1/* SPDX-License-Identifier: GPL-2.0-or-later */
2/*
3  Interval Trees
4  (C) 2012  Michel Lespinasse <walken@google.com>
5
6
7  include/linux/interval_tree_generic.h
8*/
9
10#include <linux/rbtree_augmented.h>
11
12/*
13 * Template for implementing interval trees
14 *
15 * ITSTRUCT:   struct type of the interval tree nodes
16 * ITRB:       name of struct rb_node field within ITSTRUCT
17 * ITTYPE:     type of the interval endpoints
18 * ITSUBTREE:  name of ITTYPE field within ITSTRUCT holding last-in-subtree
19 * ITSTART(n): start endpoint of ITSTRUCT node n
20 * ITLAST(n):  last endpoint of ITSTRUCT node n
21 * ITSTATIC:   'static' or empty
22 * ITPREFIX:   prefix to use for the inline tree definitions
23 *
24 * Note - before using this, please consider if generic version
25 * (interval_tree.h) would work for you...
26 */
27
28#define INTERVAL_TREE_DEFINE(ITSTRUCT, ITRB, ITTYPE, ITSUBTREE,		      \
29			     ITSTART, ITLAST, ITSTATIC, ITPREFIX)	      \
30									      \
31/* Callbacks for augmented rbtree insert and remove */			      \
32									      \
33RB_DECLARE_CALLBACKS_MAX(static, ITPREFIX ## _augment,			      \
34			 ITSTRUCT, ITRB, ITTYPE, ITSUBTREE, ITLAST)	      \
35									      \
36/* Insert / remove interval nodes from the tree */			      \
37									      \
38ITSTATIC void ITPREFIX ## _insert(ITSTRUCT *node,			      \
39				  struct rb_root_cached *root)	 	      \
40{									      \
41	struct rb_node **link = &root->rb_root.rb_node, *rb_parent = NULL;    \
42	ITTYPE start = ITSTART(node), last = ITLAST(node);		      \
43	ITSTRUCT *parent;						      \
44	bool leftmost = true;						      \
45									      \
46	while (*link) {							      \
47		rb_parent = *link;					      \
48		parent = rb_entry(rb_parent, ITSTRUCT, ITRB);		      \
49		if (parent->ITSUBTREE < last)				      \
50			parent->ITSUBTREE = last;			      \
51		if (start < ITSTART(parent))				      \
52			link = &parent->ITRB.rb_left;			      \
53		else {							      \
54			link = &parent->ITRB.rb_right;			      \
55			leftmost = false;				      \
56		}							      \
57	}								      \
58									      \
59	node->ITSUBTREE = last;						      \
60	rb_link_node(&node->ITRB, rb_parent, link);			      \
61	rb_insert_augmented_cached(&node->ITRB, root,			      \
62				   leftmost, &ITPREFIX ## _augment);	      \
63}									      \
64									      \
65ITSTATIC void ITPREFIX ## _remove(ITSTRUCT *node,			      \
66				  struct rb_root_cached *root)		      \
67{									      \
68	rb_erase_augmented_cached(&node->ITRB, root, &ITPREFIX ## _augment);  \
69}									      \
70									      \
71/*									      \
72 * Iterate over intervals intersecting [start;last]			      \
73 *									      \
74 * Note that a node's interval intersects [start;last] iff:		      \
75 *   Cond1: ITSTART(node) <= last					      \
76 * and									      \
77 *   Cond2: start <= ITLAST(node)					      \
78 */									      \
79									      \
80static ITSTRUCT *							      \
81ITPREFIX ## _subtree_search(ITSTRUCT *node, ITTYPE start, ITTYPE last)	      \
82{									      \
83	while (true) {							      \
84		/*							      \
85		 * Loop invariant: start <= node->ITSUBTREE		      \
86		 * (Cond2 is satisfied by one of the subtree nodes)	      \
87		 */							      \
88		if (node->ITRB.rb_left) {				      \
89			ITSTRUCT *left = rb_entry(node->ITRB.rb_left,	      \
90						  ITSTRUCT, ITRB);	      \
91			if (start <= left->ITSUBTREE) {			      \
92				/*					      \
93				 * Some nodes in left subtree satisfy Cond2.  \
94				 * Iterate to find the leftmost such node N.  \
95				 * If it also satisfies Cond1, that's the     \
96				 * match we are looking for. Otherwise, there \
97				 * is no matching interval as nodes to the    \
98				 * right of N can't satisfy Cond1 either.     \
99				 */					      \
100				node = left;				      \
101				continue;				      \
102			}						      \
103		}							      \
104		if (ITSTART(node) <= last) {		/* Cond1 */	      \
105			if (start <= ITLAST(node))	/* Cond2 */	      \
106				return node;	/* node is leftmost match */  \
107			if (node->ITRB.rb_right) {			      \
108				node = rb_entry(node->ITRB.rb_right,	      \
109						ITSTRUCT, ITRB);	      \
110				if (start <= node->ITSUBTREE)		      \
111					continue;			      \
112			}						      \
113		}							      \
114		return NULL;	/* No match */				      \
115	}								      \
116}									      \
117									      \
118ITSTATIC ITSTRUCT *							      \
119ITPREFIX ## _iter_first(struct rb_root_cached *root,			      \
120			ITTYPE start, ITTYPE last)			      \
121{									      \
122	ITSTRUCT *node, *leftmost;					      \
123									      \
124	if (!root->rb_root.rb_node)					      \
125		return NULL;						      \
126									      \
127	/*								      \
128	 * Fastpath range intersection/overlap between A: [a0, a1] and	      \
129	 * B: [b0, b1] is given by:					      \
130	 *								      \
131	 *         a0 <= b1 && b0 <= a1					      \
132	 *								      \
133	 *  ... where A holds the lock range and B holds the smallest	      \
134	 * 'start' and largest 'last' in the tree. For the later, we	      \
135	 * rely on the root node, which by augmented interval tree	      \
136	 * property, holds the largest value in its last-in-subtree.	      \
137	 * This allows mitigating some of the tree walk overhead for	      \
138	 * for non-intersecting ranges, maintained and consulted in O(1).     \
139	 */								      \
140	node = rb_entry(root->rb_root.rb_node, ITSTRUCT, ITRB);		      \
141	if (node->ITSUBTREE < start)					      \
142		return NULL;						      \
143									      \
144	leftmost = rb_entry(root->rb_leftmost, ITSTRUCT, ITRB);		      \
145	if (ITSTART(leftmost) > last)					      \
146		return NULL;						      \
147									      \
148	return ITPREFIX ## _subtree_search(node, start, last);		      \
149}									      \
150									      \
151ITSTATIC ITSTRUCT *							      \
152ITPREFIX ## _iter_next(ITSTRUCT *node, ITTYPE start, ITTYPE last)	      \
153{									      \
154	struct rb_node *rb = node->ITRB.rb_right, *prev;		      \
155									      \
156	while (true) {							      \
157		/*							      \
158		 * Loop invariants:					      \
159		 *   Cond1: ITSTART(node) <= last			      \
160		 *   rb == node->ITRB.rb_right				      \
161		 *							      \
162		 * First, search right subtree if suitable		      \
163		 */							      \
164		if (rb) {						      \
165			ITSTRUCT *right = rb_entry(rb, ITSTRUCT, ITRB);	      \
166			if (start <= right->ITSUBTREE)			      \
167				return ITPREFIX ## _subtree_search(right,     \
168								start, last); \
169		}							      \
170									      \
171		/* Move up the tree until we come from a node's left child */ \
172		do {							      \
173			rb = rb_parent(&node->ITRB);			      \
174			if (!rb)					      \
175				return NULL;				      \
176			prev = &node->ITRB;				      \
177			node = rb_entry(rb, ITSTRUCT, ITRB);		      \
178			rb = node->ITRB.rb_right;			      \
179		} while (prev == rb);					      \
180									      \
181		/* Check if the node intersects [start;last] */		      \
182		if (last < ITSTART(node))		/* !Cond1 */	      \
183			return NULL;					      \
184		else if (start <= ITLAST(node))		/* Cond2 */	      \
185			return node;					      \
186	}								      \
187}
188