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97e834c504
Introduce prio_set_parent() to abstract the operation which is used to attach the node to its parent. Signed-off-by: Xiao Guangrong <xiaoguangrong@linux.vnet.ibm.com> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
467 lines
12 KiB
C
467 lines
12 KiB
C
/*
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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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#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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/*
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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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* The following macros are used for implementing prio_tree for i_mmap
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*/
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#define RADIX_INDEX(vma) ((vma)->vm_pgoff)
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#define VMA_SIZE(vma) (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
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/* avoid overflow */
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#define HEAP_INDEX(vma) ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))
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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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if (root->raw) {
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struct vm_area_struct *vma = prio_tree_entry(
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node, struct vm_area_struct, shared.prio_tree_node);
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*radix = RADIX_INDEX(vma);
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*heap = HEAP_INDEX(vma);
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}
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else {
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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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void __init prio_tree_init(void)
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{
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unsigned int i;
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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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* 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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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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child->parent = parent;
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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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if (max_heap_index > prio_tree_maxindex(root->index_bits))
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root->index_bits++;
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prev = node;
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INIT_PRIO_TREE_NODE(node);
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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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root->index_bits++;
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if (prio_tree_empty(root))
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continue;
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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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prio_set_parent(prev, tmp, true);
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prev = tmp;
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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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root->prio_tree_node = node;
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return node;
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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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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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if (!prio_tree_left_empty(old))
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prio_set_parent(node, old->left, true);
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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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return old;
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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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get_index(root, node, &radix_index, &heap_index);
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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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cur = root->prio_tree_node;
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mask = 1UL << (root->index_bits - 1);
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while (mask) {
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get_index(root, cur, &r_index, &h_index);
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if (r_index == radix_index && h_index == heap_index)
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return cur;
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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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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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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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mask >>= 1;
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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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/*
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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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cur = node;
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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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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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/* 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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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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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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while (cur != node)
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cur = prio_tree_replace(root, cur->parent, cur);
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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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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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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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* 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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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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get_index(iter->root, iter->cur->left, r_index, h_index);
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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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return NULL;
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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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if (prio_tree_right_empty(iter->cur))
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return NULL;
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if (iter->size_level)
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value = iter->value;
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else
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value = iter->value | iter->mask;
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if (iter->h_index < value)
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return NULL;
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get_index(iter->root, iter->cur->right, r_index, h_index);
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if (iter->r_index <= *h_index) {
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iter->cur = iter->cur->right;
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iter_walk_down(iter);
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return iter->cur;
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}
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return NULL;
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}
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static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
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{
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iter->cur = iter->cur->parent;
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iter_walk_up(iter);
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return iter->cur;
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}
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static inline int overlap(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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return iter->h_index >= r_index && iter->r_index <= h_index;
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}
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/*
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* prio_tree_first:
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*
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* Get the first prio_tree_node that overlaps with the interval [radix_index,
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* heap_index]. Note that always radix_index <= heap_index. We do a pre-order
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* traversal of the tree.
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*/
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static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
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{
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struct prio_tree_root *root;
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unsigned long r_index, h_index;
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INIT_PRIO_TREE_ITER(iter);
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root = iter->root;
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if (prio_tree_empty(root))
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return NULL;
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get_index(root, root->prio_tree_node, &r_index, &h_index);
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if (iter->r_index > h_index)
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return NULL;
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iter->mask = 1UL << (root->index_bits - 1);
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iter->cur = root->prio_tree_node;
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while (1) {
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if (overlap(iter, r_index, h_index))
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return iter->cur;
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if (prio_tree_left(iter, &r_index, &h_index))
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continue;
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if (prio_tree_right(iter, &r_index, &h_index))
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continue;
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break;
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}
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return NULL;
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}
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/*
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* prio_tree_next:
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*
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* Get the next prio_tree_node that overlaps with the input interval in iter
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*/
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struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
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{
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unsigned long r_index, h_index;
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if (iter->cur == NULL)
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return prio_tree_first(iter);
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repeat:
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while (prio_tree_left(iter, &r_index, &h_index))
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if (overlap(iter, r_index, h_index))
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return iter->cur;
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while (!prio_tree_right(iter, &r_index, &h_index)) {
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while (!prio_tree_root(iter->cur) &&
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iter->cur->parent->right == iter->cur)
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prio_tree_parent(iter);
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if (prio_tree_root(iter->cur))
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return NULL;
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prio_tree_parent(iter);
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}
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if (overlap(iter, r_index, h_index))
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return iter->cur;
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goto repeat;
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}
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