Age Owner Branch data TLA Line data Source code
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) 1996-2024, 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 "port/pg_bitutils.h"
76 : : #include "utils/memutils.h"
77 : :
78 : :
79 : : /*
80 : : * Maximum number of integers that can be encoded in a single Simple-8b
81 : : * codeword. (Defined here before anything else, so that we can size arrays
82 : : * using this.)
83 : : */
84 : : #define SIMPLE8B_MAX_VALUES_PER_CODEWORD 240
85 : :
86 : : /*
87 : : * Parameters for shape of the in-memory B-tree.
88 : : *
89 : : * These set the size of each internal and leaf node. They don't necessarily
90 : : * need to be the same, because the tree is just an in-memory structure.
91 : : * With the default 64, each node is about 1 kb.
92 : : *
93 : : * If you change these, you must recalculate MAX_TREE_LEVELS, too!
94 : : */
95 : : #define MAX_INTERNAL_ITEMS 64
96 : : #define MAX_LEAF_ITEMS 64
97 : :
98 : : /*
99 : : * Maximum height of the tree.
100 : : *
101 : : * MAX_TREE_ITEMS is calculated from the "fan-out" of the B-tree. The
102 : : * theoretical maximum number of items that we can store in a set is 2^64,
103 : : * so MAX_TREE_LEVELS should be set so that:
104 : : *
105 : : * MAX_LEAF_ITEMS * MAX_INTERNAL_ITEMS ^ (MAX_TREE_LEVELS - 1) >= 2^64.
106 : : *
107 : : * In practice, we'll need far fewer levels, because you will run out of
108 : : * memory long before reaching that number, but let's be conservative.
109 : : */
110 : : #define MAX_TREE_LEVELS 11
111 : :
112 : : /*
113 : : * Node structures, for the in-memory B-tree.
114 : : *
115 : : * An internal node holds a number of downlink pointers to leaf nodes, or
116 : : * to internal nodes on a lower level. For each downlink, the key value
117 : : * corresponding to the lower level node is stored in a sorted array. The
118 : : * stored key values are low keys. In other words, if the downlink has value
119 : : * X, then all items stored on that child are >= X.
120 : : *
121 : : * Each leaf node holds a number of "items", with a varying number of
122 : : * integers packed into each item. Each item consists of two 64-bit words:
123 : : * The first word holds the first integer stored in the item, in plain format.
124 : : * The second word contains between 0 and 240 more integers, packed using
125 : : * Simple-8b encoding. By storing the first integer in plain, unpacked,
126 : : * format, we can use binary search to quickly find an item that holds (or
127 : : * would hold) a particular integer. And by storing the rest in packed form,
128 : : * we still get pretty good memory density, if there are clusters of integers
129 : : * with similar values.
130 : : *
131 : : * Each leaf node also has a pointer to the next leaf node, so that the leaf
132 : : * nodes can be easily walked from beginning to end when iterating.
133 : : */
134 : : typedef struct intset_node intset_node;
135 : : typedef struct intset_leaf_node intset_leaf_node;
136 : : typedef struct intset_internal_node intset_internal_node;
137 : :
138 : : /* Common structure of both leaf and internal nodes. */
139 : : struct intset_node
140 : : {
141 : : uint16 level; /* tree level of this node */
142 : : uint16 num_items; /* number of items in this node */
143 : : };
144 : :
145 : : /* Internal node */
146 : : struct intset_internal_node
147 : : {
148 : : /* common header, must match intset_node */
149 : : uint16 level; /* >= 1 on internal nodes */
150 : : uint16 num_items;
151 : :
152 : : /*
153 : : * 'values' is an array of key values, and 'downlinks' are pointers to
154 : : * lower-level nodes, corresponding to the key values.
155 : : */
156 : : uint64 values[MAX_INTERNAL_ITEMS];
157 : : intset_node *downlinks[MAX_INTERNAL_ITEMS];
158 : : };
159 : :
160 : : /* Leaf node */
161 : : typedef struct
162 : : {
163 : : uint64 first; /* first integer in this item */
164 : : uint64 codeword; /* simple8b encoded differences from 'first' */
165 : : } leaf_item;
166 : :
167 : : #define MAX_VALUES_PER_LEAF_ITEM (1 + SIMPLE8B_MAX_VALUES_PER_CODEWORD)
168 : :
169 : : struct intset_leaf_node
170 : : {
171 : : /* common header, must match intset_node */
172 : : uint16 level; /* 0 on leafs */
173 : : uint16 num_items;
174 : :
175 : : intset_leaf_node *next; /* right sibling, if any */
176 : :
177 : : leaf_item items[MAX_LEAF_ITEMS];
178 : : };
179 : :
180 : : /*
181 : : * We buffer insertions in a simple array, before packing and inserting them
182 : : * into the B-tree. MAX_BUFFERED_VALUES sets the size of the buffer. The
183 : : * encoder assumes that it is large enough that we can always fill a leaf
184 : : * item with buffered new items. In other words, MAX_BUFFERED_VALUES must be
185 : : * larger than MAX_VALUES_PER_LEAF_ITEM. For efficiency, make it much larger.
186 : : */
187 : : #define MAX_BUFFERED_VALUES (MAX_VALUES_PER_LEAF_ITEM * 2)
188 : :
189 : : /*
190 : : * IntegerSet is the top-level object representing the set.
191 : : *
192 : : * The integers are stored in an in-memory B-tree structure, plus an array
193 : : * for newly-added integers. IntegerSet also tracks information about memory
194 : : * usage, as well as the current position when iterating the set with
195 : : * intset_begin_iterate / intset_iterate_next.
196 : : */
197 : : struct IntegerSet
198 : : {
199 : : /*
200 : : * 'context' is the memory context holding this integer set and all its
201 : : * tree nodes.
202 : : *
203 : : * 'mem_used' tracks the amount of memory used. We don't do anything with
204 : : * it in integerset.c itself, but the callers can ask for it with
205 : : * intset_memory_usage().
206 : : */
207 : : MemoryContext context;
208 : : uint64 mem_used;
209 : :
210 : : uint64 num_entries; /* total # of values in the set */
211 : : uint64 highest_value; /* highest value stored in this set */
212 : :
213 : : /*
214 : : * B-tree to hold the packed values.
215 : : *
216 : : * 'rightmost_nodes' hold pointers to the rightmost node on each level.
217 : : * rightmost_parent[0] is rightmost leaf, rightmost_parent[1] is its
218 : : * parent, and so forth, all the way up to the root. These are needed when
219 : : * adding new values. (Currently, we require that new values are added at
220 : : * the end.)
221 : : */
222 : : int num_levels; /* height of the tree */
223 : : intset_node *root; /* root node */
224 : : intset_node *rightmost_nodes[MAX_TREE_LEVELS];
225 : : intset_leaf_node *leftmost_leaf; /* leftmost leaf node */
226 : :
227 : : /*
228 : : * Holding area for new items that haven't been inserted to the tree yet.
229 : : */
230 : : uint64 buffered_values[MAX_BUFFERED_VALUES];
231 : : int num_buffered_values;
232 : :
233 : : /*
234 : : * Iterator support.
235 : : *
236 : : * 'iter_values' is an array of integers ready to be returned to the
237 : : * caller; 'iter_num_values' is the length of that array, and
238 : : * 'iter_valueno' is the next index. 'iter_node' and 'iter_itemno' point
239 : : * to the leaf node, and item within the leaf node, to get the next batch
240 : : * of values from.
241 : : *
242 : : * Normally, 'iter_values' points to 'iter_values_buf', which holds items
243 : : * decoded from a leaf item. But after we have scanned the whole B-tree,
244 : : * we iterate through all the unbuffered values, too, by pointing
245 : : * iter_values to 'buffered_values'.
246 : : */
247 : : bool iter_active; /* is iteration in progress? */
248 : :
249 : : const uint64 *iter_values;
250 : : int iter_num_values; /* number of elements in 'iter_values' */
251 : : int iter_valueno; /* next index into 'iter_values' */
252 : :
253 : : intset_leaf_node *iter_node; /* current leaf node */
254 : : int iter_itemno; /* next item in 'iter_node' to decode */
255 : :
256 : : uint64 iter_values_buf[MAX_VALUES_PER_LEAF_ITEM];
257 : : };
258 : :
259 : : /*
260 : : * Prototypes for internal functions.
261 : : */
262 : : static void intset_update_upper(IntegerSet *intset, int level,
263 : : intset_node *child, uint64 child_key);
264 : : static void intset_flush_buffered_values(IntegerSet *intset);
265 : :
266 : : static int intset_binsrch_uint64(uint64 item, uint64 *arr, int arr_elems,
267 : : bool nextkey);
268 : : static int intset_binsrch_leaf(uint64 item, leaf_item *arr, int arr_elems,
269 : : bool nextkey);
270 : :
271 : : static uint64 simple8b_encode(const uint64 *ints, int *num_encoded, uint64 base);
272 : : static int simple8b_decode(uint64 codeword, uint64 *decoded, uint64 base);
273 : : static bool simple8b_contains(uint64 codeword, uint64 key, uint64 base);
274 : :
275 : :
276 : : /*
277 : : * Create a new, initially empty, integer set.
278 : : *
279 : : * The integer set is created in the current memory context.
280 : : * We will do all subsequent allocations in the same context, too, regardless
281 : : * of which memory context is current when new integers are added to the set.
282 : : */
283 : : IntegerSet *
1850 heikki.linnakangas@i 284 :CBC 108 : intset_create(void)
285 : : {
286 : : IntegerSet *intset;
287 : :
288 : 108 : intset = (IntegerSet *) palloc(sizeof(IntegerSet));
289 : 108 : intset->context = CurrentMemoryContext;
290 : 108 : intset->mem_used = GetMemoryChunkSpace(intset);
291 : :
292 : 108 : intset->num_entries = 0;
293 : 108 : intset->highest_value = 0;
294 : :
295 : 108 : intset->num_levels = 0;
296 : 108 : intset->root = NULL;
297 : 108 : memset(intset->rightmost_nodes, 0, sizeof(intset->rightmost_nodes));
298 : 108 : intset->leftmost_leaf = NULL;
299 : :
300 : 108 : intset->num_buffered_values = 0;
301 : :
1847 tgl@sss.pgh.pa.us 302 : 108 : intset->iter_active = false;
1850 heikki.linnakangas@i 303 : 108 : intset->iter_node = NULL;
304 : 108 : intset->iter_itemno = 0;
305 : 108 : intset->iter_valueno = 0;
306 : 108 : intset->iter_num_values = 0;
1847 tgl@sss.pgh.pa.us 307 : 108 : intset->iter_values = NULL;
308 : :
1850 heikki.linnakangas@i 309 : 108 : return intset;
310 : : }
311 : :
312 : : /*
313 : : * Allocate a new node.
314 : : */
315 : : static intset_internal_node *
316 : 3377 : intset_new_internal_node(IntegerSet *intset)
317 : : {
318 : : intset_internal_node *n;
319 : :
320 : 3377 : n = (intset_internal_node *) MemoryContextAlloc(intset->context,
321 : : sizeof(intset_internal_node));
322 : 3377 : intset->mem_used += GetMemoryChunkSpace(n);
323 : :
324 : 3377 : n->level = 0; /* caller must set */
325 : 3377 : n->num_items = 0;
326 : :
327 : 3377 : return n;
328 : : }
329 : :
330 : : static intset_leaf_node *
331 : 211678 : intset_new_leaf_node(IntegerSet *intset)
332 : : {
333 : : intset_leaf_node *n;
334 : :
335 : 211678 : n = (intset_leaf_node *) MemoryContextAlloc(intset->context,
336 : : sizeof(intset_leaf_node));
337 : 211678 : intset->mem_used += GetMemoryChunkSpace(n);
338 : :
339 : 211678 : n->level = 0;
340 : 211678 : n->num_items = 0;
341 : 211678 : n->next = NULL;
342 : :
343 : 211678 : return n;
344 : : }
345 : :
346 : : /*
347 : : * Return the number of entries in the integer set.
348 : : */
349 : : uint64
350 : 62 : intset_num_entries(IntegerSet *intset)
351 : : {
352 : 62 : return intset->num_entries;
353 : : }
354 : :
355 : : /*
356 : : * Return the amount of memory used by the integer set.
357 : : */
358 : : uint64
359 : 5 : intset_memory_usage(IntegerSet *intset)
360 : : {
361 : 5 : return intset->mem_used;
362 : : }
363 : :
364 : : /*
365 : : * Add a value to the set.
366 : : *
367 : : * Values must be added in order.
368 : : */
369 : : void
370 : 163004309 : intset_add_member(IntegerSet *intset, uint64 x)
371 : : {
1847 tgl@sss.pgh.pa.us 372 [ - + ]: 163004309 : if (intset->iter_active)
1847 tgl@sss.pgh.pa.us 373 [ # # ]:UBC 0 : elog(ERROR, "cannot add new values to integer set while iteration is in progress");
374 : :
1850 heikki.linnakangas@i 375 [ + + - + ]:CBC 163004309 : if (x <= intset->highest_value && intset->num_entries > 0)
1850 heikki.linnakangas@i 376 [ # # ]:UBC 0 : elog(ERROR, "cannot add value to integer set out of order");
377 : :
1850 heikki.linnakangas@i 378 [ + + ]:CBC 163004309 : if (intset->num_buffered_values >= MAX_BUFFERED_VALUES)
379 : : {
380 : : /* Time to flush our buffer */
381 : 567003 : intset_flush_buffered_values(intset);
382 [ - + ]: 567003 : Assert(intset->num_buffered_values < MAX_BUFFERED_VALUES);
383 : : }
384 : :
385 : : /* Add it to the buffer of newly-added values */
386 : 163004309 : intset->buffered_values[intset->num_buffered_values] = x;
387 : 163004309 : intset->num_buffered_values++;
388 : 163004309 : intset->num_entries++;
389 : 163004309 : intset->highest_value = x;
390 : 163004309 : }
391 : :
392 : : /*
393 : : * Take a batch of buffered values, and pack them into the B-tree.
394 : : */
395 : : static void
396 : 567003 : intset_flush_buffered_values(IntegerSet *intset)
397 : : {
398 : 567003 : uint64 *values = intset->buffered_values;
399 : 567003 : uint64 num_values = intset->num_buffered_values;
400 : 567003 : int num_packed = 0;
401 : : intset_leaf_node *leaf;
402 : :
403 : 567003 : leaf = (intset_leaf_node *) intset->rightmost_nodes[0];
404 : :
405 : : /*
406 : : * If the tree is completely empty, create the first leaf page, which is
407 : : * also the root.
408 : : */
409 [ + + ]: 567003 : if (leaf == NULL)
410 : : {
411 : : /*
412 : : * This is the very first item in the set.
413 : : *
414 : : * Allocate root node. It's also a leaf.
415 : : */
416 : 14 : leaf = intset_new_leaf_node(intset);
417 : :
418 : 14 : intset->root = (intset_node *) leaf;
419 : 14 : intset->leftmost_leaf = leaf;
420 : 14 : intset->rightmost_nodes[0] = (intset_node *) leaf;
421 : 14 : intset->num_levels = 1;
422 : : }
423 : :
424 : : /*
425 : : * If there are less than MAX_VALUES_PER_LEAF_ITEM values in the buffer,
426 : : * stop. In most cases, we cannot encode that many values in a single
427 : : * value, but this way, the encoder doesn't have to worry about running
428 : : * out of input.
429 : : */
430 [ + + ]: 14113902 : while (num_values - num_packed >= MAX_VALUES_PER_LEAF_ITEM)
431 : : {
432 : : leaf_item item;
433 : : int num_encoded;
434 : :
435 : : /*
436 : : * Construct the next leaf item, packing as many buffered values as
437 : : * possible.
438 : : */
439 : 13546899 : item.first = values[num_packed];
440 : 13546899 : item.codeword = simple8b_encode(&values[num_packed + 1],
441 : : &num_encoded,
442 : : item.first);
443 : :
444 : : /*
445 : : * Add the item to the node, allocating a new node if the old one is
446 : : * full.
447 : : */
448 [ + + ]: 13546899 : if (leaf->num_items >= MAX_LEAF_ITEMS)
449 : : {
450 : : /* Allocate new leaf and link it to the tree */
451 : 211664 : intset_leaf_node *old_leaf = leaf;
452 : :
453 : 211664 : leaf = intset_new_leaf_node(intset);
454 : 211664 : old_leaf->next = leaf;
455 : 211664 : intset->rightmost_nodes[0] = (intset_node *) leaf;
456 : 211664 : intset_update_upper(intset, 1, (intset_node *) leaf, item.first);
457 : : }
458 : 13546899 : leaf->items[leaf->num_items++] = item;
459 : :
460 : 13546899 : num_packed += 1 + num_encoded;
461 : : }
462 : :
463 : : /*
464 : : * Move any remaining buffered values to the beginning of the array.
465 : : */
466 [ + + ]: 567003 : if (num_packed < intset->num_buffered_values)
467 : : {
468 : 542105 : memmove(&intset->buffered_values[0],
469 : 542105 : &intset->buffered_values[num_packed],
470 : 542105 : (intset->num_buffered_values - num_packed) * sizeof(uint64));
471 : : }
472 : 567003 : intset->num_buffered_values -= num_packed;
473 : 567003 : }
474 : :
475 : : /*
476 : : * Insert a downlink into parent node, after creating a new node.
477 : : *
478 : : * Recurses if the parent node is full, too.
479 : : */
480 : : static void
481 : 215016 : intset_update_upper(IntegerSet *intset, int level, intset_node *child,
482 : : uint64 child_key)
483 : : {
484 : : intset_internal_node *parent;
485 : :
486 [ - + ]: 215016 : Assert(level > 0);
487 : :
488 : : /*
489 : : * Create a new root node, if necessary.
490 : : */
491 [ + + ]: 215016 : if (level >= intset->num_levels)
492 : : {
493 : 25 : intset_node *oldroot = intset->root;
494 : : uint64 downlink_key;
495 : :
496 : : /* MAX_TREE_LEVELS should be more than enough, this shouldn't happen */
497 [ - + ]: 25 : if (intset->num_levels == MAX_TREE_LEVELS)
1850 heikki.linnakangas@i 498 [ # # ]:UBC 0 : elog(ERROR, "could not expand integer set, maximum number of levels reached");
1850 heikki.linnakangas@i 499 :CBC 25 : intset->num_levels++;
500 : :
501 : : /*
502 : : * Get the first value on the old root page, to be used as the
503 : : * downlink.
504 : : */
505 [ + + ]: 25 : if (intset->root->level == 0)
506 : 10 : downlink_key = ((intset_leaf_node *) oldroot)->items[0].first;
507 : : else
508 : 15 : downlink_key = ((intset_internal_node *) oldroot)->values[0];
509 : :
510 : 25 : parent = intset_new_internal_node(intset);
511 : 25 : parent->level = level;
512 : 25 : parent->values[0] = downlink_key;
513 : 25 : parent->downlinks[0] = oldroot;
514 : 25 : parent->num_items = 1;
515 : :
516 : 25 : intset->root = (intset_node *) parent;
517 : 25 : intset->rightmost_nodes[level] = (intset_node *) parent;
518 : : }
519 : :
520 : : /*
521 : : * Place the downlink on the parent page.
522 : : */
523 : 215016 : parent = (intset_internal_node *) intset->rightmost_nodes[level];
524 : :
525 [ + + ]: 215016 : if (parent->num_items < MAX_INTERNAL_ITEMS)
526 : : {
527 : 211664 : parent->values[parent->num_items] = child_key;
528 : 211664 : parent->downlinks[parent->num_items] = child;
529 : 211664 : parent->num_items++;
530 : : }
531 : : else
532 : : {
533 : : /*
534 : : * Doesn't fit. Allocate new parent, with the downlink as the first
535 : : * item on it, and recursively insert the downlink to the new parent
536 : : * to the grandparent.
537 : : */
538 : 3352 : parent = intset_new_internal_node(intset);
539 : 3352 : parent->level = level;
540 : 3352 : parent->values[0] = child_key;
541 : 3352 : parent->downlinks[0] = child;
542 : 3352 : parent->num_items = 1;
543 : :
544 : 3352 : intset->rightmost_nodes[level] = (intset_node *) parent;
545 : :
546 : 3352 : intset_update_upper(intset, level + 1, (intset_node *) parent, child_key);
547 : : }
548 : 215016 : }
549 : :
550 : : /*
551 : : * Does the set contain the given value?
552 : : */
553 : : bool
554 : 903572 : intset_is_member(IntegerSet *intset, uint64 x)
555 : : {
556 : : intset_node *node;
557 : : intset_leaf_node *leaf;
558 : : int level;
559 : : int itemno;
560 : : leaf_item *item;
561 : :
562 : : /*
563 : : * The value might be in the buffer of newly-added values.
564 : : */
565 [ + + + + ]: 903572 : if (intset->num_buffered_values > 0 && x >= intset->buffered_values[0])
566 : : {
567 : 101173 : itemno = intset_binsrch_uint64(x,
568 : 101173 : intset->buffered_values,
569 : : intset->num_buffered_values,
570 : : false);
571 [ + + ]: 101173 : if (itemno >= intset->num_buffered_values)
572 : 16536 : return false;
573 : : else
1847 tgl@sss.pgh.pa.us 574 : 84637 : return (intset->buffered_values[itemno] == x);
575 : : }
576 : :
577 : : /*
578 : : * Start from the root, and walk down the B-tree to find the right leaf
579 : : * node.
580 : : */
1850 heikki.linnakangas@i 581 [ + + ]: 802399 : if (!intset->root)
582 : 254 : return false;
583 : 802145 : node = intset->root;
584 [ + + ]: 3004149 : for (level = intset->num_levels - 1; level > 0; level--)
585 : : {
586 : 2202006 : intset_internal_node *n = (intset_internal_node *) node;
587 : :
588 [ - + ]: 2202006 : Assert(node->level == level);
589 : :
590 : 2202006 : itemno = intset_binsrch_uint64(x, n->values, n->num_items, true);
591 [ + + ]: 2202006 : if (itemno == 0)
592 : 2 : return false;
593 : 2202004 : node = n->downlinks[itemno - 1];
594 : : }
595 [ - + ]: 802143 : Assert(node->level == 0);
596 : 802143 : leaf = (intset_leaf_node *) node;
597 : :
598 : : /*
599 : : * Binary search to find the right item on the leaf page
600 : : */
601 : 802143 : itemno = intset_binsrch_leaf(x, leaf->items, leaf->num_items, true);
602 [ + + ]: 802143 : if (itemno == 0)
603 : 9 : return false;
604 : 802134 : item = &leaf->items[itemno - 1];
605 : :
606 : : /* Is this a match to the first value on the item? */
607 [ + + ]: 802134 : if (item->first == x)
608 : 1630 : return true;
609 [ - + ]: 800504 : Assert(x > item->first);
610 : :
611 : : /* Is it in the packed codeword? */
612 [ + + ]: 800504 : if (simple8b_contains(item->codeword, x, item->first))
613 : 150225 : return true;
614 : :
615 : 650279 : return false;
616 : : }
617 : :
618 : : /*
619 : : * Begin in-order scan through all the values.
620 : : *
621 : : * While the iteration is in-progress, you cannot add new values to the set.
622 : : */
623 : : void
624 : 64 : intset_begin_iterate(IntegerSet *intset)
625 : : {
626 : : /* Note that we allow an iteration to be abandoned midway */
1847 tgl@sss.pgh.pa.us 627 : 64 : intset->iter_active = true;
1850 heikki.linnakangas@i 628 : 64 : intset->iter_node = intset->leftmost_leaf;
629 : 64 : intset->iter_itemno = 0;
630 : 64 : intset->iter_valueno = 0;
631 : 64 : intset->iter_num_values = 0;
632 : 64 : intset->iter_values = intset->iter_values_buf;
633 : 64 : }
634 : :
635 : : /*
636 : : * Returns the next integer, when iterating.
637 : : *
638 : : * intset_begin_iterate() must be called first. intset_iterate_next() returns
639 : : * the next value in the set. Returns true, if there was another value, and
640 : : * stores the value in *next. Otherwise, returns false.
641 : : */
642 : : bool
643 : 163004052 : intset_iterate_next(IntegerSet *intset, uint64 *next)
644 : : {
1847 tgl@sss.pgh.pa.us 645 [ + - ]: 163004052 : Assert(intset->iter_active);
646 : : for (;;)
647 : : {
648 : : /* Return next iter_values[] entry if any */
1850 heikki.linnakangas@i 649 [ + + ]: 176762658 : if (intset->iter_valueno < intset->iter_num_values)
650 : : {
651 : 163004035 : *next = intset->iter_values[intset->iter_valueno++];
652 : 163004035 : return true;
653 : : }
654 : :
655 : : /* Decode next item in current leaf node, if any */
1847 tgl@sss.pgh.pa.us 656 [ + + ]: 13758623 : if (intset->iter_node &&
657 [ + + ]: 13758577 : intset->iter_itemno < intset->iter_node->num_items)
1850 heikki.linnakangas@i 658 : 13546899 : {
659 : : leaf_item *item;
660 : : int num_decoded;
661 : :
662 : 13546899 : item = &intset->iter_node->items[intset->iter_itemno++];
663 : :
1847 tgl@sss.pgh.pa.us 664 : 13546899 : intset->iter_values_buf[0] = item->first;
665 : 13546899 : num_decoded = simple8b_decode(item->codeword,
666 : : &intset->iter_values_buf[1],
667 : : item->first);
1850 heikki.linnakangas@i 668 : 13546899 : intset->iter_num_values = num_decoded + 1;
669 : 13546899 : intset->iter_valueno = 0;
670 : 13546899 : continue;
671 : : }
672 : :
673 : : /* No more items on this leaf, step to next node */
674 [ + + ]: 211724 : if (intset->iter_node)
675 : : {
676 : 211678 : intset->iter_node = intset->iter_node->next;
677 : 211678 : intset->iter_itemno = 0;
678 : 211678 : continue;
679 : : }
680 : :
681 : : /*
682 : : * We have reached the end of the B-tree. But we might still have
683 : : * some integers in the buffer of newly-added values.
684 : : */
1847 tgl@sss.pgh.pa.us 685 [ + + ]: 46 : if (intset->iter_values == (const uint64 *) intset->iter_values_buf)
686 : : {
1850 heikki.linnakangas@i 687 : 29 : intset->iter_values = intset->buffered_values;
688 : 29 : intset->iter_num_values = intset->num_buffered_values;
1847 tgl@sss.pgh.pa.us 689 : 29 : intset->iter_valueno = 0;
1850 heikki.linnakangas@i 690 : 29 : continue;
691 : : }
692 : :
693 : 17 : break;
694 : : }
695 : :
696 : : /* No more results. */
1847 tgl@sss.pgh.pa.us 697 : 17 : intset->iter_active = false;
698 : 17 : *next = 0; /* prevent uninitialized-variable warnings */
1850 heikki.linnakangas@i 699 : 17 : return false;
700 : : }
701 : :
702 : : /*
703 : : * intset_binsrch_uint64() -- search a sorted array of uint64s
704 : : *
705 : : * Returns the first position with key equal or less than the given key.
706 : : * The returned position would be the "insert" location for the given key,
707 : : * that is, the position where the new key should be inserted to.
708 : : *
709 : : * 'nextkey' affects the behavior on equal keys. If true, and there is an
710 : : * equal key in the array, this returns the position immediately after the
711 : : * equal key. If false, this returns the position of the equal key itself.
712 : : */
713 : : static int
714 : 2303179 : intset_binsrch_uint64(uint64 item, uint64 *arr, int arr_elems, bool nextkey)
715 : : {
716 : : int low,
717 : : high,
718 : : mid;
719 : :
720 : 2303179 : low = 0;
721 : 2303179 : high = arr_elems;
722 [ + + ]: 13989584 : while (high > low)
723 : : {
724 : 11686405 : mid = low + (high - low) / 2;
725 : :
726 [ + + ]: 11686405 : if (nextkey)
727 : : {
728 [ + + ]: 11227096 : if (item >= arr[mid])
729 : 5564859 : low = mid + 1;
730 : : else
731 : 5662237 : high = mid;
732 : : }
733 : : else
734 : : {
735 [ + + ]: 459309 : if (item > arr[mid])
736 : 254290 : low = mid + 1;
737 : : else
738 : 205019 : high = mid;
739 : : }
740 : : }
741 : :
742 : 2303179 : return low;
743 : : }
744 : :
745 : : /* same, but for an array of leaf items */
746 : : static int
747 : 802143 : intset_binsrch_leaf(uint64 item, leaf_item *arr, int arr_elems, bool nextkey)
748 : : {
749 : : int low,
750 : : high,
751 : : mid;
752 : :
753 : 802143 : low = 0;
754 : 802143 : high = arr_elems;
755 [ + + ]: 5626570 : while (high > low)
756 : : {
757 : 4824427 : mid = low + (high - low) / 2;
758 : :
759 [ + - ]: 4824427 : if (nextkey)
760 : : {
761 [ + + ]: 4824427 : if (item >= arr[mid].first)
762 : 2435180 : low = mid + 1;
763 : : else
764 : 2389247 : high = mid;
765 : : }
766 : : else
767 : : {
1850 heikki.linnakangas@i 768 [ # # ]:UBC 0 : if (item > arr[mid].first)
769 : 0 : low = mid + 1;
770 : : else
771 : 0 : high = mid;
772 : : }
773 : : }
774 : :
1850 heikki.linnakangas@i 775 :CBC 802143 : return low;
776 : : }
777 : :
778 : : /*
779 : : * Simple-8b encoding.
780 : : *
781 : : * The simple-8b algorithm packs between 1 and 240 integers into 64-bit words,
782 : : * called "codewords". The number of integers packed into a single codeword
783 : : * depends on the integers being packed; small integers are encoded using
784 : : * fewer bits than large integers. A single codeword can store a single
785 : : * 60-bit integer, or two 30-bit integers, for example.
786 : : *
787 : : * Since we're storing a unique, sorted, set of integers, we actually encode
788 : : * the *differences* between consecutive integers. That way, clusters of
789 : : * integers that are close to each other are packed efficiently, regardless
790 : : * of their absolute values.
791 : : *
792 : : * In Simple-8b, each codeword consists of a 4-bit selector, which indicates
793 : : * how many integers are encoded in the codeword, and the encoded integers are
794 : : * packed into the remaining 60 bits. The selector allows for 16 different
795 : : * ways of using the remaining 60 bits, called "modes". The number of integers
796 : : * packed into a single codeword in each mode is listed in the simple8b_modes
797 : : * table below. For example, consider the following codeword:
798 : : *
799 : : * 20-bit integer 20-bit integer 20-bit integer
800 : : * 1101 00000000000000010010 01111010000100100000 00000000000000010100
801 : : * ^
802 : : * selector
803 : : *
804 : : * The selector 1101 is 13 in decimal. From the modes table below, we see
805 : : * that it means that the codeword encodes three 20-bit integers. In decimal,
806 : : * those integers are 18, 500000 and 20. Because we encode deltas rather than
807 : : * absolute values, the actual values that they represent are 18, 500018 and
808 : : * 500038.
809 : : *
810 : : * Modes 0 and 1 are a bit special; they encode a run of 240 or 120 zeroes
811 : : * (which means 240 or 120 consecutive integers, since we're encoding the
812 : : * deltas between integers), without using the rest of the codeword bits
813 : : * for anything.
814 : : *
815 : : * Simple-8b cannot encode integers larger than 60 bits. Values larger than
816 : : * that are always stored in the 'first' field of a leaf item, never in the
817 : : * packed codeword. If there is a sequence of integers that are more than
818 : : * 2^60 apart, the codeword will go unused on those items. To represent that,
819 : : * we use a magic EMPTY_CODEWORD codeword value.
820 : : */
821 : : static const struct simple8b_mode
822 : : {
823 : : uint8 bits_per_int;
824 : : uint8 num_ints;
825 : : } simple8b_modes[17] =
826 : :
827 : : {
828 : : {0, 240}, /* mode 0: 240 zeroes */
829 : : {0, 120}, /* mode 1: 120 zeroes */
830 : : {1, 60}, /* mode 2: sixty 1-bit integers */
831 : : {2, 30}, /* mode 3: thirty 2-bit integers */
832 : : {3, 20}, /* mode 4: twenty 3-bit integers */
833 : : {4, 15}, /* mode 5: fifteen 4-bit integers */
834 : : {5, 12}, /* mode 6: twelve 5-bit integers */
835 : : {6, 10}, /* mode 7: ten 6-bit integers */
836 : : {7, 8}, /* mode 8: eight 7-bit integers (four bits
837 : : * are wasted) */
838 : : {8, 7}, /* mode 9: seven 8-bit integers (four bits
839 : : * are wasted) */
840 : : {10, 6}, /* mode 10: six 10-bit integers */
841 : : {12, 5}, /* mode 11: five 12-bit integers */
842 : : {15, 4}, /* mode 12: four 15-bit integers */
843 : : {20, 3}, /* mode 13: three 20-bit integers */
844 : : {30, 2}, /* mode 14: two 30-bit integers */
845 : : {60, 1}, /* mode 15: one 60-bit integer */
846 : :
847 : : {0, 0} /* sentinel value */
848 : : };
849 : :
850 : : /*
851 : : * EMPTY_CODEWORD is a special value, used to indicate "no values".
852 : : * It is used if the next value is too large to be encoded with Simple-8b.
853 : : *
854 : : * This value looks like a mode-0 codeword, but we can distinguish it
855 : : * because a regular mode-0 codeword would have zeroes in the unused bits.
856 : : */
857 : : #define EMPTY_CODEWORD UINT64CONST(0x0FFFFFFFFFFFFFFF)
858 : :
859 : : /*
860 : : * Encode a number of integers into a Simple-8b codeword.
861 : : *
862 : : * (What we actually encode are deltas between successive integers.
863 : : * "base" is the value before ints[0].)
864 : : *
865 : : * The input array must contain at least SIMPLE8B_MAX_VALUES_PER_CODEWORD
866 : : * elements, ensuring that we can produce a full codeword.
867 : : *
868 : : * Returns the encoded codeword, and sets *num_encoded to the number of
869 : : * input integers that were encoded. That can be zero, if the first delta
870 : : * is too large to be encoded.
871 : : */
872 : : static uint64
1847 tgl@sss.pgh.pa.us 873 : 13546899 : simple8b_encode(const uint64 *ints, int *num_encoded, uint64 base)
874 : : {
875 : : int selector;
876 : : int nints;
877 : : int bits;
878 : : uint64 diff;
879 : : uint64 last_val;
880 : : uint64 codeword;
881 : : int i;
882 : :
1850 heikki.linnakangas@i 883 [ - + ]: 13546899 : Assert(ints[0] > base);
884 : :
885 : : /*
886 : : * Select the "mode" to use for this codeword.
887 : : *
888 : : * In each iteration, check if the next value can be represented in the
889 : : * current mode we're considering. If it's too large, then step up the
890 : : * mode to a wider one, and repeat. If it fits, move on to the next
891 : : * integer. Repeat until the codeword is full, given the current mode.
892 : : *
893 : : * Note that we don't have any way to represent unused slots in the
894 : : * codeword, so we require each codeword to be "full". It is always
895 : : * possible to produce a full codeword unless the very first delta is too
896 : : * large to be encoded. For example, if the first delta is small but the
897 : : * second is too large to be encoded, we'll end up using the last "mode",
898 : : * which has nints == 1.
899 : : */
900 : 13546899 : selector = 0;
901 : 13546899 : nints = simple8b_modes[0].num_ints;
902 : 13546899 : bits = simple8b_modes[0].bits_per_int;
903 : 13546899 : diff = ints[0] - base - 1;
904 : 13546899 : last_val = ints[0];
1847 tgl@sss.pgh.pa.us 905 : 13546899 : i = 0; /* number of deltas we have accepted */
906 : : for (;;)
907 : : {
1850 heikki.linnakangas@i 908 [ + + ]: 345945564 : if (diff >= (UINT64CONST(1) << bits))
909 : : {
910 : : /* too large, step up to next mode */
911 : 148992971 : selector++;
912 : 148992971 : nints = simple8b_modes[selector].num_ints;
913 : 148992971 : bits = simple8b_modes[selector].bits_per_int;
914 : : /* we might already have accepted enough deltas for this mode */
915 [ + + ]: 148992971 : if (i >= nints)
916 : 6499921 : break;
917 : : }
918 : : else
919 : : {
920 : : /* accept this delta; then done if codeword is full */
921 : 196952593 : i++;
922 [ + + ]: 196952593 : if (i >= nints)
923 : 7046978 : break;
924 : : /* examine next delta */
925 [ - + ]: 189905615 : Assert(ints[i] > last_val);
926 : 189905615 : diff = ints[i] - last_val - 1;
927 : 189905615 : last_val = ints[i];
928 : : }
929 : : }
930 : :
931 [ + + ]: 13546899 : if (nints == 0)
932 : : {
933 : : /*
934 : : * The first delta is too large to be encoded with Simple-8b.
935 : : *
936 : : * If there is at least one not-too-large integer in the input, we
937 : : * will encode it using mode 15 (or a more compact mode). Hence, we
938 : : * can only get here if the *first* delta is >= 2^60.
939 : : */
940 [ - + ]: 4 : Assert(i == 0);
941 : 4 : *num_encoded = 0;
942 : 4 : return EMPTY_CODEWORD;
943 : : }
944 : :
945 : : /*
946 : : * Encode the integers using the selected mode. Note that we shift them
947 : : * into the codeword in reverse order, so that they will come out in the
948 : : * correct order in the decoder.
949 : : */
950 : 13546895 : codeword = 0;
951 [ + + ]: 13546895 : if (bits > 0)
952 : : {
1847 953 [ + + ]: 137501048 : for (i = nints - 1; i > 0; i--)
954 : : {
955 : 124003952 : diff = ints[i] - ints[i - 1] - 1;
956 : 124003952 : codeword |= diff;
1850 957 : 124003952 : codeword <<= bits;
958 : : }
1847 959 : 13497096 : diff = ints[0] - base - 1;
960 : 13497096 : codeword |= diff;
961 : : }
962 : :
963 : : /* add selector to the codeword, and return */
964 : 13546895 : codeword |= (uint64) selector << 60;
965 : :
1850 966 : 13546895 : *num_encoded = nints;
967 : 13546895 : return codeword;
968 : : }
969 : :
970 : : /*
971 : : * Decode a codeword into an array of integers.
972 : : * Returns the number of integers decoded.
973 : : */
974 : : static int
975 : 13546899 : simple8b_decode(uint64 codeword, uint64 *decoded, uint64 base)
976 : : {
1847 977 : 13546899 : int selector = (codeword >> 60);
1850 978 : 13546899 : int nints = simple8b_modes[selector].num_ints;
1847 tgl@sss.pgh.pa.us 979 : 13546899 : int bits = simple8b_modes[selector].bits_per_int;
1850 heikki.linnakangas@i 980 : 13546899 : uint64 mask = (UINT64CONST(1) << bits) - 1;
981 : : uint64 curr_value;
982 : :
983 [ + + ]: 13546899 : if (codeword == EMPTY_CODEWORD)
984 : 4 : return 0;
985 : :
1847 tgl@sss.pgh.pa.us 986 : 13546895 : curr_value = base;
1850 heikki.linnakangas@i 987 [ + + ]: 162999703 : for (int i = 0; i < nints; i++)
988 : : {
989 : 149452808 : uint64 diff = codeword & mask;
990 : :
1847 tgl@sss.pgh.pa.us 991 : 149452808 : curr_value += 1 + diff;
992 : 149452808 : decoded[i] = curr_value;
1850 heikki.linnakangas@i 993 : 149452808 : codeword >>= bits;
994 : : }
995 : 13546895 : return nints;
996 : : }
997 : :
998 : : /*
999 : : * This is very similar to simple8b_decode(), but instead of decoding all
1000 : : * the values to an array, it just checks if the given "key" is part of
1001 : : * the codeword.
1002 : : */
1003 : : static bool
1004 : 800504 : simple8b_contains(uint64 codeword, uint64 key, uint64 base)
1005 : : {
1847 1006 : 800504 : int selector = (codeword >> 60);
1850 1007 : 800504 : int nints = simple8b_modes[selector].num_ints;
1008 : 800504 : int bits = simple8b_modes[selector].bits_per_int;
1009 : :
1010 [ + + ]: 800504 : if (codeword == EMPTY_CODEWORD)
1011 : 8 : return false;
1012 : :
1013 [ + + ]: 800496 : if (bits == 0)
1014 : : {
1015 : : /* Special handling for 0-bit cases. */
1847 tgl@sss.pgh.pa.us 1016 : 99603 : return (key - base) <= nints;
1017 : : }
1018 : : else
1019 : : {
1850 heikki.linnakangas@i 1020 : 700893 : uint64 mask = (UINT64CONST(1) << bits) - 1;
1021 : : uint64 curr_value;
1022 : :
1847 tgl@sss.pgh.pa.us 1023 : 700893 : curr_value = base;
1850 heikki.linnakangas@i 1024 [ + + ]: 5212627 : for (int i = 0; i < nints; i++)
1025 : : {
1026 : 4853913 : uint64 diff = codeword & mask;
1027 : :
1847 tgl@sss.pgh.pa.us 1028 : 4853913 : curr_value += 1 + diff;
1029 : :
1850 heikki.linnakangas@i 1030 [ + + ]: 4853913 : if (curr_value >= key)
1031 : : {
1032 [ + + ]: 342179 : if (curr_value == key)
1033 : 50622 : return true;
1034 : : else
1035 : 291557 : return false;
1036 : : }
1037 : :
1038 : 4511734 : codeword >>= bits;
1039 : : }
1040 : : }
1041 : 358714 : return false;
1042 : : }
|
