1 /* SPDX-License-Identifier: GPL-2.0-or-later * 1 /* SPDX-License-Identifier: GPL-2.0-or-later */
2 /* 2 /*
3 Red Black Trees 3 Red Black Trees
4 (C) 1999 Andrea Arcangeli <andrea@suse.de> 4 (C) 1999 Andrea Arcangeli <andrea@suse.de>
5 (C) 2002 David Woodhouse <dwmw2@infradead.o 5 (C) 2002 David Woodhouse <dwmw2@infradead.org>
6 (C) 2012 Michel Lespinasse <walken@google.c 6 (C) 2012 Michel Lespinasse <walken@google.com>
7 7
8 8
9 linux/include/linux/rbtree_augmented.h 9 linux/include/linux/rbtree_augmented.h
10 */ 10 */
11 11
12 #ifndef _LINUX_RBTREE_AUGMENTED_H 12 #ifndef _LINUX_RBTREE_AUGMENTED_H
13 #define _LINUX_RBTREE_AUGMENTED_H 13 #define _LINUX_RBTREE_AUGMENTED_H
14 14
15 #include <linux/compiler.h> 15 #include <linux/compiler.h>
16 #include <linux/rbtree.h> 16 #include <linux/rbtree.h>
17 #include <linux/rcupdate.h> 17 #include <linux/rcupdate.h>
18 18
19 /* 19 /*
20 * Please note - only struct rb_augment_callba 20 * Please note - only struct rb_augment_callbacks and the prototypes for
21 * rb_insert_augmented() and rb_erase_augmente 21 * rb_insert_augmented() and rb_erase_augmented() are intended to be public.
22 * The rest are implementation details you are 22 * The rest are implementation details you are not expected to depend on.
23 * 23 *
24 * See Documentation/core-api/rbtree.rst for d !! 24 * See Documentation/rbtree.txt for documentation and samples.
25 */ 25 */
26 26
27 struct rb_augment_callbacks { 27 struct rb_augment_callbacks {
28 void (*propagate)(struct rb_node *node 28 void (*propagate)(struct rb_node *node, struct rb_node *stop);
29 void (*copy)(struct rb_node *old, stru 29 void (*copy)(struct rb_node *old, struct rb_node *new);
30 void (*rotate)(struct rb_node *old, st 30 void (*rotate)(struct rb_node *old, struct rb_node *new);
31 }; 31 };
32 32
33 extern void __rb_insert_augmented(struct rb_no 33 extern void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
34 void (*augment_rotate)(struct rb_node 34 void (*augment_rotate)(struct rb_node *old, struct rb_node *new));
35 35
36 /* 36 /*
37 * Fixup the rbtree and update the augmented i 37 * Fixup the rbtree and update the augmented information when rebalancing.
38 * 38 *
39 * On insertion, the user must update the augm 39 * On insertion, the user must update the augmented information on the path
40 * leading to the inserted node, then call rb_ 40 * leading to the inserted node, then call rb_link_node() as usual and
41 * rb_insert_augmented() instead of the usual 41 * rb_insert_augmented() instead of the usual rb_insert_color() call.
42 * If rb_insert_augmented() rebalances the rbt 42 * If rb_insert_augmented() rebalances the rbtree, it will callback into
43 * a user provided function to update the augm 43 * a user provided function to update the augmented information on the
44 * affected subtrees. 44 * affected subtrees.
45 */ 45 */
46 static inline void 46 static inline void
47 rb_insert_augmented(struct rb_node *node, stru 47 rb_insert_augmented(struct rb_node *node, struct rb_root *root,
48 const struct rb_augment_ca 48 const struct rb_augment_callbacks *augment)
49 { 49 {
50 __rb_insert_augmented(node, root, augm 50 __rb_insert_augmented(node, root, augment->rotate);
51 } 51 }
52 52
53 static inline void 53 static inline void
54 rb_insert_augmented_cached(struct rb_node *nod 54 rb_insert_augmented_cached(struct rb_node *node,
55 struct rb_root_cach 55 struct rb_root_cached *root, bool newleft,
56 const struct rb_aug 56 const struct rb_augment_callbacks *augment)
57 { 57 {
58 if (newleft) 58 if (newleft)
59 root->rb_leftmost = node; 59 root->rb_leftmost = node;
60 rb_insert_augmented(node, &root->rb_ro 60 rb_insert_augmented(node, &root->rb_root, augment);
61 } 61 }
62 62
63 static __always_inline struct rb_node * <<
64 rb_add_augmented_cached(struct rb_node *node, <<
65 bool (*less)(struct rb <<
66 const struct rb_augmen <<
67 { <<
68 struct rb_node **link = &tree->rb_root <<
69 struct rb_node *parent = NULL; <<
70 bool leftmost = true; <<
71 <<
72 while (*link) { <<
73 parent = *link; <<
74 if (less(node, parent)) { <<
75 link = &parent->rb_lef <<
76 } else { <<
77 link = &parent->rb_rig <<
78 leftmost = false; <<
79 } <<
80 } <<
81 <<
82 rb_link_node(node, parent, link); <<
83 augment->propagate(parent, NULL); /* s <<
84 rb_insert_augmented_cached(node, tree, <<
85 <<
86 return leftmost ? node : NULL; <<
87 } <<
88 <<
89 /* 63 /*
90 * Template for declaring augmented rbtree cal 64 * Template for declaring augmented rbtree callbacks (generic case)
91 * 65 *
92 * RBSTATIC: 'static' or empty 66 * RBSTATIC: 'static' or empty
93 * RBNAME: name of the rb_augment_callbac 67 * RBNAME: name of the rb_augment_callbacks structure
94 * RBSTRUCT: struct type of the tree nodes 68 * RBSTRUCT: struct type of the tree nodes
95 * RBFIELD: name of struct rb_node field w 69 * RBFIELD: name of struct rb_node field within RBSTRUCT
96 * RBAUGMENTED: name of field within RBSTRUCT 70 * RBAUGMENTED: name of field within RBSTRUCT holding data for subtree
97 * RBCOMPUTE: name of function that recomput 71 * RBCOMPUTE: name of function that recomputes the RBAUGMENTED data
98 */ 72 */
99 73
100 #define RB_DECLARE_CALLBACKS(RBSTATIC, RBNAME, 74 #define RB_DECLARE_CALLBACKS(RBSTATIC, RBNAME, \
101 RBSTRUCT, RBFIELD 75 RBSTRUCT, RBFIELD, RBAUGMENTED, RBCOMPUTE) \
102 static inline void 76 static inline void \
103 RBNAME ## _propagate(struct rb_node *rb, struc 77 RBNAME ## _propagate(struct rb_node *rb, struct rb_node *stop) \
104 { 78 { \
105 while (rb != stop) { 79 while (rb != stop) { \
106 RBSTRUCT *node = rb_entry(rb, 80 RBSTRUCT *node = rb_entry(rb, RBSTRUCT, RBFIELD); \
107 if (RBCOMPUTE(node, true)) 81 if (RBCOMPUTE(node, true)) \
108 break; 82 break; \
109 rb = rb_parent(&node->RBFIELD) 83 rb = rb_parent(&node->RBFIELD); \
110 } 84 } \
111 } 85 } \
112 static inline void 86 static inline void \
113 RBNAME ## _copy(struct rb_node *rb_old, struct 87 RBNAME ## _copy(struct rb_node *rb_old, struct rb_node *rb_new) \
114 { 88 { \
115 RBSTRUCT *old = rb_entry(rb_old, RBSTR 89 RBSTRUCT *old = rb_entry(rb_old, RBSTRUCT, RBFIELD); \
116 RBSTRUCT *new = rb_entry(rb_new, RBSTR 90 RBSTRUCT *new = rb_entry(rb_new, RBSTRUCT, RBFIELD); \
117 new->RBAUGMENTED = old->RBAUGMENTED; 91 new->RBAUGMENTED = old->RBAUGMENTED; \
118 } 92 } \
119 static void 93 static void \
120 RBNAME ## _rotate(struct rb_node *rb_old, stru 94 RBNAME ## _rotate(struct rb_node *rb_old, struct rb_node *rb_new) \
121 { 95 { \
122 RBSTRUCT *old = rb_entry(rb_old, RBSTR 96 RBSTRUCT *old = rb_entry(rb_old, RBSTRUCT, RBFIELD); \
123 RBSTRUCT *new = rb_entry(rb_new, RBSTR 97 RBSTRUCT *new = rb_entry(rb_new, RBSTRUCT, RBFIELD); \
124 new->RBAUGMENTED = old->RBAUGMENTED; 98 new->RBAUGMENTED = old->RBAUGMENTED; \
125 RBCOMPUTE(old, false); 99 RBCOMPUTE(old, false); \
126 } 100 } \
127 RBSTATIC const struct rb_augment_callbacks RBN 101 RBSTATIC const struct rb_augment_callbacks RBNAME = { \
128 .propagate = RBNAME ## _propagate, 102 .propagate = RBNAME ## _propagate, \
129 .copy = RBNAME ## _copy, 103 .copy = RBNAME ## _copy, \
130 .rotate = RBNAME ## _rotate 104 .rotate = RBNAME ## _rotate \
131 }; 105 };
132 106
133 /* 107 /*
134 * Template for declaring augmented rbtree cal 108 * Template for declaring augmented rbtree callbacks,
135 * computing RBAUGMENTED scalar as max(RBCOMPU 109 * computing RBAUGMENTED scalar as max(RBCOMPUTE(node)) for all subtree nodes.
136 * 110 *
137 * RBSTATIC: 'static' or empty 111 * RBSTATIC: 'static' or empty
138 * RBNAME: name of the rb_augment_callbac 112 * RBNAME: name of the rb_augment_callbacks structure
139 * RBSTRUCT: struct type of the tree nodes 113 * RBSTRUCT: struct type of the tree nodes
140 * RBFIELD: name of struct rb_node field w 114 * RBFIELD: name of struct rb_node field within RBSTRUCT
141 * RBTYPE: type of the RBAUGMENTED field 115 * RBTYPE: type of the RBAUGMENTED field
142 * RBAUGMENTED: name of RBTYPE field within RB 116 * RBAUGMENTED: name of RBTYPE field within RBSTRUCT holding data for subtree
143 * RBCOMPUTE: name of function that returns 117 * RBCOMPUTE: name of function that returns the per-node RBTYPE scalar
144 */ 118 */
145 119
146 #define RB_DECLARE_CALLBACKS_MAX(RBSTATIC, RBN 120 #define RB_DECLARE_CALLBACKS_MAX(RBSTATIC, RBNAME, RBSTRUCT, RBFIELD, \
147 RBTYPE, RBAUG 121 RBTYPE, RBAUGMENTED, RBCOMPUTE) \
148 static inline bool RBNAME ## _compute_max(RBST 122 static inline bool RBNAME ## _compute_max(RBSTRUCT *node, bool exit) \
149 { 123 { \
150 RBSTRUCT *child; 124 RBSTRUCT *child; \
151 RBTYPE max = RBCOMPUTE(node); 125 RBTYPE max = RBCOMPUTE(node); \
152 if (node->RBFIELD.rb_left) { 126 if (node->RBFIELD.rb_left) { \
153 child = rb_entry(node->RBFIELD 127 child = rb_entry(node->RBFIELD.rb_left, RBSTRUCT, RBFIELD); \
154 if (child->RBAUGMENTED > max) 128 if (child->RBAUGMENTED > max) \
155 max = child->RBAUGMENT 129 max = child->RBAUGMENTED; \
156 } 130 } \
157 if (node->RBFIELD.rb_right) { 131 if (node->RBFIELD.rb_right) { \
158 child = rb_entry(node->RBFIELD 132 child = rb_entry(node->RBFIELD.rb_right, RBSTRUCT, RBFIELD); \
159 if (child->RBAUGMENTED > max) 133 if (child->RBAUGMENTED > max) \
160 max = child->RBAUGMENT 134 max = child->RBAUGMENTED; \
161 } 135 } \
162 if (exit && node->RBAUGMENTED == max) 136 if (exit && node->RBAUGMENTED == max) \
163 return true; 137 return true; \
164 node->RBAUGMENTED = max; 138 node->RBAUGMENTED = max; \
165 return false; 139 return false; \
166 } 140 } \
167 RB_DECLARE_CALLBACKS(RBSTATIC, RBNAME, 141 RB_DECLARE_CALLBACKS(RBSTATIC, RBNAME, \
168 RBSTRUCT, RBFIELD, RBAUGM 142 RBSTRUCT, RBFIELD, RBAUGMENTED, RBNAME ## _compute_max)
169 143
170 144
171 #define RB_RED 0 145 #define RB_RED 0
172 #define RB_BLACK 1 146 #define RB_BLACK 1
173 147
174 #define __rb_parent(pc) ((struct rb_node *) 148 #define __rb_parent(pc) ((struct rb_node *)(pc & ~3))
175 149
176 #define __rb_color(pc) ((pc) & 1) 150 #define __rb_color(pc) ((pc) & 1)
177 #define __rb_is_black(pc) __rb_color(pc) 151 #define __rb_is_black(pc) __rb_color(pc)
178 #define __rb_is_red(pc) (!__rb_color(pc)) 152 #define __rb_is_red(pc) (!__rb_color(pc))
179 #define rb_color(rb) __rb_color((rb)->__ 153 #define rb_color(rb) __rb_color((rb)->__rb_parent_color)
180 #define rb_is_red(rb) __rb_is_red((rb)->_ 154 #define rb_is_red(rb) __rb_is_red((rb)->__rb_parent_color)
181 #define rb_is_black(rb) __rb_is_black((rb)- 155 #define rb_is_black(rb) __rb_is_black((rb)->__rb_parent_color)
182 156
183 static inline void rb_set_parent(struct rb_nod 157 static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
184 { 158 {
185 rb->__rb_parent_color = rb_color(rb) + !! 159 rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
186 } 160 }
187 161
188 static inline void rb_set_parent_color(struct 162 static inline void rb_set_parent_color(struct rb_node *rb,
189 struct 163 struct rb_node *p, int color)
190 { 164 {
191 rb->__rb_parent_color = (unsigned long !! 165 rb->__rb_parent_color = (unsigned long)p | color;
192 } 166 }
193 167
194 static inline void 168 static inline void
195 __rb_change_child(struct rb_node *old, struct 169 __rb_change_child(struct rb_node *old, struct rb_node *new,
196 struct rb_node *parent, stru 170 struct rb_node *parent, struct rb_root *root)
197 { 171 {
198 if (parent) { 172 if (parent) {
199 if (parent->rb_left == old) 173 if (parent->rb_left == old)
200 WRITE_ONCE(parent->rb_ 174 WRITE_ONCE(parent->rb_left, new);
201 else 175 else
202 WRITE_ONCE(parent->rb_ 176 WRITE_ONCE(parent->rb_right, new);
203 } else 177 } else
204 WRITE_ONCE(root->rb_node, new) 178 WRITE_ONCE(root->rb_node, new);
205 } 179 }
206 180
207 static inline void 181 static inline void
208 __rb_change_child_rcu(struct rb_node *old, str 182 __rb_change_child_rcu(struct rb_node *old, struct rb_node *new,
209 struct rb_node *parent, 183 struct rb_node *parent, struct rb_root *root)
210 { 184 {
211 if (parent) { 185 if (parent) {
212 if (parent->rb_left == old) 186 if (parent->rb_left == old)
213 rcu_assign_pointer(par 187 rcu_assign_pointer(parent->rb_left, new);
214 else 188 else
215 rcu_assign_pointer(par 189 rcu_assign_pointer(parent->rb_right, new);
216 } else 190 } else
217 rcu_assign_pointer(root->rb_no 191 rcu_assign_pointer(root->rb_node, new);
218 } 192 }
219 193
220 extern void __rb_erase_color(struct rb_node *p 194 extern void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
221 void (*augment_rotate)(struct rb_node 195 void (*augment_rotate)(struct rb_node *old, struct rb_node *new));
222 196
223 static __always_inline struct rb_node * 197 static __always_inline struct rb_node *
224 __rb_erase_augmented(struct rb_node *node, str 198 __rb_erase_augmented(struct rb_node *node, struct rb_root *root,
225 const struct rb_augment_c 199 const struct rb_augment_callbacks *augment)
226 { 200 {
227 struct rb_node *child = node->rb_right 201 struct rb_node *child = node->rb_right;
228 struct rb_node *tmp = node->rb_left; 202 struct rb_node *tmp = node->rb_left;
229 struct rb_node *parent, *rebalance; 203 struct rb_node *parent, *rebalance;
230 unsigned long pc; 204 unsigned long pc;
231 205
232 if (!tmp) { 206 if (!tmp) {
233 /* 207 /*
234 * Case 1: node to erase has n 208 * Case 1: node to erase has no more than 1 child (easy!)
235 * 209 *
236 * Note that if there is one c 210 * Note that if there is one child it must be red due to 5)
237 * and node must be black due 211 * and node must be black due to 4). We adjust colors locally
238 * so as to bypass __rb_erase_ 212 * so as to bypass __rb_erase_color() later on.
239 */ 213 */
240 pc = node->__rb_parent_color; 214 pc = node->__rb_parent_color;
241 parent = __rb_parent(pc); 215 parent = __rb_parent(pc);
242 __rb_change_child(node, child, 216 __rb_change_child(node, child, parent, root);
243 if (child) { 217 if (child) {
244 child->__rb_parent_col 218 child->__rb_parent_color = pc;
245 rebalance = NULL; 219 rebalance = NULL;
246 } else 220 } else
247 rebalance = __rb_is_bl 221 rebalance = __rb_is_black(pc) ? parent : NULL;
248 tmp = parent; 222 tmp = parent;
249 } else if (!child) { 223 } else if (!child) {
250 /* Still case 1, but this time 224 /* Still case 1, but this time the child is node->rb_left */
251 tmp->__rb_parent_color = pc = 225 tmp->__rb_parent_color = pc = node->__rb_parent_color;
252 parent = __rb_parent(pc); 226 parent = __rb_parent(pc);
253 __rb_change_child(node, tmp, p 227 __rb_change_child(node, tmp, parent, root);
254 rebalance = NULL; 228 rebalance = NULL;
255 tmp = parent; 229 tmp = parent;
256 } else { 230 } else {
257 struct rb_node *successor = ch 231 struct rb_node *successor = child, *child2;
258 232
259 tmp = child->rb_left; 233 tmp = child->rb_left;
260 if (!tmp) { 234 if (!tmp) {
261 /* 235 /*
262 * Case 2: node's succ 236 * Case 2: node's successor is its right child
263 * 237 *
264 * (n) (s) 238 * (n) (s)
265 * / \ / \ 239 * / \ / \
266 * (x) (s) -> (x) ( 240 * (x) (s) -> (x) (c)
267 * \ 241 * \
268 * (c) 242 * (c)
269 */ 243 */
270 parent = successor; 244 parent = successor;
271 child2 = successor->rb 245 child2 = successor->rb_right;
272 246
273 augment->copy(node, su 247 augment->copy(node, successor);
274 } else { 248 } else {
275 /* 249 /*
276 * Case 3: node's succ 250 * Case 3: node's successor is leftmost under
277 * node's right child 251 * node's right child subtree
278 * 252 *
279 * (n) (s) 253 * (n) (s)
280 * / \ / \ 254 * / \ / \
281 * (x) (y) -> (x) ( 255 * (x) (y) -> (x) (y)
282 * / / 256 * / /
283 * (p) (p) 257 * (p) (p)
284 * / / 258 * / /
285 * (s) (c) 259 * (s) (c)
286 * \ 260 * \
287 * (c) 261 * (c)
288 */ 262 */
289 do { 263 do {
290 parent = succe 264 parent = successor;
291 successor = tm 265 successor = tmp;
292 tmp = tmp->rb_ 266 tmp = tmp->rb_left;
293 } while (tmp); 267 } while (tmp);
294 child2 = successor->rb 268 child2 = successor->rb_right;
295 WRITE_ONCE(parent->rb_ 269 WRITE_ONCE(parent->rb_left, child2);
296 WRITE_ONCE(successor-> 270 WRITE_ONCE(successor->rb_right, child);
297 rb_set_parent(child, s 271 rb_set_parent(child, successor);
298 272
299 augment->copy(node, su 273 augment->copy(node, successor);
300 augment->propagate(par 274 augment->propagate(parent, successor);
301 } 275 }
302 276
303 tmp = node->rb_left; 277 tmp = node->rb_left;
304 WRITE_ONCE(successor->rb_left, 278 WRITE_ONCE(successor->rb_left, tmp);
305 rb_set_parent(tmp, successor); 279 rb_set_parent(tmp, successor);
306 280
307 pc = node->__rb_parent_color; 281 pc = node->__rb_parent_color;
308 tmp = __rb_parent(pc); 282 tmp = __rb_parent(pc);
309 __rb_change_child(node, succes 283 __rb_change_child(node, successor, tmp, root);
310 284
311 if (child2) { 285 if (child2) {
>> 286 successor->__rb_parent_color = pc;
312 rb_set_parent_color(ch 287 rb_set_parent_color(child2, parent, RB_BLACK);
313 rebalance = NULL; 288 rebalance = NULL;
314 } else { 289 } else {
315 rebalance = rb_is_blac !! 290 unsigned long pc2 = successor->__rb_parent_color;
>> 291 successor->__rb_parent_color = pc;
>> 292 rebalance = __rb_is_black(pc2) ? parent : NULL;
316 } 293 }
317 successor->__rb_parent_color = <<
318 tmp = successor; 294 tmp = successor;
319 } 295 }
320 296
321 augment->propagate(tmp, NULL); 297 augment->propagate(tmp, NULL);
322 return rebalance; 298 return rebalance;
323 } 299 }
324 300
325 static __always_inline void 301 static __always_inline void
326 rb_erase_augmented(struct rb_node *node, struc 302 rb_erase_augmented(struct rb_node *node, struct rb_root *root,
327 const struct rb_augment_cal 303 const struct rb_augment_callbacks *augment)
328 { 304 {
329 struct rb_node *rebalance = __rb_erase 305 struct rb_node *rebalance = __rb_erase_augmented(node, root, augment);
330 if (rebalance) 306 if (rebalance)
331 __rb_erase_color(rebalance, ro 307 __rb_erase_color(rebalance, root, augment->rotate);
332 } 308 }
333 309
334 static __always_inline void 310 static __always_inline void
335 rb_erase_augmented_cached(struct rb_node *node 311 rb_erase_augmented_cached(struct rb_node *node, struct rb_root_cached *root,
336 const struct rb_augm 312 const struct rb_augment_callbacks *augment)
337 { 313 {
338 if (root->rb_leftmost == node) 314 if (root->rb_leftmost == node)
339 root->rb_leftmost = rb_next(no 315 root->rb_leftmost = rb_next(node);
340 rb_erase_augmented(node, &root->rb_roo 316 rb_erase_augmented(node, &root->rb_root, augment);
341 } 317 }
342 318
343 #endif /* _LINUX_RBTREE_AUGMENTED_H */ 319 #endif /* _LINUX_RBTREE_AUGMENTED_H */
344 320
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