1 /*
2 * Copyright (c) 2018 Intel Corporation
3 *
4 * SPDX-License-Identifier: Apache-2.0
5 */
6
7 /**
8 * @file
9 * @defgroup rbtree_apis Balanced Red/Black Tree
10 * @ingroup datastructure_apis
11 *
12 * @brief Balanced Red/Black Tree implementation
13 *
14 * This implements an intrusive balanced tree that guarantees
15 * O(log2(N)) runtime for all operations and amortized O(1) behavior
16 * for creation and destruction of whole trees. The algorithms and
17 * naming are conventional per existing academic and didactic
18 * implementations, c.f.:
19 *
20 * https://en.wikipedia.org/wiki/Red%E2%80%93black_tree
21 *
22 * The implementation is size-optimized to prioritize runtime memory
23 * usage. The data structure is intrusive, which is to say the @ref
24 * rbnode handle is intended to be placed in a separate struct, in the
25 * same way as with other such structures (e.g. Zephyr's @ref
26 * doubly-linked-list_apis), and requires no data pointer to be stored
27 * in the node. The color bit is unioned with a pointer (fairly common
28 * for such libraries). Most notably, there is no "parent" pointer
29 * stored in the node, the upper structure of the tree being generated
30 * dynamically via a stack as the tree is recursed. So the overall
31 * memory overhead of a node is just two pointers, identical with a
32 * doubly-linked list.
33 *
34 * @{
35 */
36
37 #ifndef ZEPHYR_INCLUDE_SYS_RB_H_
38 #define ZEPHYR_INCLUDE_SYS_RB_H_
39
40 #include <stdbool.h>
41 #include <stdint.h>
42
43 /* Our SDK/toolchains integration seems to be inconsistent about
44 * whether they expose alloca.h or not. On gcc it's a moot point as
45 * it's always builtin.
46 */
47 #ifdef __GNUC__
48 #ifndef alloca
49 #define alloca __builtin_alloca
50 #endif
51 #else
52 #include <alloca.h>
53 #endif
54
55 /**
56 * @brief Balanced red/black tree node structure
57 */
58 struct rbnode {
59 /** @cond INTERNAL_HIDDEN */
60 struct rbnode *children[2];
61 /** @endcond */
62 };
63
64 /* Theoretical maximum depth of tree based on pointer size. If memory
65 * is filled with 2-pointer nodes, and the tree can be twice as a
66 * packed binary tree, plus root... Works out to 59 entries for 32
67 * bit pointers and 121 at 64 bits.
68 */
69 #define Z_TBITS(t) ((sizeof(t)) < 8 ? 2 : 3)
70 #define Z_PBITS(t) (8 * sizeof(t))
71 #define Z_MAX_RBTREE_DEPTH (2 * (Z_PBITS(int *) - Z_TBITS(int *) - 1) + 1)
72
73 /**
74 * @typedef rb_lessthan_t
75 * @brief Red/black tree comparison predicate
76 *
77 * Compares the two nodes and returns true if node A is strictly less
78 * than B according to the tree's sorting criteria, false otherwise.
79 *
80 * Note that during insert, the new node being inserted will always be
81 * "A", where "B" is the existing node within the tree against which
82 * it is being compared. This trait can be used (with care!) to
83 * implement "most/least recently added" semantics between nodes which
84 * would otherwise compare as equal.
85 */
86 typedef bool (*rb_lessthan_t)(struct rbnode *a, struct rbnode *b);
87
88 /**
89 * @brief Balanced red/black tree structure
90 */
91 struct rbtree {
92 /** Root node of the tree */
93 struct rbnode *root;
94 /** Comparison function for nodes in the tree */
95 rb_lessthan_t lessthan_fn;
96 /** @cond INTERNAL_HIDDEN */
97 int max_depth;
98 #ifdef CONFIG_MISRA_SANE
99 struct rbnode *iter_stack[Z_MAX_RBTREE_DEPTH];
100 unsigned char iter_left[Z_MAX_RBTREE_DEPTH];
101 #endif
102 /** @endcond */
103 };
104
105 /**
106 * @brief Prototype for node visitor callback.
107 * @param node Node being visited
108 * @param cookie User-specified data
109 */
110 typedef void (*rb_visit_t)(struct rbnode *node, void *cookie);
111
112 struct rbnode *z_rb_child(struct rbnode *node, uint8_t side);
113 int z_rb_is_black(struct rbnode *node);
114 #ifndef CONFIG_MISRA_SANE
115 void z_rb_walk(struct rbnode *node, rb_visit_t visit_fn, void *cookie);
116 #endif
117 struct rbnode *z_rb_get_minmax(struct rbtree *tree, uint8_t side);
118
119 /**
120 * @brief Insert node into tree
121 */
122 void rb_insert(struct rbtree *tree, struct rbnode *node);
123
124 /**
125 * @brief Remove node from tree
126 */
127 void rb_remove(struct rbtree *tree, struct rbnode *node);
128
129 /**
130 * @brief Returns the lowest-sorted member of the tree
131 */
rb_get_min(struct rbtree * tree)132 static inline struct rbnode *rb_get_min(struct rbtree *tree)
133 {
134 return z_rb_get_minmax(tree, 0U);
135 }
136
137 /**
138 * @brief Returns the highest-sorted member of the tree
139 */
rb_get_max(struct rbtree * tree)140 static inline struct rbnode *rb_get_max(struct rbtree *tree)
141 {
142 return z_rb_get_minmax(tree, 1U);
143 }
144
145 /**
146 * @brief Returns true if the given node is part of the tree
147 *
148 * Note that this does not internally dereference the node pointer
149 * (though the tree's lessthan callback might!), it just tests it for
150 * equality with items in the tree. So it's feasible to use this to
151 * implement a "set" construct by simply testing the pointer value
152 * itself.
153 */
154 bool rb_contains(struct rbtree *tree, struct rbnode *node);
155
156 #ifndef CONFIG_MISRA_SANE
157 /**
158 * @brief Walk/enumerate a rbtree
159 *
160 * Very simple recursive enumeration. Low code size, but requiring a
161 * separate function can be clumsy for the user and there is no way to
162 * break out of the loop early. See RB_FOR_EACH for an iterative
163 * implementation.
164 */
rb_walk(struct rbtree * tree,rb_visit_t visit_fn,void * cookie)165 static inline void rb_walk(struct rbtree *tree, rb_visit_t visit_fn,
166 void *cookie)
167 {
168 z_rb_walk(tree->root, visit_fn, cookie);
169 }
170 #endif
171
172 struct _rb_foreach {
173 struct rbnode **stack;
174 uint8_t *is_left;
175 int32_t top;
176 };
177
178 #ifdef CONFIG_MISRA_SANE
179 #define _RB_FOREACH_INIT(tree, node) { \
180 .stack = &(tree)->iter_stack[0], \
181 .is_left = &(tree)->iter_left[0], \
182 .top = -1 \
183 }
184 #else
185 #define _RB_FOREACH_INIT(tree, node) { \
186 .stack = (struct rbnode **) \
187 alloca((tree)->max_depth * sizeof(struct rbnode *)), \
188 .is_left = (uint8_t *)alloca((tree)->max_depth * sizeof(uint8_t)),\
189 .top = -1 \
190 }
191 #endif
192
193 struct rbnode *z_rb_foreach_next(struct rbtree *tree, struct _rb_foreach *f);
194
195 /**
196 * @brief Walk a tree in-order without recursing
197 *
198 * While @ref rb_walk() is very simple, recursing on the C stack can
199 * be clumsy for some purposes and on some architectures wastes
200 * significant memory in stack frames. This macro implements a
201 * non-recursive "foreach" loop that can iterate directly on the tree,
202 * at a moderate cost in code size.
203 *
204 * Note that the resulting loop is not safe against modifications to
205 * the tree. Changes to the tree structure during the loop will
206 * produce incorrect results, as nodes may be skipped or duplicated.
207 * Unlike linked lists, no _SAFE variant exists.
208 *
209 * Note also that the macro expands its arguments multiple times, so
210 * they should not be expressions with side effects.
211 *
212 * @param tree A pointer to a struct rbtree to walk
213 * @param node The symbol name of a local struct rbnode* variable to
214 * use as the iterator
215 */
216 #define RB_FOR_EACH(tree, node) \
217 for (struct _rb_foreach __f = _RB_FOREACH_INIT(tree, node); \
218 (node = z_rb_foreach_next(tree, &__f)); \
219 /**/)
220
221 /**
222 * @brief Loop over rbtree with implicit container field logic
223 *
224 * As for RB_FOR_EACH(), but "node" can have an arbitrary type
225 * containing a struct rbnode.
226 *
227 * @param tree A pointer to a struct rbtree to walk
228 * @param node The symbol name of a local iterator
229 * @param field The field name of a struct rbnode inside node
230 */
231 #define RB_FOR_EACH_CONTAINER(tree, node, field) \
232 for (struct _rb_foreach __f = _RB_FOREACH_INIT(tree, node); \
233 ({struct rbnode *n = z_rb_foreach_next(tree, &__f); \
234 node = n ? CONTAINER_OF(n, __typeof__(*(node)), \
235 field) : NULL; }) != NULL; \
236 /**/)
237
238 /** @} */
239
240 #endif /* ZEPHYR_INCLUDE_SYS_RB_H_ */
241
