Root/lib/prio_tree.c

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
88/*
89 * Extend a priority search tree so that it can store a node with heap_index
90 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
91 * However, this function is used rarely and the common case performance is
92 * not bad.
93 */
94static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
95        struct prio_tree_node *node, unsigned long max_heap_index)
96{
97    struct prio_tree_node *first = NULL, *prev, *last = NULL;
98
99    if (max_heap_index > prio_tree_maxindex(root->index_bits))
100        root->index_bits++;
101
102    while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
103        root->index_bits++;
104
105        if (prio_tree_empty(root))
106            continue;
107
108        if (first == NULL) {
109            first = root->prio_tree_node;
110            prio_tree_remove(root, root->prio_tree_node);
111            INIT_PRIO_TREE_NODE(first);
112            last = first;
113        } else {
114            prev = last;
115            last = root->prio_tree_node;
116            prio_tree_remove(root, root->prio_tree_node);
117            INIT_PRIO_TREE_NODE(last);
118            prev->left = last;
119            last->parent = prev;
120        }
121    }
122
123    INIT_PRIO_TREE_NODE(node);
124
125    if (first) {
126        node->left = first;
127        first->parent = node;
128    } else
129        last = node;
130
131    if (!prio_tree_empty(root)) {
132        last->left = root->prio_tree_node;
133        last->left->parent = last;
134    }
135
136    root->prio_tree_node = node;
137    return node;
138}
139
140/*
141 * Replace a prio_tree_node with a new node and return the old node
142 */
143struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
144        struct prio_tree_node *old, struct prio_tree_node *node)
145{
146    INIT_PRIO_TREE_NODE(node);
147
148    if (prio_tree_root(old)) {
149        BUG_ON(root->prio_tree_node != old);
150        /*
151         * We can reduce root->index_bits here. However, it is complex
152         * and does not help much to improve performance (IMO).
153         */
154        node->parent = node;
155        root->prio_tree_node = node;
156    } else {
157        node->parent = old->parent;
158        if (old->parent->left == old)
159            old->parent->left = node;
160        else
161            old->parent->right = node;
162    }
163
164    if (!prio_tree_left_empty(old)) {
165        node->left = old->left;
166        old->left->parent = node;
167    }
168
169    if (!prio_tree_right_empty(old)) {
170        node->right = old->right;
171        old->right->parent = node;
172    }
173
174    return old;
175}
176
177/*
178 * Insert a prio_tree_node @node into a radix priority search tree @root. The
179 * algorithm typically takes O(log n) time where 'log n' is the number of bits
180 * required to represent the maximum heap_index. In the worst case, the algo
181 * can take O((log n)^2) - check prio_tree_expand.
182 *
183 * If a prior node with same radix_index and heap_index is already found in
184 * the tree, then returns the address of the prior node. Otherwise, inserts
185 * @node into the tree and returns @node.
186 */
187struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
188        struct prio_tree_node *node)
189{
190    struct prio_tree_node *cur, *res = node;
191    unsigned long radix_index, heap_index;
192    unsigned long r_index, h_index, index, mask;
193    int size_flag = 0;
194
195    get_index(root, node, &radix_index, &heap_index);
196
197    if (prio_tree_empty(root) ||
198            heap_index > prio_tree_maxindex(root->index_bits))
199        return prio_tree_expand(root, node, heap_index);
200
201    cur = root->prio_tree_node;
202    mask = 1UL << (root->index_bits - 1);
203
204    while (mask) {
205        get_index(root, cur, &r_index, &h_index);
206
207        if (r_index == radix_index && h_index == heap_index)
208            return cur;
209
210                if (h_index < heap_index ||
211            (h_index == heap_index && r_index > radix_index)) {
212            struct prio_tree_node *tmp = node;
213            node = prio_tree_replace(root, cur, node);
214            cur = tmp;
215            /* swap indices */
216            index = r_index;
217            r_index = radix_index;
218            radix_index = index;
219            index = h_index;
220            h_index = heap_index;
221            heap_index = index;
222        }
223
224        if (size_flag)
225            index = heap_index - radix_index;
226        else
227            index = radix_index;
228
229        if (index & mask) {
230            if (prio_tree_right_empty(cur)) {
231                INIT_PRIO_TREE_NODE(node);
232                cur->right = node;
233                node->parent = cur;
234                return res;
235            } else
236                cur = cur->right;
237        } else {
238            if (prio_tree_left_empty(cur)) {
239                INIT_PRIO_TREE_NODE(node);
240                cur->left = node;
241                node->parent = cur;
242                return res;
243            } else
244                cur = cur->left;
245        }
246
247        mask >>= 1;
248
249        if (!mask) {
250            mask = 1UL << (BITS_PER_LONG - 1);
251            size_flag = 1;
252        }
253    }
254    /* Should not reach here */
255    BUG();
256    return NULL;
257}
258
259/*
260 * Remove a prio_tree_node @node from a radix priority search tree @root. The
261 * algorithm takes O(log n) time where 'log n' is the number of bits required
262 * to represent the maximum heap_index.
263 */
264void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
265{
266    struct prio_tree_node *cur;
267    unsigned long r_index, h_index_right, h_index_left;
268
269    cur = node;
270
271    while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
272        if (!prio_tree_left_empty(cur))
273            get_index(root, cur->left, &r_index, &h_index_left);
274        else {
275            cur = cur->right;
276            continue;
277        }
278
279        if (!prio_tree_right_empty(cur))
280            get_index(root, cur->right, &r_index, &h_index_right);
281        else {
282            cur = cur->left;
283            continue;
284        }
285
286        /* both h_index_left and h_index_right cannot be 0 */
287        if (h_index_left >= h_index_right)
288            cur = cur->left;
289        else
290            cur = cur->right;
291    }
292
293    if (prio_tree_root(cur)) {
294        BUG_ON(root->prio_tree_node != cur);
295        __INIT_PRIO_TREE_ROOT(root, root->raw);
296        return;
297    }
298
299    if (cur->parent->right == cur)
300        cur->parent->right = cur->parent;
301    else
302        cur->parent->left = cur->parent;
303
304    while (cur != node)
305        cur = prio_tree_replace(root, cur->parent, cur);
306}
307
308/*
309 * Following functions help to enumerate all prio_tree_nodes in the tree that
310 * overlap with the input interval X [radix_index, heap_index]. The enumeration
311 * takes O(log n + m) time where 'log n' is the height of the tree (which is
312 * proportional to # of bits required to represent the maximum heap_index) and
313 * 'm' is the number of prio_tree_nodes that overlap the interval X.
314 */
315
316static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
317        unsigned long *r_index, unsigned long *h_index)
318{
319    if (prio_tree_left_empty(iter->cur))
320        return NULL;
321
322    get_index(iter->root, iter->cur->left, r_index, h_index);
323
324    if (iter->r_index <= *h_index) {
325        iter->cur = iter->cur->left;
326        iter->mask >>= 1;
327        if (iter->mask) {
328            if (iter->size_level)
329                iter->size_level++;
330        } else {
331            if (iter->size_level) {
332                BUG_ON(!prio_tree_left_empty(iter->cur));
333                BUG_ON(!prio_tree_right_empty(iter->cur));
334                iter->size_level++;
335                iter->mask = ULONG_MAX;
336            } else {
337                iter->size_level = 1;
338                iter->mask = 1UL << (BITS_PER_LONG - 1);
339            }
340        }
341        return iter->cur;
342    }
343
344    return NULL;
345}
346
347static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
348        unsigned long *r_index, unsigned long *h_index)
349{
350    unsigned long value;
351
352    if (prio_tree_right_empty(iter->cur))
353        return NULL;
354
355    if (iter->size_level)
356        value = iter->value;
357    else
358        value = iter->value | iter->mask;
359
360    if (iter->h_index < value)
361        return NULL;
362
363    get_index(iter->root, iter->cur->right, r_index, h_index);
364
365    if (iter->r_index <= *h_index) {
366        iter->cur = iter->cur->right;
367        iter->mask >>= 1;
368        iter->value = value;
369        if (iter->mask) {
370            if (iter->size_level)
371                iter->size_level++;
372        } else {
373            if (iter->size_level) {
374                BUG_ON(!prio_tree_left_empty(iter->cur));
375                BUG_ON(!prio_tree_right_empty(iter->cur));
376                iter->size_level++;
377                iter->mask = ULONG_MAX;
378            } else {
379                iter->size_level = 1;
380                iter->mask = 1UL << (BITS_PER_LONG - 1);
381            }
382        }
383        return iter->cur;
384    }
385
386    return NULL;
387}
388
389static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
390{
391    iter->cur = iter->cur->parent;
392    if (iter->mask == ULONG_MAX)
393        iter->mask = 1UL;
394    else if (iter->size_level == 1)
395        iter->mask = 1UL;
396    else
397        iter->mask <<= 1;
398    if (iter->size_level)
399        iter->size_level--;
400    if (!iter->size_level && (iter->value & iter->mask))
401        iter->value ^= iter->mask;
402    return iter->cur;
403}
404
405static inline int overlap(struct prio_tree_iter *iter,
406        unsigned long r_index, unsigned long h_index)
407{
408    return iter->h_index >= r_index && iter->r_index <= h_index;
409}
410
411/*
412 * prio_tree_first:
413 *
414 * Get the first prio_tree_node that overlaps with the interval [radix_index,
415 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
416 * traversal of the tree.
417 */
418static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
419{
420    struct prio_tree_root *root;
421    unsigned long r_index, h_index;
422
423    INIT_PRIO_TREE_ITER(iter);
424
425    root = iter->root;
426    if (prio_tree_empty(root))
427        return NULL;
428
429    get_index(root, root->prio_tree_node, &r_index, &h_index);
430
431    if (iter->r_index > h_index)
432        return NULL;
433
434    iter->mask = 1UL << (root->index_bits - 1);
435    iter->cur = root->prio_tree_node;
436
437    while (1) {
438        if (overlap(iter, r_index, h_index))
439            return iter->cur;
440
441        if (prio_tree_left(iter, &r_index, &h_index))
442            continue;
443
444        if (prio_tree_right(iter, &r_index, &h_index))
445            continue;
446
447        break;
448    }
449    return NULL;
450}
451
452/*
453 * prio_tree_next:
454 *
455 * Get the next prio_tree_node that overlaps with the input interval in iter
456 */
457struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
458{
459    unsigned long r_index, h_index;
460
461    if (iter->cur == NULL)
462        return prio_tree_first(iter);
463
464repeat:
465    while (prio_tree_left(iter, &r_index, &h_index))
466        if (overlap(iter, r_index, h_index))
467            return iter->cur;
468
469    while (!prio_tree_right(iter, &r_index, &h_index)) {
470            while (!prio_tree_root(iter->cur) &&
471                iter->cur->parent->right == iter->cur)
472            prio_tree_parent(iter);
473
474        if (prio_tree_root(iter->cur))
475            return NULL;
476
477        prio_tree_parent(iter);
478    }
479
480    if (overlap(iter, r_index, h_index))
481        return iter->cur;
482
483    goto repeat;
484}
485

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