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1 : : /*-------------------------------------------------------------------------
2 : : *
3 : : * ts_typanalyze.c
4 : : * functions for gathering statistics from tsvector columns
5 : : *
6 : : * Portions Copyright (c) 1996-2026, PostgreSQL Global Development Group
7 : : *
8 : : *
9 : : * IDENTIFICATION
10 : : * src/backend/tsearch/ts_typanalyze.c
11 : : *
12 : : *-------------------------------------------------------------------------
13 : : */
14 : : #include "postgres.h"
15 : :
16 : : #include "catalog/pg_collation.h"
17 : : #include "catalog/pg_operator.h"
18 : : #include "commands/vacuum.h"
19 : : #include "common/hashfn.h"
20 : : #include "tsearch/ts_type.h"
21 : : #include "utils/builtins.h"
22 : : #include "varatt.h"
23 : :
24 : :
25 : : /* A hash key for lexemes */
26 : : typedef struct
27 : : {
28 : : char *lexeme; /* lexeme (not NULL terminated!) */
29 : : int length; /* its length in bytes */
30 : : } LexemeHashKey;
31 : :
32 : : /* A hash table entry for the Lossy Counting algorithm */
33 : : typedef struct
34 : : {
35 : : LexemeHashKey key; /* This is 'e' from the LC algorithm. */
36 : : int frequency; /* This is 'f'. */
37 : : int delta; /* And this is 'delta'. */
38 : : } TrackItem;
39 : :
40 : : static void compute_tsvector_stats(VacAttrStats *stats,
41 : : AnalyzeAttrFetchFunc fetchfunc,
42 : : int samplerows,
43 : : double totalrows);
44 : : static void prune_lexemes_hashtable(HTAB *lexemes_tab, int b_current);
45 : : static uint32 lexeme_hash(const void *key, Size keysize);
46 : : static int lexeme_match(const void *key1, const void *key2, Size keysize);
47 : : static int lexeme_compare(const void *key1, const void *key2);
48 : : static int trackitem_compare_frequencies_desc(const void *e1, const void *e2,
49 : : void *arg);
50 : : static int trackitem_compare_lexemes(const void *e1, const void *e2,
51 : : void *arg);
52 : :
53 : :
54 : : /*
55 : : * ts_typanalyze -- a custom typanalyze function for tsvector columns
56 : : */
57 : : Datum
58 : 1 : ts_typanalyze(PG_FUNCTION_ARGS)
59 : : {
60 : 1 : VacAttrStats *stats = (VacAttrStats *) PG_GETARG_POINTER(0);
61 : :
62 : : /* If the attstattarget column is negative, use the default value */
63 [ - + ]: 1 : if (stats->attstattarget < 0)
64 : 1 : stats->attstattarget = default_statistics_target;
65 : :
66 : 1 : stats->compute_stats = compute_tsvector_stats;
67 : : /* see comment about the choice of minrows in commands/analyze.c */
68 : 1 : stats->minrows = 300 * stats->attstattarget;
69 : :
70 : 2 : PG_RETURN_BOOL(true);
71 : 1 : }
72 : :
73 : : /*
74 : : * compute_tsvector_stats() -- compute statistics for a tsvector column
75 : : *
76 : : * This function computes statistics that are useful for determining @@
77 : : * operations' selectivity, along with the fraction of non-null rows and
78 : : * average width.
79 : : *
80 : : * Instead of finding the most common values, as we do for most datatypes,
81 : : * we're looking for the most common lexemes. This is more useful, because
82 : : * there most probably won't be any two rows with the same tsvector and thus
83 : : * the notion of a MCV is a bit bogus with this datatype. With a list of the
84 : : * most common lexemes we can do a better job at figuring out @@ selectivity.
85 : : *
86 : : * For the same reasons we assume that tsvector columns are unique when
87 : : * determining the number of distinct values.
88 : : *
89 : : * The algorithm used is Lossy Counting, as proposed in the paper "Approximate
90 : : * frequency counts over data streams" by G. S. Manku and R. Motwani, in
91 : : * Proceedings of the 28th International Conference on Very Large Data Bases,
92 : : * Hong Kong, China, August 2002, section 4.2. The paper is available at
93 : : * http://www.vldb.org/conf/2002/S10P03.pdf
94 : : *
95 : : * The Lossy Counting (aka LC) algorithm goes like this:
96 : : * Let s be the threshold frequency for an item (the minimum frequency we
97 : : * are interested in) and epsilon the error margin for the frequency. Let D
98 : : * be a set of triples (e, f, delta), where e is an element value, f is that
99 : : * element's frequency (actually, its current occurrence count) and delta is
100 : : * the maximum error in f. We start with D empty and process the elements in
101 : : * batches of size w. (The batch size is also known as "bucket size" and is
102 : : * equal to 1/epsilon.) Let the current batch number be b_current, starting
103 : : * with 1. For each element e we either increment its f count, if it's
104 : : * already in D, or insert a new triple into D with values (e, 1, b_current
105 : : * - 1). After processing each batch we prune D, by removing from it all
106 : : * elements with f + delta <= b_current. After the algorithm finishes we
107 : : * suppress all elements from D that do not satisfy f >= (s - epsilon) * N,
108 : : * where N is the total number of elements in the input. We emit the
109 : : * remaining elements with estimated frequency f/N. The LC paper proves
110 : : * that this algorithm finds all elements with true frequency at least s,
111 : : * and that no frequency is overestimated or is underestimated by more than
112 : : * epsilon. Furthermore, given reasonable assumptions about the input
113 : : * distribution, the required table size is no more than about 7 times w.
114 : : *
115 : : * We set s to be the estimated frequency of the K'th word in a natural
116 : : * language's frequency table, where K is the target number of entries in
117 : : * the MCELEM array plus an arbitrary constant, meant to reflect the fact
118 : : * that the most common words in any language would usually be stopwords
119 : : * so we will not actually see them in the input. We assume that the
120 : : * distribution of word frequencies (including the stopwords) follows Zipf's
121 : : * law with an exponent of 1.
122 : : *
123 : : * Assuming Zipfian distribution, the frequency of the K'th word is equal
124 : : * to 1/(K * H(W)) where H(n) is 1/2 + 1/3 + ... + 1/n and W is the number of
125 : : * words in the language. Putting W as one million, we get roughly 0.07/K.
126 : : * Assuming top 10 words are stopwords gives s = 0.07/(K + 10). We set
127 : : * epsilon = s/10, which gives bucket width w = (K + 10)/0.007 and
128 : : * maximum expected hashtable size of about 1000 * (K + 10).
129 : : *
130 : : * Note: in the above discussion, s, epsilon, and f/N are in terms of a
131 : : * lexeme's frequency as a fraction of all lexemes seen in the input.
132 : : * However, what we actually want to store in the finished pg_statistic
133 : : * entry is each lexeme's frequency as a fraction of all rows that it occurs
134 : : * in. Assuming that the input tsvectors are correctly constructed, no
135 : : * lexeme occurs more than once per tsvector, so the final count f is a
136 : : * correct estimate of the number of input tsvectors it occurs in, and we
137 : : * need only change the divisor from N to nonnull_cnt to get the number we
138 : : * want.
139 : : */
140 : : static void
141 : 1 : compute_tsvector_stats(VacAttrStats *stats,
142 : : AnalyzeAttrFetchFunc fetchfunc,
143 : : int samplerows,
144 : : double totalrows)
145 : : {
146 : 1 : int num_mcelem;
147 : 1 : int null_cnt = 0;
148 : 1 : double total_width = 0;
149 : :
150 : : /* This is D from the LC algorithm. */
151 : 1 : HTAB *lexemes_tab;
152 : 1 : HASHCTL hash_ctl;
153 : 1 : HASH_SEQ_STATUS scan_status;
154 : :
155 : : /* This is the current bucket number from the LC algorithm */
156 : 1 : int b_current;
157 : :
158 : : /* This is 'w' from the LC algorithm */
159 : 1 : int bucket_width;
160 : 1 : int vector_no,
161 : : lexeme_no;
162 : 1 : LexemeHashKey hash_key;
163 : :
164 : : /*
165 : : * We want statistics_target * 10 lexemes in the MCELEM array. This
166 : : * multiplier is pretty arbitrary, but is meant to reflect the fact that
167 : : * the number of individual lexeme values tracked in pg_statistic ought to
168 : : * be more than the number of values for a simple scalar column.
169 : : */
170 : 1 : num_mcelem = stats->attstattarget * 10;
171 : :
172 : : /*
173 : : * We set bucket width equal to (num_mcelem + 10) / 0.007 as per the
174 : : * comment above.
175 : : */
176 : 1 : bucket_width = (num_mcelem + 10) * 1000 / 7;
177 : :
178 : : /*
179 : : * Create the hashtable. It will be in local memory, so we don't need to
180 : : * worry about overflowing the initial size. Also we don't need to pay any
181 : : * attention to locking and memory management.
182 : : */
183 : 1 : hash_ctl.keysize = sizeof(LexemeHashKey);
184 : 1 : hash_ctl.entrysize = sizeof(TrackItem);
185 : 1 : hash_ctl.hash = lexeme_hash;
186 : 1 : hash_ctl.match = lexeme_match;
187 : 1 : hash_ctl.hcxt = CurrentMemoryContext;
188 : 1 : lexemes_tab = hash_create("Analyzed lexemes table",
189 : 1 : num_mcelem,
190 : : &hash_ctl,
191 : : HASH_ELEM | HASH_FUNCTION | HASH_COMPARE | HASH_CONTEXT);
192 : :
193 : : /* Initialize counters. */
194 : 1 : b_current = 1;
195 : 1 : lexeme_no = 0;
196 : :
197 : : /* Loop over the tsvectors. */
198 [ + + ]: 509 : for (vector_no = 0; vector_no < samplerows; vector_no++)
199 : : {
200 : 508 : Datum value;
201 : 508 : bool isnull;
202 : 508 : TSVector vector;
203 : 508 : WordEntry *curentryptr;
204 : 508 : char *lexemesptr;
205 : 508 : int j;
206 : :
207 : 508 : vacuum_delay_point(true);
208 : :
209 : 508 : value = fetchfunc(stats, vector_no, &isnull);
210 : :
211 : : /*
212 : : * Check for null/nonnull.
213 : : */
214 [ - + ]: 508 : if (isnull)
215 : : {
216 : 0 : null_cnt++;
217 : 0 : continue;
218 : : }
219 : :
220 : : /*
221 : : * Add up widths for average-width calculation. Since it's a
222 : : * tsvector, we know it's varlena. As in the regular
223 : : * compute_minimal_stats function, we use the toasted width for this
224 : : * calculation.
225 : : */
226 : 508 : total_width += VARSIZE_ANY(DatumGetPointer(value));
227 : :
228 : : /*
229 : : * Now detoast the tsvector if needed.
230 : : */
231 : 508 : vector = DatumGetTSVector(value);
232 : :
233 : : /*
234 : : * We loop through the lexemes in the tsvector and add them to our
235 : : * tracking hashtable.
236 : : */
237 : 508 : lexemesptr = STRPTR(vector);
238 : 508 : curentryptr = ARRPTR(vector);
239 [ + + ]: 29308 : for (j = 0; j < vector->size; j++)
240 : : {
241 : 28800 : TrackItem *item;
242 : 28800 : bool found;
243 : :
244 : : /*
245 : : * Construct a hash key. The key points into the (detoasted)
246 : : * tsvector value at this point, but if a new entry is created, we
247 : : * make a copy of it. This way we can free the tsvector value
248 : : * once we've processed all its lexemes.
249 : : */
250 : 28800 : hash_key.lexeme = lexemesptr + curentryptr->pos;
251 : 28800 : hash_key.length = curentryptr->len;
252 : :
253 : : /* Lookup current lexeme in hashtable, adding it if new */
254 : 28800 : item = (TrackItem *) hash_search(lexemes_tab,
255 : : &hash_key,
256 : : HASH_ENTER, &found);
257 : :
258 [ + + ]: 28800 : if (found)
259 : : {
260 : : /* The lexeme is already on the tracking list */
261 : 27659 : item->frequency++;
262 : 27659 : }
263 : : else
264 : : {
265 : : /* Initialize new tracking list element */
266 : 1141 : item->frequency = 1;
267 : 1141 : item->delta = b_current - 1;
268 : :
269 : 1141 : item->key.lexeme = palloc(hash_key.length);
270 : 1141 : memcpy(item->key.lexeme, hash_key.lexeme, hash_key.length);
271 : : }
272 : :
273 : : /* lexeme_no is the number of elements processed (ie N) */
274 : 28800 : lexeme_no++;
275 : :
276 : : /* We prune the D structure after processing each bucket */
277 [ + - ]: 28800 : if (lexeme_no % bucket_width == 0)
278 : : {
279 : 0 : prune_lexemes_hashtable(lexemes_tab, b_current);
280 : 0 : b_current++;
281 : 0 : }
282 : :
283 : : /* Advance to the next WordEntry in the tsvector */
284 : 28800 : curentryptr++;
285 : 28800 : }
286 : :
287 : : /* If the vector was toasted, free the detoasted copy. */
288 [ + + ]: 508 : if (TSVectorGetDatum(vector) != value)
289 : 64 : pfree(vector);
290 [ + - - ]: 508 : }
291 : :
292 : : /* We can only compute real stats if we found some non-null values. */
293 [ + - ]: 1 : if (null_cnt < samplerows)
294 : : {
295 : 1 : int nonnull_cnt = samplerows - null_cnt;
296 : 1 : int i;
297 : 1 : TrackItem **sort_table;
298 : 1 : TrackItem *item;
299 : 1 : int track_len;
300 : 1 : int cutoff_freq;
301 : 1 : int minfreq,
302 : : maxfreq;
303 : :
304 : 1 : stats->stats_valid = true;
305 : : /* Do the simple null-frac and average width stats */
306 : 1 : stats->stanullfrac = (double) null_cnt / (double) samplerows;
307 : 1 : stats->stawidth = total_width / (double) nonnull_cnt;
308 : :
309 : : /* Assume it's a unique column (see notes above) */
310 : 1 : stats->stadistinct = -1.0 * (1.0 - stats->stanullfrac);
311 : :
312 : : /*
313 : : * Construct an array of the interesting hashtable items, that is,
314 : : * those meeting the cutoff frequency (s - epsilon)*N. Also identify
315 : : * the maximum frequency among these items.
316 : : *
317 : : * Since epsilon = s/10 and bucket_width = 1/epsilon, the cutoff
318 : : * frequency is 9*N / bucket_width.
319 : : */
320 : 1 : cutoff_freq = 9 * lexeme_no / bucket_width;
321 : :
322 : 1 : i = hash_get_num_entries(lexemes_tab); /* surely enough space */
323 : 1 : sort_table = palloc_array(TrackItem *, i);
324 : :
325 : 1 : hash_seq_init(&scan_status, lexemes_tab);
326 : 1 : track_len = 0;
327 : 1 : maxfreq = 0;
328 [ + + ]: 1142 : while ((item = (TrackItem *) hash_seq_search(&scan_status)) != NULL)
329 : : {
330 [ + + ]: 1141 : if (item->frequency > cutoff_freq)
331 : : {
332 : 1053 : sort_table[track_len++] = item;
333 [ + + ]: 1053 : maxfreq = Max(maxfreq, item->frequency);
334 : 1053 : }
335 : : }
336 [ + - ]: 1 : Assert(track_len <= i);
337 : :
338 : : /* emit some statistics for debug purposes */
339 [ - + - + ]: 1 : elog(DEBUG3, "tsvector_stats: target # mces = %d, bucket width = %d, "
340 : : "# lexemes = %d, hashtable size = %d, usable entries = %d",
341 : : num_mcelem, bucket_width, lexeme_no, i, track_len);
342 : :
343 : : /*
344 : : * If we obtained more lexemes than we really want, get rid of those
345 : : * with least frequencies. The easiest way is to qsort the array into
346 : : * descending frequency order and truncate the array.
347 : : *
348 : : * If we did not find more elements than we want, then it is safe to
349 : : * assume that the stored MCE array will contain every element with
350 : : * frequency above the cutoff. In that case, rather than storing the
351 : : * smallest frequency we are keeping, we want to store the minimum
352 : : * frequency that would have been accepted as a valid MCE. The
353 : : * selectivity functions can assume that that is an upper bound on the
354 : : * frequency of elements not present in the array.
355 : : *
356 : : * If we found no candidate MCEs at all, we still want to record the
357 : : * cutoff frequency, since it's still valid to assume that no element
358 : : * has frequency more than that.
359 : : */
360 [ + - ]: 1 : if (num_mcelem < track_len)
361 : : {
362 : 1 : qsort_interruptible(sort_table, track_len, sizeof(TrackItem *),
363 : : trackitem_compare_frequencies_desc, NULL);
364 : : /* set minfreq to the smallest frequency we're keeping */
365 : 1 : minfreq = sort_table[num_mcelem - 1]->frequency;
366 : 1 : }
367 : : else
368 : : {
369 : 0 : num_mcelem = track_len;
370 : : /* set minfreq to the minimum frequency above the cutoff */
371 : 0 : minfreq = cutoff_freq + 1;
372 : : /* ensure maxfreq is nonzero, too */
373 [ # # ]: 0 : if (track_len == 0)
374 : 0 : maxfreq = minfreq;
375 : : }
376 : :
377 : : /* Generate MCELEM slot entry */
378 [ - + ]: 1 : if (num_mcelem >= 0)
379 : : {
380 : 1 : MemoryContext old_context;
381 : 1 : Datum *mcelem_values;
382 : 1 : float4 *mcelem_freqs;
383 : :
384 : : /*
385 : : * We want to store statistics sorted on the lexeme value using
386 : : * first length, then byte-for-byte comparison. The reason for
387 : : * doing length comparison first is that we don't care about the
388 : : * ordering so long as it's consistent, and comparing lengths
389 : : * first gives us a chance to avoid a strncmp() call.
390 : : *
391 : : * This is different from what we do with scalar statistics --
392 : : * they get sorted on frequencies. The rationale is that we
393 : : * usually search through most common elements looking for a
394 : : * specific value, so we can grab its frequency. When values are
395 : : * presorted we can employ binary search for that. See
396 : : * ts_selfuncs.c for a real usage scenario.
397 : : */
398 : 1 : qsort_interruptible(sort_table, num_mcelem, sizeof(TrackItem *),
399 : : trackitem_compare_lexemes, NULL);
400 : :
401 : : /* Must copy the target values into anl_context */
402 : 1 : old_context = MemoryContextSwitchTo(stats->anl_context);
403 : :
404 : : /*
405 : : * We sorted statistics on the lexeme value, but we want to be
406 : : * able to find out the minimal and maximal frequency without
407 : : * going through all the values. We keep those two extra
408 : : * frequencies in two extra cells in mcelem_freqs.
409 : : *
410 : : * (Note: the MCELEM statistics slot definition allows for a third
411 : : * extra number containing the frequency of nulls, but we don't
412 : : * create that for a tsvector column, since null elements aren't
413 : : * possible.)
414 : : */
415 : 1 : mcelem_values = palloc_array(Datum, num_mcelem);
416 : 1 : mcelem_freqs = palloc_array(float4, num_mcelem + 2);
417 : :
418 : : /*
419 : : * See comments above about use of nonnull_cnt as the divisor for
420 : : * the final frequency estimates.
421 : : */
422 [ + + ]: 1001 : for (i = 0; i < num_mcelem; i++)
423 : : {
424 : 1000 : TrackItem *titem = sort_table[i];
425 : :
426 : 1000 : mcelem_values[i] =
427 : 2000 : PointerGetDatum(cstring_to_text_with_len(titem->key.lexeme,
428 : 1000 : titem->key.length));
429 : 1000 : mcelem_freqs[i] = (double) titem->frequency / (double) nonnull_cnt;
430 : 1000 : }
431 : 1 : mcelem_freqs[i++] = (double) minfreq / (double) nonnull_cnt;
432 : 1 : mcelem_freqs[i] = (double) maxfreq / (double) nonnull_cnt;
433 : 1 : MemoryContextSwitchTo(old_context);
434 : :
435 : 1 : stats->stakind[0] = STATISTIC_KIND_MCELEM;
436 : 1 : stats->staop[0] = TextEqualOperator;
437 : 1 : stats->stacoll[0] = DEFAULT_COLLATION_OID;
438 : 1 : stats->stanumbers[0] = mcelem_freqs;
439 : : /* See above comment about two extra frequency fields */
440 : 1 : stats->numnumbers[0] = num_mcelem + 2;
441 : 1 : stats->stavalues[0] = mcelem_values;
442 : 1 : stats->numvalues[0] = num_mcelem;
443 : : /* We are storing text values */
444 : 1 : stats->statypid[0] = TEXTOID;
445 : 1 : stats->statyplen[0] = -1; /* typlen, -1 for varlena */
446 : 1 : stats->statypbyval[0] = false;
447 : 1 : stats->statypalign[0] = 'i';
448 : 1 : }
449 : 1 : }
450 : : else
451 : : {
452 : : /* We found only nulls; assume the column is entirely null */
453 : 0 : stats->stats_valid = true;
454 : 0 : stats->stanullfrac = 1.0;
455 : 0 : stats->stawidth = 0; /* "unknown" */
456 : 0 : stats->stadistinct = 0.0; /* "unknown" */
457 : : }
458 : :
459 : : /*
460 : : * We don't need to bother cleaning up any of our temporary palloc's. The
461 : : * hashtable should also go away, as it used a child memory context.
462 : : */
463 : 1 : }
464 : :
465 : : /*
466 : : * A function to prune the D structure from the Lossy Counting algorithm.
467 : : * Consult compute_tsvector_stats() for wider explanation.
468 : : */
469 : : static void
470 : 0 : prune_lexemes_hashtable(HTAB *lexemes_tab, int b_current)
471 : : {
472 : 0 : HASH_SEQ_STATUS scan_status;
473 : 0 : TrackItem *item;
474 : :
475 : 0 : hash_seq_init(&scan_status, lexemes_tab);
476 [ # # ]: 0 : while ((item = (TrackItem *) hash_seq_search(&scan_status)) != NULL)
477 : : {
478 [ # # ]: 0 : if (item->frequency + item->delta <= b_current)
479 : : {
480 : 0 : char *lexeme = item->key.lexeme;
481 : :
482 : 0 : if (hash_search(lexemes_tab, &item->key,
483 [ # # ]: 0 : HASH_REMOVE, NULL) == NULL)
484 [ # # # # ]: 0 : elog(ERROR, "hash table corrupted");
485 : 0 : pfree(lexeme);
486 : 0 : }
487 : : }
488 : 0 : }
489 : :
490 : : /*
491 : : * Hash functions for lexemes. They are strings, but not NULL terminated,
492 : : * so we need a special hash function.
493 : : */
494 : : static uint32
495 : 28800 : lexeme_hash(const void *key, Size keysize)
496 : : {
497 : 28800 : const LexemeHashKey *l = (const LexemeHashKey *) key;
498 : :
499 : 86400 : return DatumGetUInt32(hash_any((const unsigned char *) l->lexeme,
500 : 28800 : l->length));
501 : 28800 : }
502 : :
503 : : /*
504 : : * Matching function for lexemes, to be used in hashtable lookups.
505 : : */
506 : : static int
507 : 27659 : lexeme_match(const void *key1, const void *key2, Size keysize)
508 : : {
509 : : /* The keysize parameter is superfluous, the keys store their lengths */
510 : 27659 : return lexeme_compare(key1, key2);
511 : : }
512 : :
513 : : /*
514 : : * Comparison function for lexemes.
515 : : */
516 : : static int
517 : 37838 : lexeme_compare(const void *key1, const void *key2)
518 : : {
519 : 37838 : const LexemeHashKey *d1 = (const LexemeHashKey *) key1;
520 : 37838 : const LexemeHashKey *d2 = (const LexemeHashKey *) key2;
521 : :
522 : : /* First, compare by length */
523 [ - + ]: 37838 : if (d1->length > d2->length)
524 : 0 : return 1;
525 [ - + ]: 37838 : else if (d1->length < d2->length)
526 : 0 : return -1;
527 : : /* Lengths are equal, do a byte-by-byte comparison */
528 : 37838 : return strncmp(d1->lexeme, d2->lexeme, d1->length);
529 : 37838 : }
530 : :
531 : : /*
532 : : * Comparator for sorting TrackItems on frequencies (descending sort)
533 : : */
534 : : static int
535 : 6410 : trackitem_compare_frequencies_desc(const void *e1, const void *e2, void *arg)
536 : : {
537 : 6410 : const TrackItem *const *t1 = (const TrackItem *const *) e1;
538 : 6410 : const TrackItem *const *t2 = (const TrackItem *const *) e2;
539 : :
540 : 12820 : return (*t2)->frequency - (*t1)->frequency;
541 : 6410 : }
542 : :
543 : : /*
544 : : * Comparator for sorting TrackItems on lexemes
545 : : */
546 : : static int
547 : 10179 : trackitem_compare_lexemes(const void *e1, const void *e2, void *arg)
548 : : {
549 : 10179 : const TrackItem *const *t1 = (const TrackItem *const *) e1;
550 : 10179 : const TrackItem *const *t2 = (const TrackItem *const *) e2;
551 : :
552 : 20358 : return lexeme_compare(&(*t1)->key, &(*t2)->key);
553 : 10179 : }
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