes on the right until the match length has decreased to
422 * the next match length on the left or to below the minimum match
425 lz_sarray_pos_t offset;
426 lz_sarray_cost_t cost;
427 lz_sarray_pos_t old_R;
428 lz_sarray_pos_t old_lenR;
430 /* Check for hard cutoff on amount of work done. */
431 if (count_remaining-- == 0) {
432 if (pending_offset != 0) {
433 /* Save pending match. */
434 matches[nmatches++] = (struct raw_match){
436 .offset = pending_offset,
443 /* Suffix is in LZ77 dictionary. (Check was needed
444 * because the salink array caps distances to save
449 /* Save match offset if it results in lower cost. */
450 cost = (*eval_match_cost)(lenR,
452 eval_match_cost_ctx);
453 if (cost < best_cost) {
455 pending_offset = offset;
459 /* Advance right to next suffix. */
464 R += link[R].dist_to_next;
466 if (link[old_R].lcpnext < lenR) {
467 /* Match length decreased. */
469 lenR = link[old_R].lcpnext;
471 /* Neither the right side nor the left size has any more
472 * matches of length @old_lenR. If a pending match
473 * exists, save it. */
474 if (pending_offset != 0) {
475 matches[nmatches++] = (struct raw_match){
477 .offset = pending_offset,
479 if (nmatches == max_matches_to_return)
486 /* lenL >= lenR: Extend left, unless the
487 * minimum match length would be underrun, in
488 * which case we are done. */
494 /* lenR > lenL: Keep extending right.
495 * (No check for whether the minimum match length has
496 * been underrun is needed, provided that such lengths
497 * are marked as 0.) */
502 #endif /* _WIMLIB_LZ_SARRAY_H */