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1 : : /*-------------------------------------------------------------------------
2 : : *
3 : : * integerset.c
4 : : * Data structure to hold a large set of 64-bit integers efficiently
5 : : *
6 : : * IntegerSet provides an in-memory data structure to hold a set of
7 : : * arbitrary 64-bit integers. Internally, the values are stored in a
8 : : * B-tree, with a special packed representation at the leaf level using
9 : : * the Simple-8b algorithm, which can pack clusters of nearby values
10 : : * very tightly.
11 : : *
12 : : * Memory consumption depends on the number of values stored, but also
13 : : * on how far the values are from each other. In the best case, with
14 : : * long runs of consecutive integers, memory consumption can be as low as
15 : : * 0.1 bytes per integer. In the worst case, if integers are more than
16 : : * 2^32 apart, it uses about 8 bytes per integer. In typical use, the
17 : : * consumption per integer is somewhere between those extremes, depending
18 : : * on the range of integers stored, and how "clustered" they are.
19 : : *
20 : : *
21 : : * Interface
22 : : * ---------
23 : : *
24 : : * intset_create - Create a new, empty set
25 : : * intset_add_member - Add an integer to the set
26 : : * intset_is_member - Test if an integer is in the set
27 : : * intset_begin_iterate - Begin iterating through all integers in set
28 : : * intset_iterate_next - Return next set member, if any
29 : : *
30 : : * intset_create() creates the set in the current memory context. Subsequent
31 : : * operations that add to the data structure will continue to allocate from
32 : : * that same context, even if it's not current anymore.
33 : : *
34 : : * Note that there is no function to free an integer set. If you need to do
35 : : * that, create a dedicated memory context to hold it, and destroy the memory
36 : : * context instead.
37 : : *
38 : : *
39 : : * Limitations
40 : : * -----------
41 : : *
42 : : * - Values must be added in order. (Random insertions would require
43 : : * splitting nodes, which hasn't been implemented.)
44 : : *
45 : : * - Values cannot be added while iteration is in progress.
46 : : *
47 : : * - No support for removing values.
48 : : *
49 : : * None of these limitations are fundamental to the data structure, so they
50 : : * could be lifted if needed, by writing some new code. But the current
51 : : * users of this facility don't need them.
52 : : *
53 : : *
54 : : * References
55 : : * ----------
56 : : *
57 : : * Simple-8b encoding is based on:
58 : : *
59 : : * Vo Ngoc Anh, Alistair Moffat, Index compression using 64-bit words,
60 : : * Software - Practice & Experience, v.40 n.2, p.131-147, February 2010
61 : : * (https://doi.org/10.1002/spe.948)
62 : : *
63 : : *
64 : : * Portions Copyright (c) 1996-2026, PostgreSQL Global Development Group
65 : : * Portions Copyright (c) 1994, Regents of the University of California
66 : : *
67 : : * IDENTIFICATION
68 : : * src/backend/lib/integerset.c
69 : : *
70 : : *-------------------------------------------------------------------------
71 : : */
72 : : #include "postgres.h"
73 : :
74 : : #include "lib/integerset.h"
75 : : #include "utils/memutils.h"
76 : :
77 : :
78 : : /*
79 : : * Maximum number of integers that can be encoded in a single Simple-8b
80 : : * codeword. (Defined here before anything else, so that we can size arrays
81 : : * using this.)
82 : : */
83 : : #define SIMPLE8B_MAX_VALUES_PER_CODEWORD 240
84 : :
85 : : /*
86 : : * Parameters for shape of the in-memory B-tree.
87 : : *
88 : : * These set the size of each internal and leaf node. They don't necessarily
89 : : * need to be the same, because the tree is just an in-memory structure.
90 : : * With the default 64, each node is about 1 kb.
91 : : *
92 : : * If you change these, you must recalculate MAX_TREE_LEVELS, too!
93 : : */
94 : : #define MAX_INTERNAL_ITEMS 64
95 : : #define MAX_LEAF_ITEMS 64
96 : :
97 : : /*
98 : : * Maximum height of the tree.
99 : : *
100 : : * MAX_TREE_ITEMS is calculated from the "fan-out" of the B-tree. The
101 : : * theoretical maximum number of items that we can store in a set is 2^64,
102 : : * so MAX_TREE_LEVELS should be set so that:
103 : : *
104 : : * MAX_LEAF_ITEMS * MAX_INTERNAL_ITEMS ^ (MAX_TREE_LEVELS - 1) >= 2^64.
105 : : *
106 : : * In practice, we'll need far fewer levels, because you will run out of
107 : : * memory long before reaching that number, but let's be conservative.
108 : : */
109 : : #define MAX_TREE_LEVELS 11
110 : :
111 : : /*
112 : : * Node structures, for the in-memory B-tree.
113 : : *
114 : : * An internal node holds a number of downlink pointers to leaf nodes, or
115 : : * to internal nodes on a lower level. For each downlink, the key value
116 : : * corresponding to the lower level node is stored in a sorted array. The
117 : : * stored key values are low keys. In other words, if the downlink has value
118 : : * X, then all items stored on that child are >= X.
119 : : *
120 : : * Each leaf node holds a number of "items", with a varying number of
121 : : * integers packed into each item. Each item consists of two 64-bit words:
122 : : * The first word holds the first integer stored in the item, in plain format.
123 : : * The second word contains between 0 and 240 more integers, packed using
124 : : * Simple-8b encoding. By storing the first integer in plain, unpacked,
125 : : * format, we can use binary search to quickly find an item that holds (or
126 : : * would hold) a particular integer. And by storing the rest in packed form,
127 : : * we still get pretty good memory density, if there are clusters of integers
128 : : * with similar values.
129 : : *
130 : : * Each leaf node also has a pointer to the next leaf node, so that the leaf
131 : : * nodes can be easily walked from beginning to end when iterating.
132 : : */
133 : : typedef struct intset_node intset_node;
134 : : typedef struct intset_leaf_node intset_leaf_node;
135 : : typedef struct intset_internal_node intset_internal_node;
136 : :
137 : : /* Common structure of both leaf and internal nodes. */
138 : : struct intset_node
139 : : {
140 : : uint16 level; /* tree level of this node */
141 : : uint16 num_items; /* number of items in this node */
142 : : };
143 : :
144 : : /* Internal node */
145 : : struct intset_internal_node
146 : : {
147 : : /* common header, must match intset_node */
148 : : uint16 level; /* >= 1 on internal nodes */
149 : : uint16 num_items;
150 : :
151 : : /*
152 : : * 'values' is an array of key values, and 'downlinks' are pointers to
153 : : * lower-level nodes, corresponding to the key values.
154 : : */
155 : : uint64 values[MAX_INTERNAL_ITEMS];
156 : : intset_node *downlinks[MAX_INTERNAL_ITEMS];
157 : : };
158 : :
159 : : /* Leaf node */
160 : : typedef struct
161 : : {
162 : : uint64 first; /* first integer in this item */
163 : : uint64 codeword; /* simple8b encoded differences from 'first' */
164 : : } leaf_item;
165 : :
166 : : #define MAX_VALUES_PER_LEAF_ITEM (1 + SIMPLE8B_MAX_VALUES_PER_CODEWORD)
167 : :
168 : : struct intset_leaf_node
169 : : {
170 : : /* common header, must match intset_node */
171 : : uint16 level; /* 0 on leafs */
172 : : uint16 num_items;
173 : :
174 : : intset_leaf_node *next; /* right sibling, if any */
175 : :
176 : : leaf_item items[MAX_LEAF_ITEMS];
177 : : };
178 : :
179 : : /*
180 : : * We buffer insertions in a simple array, before packing and inserting them
181 : : * into the B-tree. MAX_BUFFERED_VALUES sets the size of the buffer. The
182 : : * encoder assumes that it is large enough that we can always fill a leaf
183 : : * item with buffered new items. In other words, MAX_BUFFERED_VALUES must be
184 : : * larger than MAX_VALUES_PER_LEAF_ITEM. For efficiency, make it much larger.
185 : : */
186 : : #define MAX_BUFFERED_VALUES (MAX_VALUES_PER_LEAF_ITEM * 2)
187 : :
188 : : /*
189 : : * IntegerSet is the top-level object representing the set.
190 : : *
191 : : * The integers are stored in an in-memory B-tree structure, plus an array
192 : : * for newly-added integers. IntegerSet also tracks information about memory
193 : : * usage, as well as the current position when iterating the set with
194 : : * intset_begin_iterate / intset_iterate_next.
195 : : */
196 : : struct IntegerSet
197 : : {
198 : : /*
199 : : * 'context' is the memory context holding this integer set and all its
200 : : * tree nodes.
201 : : *
202 : : * 'mem_used' tracks the amount of memory used. We don't do anything with
203 : : * it in integerset.c itself, but the callers can ask for it with
204 : : * intset_memory_usage().
205 : : */
206 : : MemoryContext context;
207 : : uint64 mem_used;
208 : :
209 : : uint64 num_entries; /* total # of values in the set */
210 : : uint64 highest_value; /* highest value stored in this set */
211 : :
212 : : /*
213 : : * B-tree to hold the packed values.
214 : : *
215 : : * 'rightmost_nodes' hold pointers to the rightmost node on each level.
216 : : * rightmost_parent[0] is rightmost leaf, rightmost_parent[1] is its
217 : : * parent, and so forth, all the way up to the root. These are needed when
218 : : * adding new values. (Currently, we require that new values are added at
219 : : * the end.)
220 : : */
221 : : int num_levels; /* height of the tree */
222 : : intset_node *root; /* root node */
223 : : intset_node *rightmost_nodes[MAX_TREE_LEVELS];
224 : : intset_leaf_node *leftmost_leaf; /* leftmost leaf node */
225 : :
226 : : /*
227 : : * Holding area for new items that haven't been inserted to the tree yet.
228 : : */
229 : : uint64 buffered_values[MAX_BUFFERED_VALUES];
230 : : int num_buffered_values;
231 : :
232 : : /*
233 : : * Iterator support.
234 : : *
235 : : * 'iter_values' is an array of integers ready to be returned to the
236 : : * caller; 'iter_num_values' is the length of that array, and
237 : : * 'iter_valueno' is the next index. 'iter_node' and 'iter_itemno' point
238 : : * to the leaf node, and item within the leaf node, to get the next batch
239 : : * of values from.
240 : : *
241 : : * Normally, 'iter_values' points to 'iter_values_buf', which holds items
242 : : * decoded from a leaf item. But after we have scanned the whole B-tree,
243 : : * we iterate through all the unbuffered values, too, by pointing
244 : : * iter_values to 'buffered_values'.
245 : : */
246 : : bool iter_active; /* is iteration in progress? */
247 : :
248 : : const uint64 *iter_values;
249 : : int iter_num_values; /* number of elements in 'iter_values' */
250 : : int iter_valueno; /* next index into 'iter_values' */
251 : :
252 : : intset_leaf_node *iter_node; /* current leaf node */
253 : : int iter_itemno; /* next item in 'iter_node' to decode */
254 : :
255 : : uint64 iter_values_buf[MAX_VALUES_PER_LEAF_ITEM];
256 : : };
257 : :
258 : : /*
259 : : * Prototypes for internal functions.
260 : : */
261 : : static void intset_update_upper(IntegerSet *intset, int level,
262 : : intset_node *child, uint64 child_key);
263 : : static void intset_flush_buffered_values(IntegerSet *intset);
264 : :
265 : : static int intset_binsrch_uint64(uint64 item, uint64 *arr, int arr_elems,
266 : : bool nextkey);
267 : : static int intset_binsrch_leaf(uint64 item, leaf_item *arr, int arr_elems,
268 : : bool nextkey);
269 : :
270 : : static uint64 simple8b_encode(const uint64 *ints, int *num_encoded, uint64 base);
271 : : static int simple8b_decode(uint64 codeword, uint64 *decoded, uint64 base);
272 : : static bool simple8b_contains(uint64 codeword, uint64 key, uint64 base);
273 : :
274 : :
275 : : /*
276 : : * Create a new, initially empty, integer set.
277 : : *
278 : : * The integer set is created in the current memory context.
279 : : * We will do all subsequent allocations in the same context, too, regardless
280 : : * of which memory context is current when new integers are added to the set.
281 : : */
282 : : IntegerSet *
283 : 146 : intset_create(void)
284 : : {
285 : : IntegerSet *intset;
286 : :
287 : 146 : intset = palloc_object(IntegerSet);
288 : 146 : intset->context = CurrentMemoryContext;
289 : 146 : intset->mem_used = GetMemoryChunkSpace(intset);
290 : :
291 : 146 : intset->num_entries = 0;
292 : 146 : intset->highest_value = 0;
293 : :
294 : 146 : intset->num_levels = 0;
295 : 146 : intset->root = NULL;
296 : 146 : memset(intset->rightmost_nodes, 0, sizeof(intset->rightmost_nodes));
297 : 146 : intset->leftmost_leaf = NULL;
298 : :
299 : 146 : intset->num_buffered_values = 0;
300 : :
301 : 146 : intset->iter_active = false;
302 : 146 : intset->iter_node = NULL;
303 : 146 : intset->iter_itemno = 0;
304 : 146 : intset->iter_valueno = 0;
305 : 146 : intset->iter_num_values = 0;
306 : 146 : intset->iter_values = NULL;
307 : :
308 : 146 : return intset;
309 : : }
310 : :
311 : : /*
312 : : * Allocate a new node.
313 : : */
314 : : static intset_internal_node *
315 : 3377 : intset_new_internal_node(IntegerSet *intset)
316 : : {
317 : : intset_internal_node *n;
318 : :
319 : 3377 : n = (intset_internal_node *) MemoryContextAlloc(intset->context,
320 : : sizeof(intset_internal_node));
321 : 3377 : intset->mem_used += GetMemoryChunkSpace(n);
322 : :
323 : 3377 : n->level = 0; /* caller must set */
324 : 3377 : n->num_items = 0;
325 : :
326 : 3377 : return n;
327 : : }
328 : :
329 : : static intset_leaf_node *
330 : 211678 : intset_new_leaf_node(IntegerSet *intset)
331 : : {
332 : : intset_leaf_node *n;
333 : :
334 : 211678 : n = (intset_leaf_node *) MemoryContextAlloc(intset->context,
335 : : sizeof(intset_leaf_node));
336 : 211678 : intset->mem_used += GetMemoryChunkSpace(n);
337 : :
338 : 211678 : n->level = 0;
339 : 211678 : n->num_items = 0;
340 : 211678 : n->next = NULL;
341 : :
342 : 211678 : return n;
343 : : }
344 : :
345 : : /*
346 : : * Return the number of entries in the integer set.
347 : : */
348 : : uint64
349 : 81 : intset_num_entries(IntegerSet *intset)
350 : : {
351 : 81 : return intset->num_entries;
352 : : }
353 : :
354 : : /*
355 : : * Return the amount of memory used by the integer set.
356 : : */
357 : : uint64
358 : 5 : intset_memory_usage(IntegerSet *intset)
359 : : {
360 : 5 : return intset->mem_used;
361 : : }
362 : :
363 : : /*
364 : : * Add a value to the set.
365 : : *
366 : : * Values must be added in order.
367 : : */
368 : : void
369 : 163004155 : intset_add_member(IntegerSet *intset, uint64 x)
370 : : {
371 [ - + ]: 163004155 : if (intset->iter_active)
372 [ # # ]: 0 : elog(ERROR, "cannot add new values to integer set while iteration is in progress");
373 : :
374 [ + + - + ]: 163004155 : if (x <= intset->highest_value && intset->num_entries > 0)
375 [ # # ]: 0 : elog(ERROR, "cannot add value to integer set out of order");
376 : :
377 [ + + ]: 163004155 : if (intset->num_buffered_values >= MAX_BUFFERED_VALUES)
378 : : {
379 : : /* Time to flush our buffer */
380 : 567003 : intset_flush_buffered_values(intset);
381 : : Assert(intset->num_buffered_values < MAX_BUFFERED_VALUES);
382 : : }
383 : :
384 : : /* Add it to the buffer of newly-added values */
385 : 163004155 : intset->buffered_values[intset->num_buffered_values] = x;
386 : 163004155 : intset->num_buffered_values++;
387 : 163004155 : intset->num_entries++;
388 : 163004155 : intset->highest_value = x;
389 : 163004155 : }
390 : :
391 : : /*
392 : : * Take a batch of buffered values, and pack them into the B-tree.
393 : : */
394 : : static void
395 : 567003 : intset_flush_buffered_values(IntegerSet *intset)
396 : : {
397 : 567003 : uint64 *values = intset->buffered_values;
398 : 567003 : uint64 num_values = intset->num_buffered_values;
399 : 567003 : int num_packed = 0;
400 : : intset_leaf_node *leaf;
401 : :
402 : 567003 : leaf = (intset_leaf_node *) intset->rightmost_nodes[0];
403 : :
404 : : /*
405 : : * If the tree is completely empty, create the first leaf page, which is
406 : : * also the root.
407 : : */
408 [ + + ]: 567003 : if (leaf == NULL)
409 : : {
410 : : /*
411 : : * This is the very first item in the set.
412 : : *
413 : : * Allocate root node. It's also a leaf.
414 : : */
415 : 14 : leaf = intset_new_leaf_node(intset);
416 : :
417 : 14 : intset->root = (intset_node *) leaf;
418 : 14 : intset->leftmost_leaf = leaf;
419 : 14 : intset->rightmost_nodes[0] = (intset_node *) leaf;
420 : 14 : intset->num_levels = 1;
421 : : }
422 : :
423 : : /*
424 : : * If there are less than MAX_VALUES_PER_LEAF_ITEM values in the buffer,
425 : : * stop. In most cases, we cannot encode that many values in a single
426 : : * value, but this way, the encoder doesn't have to worry about running
427 : : * out of input.
428 : : */
429 [ + + ]: 14113901 : while (num_values - num_packed >= MAX_VALUES_PER_LEAF_ITEM)
430 : : {
431 : : leaf_item item;
432 : : int num_encoded;
433 : :
434 : : /*
435 : : * Construct the next leaf item, packing as many buffered values as
436 : : * possible.
437 : : */
438 : 13546898 : item.first = values[num_packed];
439 : 13546898 : item.codeword = simple8b_encode(&values[num_packed + 1],
440 : : &num_encoded,
441 : : item.first);
442 : :
443 : : /*
444 : : * Add the item to the node, allocating a new node if the old one is
445 : : * full.
446 : : */
447 [ + + ]: 13546898 : if (leaf->num_items >= MAX_LEAF_ITEMS)
448 : : {
449 : : /* Allocate new leaf and link it to the tree */
450 : 211664 : intset_leaf_node *old_leaf = leaf;
451 : :
452 : 211664 : leaf = intset_new_leaf_node(intset);
453 : 211664 : old_leaf->next = leaf;
454 : 211664 : intset->rightmost_nodes[0] = (intset_node *) leaf;
455 : 211664 : intset_update_upper(intset, 1, (intset_node *) leaf, item.first);
456 : : }
457 : 13546898 : leaf->items[leaf->num_items++] = item;
458 : :
459 : 13546898 : num_packed += 1 + num_encoded;
460 : : }
461 : :
462 : : /*
463 : : * Move any remaining buffered values to the beginning of the array.
464 : : */
465 [ + + ]: 567003 : if (num_packed < intset->num_buffered_values)
466 : : {
467 : 542105 : memmove(&intset->buffered_values[0],
468 : 542105 : &intset->buffered_values[num_packed],
469 : 542105 : (intset->num_buffered_values - num_packed) * sizeof(uint64));
470 : : }
471 : 567003 : intset->num_buffered_values -= num_packed;
472 : 567003 : }
473 : :
474 : : /*
475 : : * Insert a downlink into parent node, after creating a new node.
476 : : *
477 : : * Recurses if the parent node is full, too.
478 : : */
479 : : static void
480 : 215016 : intset_update_upper(IntegerSet *intset, int level, intset_node *child,
481 : : uint64 child_key)
482 : : {
483 : : intset_internal_node *parent;
484 : :
485 : : Assert(level > 0);
486 : :
487 : : /*
488 : : * Create a new root node, if necessary.
489 : : */
490 [ + + ]: 215016 : if (level >= intset->num_levels)
491 : : {
492 : 25 : intset_node *oldroot = intset->root;
493 : : uint64 downlink_key;
494 : :
495 : : /* MAX_TREE_LEVELS should be more than enough, this shouldn't happen */
496 [ - + ]: 25 : if (intset->num_levels == MAX_TREE_LEVELS)
497 [ # # ]: 0 : elog(ERROR, "could not expand integer set, maximum number of levels reached");
498 : 25 : intset->num_levels++;
499 : :
500 : : /*
501 : : * Get the first value on the old root page, to be used as the
502 : : * downlink.
503 : : */
504 [ + + ]: 25 : if (intset->root->level == 0)
505 : 10 : downlink_key = ((intset_leaf_node *) oldroot)->items[0].first;
506 : : else
507 : 15 : downlink_key = ((intset_internal_node *) oldroot)->values[0];
508 : :
509 : 25 : parent = intset_new_internal_node(intset);
510 : 25 : parent->level = level;
511 : 25 : parent->values[0] = downlink_key;
512 : 25 : parent->downlinks[0] = oldroot;
513 : 25 : parent->num_items = 1;
514 : :
515 : 25 : intset->root = (intset_node *) parent;
516 : 25 : intset->rightmost_nodes[level] = (intset_node *) parent;
517 : : }
518 : :
519 : : /*
520 : : * Place the downlink on the parent page.
521 : : */
522 : 215016 : parent = (intset_internal_node *) intset->rightmost_nodes[level];
523 : :
524 [ + + ]: 215016 : if (parent->num_items < MAX_INTERNAL_ITEMS)
525 : : {
526 : 211664 : parent->values[parent->num_items] = child_key;
527 : 211664 : parent->downlinks[parent->num_items] = child;
528 : 211664 : parent->num_items++;
529 : : }
530 : : else
531 : : {
532 : : /*
533 : : * Doesn't fit. Allocate new parent, with the downlink as the first
534 : : * item on it, and recursively insert the downlink to the new parent
535 : : * to the grandparent.
536 : : */
537 : 3352 : parent = intset_new_internal_node(intset);
538 : 3352 : parent->level = level;
539 : 3352 : parent->values[0] = child_key;
540 : 3352 : parent->downlinks[0] = child;
541 : 3352 : parent->num_items = 1;
542 : :
543 : 3352 : intset->rightmost_nodes[level] = (intset_node *) parent;
544 : :
545 : 3352 : intset_update_upper(intset, level + 1, (intset_node *) parent, child_key);
546 : : }
547 : 215016 : }
548 : :
549 : : /*
550 : : * Does the set contain the given value?
551 : : */
552 : : bool
553 : 903246 : intset_is_member(IntegerSet *intset, uint64 x)
554 : : {
555 : : intset_node *node;
556 : : intset_leaf_node *leaf;
557 : : int level;
558 : : int itemno;
559 : : leaf_item *item;
560 : :
561 : : /*
562 : : * The value might be in the buffer of newly-added values.
563 : : */
564 [ + + + + ]: 903246 : if (intset->num_buffered_values > 0 && x >= intset->buffered_values[0])
565 : : {
566 : 101006 : itemno = intset_binsrch_uint64(x,
567 : 101006 : intset->buffered_values,
568 : : intset->num_buffered_values,
569 : : false);
570 [ + + ]: 101006 : if (itemno >= intset->num_buffered_values)
571 : 16606 : return false;
572 : : else
573 : 84400 : return (intset->buffered_values[itemno] == x);
574 : : }
575 : :
576 : : /*
577 : : * Start from the root, and walk down the B-tree to find the right leaf
578 : : * node.
579 : : */
580 [ + + ]: 802240 : if (!intset->root)
581 : 90 : return false;
582 : 802150 : node = intset->root;
583 [ + + ]: 3004167 : for (level = intset->num_levels - 1; level > 0; level--)
584 : : {
585 : 2202019 : intset_internal_node *n = (intset_internal_node *) node;
586 : :
587 : : Assert(node->level == level);
588 : :
589 : 2202019 : itemno = intset_binsrch_uint64(x, n->values, n->num_items, true);
590 [ + + ]: 2202019 : if (itemno == 0)
591 : 2 : return false;
592 : 2202017 : node = n->downlinks[itemno - 1];
593 : : }
594 : : Assert(node->level == 0);
595 : 802148 : leaf = (intset_leaf_node *) node;
596 : :
597 : : /*
598 : : * Binary search to find the right item on the leaf page
599 : : */
600 : 802148 : itemno = intset_binsrch_leaf(x, leaf->items, leaf->num_items, true);
601 [ + + ]: 802148 : if (itemno == 0)
602 : 9 : return false;
603 : 802139 : item = &leaf->items[itemno - 1];
604 : :
605 : : /* Is this a match to the first value on the item? */
606 [ + + ]: 802139 : if (item->first == x)
607 : 1681 : return true;
608 : : Assert(x > item->first);
609 : :
610 : : /* Is it in the packed codeword? */
611 [ + + ]: 800458 : if (simple8b_contains(item->codeword, x, item->first))
612 : 149978 : return true;
613 : :
614 : 650480 : return false;
615 : : }
616 : :
617 : : /*
618 : : * Begin in-order scan through all the values.
619 : : *
620 : : * While the iteration is in-progress, you cannot add new values to the set.
621 : : */
622 : : void
623 : 83 : intset_begin_iterate(IntegerSet *intset)
624 : : {
625 : : /* Note that we allow an iteration to be abandoned midway */
626 : 83 : intset->iter_active = true;
627 : 83 : intset->iter_node = intset->leftmost_leaf;
628 : 83 : intset->iter_itemno = 0;
629 : 83 : intset->iter_valueno = 0;
630 : 83 : intset->iter_num_values = 0;
631 : 83 : intset->iter_values = intset->iter_values_buf;
632 : 83 : }
633 : :
634 : : /*
635 : : * Returns the next integer, when iterating.
636 : : *
637 : : * intset_begin_iterate() must be called first. intset_iterate_next() returns
638 : : * the next value in the set. Returns true, if there was another value, and
639 : : * stores the value in *next. Otherwise, returns false.
640 : : */
641 : : bool
642 : 163004052 : intset_iterate_next(IntegerSet *intset, uint64 *next)
643 : : {
644 : : Assert(intset->iter_active);
645 : : for (;;)
646 : : {
647 : : /* Return next iter_values[] entry if any */
648 [ + + ]: 176762657 : if (intset->iter_valueno < intset->iter_num_values)
649 : : {
650 : 163004033 : *next = intset->iter_values[intset->iter_valueno++];
651 : 163004033 : return true;
652 : : }
653 : :
654 : : /* Decode next item in current leaf node, if any */
655 [ + + ]: 13758624 : if (intset->iter_node &&
656 [ + + ]: 13758576 : intset->iter_itemno < intset->iter_node->num_items)
657 : 13546898 : {
658 : : leaf_item *item;
659 : : int num_decoded;
660 : :
661 : 13546898 : item = &intset->iter_node->items[intset->iter_itemno++];
662 : :
663 : 13546898 : intset->iter_values_buf[0] = item->first;
664 : 13546898 : num_decoded = simple8b_decode(item->codeword,
665 : : &intset->iter_values_buf[1],
666 : : item->first);
667 : 13546898 : intset->iter_num_values = num_decoded + 1;
668 : 13546898 : intset->iter_valueno = 0;
669 : 13546898 : continue;
670 : : }
671 : :
672 : : /* No more items on this leaf, step to next node */
673 [ + + ]: 211726 : if (intset->iter_node)
674 : : {
675 : 211678 : intset->iter_node = intset->iter_node->next;
676 : 211678 : intset->iter_itemno = 0;
677 : 211678 : continue;
678 : : }
679 : :
680 : : /*
681 : : * We have reached the end of the B-tree. But we might still have
682 : : * some integers in the buffer of newly-added values.
683 : : */
684 [ + + ]: 48 : if (intset->iter_values == (const uint64 *) intset->iter_values_buf)
685 : : {
686 : 29 : intset->iter_values = intset->buffered_values;
687 : 29 : intset->iter_num_values = intset->num_buffered_values;
688 : 29 : intset->iter_valueno = 0;
689 : 29 : continue;
690 : : }
691 : :
692 : 19 : break;
693 : : }
694 : :
695 : : /* No more results. */
696 : 19 : intset->iter_active = false;
697 : 19 : *next = 0; /* prevent uninitialized-variable warnings */
698 : 19 : return false;
699 : : }
700 : :
701 : : /*
702 : : * intset_binsrch_uint64() -- search a sorted array of uint64s
703 : : *
704 : : * Returns the first position with key equal or less than the given key.
705 : : * The returned position would be the "insert" location for the given key,
706 : : * that is, the position where the new key should be inserted to.
707 : : *
708 : : * 'nextkey' affects the behavior on equal keys. If true, and there is an
709 : : * equal key in the array, this returns the position immediately after the
710 : : * equal key. If false, this returns the position of the equal key itself.
711 : : */
712 : : static int
713 : 2303025 : intset_binsrch_uint64(uint64 item, uint64 *arr, int arr_elems, bool nextkey)
714 : : {
715 : : int low,
716 : : high,
717 : : mid;
718 : :
719 : 2303025 : low = 0;
720 : 2303025 : high = arr_elems;
721 [ + + ]: 13987736 : while (high > low)
722 : : {
723 : 11684711 : mid = low + (high - low) / 2;
724 : :
725 [ + + ]: 11684711 : if (nextkey)
726 : : {
727 [ + + ]: 11226639 : if (item >= arr[mid])
728 : 5569415 : low = mid + 1;
729 : : else
730 : 5657224 : high = mid;
731 : : }
732 : : else
733 : : {
734 [ + + ]: 458072 : if (item > arr[mid])
735 : 253540 : low = mid + 1;
736 : : else
737 : 204532 : high = mid;
738 : : }
739 : : }
740 : :
741 : 2303025 : return low;
742 : : }
743 : :
744 : : /* same, but for an array of leaf items */
745 : : static int
746 : 802148 : intset_binsrch_leaf(uint64 item, leaf_item *arr, int arr_elems, bool nextkey)
747 : : {
748 : : int low,
749 : : high,
750 : : mid;
751 : :
752 : 802148 : low = 0;
753 : 802148 : high = arr_elems;
754 [ + + ]: 5626555 : while (high > low)
755 : : {
756 : 4824407 : mid = low + (high - low) / 2;
757 : :
758 [ + - ]: 4824407 : if (nextkey)
759 : : {
760 [ + + ]: 4824407 : if (item >= arr[mid].first)
761 : 2436370 : low = mid + 1;
762 : : else
763 : 2388037 : high = mid;
764 : : }
765 : : else
766 : : {
767 [ # # ]: 0 : if (item > arr[mid].first)
768 : 0 : low = mid + 1;
769 : : else
770 : 0 : high = mid;
771 : : }
772 : : }
773 : :
774 : 802148 : return low;
775 : : }
776 : :
777 : : /*
778 : : * Simple-8b encoding.
779 : : *
780 : : * The simple-8b algorithm packs between 1 and 240 integers into 64-bit words,
781 : : * called "codewords". The number of integers packed into a single codeword
782 : : * depends on the integers being packed; small integers are encoded using
783 : : * fewer bits than large integers. A single codeword can store a single
784 : : * 60-bit integer, or two 30-bit integers, for example.
785 : : *
786 : : * Since we're storing a unique, sorted, set of integers, we actually encode
787 : : * the *differences* between consecutive integers. That way, clusters of
788 : : * integers that are close to each other are packed efficiently, regardless
789 : : * of their absolute values.
790 : : *
791 : : * In Simple-8b, each codeword consists of a 4-bit selector, which indicates
792 : : * how many integers are encoded in the codeword, and the encoded integers are
793 : : * packed into the remaining 60 bits. The selector allows for 16 different
794 : : * ways of using the remaining 60 bits, called "modes". The number of integers
795 : : * packed into a single codeword in each mode is listed in the simple8b_modes
796 : : * table below. For example, consider the following codeword:
797 : : *
798 : : * 20-bit integer 20-bit integer 20-bit integer
799 : : * 1101 00000000000000010010 01111010000100100000 00000000000000010100
800 : : * ^
801 : : * selector
802 : : *
803 : : * The selector 1101 is 13 in decimal. From the modes table below, we see
804 : : * that it means that the codeword encodes three 20-bit integers. In decimal,
805 : : * those integers are 18, 500000 and 20. Because we encode deltas rather than
806 : : * absolute values, the actual values that they represent are 18, 500018 and
807 : : * 500038.
808 : : *
809 : : * Modes 0 and 1 are a bit special; they encode a run of 240 or 120 zeroes
810 : : * (which means 240 or 120 consecutive integers, since we're encoding the
811 : : * deltas between integers), without using the rest of the codeword bits
812 : : * for anything.
813 : : *
814 : : * Simple-8b cannot encode integers larger than 60 bits. Values larger than
815 : : * that are always stored in the 'first' field of a leaf item, never in the
816 : : * packed codeword. If there is a sequence of integers that are more than
817 : : * 2^60 apart, the codeword will go unused on those items. To represent that,
818 : : * we use a magic EMPTY_CODEWORD codeword value.
819 : : */
820 : : static const struct simple8b_mode
821 : : {
822 : : uint8 bits_per_int;
823 : : uint8 num_ints;
824 : : } simple8b_modes[17] =
825 : :
826 : : {
827 : : {0, 240}, /* mode 0: 240 zeroes */
828 : : {0, 120}, /* mode 1: 120 zeroes */
829 : : {1, 60}, /* mode 2: sixty 1-bit integers */
830 : : {2, 30}, /* mode 3: thirty 2-bit integers */
831 : : {3, 20}, /* mode 4: twenty 3-bit integers */
832 : : {4, 15}, /* mode 5: fifteen 4-bit integers */
833 : : {5, 12}, /* mode 6: twelve 5-bit integers */
834 : : {6, 10}, /* mode 7: ten 6-bit integers */
835 : : {7, 8}, /* mode 8: eight 7-bit integers (four bits
836 : : * are wasted) */
837 : : {8, 7}, /* mode 9: seven 8-bit integers (four bits
838 : : * are wasted) */
839 : : {10, 6}, /* mode 10: six 10-bit integers */
840 : : {12, 5}, /* mode 11: five 12-bit integers */
841 : : {15, 4}, /* mode 12: four 15-bit integers */
842 : : {20, 3}, /* mode 13: three 20-bit integers */
843 : : {30, 2}, /* mode 14: two 30-bit integers */
844 : : {60, 1}, /* mode 15: one 60-bit integer */
845 : :
846 : : {0, 0} /* sentinel value */
847 : : };
848 : :
849 : : /*
850 : : * EMPTY_CODEWORD is a special value, used to indicate "no values".
851 : : * It is used if the next value is too large to be encoded with Simple-8b.
852 : : *
853 : : * This value looks like a mode-0 codeword, but we can distinguish it
854 : : * because a regular mode-0 codeword would have zeroes in the unused bits.
855 : : */
856 : : #define EMPTY_CODEWORD UINT64CONST(0x0FFFFFFFFFFFFFFF)
857 : :
858 : : /*
859 : : * Encode a number of integers into a Simple-8b codeword.
860 : : *
861 : : * (What we actually encode are deltas between successive integers.
862 : : * "base" is the value before ints[0].)
863 : : *
864 : : * The input array must contain at least SIMPLE8B_MAX_VALUES_PER_CODEWORD
865 : : * elements, ensuring that we can produce a full codeword.
866 : : *
867 : : * Returns the encoded codeword, and sets *num_encoded to the number of
868 : : * input integers that were encoded. That can be zero, if the first delta
869 : : * is too large to be encoded.
870 : : */
871 : : static uint64
872 : 13546898 : simple8b_encode(const uint64 *ints, int *num_encoded, uint64 base)
873 : : {
874 : : int selector;
875 : : int nints;
876 : : int bits;
877 : : uint64 diff;
878 : : uint64 last_val;
879 : : uint64 codeword;
880 : : int i;
881 : :
882 : : Assert(ints[0] > base);
883 : :
884 : : /*
885 : : * Select the "mode" to use for this codeword.
886 : : *
887 : : * In each iteration, check if the next value can be represented in the
888 : : * current mode we're considering. If it's too large, then step up the
889 : : * mode to a wider one, and repeat. If it fits, move on to the next
890 : : * integer. Repeat until the codeword is full, given the current mode.
891 : : *
892 : : * Note that we don't have any way to represent unused slots in the
893 : : * codeword, so we require each codeword to be "full". It is always
894 : : * possible to produce a full codeword unless the very first delta is too
895 : : * large to be encoded. For example, if the first delta is small but the
896 : : * second is too large to be encoded, we'll end up using the last "mode",
897 : : * which has nints == 1.
898 : : */
899 : 13546898 : selector = 0;
900 : 13546898 : nints = simple8b_modes[0].num_ints;
901 : 13546898 : bits = simple8b_modes[0].bits_per_int;
902 : 13546898 : diff = ints[0] - base - 1;
903 : 13546898 : last_val = ints[0];
904 : 13546898 : i = 0; /* number of deltas we have accepted */
905 : : for (;;)
906 : : {
907 [ + + ]: 345945548 : if (diff >= (UINT64CONST(1) << bits))
908 : : {
909 : : /* too large, step up to next mode */
910 : 148992954 : selector++;
911 : 148992954 : nints = simple8b_modes[selector].num_ints;
912 : 148992954 : bits = simple8b_modes[selector].bits_per_int;
913 : : /* we might already have accepted enough deltas for this mode */
914 [ + + ]: 148992954 : if (i >= nints)
915 : 6499933 : break;
916 : : }
917 : : else
918 : : {
919 : : /* accept this delta; then done if codeword is full */
920 : 196952594 : i++;
921 [ + + ]: 196952594 : if (i >= nints)
922 : 7046965 : break;
923 : : /* examine next delta */
924 : : Assert(ints[i] > last_val);
925 : 189905629 : diff = ints[i] - last_val - 1;
926 : 189905629 : last_val = ints[i];
927 : : }
928 : : }
929 : :
930 [ + + ]: 13546898 : if (nints == 0)
931 : : {
932 : : /*
933 : : * The first delta is too large to be encoded with Simple-8b.
934 : : *
935 : : * If there is at least one not-too-large integer in the input, we
936 : : * will encode it using mode 15 (or a more compact mode). Hence, we
937 : : * can only get here if the *first* delta is >= 2^60.
938 : : */
939 : : Assert(i == 0);
940 : 4 : *num_encoded = 0;
941 : 4 : return EMPTY_CODEWORD;
942 : : }
943 : :
944 : : /*
945 : : * Encode the integers using the selected mode. Note that we shift them
946 : : * into the codeword in reverse order, so that they will come out in the
947 : : * correct order in the decoder.
948 : : */
949 : 13546894 : codeword = 0;
950 [ + + ]: 13546894 : if (bits > 0)
951 : : {
952 [ + + ]: 137501049 : for (i = nints - 1; i > 0; i--)
953 : : {
954 : 124003954 : diff = ints[i] - ints[i - 1] - 1;
955 : 124003954 : codeword |= diff;
956 : 124003954 : codeword <<= bits;
957 : : }
958 : 13497095 : diff = ints[0] - base - 1;
959 : 13497095 : codeword |= diff;
960 : : }
961 : :
962 : : /* add selector to the codeword, and return */
963 : 13546894 : codeword |= (uint64) selector << 60;
964 : :
965 : 13546894 : *num_encoded = nints;
966 : 13546894 : return codeword;
967 : : }
968 : :
969 : : /*
970 : : * Decode a codeword into an array of integers.
971 : : * Returns the number of integers decoded.
972 : : */
973 : : static int
974 : 13546898 : simple8b_decode(uint64 codeword, uint64 *decoded, uint64 base)
975 : : {
976 : 13546898 : int selector = (codeword >> 60);
977 : 13546898 : int nints = simple8b_modes[selector].num_ints;
978 : 13546898 : int bits = simple8b_modes[selector].bits_per_int;
979 : 13546898 : uint64 mask = (UINT64CONST(1) << bits) - 1;
980 : : uint64 curr_value;
981 : :
982 [ + + ]: 13546898 : if (codeword == EMPTY_CODEWORD)
983 : 4 : return 0;
984 : :
985 : 13546894 : curr_value = base;
986 [ + + ]: 162999703 : for (int i = 0; i < nints; i++)
987 : : {
988 : 149452809 : uint64 diff = codeword & mask;
989 : :
990 : 149452809 : curr_value += 1 + diff;
991 : 149452809 : decoded[i] = curr_value;
992 : 149452809 : codeword >>= bits;
993 : : }
994 : 13546894 : return nints;
995 : : }
996 : :
997 : : /*
998 : : * This is very similar to simple8b_decode(), but instead of decoding all
999 : : * the values to an array, it just checks if the given "key" is part of
1000 : : * the codeword.
1001 : : */
1002 : : static bool
1003 : 800458 : simple8b_contains(uint64 codeword, uint64 key, uint64 base)
1004 : : {
1005 : 800458 : int selector = (codeword >> 60);
1006 : 800458 : int nints = simple8b_modes[selector].num_ints;
1007 : 800458 : int bits = simple8b_modes[selector].bits_per_int;
1008 : :
1009 [ + + ]: 800458 : if (codeword == EMPTY_CODEWORD)
1010 : 8 : return false;
1011 : :
1012 [ + + ]: 800450 : if (bits == 0)
1013 : : {
1014 : : /* Special handling for 0-bit cases. */
1015 : 99564 : return (key - base) <= nints;
1016 : : }
1017 : : else
1018 : : {
1019 : 700886 : uint64 mask = (UINT64CONST(1) << bits) - 1;
1020 : : uint64 curr_value;
1021 : :
1022 : 700886 : curr_value = base;
1023 [ + + ]: 5220249 : for (int i = 0; i < nints; i++)
1024 : : {
1025 : 4861926 : uint64 diff = codeword & mask;
1026 : :
1027 : 4861926 : curr_value += 1 + diff;
1028 : :
1029 [ + + ]: 4861926 : if (curr_value >= key)
1030 : : {
1031 [ + + ]: 342563 : if (curr_value == key)
1032 : 50414 : return true;
1033 : : else
1034 : 292149 : return false;
1035 : : }
1036 : :
1037 : 4519363 : codeword >>= bits;
1038 : : }
1039 : : }
1040 : 358323 : return false;
1041 : : }
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