218 lines
8 KiB
C
218 lines
8 KiB
C
/*
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Interval Trees
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(C) 2012 Michel Lespinasse <walken@google.com>
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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include/linux/interval_tree_generic.h
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*/
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#include <linux/rbtree_augmented.h>
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/*
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* Template for implementing interval trees
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*
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* ITSTRUCT: struct type of the interval tree nodes
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* ITRB: name of struct rb_node field within ITSTRUCT
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* ITTYPE: type of the interval endpoints
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* ITSUBTREE: name of ITTYPE field within ITSTRUCT holding last-in-subtree
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* ITSTART(n): start endpoint of ITSTRUCT node n
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* ITLAST(n): last endpoint of ITSTRUCT node n
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* ITSTATIC: 'static' or empty
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* ITPREFIX: prefix to use for the inline tree definitions
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*
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* Note - before using this, please consider if generic version
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* (interval_tree.h) would work for you...
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*/
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#define INTERVAL_TREE_DEFINE(ITSTRUCT, ITRB, ITTYPE, ITSUBTREE, \
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ITSTART, ITLAST, ITSTATIC, ITPREFIX) \
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\
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/* Callbacks for augmented rbtree insert and remove */ \
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\
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static inline ITTYPE ITPREFIX ## _compute_subtree_last(ITSTRUCT *node) \
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{ \
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ITTYPE max = ITLAST(node), subtree_last; \
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if (node->ITRB.rb_left) { \
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subtree_last = rb_entry(node->ITRB.rb_left, \
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ITSTRUCT, ITRB)->ITSUBTREE; \
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if (max < subtree_last) \
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max = subtree_last; \
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} \
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if (node->ITRB.rb_right) { \
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subtree_last = rb_entry(node->ITRB.rb_right, \
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ITSTRUCT, ITRB)->ITSUBTREE; \
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if (max < subtree_last) \
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max = subtree_last; \
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} \
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return max; \
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} \
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\
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RB_DECLARE_CALLBACKS(static, ITPREFIX ## _augment, ITSTRUCT, ITRB, \
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ITTYPE, ITSUBTREE, ITPREFIX ## _compute_subtree_last) \
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\
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/* Insert / remove interval nodes from the tree */ \
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\
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ITSTATIC void ITPREFIX ## _insert(ITSTRUCT *node, \
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struct rb_root_cached *root) \
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{ \
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struct rb_node **link = &root->rb_root.rb_node, *rb_parent = NULL; \
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ITTYPE start = ITSTART(node), last = ITLAST(node); \
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ITSTRUCT *parent; \
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bool leftmost = true; \
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\
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while (*link) { \
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rb_parent = *link; \
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parent = rb_entry(rb_parent, ITSTRUCT, ITRB); \
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if (parent->ITSUBTREE < last) \
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parent->ITSUBTREE = last; \
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if (start < ITSTART(parent)) \
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link = &parent->ITRB.rb_left; \
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else { \
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link = &parent->ITRB.rb_right; \
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leftmost = false; \
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} \
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} \
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\
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node->ITSUBTREE = last; \
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rb_link_node(&node->ITRB, rb_parent, link); \
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rb_insert_augmented_cached(&node->ITRB, root, \
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leftmost, &ITPREFIX ## _augment); \
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} \
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\
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ITSTATIC void ITPREFIX ## _remove(ITSTRUCT *node, \
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struct rb_root_cached *root) \
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{ \
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rb_erase_augmented_cached(&node->ITRB, root, &ITPREFIX ## _augment); \
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} \
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\
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/* \
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* Iterate over intervals intersecting [start;last] \
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* \
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* Note that a node's interval intersects [start;last] iff: \
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* Cond1: ITSTART(node) <= last \
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* and \
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* Cond2: start <= ITLAST(node) \
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*/ \
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\
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static ITSTRUCT * \
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ITPREFIX ## _subtree_search(ITSTRUCT *node, ITTYPE start, ITTYPE last) \
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{ \
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while (true) { \
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/* \
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* Loop invariant: start <= node->ITSUBTREE \
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* (Cond2 is satisfied by one of the subtree nodes) \
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*/ \
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if (node->ITRB.rb_left) { \
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ITSTRUCT *left = rb_entry(node->ITRB.rb_left, \
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ITSTRUCT, ITRB); \
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if (start <= left->ITSUBTREE) { \
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/* \
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* Some nodes in left subtree satisfy Cond2. \
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* Iterate to find the leftmost such node N. \
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* If it also satisfies Cond1, that's the \
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* match we are looking for. Otherwise, there \
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* is no matching interval as nodes to the \
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* right of N can't satisfy Cond1 either. \
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*/ \
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node = left; \
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continue; \
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} \
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} \
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if (ITSTART(node) <= last) { /* Cond1 */ \
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if (start <= ITLAST(node)) /* Cond2 */ \
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return node; /* node is leftmost match */ \
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if (node->ITRB.rb_right) { \
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node = rb_entry(node->ITRB.rb_right, \
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ITSTRUCT, ITRB); \
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if (start <= node->ITSUBTREE) \
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continue; \
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} \
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} \
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return NULL; /* No match */ \
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} \
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} \
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\
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ITSTATIC ITSTRUCT * \
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ITPREFIX ## _iter_first(struct rb_root_cached *root, \
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ITTYPE start, ITTYPE last) \
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{ \
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ITSTRUCT *node, *leftmost; \
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\
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if (!root->rb_root.rb_node) \
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return NULL; \
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\
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/* \
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* Fastpath range intersection/overlap between A: [a0, a1] and \
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* B: [b0, b1] is given by: \
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* \
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* a0 <= b1 && b0 <= a1 \
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* \
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* ... where A holds the lock range and B holds the smallest \
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* 'start' and largest 'last' in the tree. For the later, we \
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* rely on the root node, which by augmented interval tree \
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* property, holds the largest value in its last-in-subtree. \
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* This allows mitigating some of the tree walk overhead for \
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* for non-intersecting ranges, maintained and consulted in O(1). \
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*/ \
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node = rb_entry(root->rb_root.rb_node, ITSTRUCT, ITRB); \
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if (node->ITSUBTREE < start) \
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return NULL; \
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\
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leftmost = rb_entry(root->rb_leftmost, ITSTRUCT, ITRB); \
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if (ITSTART(leftmost) > last) \
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return NULL; \
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\
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return ITPREFIX ## _subtree_search(node, start, last); \
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} \
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\
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ITSTATIC ITSTRUCT * \
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ITPREFIX ## _iter_next(ITSTRUCT *node, ITTYPE start, ITTYPE last) \
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{ \
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struct rb_node *rb = node->ITRB.rb_right, *prev; \
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\
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while (true) { \
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/* \
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* Loop invariants: \
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* Cond1: ITSTART(node) <= last \
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* rb == node->ITRB.rb_right \
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* \
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* First, search right subtree if suitable \
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*/ \
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if (rb) { \
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ITSTRUCT *right = rb_entry(rb, ITSTRUCT, ITRB); \
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if (start <= right->ITSUBTREE) \
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return ITPREFIX ## _subtree_search(right, \
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start, last); \
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} \
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\
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/* Move up the tree until we come from a node's left child */ \
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do { \
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rb = rb_parent(&node->ITRB); \
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if (!rb) \
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return NULL; \
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prev = &node->ITRB; \
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node = rb_entry(rb, ITSTRUCT, ITRB); \
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rb = node->ITRB.rb_right; \
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} while (prev == rb); \
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\
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/* Check if the node intersects [start;last] */ \
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if (last < ITSTART(node)) /* !Cond1 */ \
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return NULL; \
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else if (start <= ITLAST(node)) /* Cond2 */ \
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return node; \
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} \
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}
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