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