+++ /dev/null
-/*
- * 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>
-#include <linux/export.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
- */
-
-static void get_index(const struct prio_tree_root *root,
- const struct prio_tree_node *node,
- unsigned long *radix, unsigned long *heap)
-{
- *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];
-}
-
-static void prio_set_parent(struct prio_tree_node *parent,
- struct prio_tree_node *child, bool left)
-{
- if (left)
- parent->left = child;
- else
- parent->right = child;
-
- child->parent = parent;
-}
-
-/*
- * 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 *prev;
-
- if (max_heap_index > prio_tree_maxindex(root->index_bits))
- root->index_bits++;
-
- prev = node;
- INIT_PRIO_TREE_NODE(node);
-
- while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
- struct prio_tree_node *tmp = root->prio_tree_node;
-
- root->index_bits++;
-
- if (prio_tree_empty(root))
- continue;
-
- prio_tree_remove(root, root->prio_tree_node);
- INIT_PRIO_TREE_NODE(tmp);
-
- prio_set_parent(prev, tmp, true);
- prev = tmp;
- }
-
- if (!prio_tree_empty(root))
- prio_set_parent(prev, root->prio_tree_node, true);
-
- 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).
- */
- root->prio_tree_node = node;
- } else
- prio_set_parent(old->parent, node, old->parent->left == old);
-
- if (!prio_tree_left_empty(old))
- prio_set_parent(node, old->left, true);
-
- if (!prio_tree_right_empty(old))
- prio_set_parent(node, old->right, false);
-
- 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);
- prio_set_parent(cur, node, false);
- return res;
- } else
- cur = cur->right;
- } else {
- if (prio_tree_left_empty(cur)) {
- INIT_PRIO_TREE_NODE(node);
- prio_set_parent(cur, node, true);
- 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;
-}
-EXPORT_SYMBOL(prio_tree_insert);
-
-/*
- * 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);
-}
-EXPORT_SYMBOL(prio_tree_remove);
-
-static void iter_walk_down(struct prio_tree_iter *iter)
-{
- iter->mask >>= 1;
- if (iter->mask) {
- if (iter->size_level)
- iter->size_level++;
- return;
- }
-
- 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);
- }
-}
-
-static void iter_walk_up(struct prio_tree_iter *iter)
-{
- 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;
-}
-
-/*
- * 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_walk_down(iter);
- 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_walk_down(iter);
- return iter->cur;
- }
-
- return NULL;
-}
-
-static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
-{
- iter->cur = iter->cur->parent;
- iter_walk_up(iter);
- 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;
-}
-EXPORT_SYMBOL(prio_tree_next);
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