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  1/*
  2 * lib/prio_tree.c - priority search tree
  3 *
  4 * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
  5 *
  6 * This file is released under the GPL v2.
  7 *
  8 * Based on the radix priority search tree proposed by Edward M. McCreight
  9 * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
 10 *
 11 * 02Feb2004	Initial version
 12 */
 13
 14#include <linux/init.h>
 15#include <linux/mm.h>
 16#include <linux/prio_tree.h>
 17
 18/*
 19 * A clever mix of heap and radix trees forms a radix priority search tree (PST)
 20 * which is useful for storing intervals, e.g, we can consider a vma as a closed
 21 * interval of file pages [offset_begin, offset_end], and store all vmas that
 22 * map a file in a PST. Then, using the PST, we can answer a stabbing query,
 23 * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
 24 * given input interval X (a set of consecutive file pages), in "O(log n + m)"
 25 * time where 'log n' is the height of the PST, and 'm' is the number of stored
 26 * intervals (vmas) that overlap (map) with the input interval X (the set of
 27 * consecutive file pages).
 28 *
 29 * In our implementation, we store closed intervals of the form [radix_index,
 30 * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
 31 * is designed for storing intervals with unique radix indices, i.e., each
 32 * interval have different radix_index. However, this limitation can be easily
 33 * overcome by using the size, i.e., heap_index - radix_index, as part of the
 34 * index, so we index the tree using [(radix_index,size), heap_index].
 35 *
 36 * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
 37 * machine, the maximum height of a PST can be 64. We can use a balanced version
 38 * of the priority search tree to optimize the tree height, but the balanced
 39 * tree proposed by McCreight is too complex and memory-hungry for our purpose.
 40 */
 41
 42/*
 43 * The following macros are used for implementing prio_tree for i_mmap
 44 */
 45
 46#define RADIX_INDEX(vma)  ((vma)->vm_pgoff)
 47#define VMA_SIZE(vma)	  (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
 48/* avoid overflow */
 49#define HEAP_INDEX(vma)	  ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
 50
 51
 52static void get_index(const struct prio_tree_root *root,
 53    const struct prio_tree_node *node,
 54    unsigned long *radix, unsigned long *heap)
 55{
 56	if (root->raw) {
 57		struct vm_area_struct *vma = prio_tree_entry(
 58		    node, struct vm_area_struct, shared.prio_tree_node);
 59
 60		*radix = RADIX_INDEX(vma);
 61		*heap = HEAP_INDEX(vma);
 62	}
 63	else {
 64		*radix = node->start;
 65		*heap = node->last;
 66	}
 67}
 68
 69static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
 70
 71void __init prio_tree_init(void)
 72{
 73	unsigned int i;
 74
 75	for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
 76		index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
 77	index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
 78}
 79
 80/*
 81 * Maximum heap_index that can be stored in a PST with index_bits bits
 82 */
 83static inline unsigned long prio_tree_maxindex(unsigned int bits)
 84{
 85	return index_bits_to_maxindex[bits - 1];
 86}
 87
 88static void prio_set_parent(struct prio_tree_node *parent,
 89			    struct prio_tree_node *child, bool left)
 90{
 91	if (left)
 92		parent->left = child;
 93	else
 94		parent->right = child;
 95
 96	child->parent = parent;
 97}
 98
 99/*
100 * Extend a priority search tree so that it can store a node with heap_index
101 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
102 * However, this function is used rarely and the common case performance is
103 * not bad.
104 */
105static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
106		struct prio_tree_node *node, unsigned long max_heap_index)
107{
108	struct prio_tree_node *prev;
109
110	if (max_heap_index > prio_tree_maxindex(root->index_bits))
111		root->index_bits++;
112
113	prev = node;
114	INIT_PRIO_TREE_NODE(node);
115
116	while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
117		struct prio_tree_node *tmp = root->prio_tree_node;
118
119		root->index_bits++;
120
121		if (prio_tree_empty(root))
122			continue;
123
124		prio_tree_remove(root, root->prio_tree_node);
125		INIT_PRIO_TREE_NODE(tmp);
126
127		prio_set_parent(prev, tmp, true);
128		prev = tmp;
129	}
130
131	if (!prio_tree_empty(root))
132		prio_set_parent(prev, root->prio_tree_node, true);
133
134	root->prio_tree_node = node;
135	return node;
136}
137
138/*
139 * Replace a prio_tree_node with a new node and return the old node
140 */
141struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
142		struct prio_tree_node *old, struct prio_tree_node *node)
143{
144	INIT_PRIO_TREE_NODE(node);
145
146	if (prio_tree_root(old)) {
147		BUG_ON(root->prio_tree_node != old);
148		/*
149		 * We can reduce root->index_bits here. However, it is complex
150		 * and does not help much to improve performance (IMO).
151		 */
152		root->prio_tree_node = node;
153	} else
154		prio_set_parent(old->parent, node, old->parent->left == old);
155
156	if (!prio_tree_left_empty(old))
157		prio_set_parent(node, old->left, true);
158
159	if (!prio_tree_right_empty(old))
160		prio_set_parent(node, old->right, false);
161
162	return old;
163}
164
165/*
166 * Insert a prio_tree_node @node into a radix priority search tree @root. The
167 * algorithm typically takes O(log n) time where 'log n' is the number of bits
168 * required to represent the maximum heap_index. In the worst case, the algo
169 * can take O((log n)^2) - check prio_tree_expand.
170 *
171 * If a prior node with same radix_index and heap_index is already found in
172 * the tree, then returns the address of the prior node. Otherwise, inserts
173 * @node into the tree and returns @node.
174 */
175struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
176		struct prio_tree_node *node)
177{
178	struct prio_tree_node *cur, *res = node;
179	unsigned long radix_index, heap_index;
180	unsigned long r_index, h_index, index, mask;
181	int size_flag = 0;
182
183	get_index(root, node, &radix_index, &heap_index);
184
185	if (prio_tree_empty(root) ||
186			heap_index > prio_tree_maxindex(root->index_bits))
187		return prio_tree_expand(root, node, heap_index);
188
189	cur = root->prio_tree_node;
190	mask = 1UL << (root->index_bits - 1);
191
192	while (mask) {
193		get_index(root, cur, &r_index, &h_index);
194
195		if (r_index == radix_index && h_index == heap_index)
196			return cur;
197
198                if (h_index < heap_index ||
199		    (h_index == heap_index && r_index > radix_index)) {
200			struct prio_tree_node *tmp = node;
201			node = prio_tree_replace(root, cur, node);
202			cur = tmp;
203			/* swap indices */
204			index = r_index;
205			r_index = radix_index;
206			radix_index = index;
207			index = h_index;
208			h_index = heap_index;
209			heap_index = index;
210		}
211
212		if (size_flag)
213			index = heap_index - radix_index;
214		else
215			index = radix_index;
216
217		if (index & mask) {
218			if (prio_tree_right_empty(cur)) {
219				INIT_PRIO_TREE_NODE(node);
220				prio_set_parent(cur, node, false);
221				return res;
222			} else
223				cur = cur->right;
224		} else {
225			if (prio_tree_left_empty(cur)) {
226				INIT_PRIO_TREE_NODE(node);
227				prio_set_parent(cur, node, true);
228				return res;
229			} else
230				cur = cur->left;
231		}
232
233		mask >>= 1;
234
235		if (!mask) {
236			mask = 1UL << (BITS_PER_LONG - 1);
237			size_flag = 1;
238		}
239	}
240	/* Should not reach here */
241	BUG();
242	return NULL;
243}
244
245/*
246 * Remove a prio_tree_node @node from a radix priority search tree @root. The
247 * algorithm takes O(log n) time where 'log n' is the number of bits required
248 * to represent the maximum heap_index.
249 */
250void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
251{
252	struct prio_tree_node *cur;
253	unsigned long r_index, h_index_right, h_index_left;
254
255	cur = node;
256
257	while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
258		if (!prio_tree_left_empty(cur))
259			get_index(root, cur->left, &r_index, &h_index_left);
260		else {
261			cur = cur->right;
262			continue;
263		}
264
265		if (!prio_tree_right_empty(cur))
266			get_index(root, cur->right, &r_index, &h_index_right);
267		else {
268			cur = cur->left;
269			continue;
270		}
271
272		/* both h_index_left and h_index_right cannot be 0 */
273		if (h_index_left >= h_index_right)
274			cur = cur->left;
275		else
276			cur = cur->right;
277	}
278
279	if (prio_tree_root(cur)) {
280		BUG_ON(root->prio_tree_node != cur);
281		__INIT_PRIO_TREE_ROOT(root, root->raw);
282		return;
283	}
284
285	if (cur->parent->right == cur)
286		cur->parent->right = cur->parent;
287	else
288		cur->parent->left = cur->parent;
289
290	while (cur != node)
291		cur = prio_tree_replace(root, cur->parent, cur);
292}
293
294static void iter_walk_down(struct prio_tree_iter *iter)
295{
296	iter->mask >>= 1;
297	if (iter->mask) {
298		if (iter->size_level)
299			iter->size_level++;
300		return;
301	}
302
303	if (iter->size_level) {
304		BUG_ON(!prio_tree_left_empty(iter->cur));
305		BUG_ON(!prio_tree_right_empty(iter->cur));
306		iter->size_level++;
307		iter->mask = ULONG_MAX;
308	} else {
309		iter->size_level = 1;
310		iter->mask = 1UL << (BITS_PER_LONG - 1);
311	}
312}
313
314static void iter_walk_up(struct prio_tree_iter *iter)
315{
316	if (iter->mask == ULONG_MAX)
317		iter->mask = 1UL;
318	else if (iter->size_level == 1)
319		iter->mask = 1UL;
320	else
321		iter->mask <<= 1;
322	if (iter->size_level)
323		iter->size_level--;
324	if (!iter->size_level && (iter->value & iter->mask))
325		iter->value ^= iter->mask;
326}
327
328/*
329 * Following functions help to enumerate all prio_tree_nodes in the tree that
330 * overlap with the input interval X [radix_index, heap_index]. The enumeration
331 * takes O(log n + m) time where 'log n' is the height of the tree (which is
332 * proportional to # of bits required to represent the maximum heap_index) and
333 * 'm' is the number of prio_tree_nodes that overlap the interval X.
334 */
335
336static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
337		unsigned long *r_index, unsigned long *h_index)
338{
339	if (prio_tree_left_empty(iter->cur))
340		return NULL;
341
342	get_index(iter->root, iter->cur->left, r_index, h_index);
343
344	if (iter->r_index <= *h_index) {
345		iter->cur = iter->cur->left;
346		iter_walk_down(iter);
347		return iter->cur;
348	}
349
350	return NULL;
351}
352
353static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
354		unsigned long *r_index, unsigned long *h_index)
355{
356	unsigned long value;
357
358	if (prio_tree_right_empty(iter->cur))
359		return NULL;
360
361	if (iter->size_level)
362		value = iter->value;
363	else
364		value = iter->value | iter->mask;
365
366	if (iter->h_index < value)
367		return NULL;
368
369	get_index(iter->root, iter->cur->right, r_index, h_index);
370
371	if (iter->r_index <= *h_index) {
372		iter->cur = iter->cur->right;
373		iter_walk_down(iter);
374		return iter->cur;
375	}
376
377	return NULL;
378}
379
380static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
381{
382	iter->cur = iter->cur->parent;
383	iter_walk_up(iter);
384	return iter->cur;
385}
386
387static inline int overlap(struct prio_tree_iter *iter,
388		unsigned long r_index, unsigned long h_index)
389{
390	return iter->h_index >= r_index && iter->r_index <= h_index;
391}
392
393/*
394 * prio_tree_first:
395 *
396 * Get the first prio_tree_node that overlaps with the interval [radix_index,
397 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
398 * traversal of the tree.
399 */
400static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
401{
402	struct prio_tree_root *root;
403	unsigned long r_index, h_index;
404
405	INIT_PRIO_TREE_ITER(iter);
406
407	root = iter->root;
408	if (prio_tree_empty(root))
409		return NULL;
410
411	get_index(root, root->prio_tree_node, &r_index, &h_index);
412
413	if (iter->r_index > h_index)
414		return NULL;
415
416	iter->mask = 1UL << (root->index_bits - 1);
417	iter->cur = root->prio_tree_node;
418
419	while (1) {
420		if (overlap(iter, r_index, h_index))
421			return iter->cur;
422
423		if (prio_tree_left(iter, &r_index, &h_index))
424			continue;
425
426		if (prio_tree_right(iter, &r_index, &h_index))
427			continue;
428
429		break;
430	}
431	return NULL;
432}
433
434/*
435 * prio_tree_next:
436 *
437 * Get the next prio_tree_node that overlaps with the input interval in iter
438 */
439struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
440{
441	unsigned long r_index, h_index;
442
443	if (iter->cur == NULL)
444		return prio_tree_first(iter);
445
446repeat:
447	while (prio_tree_left(iter, &r_index, &h_index))
448		if (overlap(iter, r_index, h_index))
449			return iter->cur;
450
451	while (!prio_tree_right(iter, &r_index, &h_index)) {
452	    	while (!prio_tree_root(iter->cur) &&
453				iter->cur->parent->right == iter->cur)
454			prio_tree_parent(iter);
455
456		if (prio_tree_root(iter->cur))
457			return NULL;
458
459		prio_tree_parent(iter);
460	}
461
462	if (overlap(iter, r_index, h_index))
463		return iter->cur;
464
465	goto repeat;
466}