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-/*
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- * lib/prio_tree.c - priority search tree
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- *
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- * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
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- *
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- * This file is released under the GPL v2.
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- *
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- * Based on the radix priority search tree proposed by Edward M. McCreight
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- * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
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- *
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- * 02Feb2004 Initial version
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- */
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-
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-#include <linux/init.h>
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-#include <linux/mm.h>
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-#include <linux/prio_tree.h>
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-#include <linux/export.h>
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-
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-/*
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- * A clever mix of heap and radix trees forms a radix priority search tree (PST)
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- * which is useful for storing intervals, e.g, we can consider a vma as a closed
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- * interval of file pages [offset_begin, offset_end], and store all vmas that
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- * map a file in a PST. Then, using the PST, we can answer a stabbing query,
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- * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
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- * given input interval X (a set of consecutive file pages), in "O(log n + m)"
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- * time where 'log n' is the height of the PST, and 'm' is the number of stored
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- * intervals (vmas) that overlap (map) with the input interval X (the set of
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- * consecutive file pages).
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- *
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- * In our implementation, we store closed intervals of the form [radix_index,
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- * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
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- * is designed for storing intervals with unique radix indices, i.e., each
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- * interval have different radix_index. However, this limitation can be easily
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- * overcome by using the size, i.e., heap_index - radix_index, as part of the
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- * index, so we index the tree using [(radix_index,size), heap_index].
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- *
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- * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
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- * machine, the maximum height of a PST can be 64. We can use a balanced version
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- * of the priority search tree to optimize the tree height, but the balanced
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- * tree proposed by McCreight is too complex and memory-hungry for our purpose.
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- */
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-
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-/*
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- * The following macros are used for implementing prio_tree for i_mmap
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- */
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-
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-static void get_index(const struct prio_tree_root *root,
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- const struct prio_tree_node *node,
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- unsigned long *radix, unsigned long *heap)
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-{
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- *radix = node->start;
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- *heap = node->last;
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-}
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-
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-static unsigned long index_bits_to_maxindex[BITS_PER_LONG];
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-
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-void __init prio_tree_init(void)
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-{
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- unsigned int i;
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-
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- for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
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- index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
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- index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
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-}
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-
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-/*
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- * Maximum heap_index that can be stored in a PST with index_bits bits
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- */
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-static inline unsigned long prio_tree_maxindex(unsigned int bits)
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-{
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- return index_bits_to_maxindex[bits - 1];
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-}
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-
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-static void prio_set_parent(struct prio_tree_node *parent,
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- struct prio_tree_node *child, bool left)
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-{
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- if (left)
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- parent->left = child;
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- else
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- parent->right = child;
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-
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- child->parent = parent;
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-}
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-
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-/*
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- * Extend a priority search tree so that it can store a node with heap_index
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- * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
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- * However, this function is used rarely and the common case performance is
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- * not bad.
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- */
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-static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
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- struct prio_tree_node *node, unsigned long max_heap_index)
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-{
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- struct prio_tree_node *prev;
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-
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- if (max_heap_index > prio_tree_maxindex(root->index_bits))
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- root->index_bits++;
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-
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- prev = node;
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- INIT_PRIO_TREE_NODE(node);
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-
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- while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
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- struct prio_tree_node *tmp = root->prio_tree_node;
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-
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- root->index_bits++;
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-
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- if (prio_tree_empty(root))
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- continue;
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-
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- prio_tree_remove(root, root->prio_tree_node);
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- INIT_PRIO_TREE_NODE(tmp);
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-
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- prio_set_parent(prev, tmp, true);
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- prev = tmp;
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- }
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-
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- if (!prio_tree_empty(root))
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- prio_set_parent(prev, root->prio_tree_node, true);
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-
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- root->prio_tree_node = node;
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- return node;
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-}
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-
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-/*
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- * Replace a prio_tree_node with a new node and return the old node
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- */
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-struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
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- struct prio_tree_node *old, struct prio_tree_node *node)
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-{
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- INIT_PRIO_TREE_NODE(node);
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-
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- if (prio_tree_root(old)) {
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- BUG_ON(root->prio_tree_node != old);
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- /*
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- * We can reduce root->index_bits here. However, it is complex
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- * and does not help much to improve performance (IMO).
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- */
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- root->prio_tree_node = node;
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- } else
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- prio_set_parent(old->parent, node, old->parent->left == old);
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-
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- if (!prio_tree_left_empty(old))
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- prio_set_parent(node, old->left, true);
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-
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- if (!prio_tree_right_empty(old))
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- prio_set_parent(node, old->right, false);
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-
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- return old;
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-}
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-
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-/*
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- * Insert a prio_tree_node @node into a radix priority search tree @root. The
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- * algorithm typically takes O(log n) time where 'log n' is the number of bits
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- * required to represent the maximum heap_index. In the worst case, the algo
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- * can take O((log n)^2) - check prio_tree_expand.
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- *
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- * If a prior node with same radix_index and heap_index is already found in
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- * the tree, then returns the address of the prior node. Otherwise, inserts
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- * @node into the tree and returns @node.
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- */
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-struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
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- struct prio_tree_node *node)
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-{
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- struct prio_tree_node *cur, *res = node;
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- unsigned long radix_index, heap_index;
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- unsigned long r_index, h_index, index, mask;
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- int size_flag = 0;
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-
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- get_index(root, node, &radix_index, &heap_index);
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-
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- if (prio_tree_empty(root) ||
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- heap_index > prio_tree_maxindex(root->index_bits))
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- return prio_tree_expand(root, node, heap_index);
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-
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- cur = root->prio_tree_node;
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- mask = 1UL << (root->index_bits - 1);
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-
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- while (mask) {
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- get_index(root, cur, &r_index, &h_index);
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-
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- if (r_index == radix_index && h_index == heap_index)
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- return cur;
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-
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- if (h_index < heap_index ||
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- (h_index == heap_index && r_index > radix_index)) {
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- struct prio_tree_node *tmp = node;
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- node = prio_tree_replace(root, cur, node);
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- cur = tmp;
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- /* swap indices */
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- index = r_index;
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- r_index = radix_index;
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- radix_index = index;
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- index = h_index;
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- h_index = heap_index;
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- heap_index = index;
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- }
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-
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- if (size_flag)
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- index = heap_index - radix_index;
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- else
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- index = radix_index;
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-
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- if (index & mask) {
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- if (prio_tree_right_empty(cur)) {
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- INIT_PRIO_TREE_NODE(node);
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- prio_set_parent(cur, node, false);
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- return res;
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- } else
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- cur = cur->right;
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- } else {
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- if (prio_tree_left_empty(cur)) {
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- INIT_PRIO_TREE_NODE(node);
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- prio_set_parent(cur, node, true);
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- return res;
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- } else
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- cur = cur->left;
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- }
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-
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- mask >>= 1;
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-
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- if (!mask) {
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- mask = 1UL << (BITS_PER_LONG - 1);
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- size_flag = 1;
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- }
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- }
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- /* Should not reach here */
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- BUG();
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- return NULL;
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-}
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-EXPORT_SYMBOL(prio_tree_insert);
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-
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-/*
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- * Remove a prio_tree_node @node from a radix priority search tree @root. The
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- * algorithm takes O(log n) time where 'log n' is the number of bits required
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- * to represent the maximum heap_index.
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- */
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-void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
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-{
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- struct prio_tree_node *cur;
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- unsigned long r_index, h_index_right, h_index_left;
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-
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- cur = node;
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-
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- while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
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- if (!prio_tree_left_empty(cur))
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- get_index(root, cur->left, &r_index, &h_index_left);
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- else {
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- cur = cur->right;
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- continue;
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- }
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-
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- if (!prio_tree_right_empty(cur))
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- get_index(root, cur->right, &r_index, &h_index_right);
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- else {
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- cur = cur->left;
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- continue;
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- }
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-
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- /* both h_index_left and h_index_right cannot be 0 */
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- if (h_index_left >= h_index_right)
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- cur = cur->left;
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- else
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- cur = cur->right;
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- }
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-
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- if (prio_tree_root(cur)) {
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- BUG_ON(root->prio_tree_node != cur);
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- __INIT_PRIO_TREE_ROOT(root, root->raw);
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- return;
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- }
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-
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- if (cur->parent->right == cur)
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- cur->parent->right = cur->parent;
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- else
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- cur->parent->left = cur->parent;
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-
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- while (cur != node)
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- cur = prio_tree_replace(root, cur->parent, cur);
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-}
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-EXPORT_SYMBOL(prio_tree_remove);
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-
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-static void iter_walk_down(struct prio_tree_iter *iter)
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-{
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- iter->mask >>= 1;
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- if (iter->mask) {
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- if (iter->size_level)
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- iter->size_level++;
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- return;
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- }
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-
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- if (iter->size_level) {
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- BUG_ON(!prio_tree_left_empty(iter->cur));
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- BUG_ON(!prio_tree_right_empty(iter->cur));
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- iter->size_level++;
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- iter->mask = ULONG_MAX;
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- } else {
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- iter->size_level = 1;
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- iter->mask = 1UL << (BITS_PER_LONG - 1);
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- }
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-}
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-
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-static void iter_walk_up(struct prio_tree_iter *iter)
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-{
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- if (iter->mask == ULONG_MAX)
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- iter->mask = 1UL;
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- else if (iter->size_level == 1)
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- iter->mask = 1UL;
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- else
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- iter->mask <<= 1;
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- if (iter->size_level)
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- iter->size_level--;
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- if (!iter->size_level && (iter->value & iter->mask))
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- iter->value ^= iter->mask;
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-}
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-
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-/*
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- * Following functions help to enumerate all prio_tree_nodes in the tree that
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- * overlap with the input interval X [radix_index, heap_index]. The enumeration
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- * takes O(log n + m) time where 'log n' is the height of the tree (which is
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- * proportional to # of bits required to represent the maximum heap_index) and
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- * 'm' is the number of prio_tree_nodes that overlap the interval X.
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- */
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-
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-static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
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- unsigned long *r_index, unsigned long *h_index)
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-{
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- if (prio_tree_left_empty(iter->cur))
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- return NULL;
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-
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- get_index(iter->root, iter->cur->left, r_index, h_index);
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-
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- if (iter->r_index <= *h_index) {
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- iter->cur = iter->cur->left;
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- iter_walk_down(iter);
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- return iter->cur;
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- }
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-
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- return NULL;
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-}
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-
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-static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
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- unsigned long *r_index, unsigned long *h_index)
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-{
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- unsigned long value;
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-
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- if (prio_tree_right_empty(iter->cur))
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- return NULL;
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-
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- if (iter->size_level)
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- value = iter->value;
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|
- 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);
|
|
|