aboutsummaryrefslogtreecommitdiff
path: root/lib/prio_tree.c
blob: ccfd850b0dec5e5d9317801e4fdbbc54cbabecbd (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
/*
 * lib/prio_tree.c - priority search tree
 *
 * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
 *
 * This file is released under the GPL v2.
 *
 * Based on the radix priority search tree proposed by Edward M. McCreight
 * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
 *
 * 02Feb2004	Initial version
 */

#include <linux/init.h>
#include <linux/mm.h>
#include <linux/prio_tree.h>

/*
 * A clever mix of heap and radix trees forms a radix priority search tree (PST)
 * which is useful for storing intervals, e.g, we can consider a vma as a closed
 * interval of file pages [offset_begin, offset_end], and store all vmas that
 * map a file in a PST. Then, using the PST, we can answer a stabbing query,
 * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
 * given input interval X (a set of consecutive file pages), in "O(log n + m)"
 * time where 'log n' is the height of the PST, and 'm' is the number of stored
 * intervals (vmas) that overlap (map) with the input interval X (the set of
 * consecutive file pages).
 *
 * In our implementation, we store closed intervals of the form [radix_index,
 * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
 * is designed for storing intervals with unique radix indices, i.e., each
 * interval have different radix_index. However, this limitation can be easily
 * overcome by using the size, i.e., heap_index - radix_index, as part of the
 * index, so we index the tree using [(radix_index,size), heap_index].
 *
 * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
 * machine, the maximum height of a PST can be 64. We can use a balanced version
 * of the priority search tree to optimize the tree height, but the balanced
 * tree proposed by McCreight is too complex and memory-hungry for our purpose.
 */

/*
 * The following macros are used for implementing prio_tree for i_mmap
 */

#define RADIX_INDEX(vma)  ((vma)->vm_pgoff)
#define VMA_SIZE(vma)	  (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
/* avoid overflow */
#define HEAP_INDEX(vma)	  ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))


static void get_index(const struct prio_tree_root *root,
    const struct prio_tree_node *node,
    unsigned long *radix, unsigned long *heap)
{
	if (root->raw) {
		struct vm_area_struct *vma = prio_tree_entry(
		    node, struct vm_area_struct, shared.prio_tree_node);

		*radix = RADIX_INDEX(vma);
		*heap = HEAP_INDEX(vma);
	}
	else {
		*radix = node->start;
		*heap = node->last;
	}
}

static unsigned long index_bits_to_maxindex[BITS_PER_LONG];

void __init prio_tree_init(void)
{
	unsigned int i;

	for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
		index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
	index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
}

/*
 * Maximum heap_index that can be stored in a PST with index_bits bits
 */
static inline unsigned long prio_tree_maxindex(unsigned int bits)
{
	return index_bits_to_maxindex[bits - 1];
}

/*
 * Extend a priority search tree so that it can store a node with heap_index
 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
 * However, this function is used rarely and the common case performance is
 * not bad.
 */
static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
		struct prio_tree_node *node, unsigned long max_heap_index)
{
	struct prio_tree_node *first = NULL, *prev, *last = NULL;

	if (max_heap_index > prio_tree_maxindex(root->index_bits))
		root->index_bits++;

	while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
		root->index_bits++;

		if (prio_tree_empty(root))
			continue;

		if (first == NULL) {
			first = root->prio_tree_node;
			prio_tree_remove(root, root->prio_tree_node);
			INIT_PRIO_TREE_NODE(first);
			last = first;
		} else {
			prev = last;
			last = root->prio_tree_node;
			prio_tree_remove(root, root->prio_tree_node);
			INIT_PRIO_TREE_NODE(last);
			prev->left = last;
			last->parent = prev;
		}
	}

	INIT_PRIO_TREE_NODE(node);

	if (first) {
		node->left = first;
		first->parent = node;
	} else
		last = node;

	if (!prio_tree_empty(root)) {
		last->left = root->prio_tree_node;
		last->left->parent = last;
	}

	root->prio_tree_node = node;
	return node;
}

/*
 * Replace a prio_tree_node with a new node and return the old node
 */
struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
		struct prio_tree_node *old, struct prio_tree_node *node)
{
	INIT_PRIO_TREE_NODE(node);

	if (prio_tree_root(old)) {
		BUG_ON(root->prio_tree_node != old);
		/*
		 * We can reduce root->index_bits here. However, it is complex
		 * and does not help much to improve performance (IMO).
		 */
		node->parent = node;
		root->prio_tree_node = node;
	} else {
		node->parent = old->parent;
		if (old->parent->left == old)
			old->parent->left = node;
		else
			old->parent->right = node;
	}

	if (!prio_tree_left_empty(old)) {
		node->left = old->left;
		old->left->parent = node;
	}

	if (!prio_tree_right_empty(old)) {
		node->right = old->right;
		old->right->parent = node;
	}

	return old;
}

/*
 * Insert a prio_tree_node @node into a radix priority search tree @root. The
 * algorithm typically takes O(log n) time where 'log n' is the number of bits
 * required to represent the maximum heap_index. In the worst case, the algo
 * can take O((log n)^2) - check prio_tree_expand.
 *
 * If a prior node with same radix_index and heap_index is already found in
 * the tree, then returns the address of the prior node. Otherwise, inserts
 * @node into the tree and returns @node.
 */
struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
		struct prio_tree_node *node)
{
	struct prio_tree_node *cur, *res = node;
	unsigned long radix_index, heap_index;
	unsigned long r_index, h_index, index, mask;
	int size_flag = 0;

	get_index(root, node, &radix_index, &heap_index);

	if (prio_tree_empty(root) ||
			heap_index > prio_tree_maxindex(root->index_bits))
		return prio_tree_expand(root, node, heap_index);

	cur = root->prio_tree_node;
	mask = 1UL << (root->index_bits - 1);

	while (mask) {
		get_index(root, cur, &r_index, &h_index);

		if (r_index == radix_index && h_index == heap_index)
			return cur;

                if (h_index < heap_index ||
		    (h_index == heap_index && r_index > radix_index)) {
			struct prio_tree_node *tmp = node;
			node = prio_tree_replace(root, cur, node);
			cur = tmp;
			/* swap indices */
			index = r_index;
			r_index = radix_index;
			radix_index = index;
			index = h_index;
			h_index = heap_index;
			heap_index = index;
		}

		if (size_flag)
			index = heap_index - radix_index;
		else
			index = radix_index;

		if (index & mask) {
			if (prio_tree_right_empty(cur)) {
				INIT_PRIO_TREE_NODE(node);
				cur->right = node;
				node->parent = cur;
				return res;
			} else
				cur = cur->right;
		} else {
			if (prio_tree_left_empty(cur)) {
				INIT_PRIO_TREE_NODE(node);
				cur->left = node;
				node->parent = cur;
				return res;
			} else
				cur = cur->left;
		}

		mask >>= 1;

		if (!mask) {
			mask = 1UL << (BITS_PER_LONG - 1);
			size_flag = 1;
		}
	}
	/* Should not reach here */
	BUG();
	return NULL;
}

/*
 * Remove a prio_tree_node @node from a radix priority search tree @root. The
 * algorithm takes O(log n) time where 'log n' is the number of bits required
 * to represent the maximum heap_index.
 */
void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
{
	struct prio_tree_node *cur;
	unsigned long r_index, h_index_right, h_index_left;

	cur = node;

	while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
		if (!prio_tree_left_empty(cur))
			get_index(root, cur->left, &r_index, &h_index_left);
		else {
			cur = cur->right;
			continue;
		}

		if (!prio_tree_right_empty(cur))
			get_index(root, cur->right, &r_index, &h_index_right);
		else {
			cur = cur->left;
			continue;
		}

		/* both h_index_left and h_index_right cannot be 0 */
		if (h_index_left >= h_index_right)
			cur = cur->left;
		else
			cur = cur->right;
	}

	if (prio_tree_root(cur)) {
		BUG_ON(root->prio_tree_node != cur);
		__INIT_PRIO_TREE_ROOT(root, root->raw);
		return;
	}

	if (cur->parent->right == cur)
		cur->parent->right = cur->parent;
	else
		cur->parent->left = cur->parent;

	while (cur != node)
		cur = prio_tree_replace(root, cur->parent, cur);
}

/*
 * Following functions help to enumerate all prio_tree_nodes in the tree that
 * overlap with the input interval X [radix_index, heap_index]. The enumeration
 * takes O(log n + m) time where 'log n' is the height of the tree (which is
 * proportional to # of bits required to represent the maximum heap_index) and
 * 'm' is the number of prio_tree_nodes that overlap the interval X.
 */

static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
		unsigned long *r_index, unsigned long *h_index)
{
	if (prio_tree_left_empty(iter->cur))
		return NULL;

	get_index(iter->root, iter->cur->left, r_index, h_index);

	if (iter->r_index <= *h_index) {
		iter->cur = iter->cur->left;
		iter->mask >>= 1;
		if (iter->mask) {
			if (iter->size_level)
				iter->size_level++;
		} else {
			if (iter->size_level) {
				BUG_ON(!prio_tree_left_empty(iter->cur));
				BUG_ON(!prio_tree_right_empty(iter->cur));
				iter->size_level++;
				iter->mask = ULONG_MAX;
			} else {
				iter->size_level = 1;
				iter->mask = 1UL << (BITS_PER_LONG - 1);
			}
		}
		return iter->cur;
	}

	return NULL;
}

static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
		unsigned long *r_index, unsigned long *h_index)
{
	unsigned long value;

	if (prio_tree_right_empty(iter->cur))
		return NULL;

	if (iter->size_level)
		value = iter->value;
	else
		value = iter->value | iter->mask;

	if (iter->h_index < value)
		return NULL;

	get_index(iter->root, iter->cur->right, r_index, h_index);

	if (iter->r_index <= *h_index) {
		iter->cur = iter->cur->right;
		iter->mask >>= 1;
		iter->value = value;
		if (iter->mask) {
			if (iter->size_level)
				iter->size_level++;
		} else {
			if (iter->size_level) {
				BUG_ON(!prio_tree_left_empty(iter->cur));
				BUG_ON(!prio_tree_right_empty(iter->cur));
				iter->size_level++;
				iter->mask = ULONG_MAX;
			} else {
				iter->size_level = 1;
				iter->mask = 1UL << (BITS_PER_LONG - 1);
			}
		}
		return iter->cur;
	}

	return NULL;
}

static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
{
	iter->cur = iter->cur->parent;
	if (iter->mask == ULONG_MAX)
		iter->mask = 1UL;
	else if (iter->size_level == 1)
		iter->mask = 1UL;
	else
		iter->mask <<= 1;
	if (iter->size_level)
		iter->size_level--;
	if (!iter->size_level && (iter->value & iter->mask))
		iter->value ^= iter->mask;
	return iter->cur;
}

static inline int overlap(struct prio_tree_iter *iter,
		unsigned long r_index, unsigned long h_index)
{
	return iter->h_index >= r_index && iter->r_index <= h_index;
}

/*
 * prio_tree_first:
 *
 * Get the first prio_tree_node that overlaps with the interval [radix_index,
 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
 * traversal of the tree.
 */
static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
{
	struct prio_tree_root *root;
	unsigned long r_index, h_index;

	INIT_PRIO_TREE_ITER(iter);

	root = iter->root;
	if (prio_tree_empty(root))
		return NULL;

	get_index(root, root->prio_tree_node, &r_index, &h_index);

	if (iter->r_index > h_index)
		return NULL;

	iter->mask = 1UL << (root->index_bits - 1);
	iter->cur = root->prio_tree_node;

	while (1) {
		if (overlap(iter, r_index, h_index))
			return iter->cur;

		if (prio_tree_left(iter, &r_index, &h_index))
			continue;

		if (prio_tree_right(iter, &r_index, &h_index))
			continue;

		break;
	}
	return NULL;
}

/*
 * prio_tree_next:
 *
 * Get the next prio_tree_node that overlaps with the input interval in iter
 */
struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
{
	unsigned long r_index, h_index;

	if (iter->cur == NULL)
		return prio_tree_first(iter);

repeat:
	while (prio_tree_left(iter, &r_index, &h_index))
		if (overlap(iter, r_index, h_index))
			return iter->cur;

	while (!prio_tree_right(iter, &r_index, &h_index)) {
	    	while (!prio_tree_root(iter->cur) &&
				iter->cur->parent->right == iter->cur)
			prio_tree_parent(iter);

		if (prio_tree_root(iter->cur))
			return NULL;

		prio_tree_parent(iter);
	}

	if (overlap(iter, r_index, h_index))
		return iter->cur;

	goto repeat;
}