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/lib/rbtree.c 9 linux/lib/rbtree.c
10 */ 10 */
11 11
12 #include <linux/rbtree_augmented.h> 12 #include <linux/rbtree_augmented.h>
13 #include <linux/export.h> 13 #include <linux/export.h>
14 14
15 /* 15 /*
16 * red-black trees properties: https://en.wik !! 16 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
17 * 17 *
18 * 1) A node is either red or black 18 * 1) A node is either red or black
19 * 2) The root is black 19 * 2) The root is black
20 * 3) All leaves (NULL) are black 20 * 3) All leaves (NULL) are black
21 * 4) Both children of every red node are bla 21 * 4) Both children of every red node are black
22 * 5) Every simple path from root to leaves c 22 * 5) Every simple path from root to leaves contains the same number
23 * of black nodes. 23 * of black nodes.
24 * 24 *
25 * 4 and 5 give the O(log n) guarantee, since 25 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
26 * consecutive red nodes in a path and every 26 * consecutive red nodes in a path and every red node is therefore followed by
27 * a black. So if B is the number of black no 27 * a black. So if B is the number of black nodes on every simple path (as per
28 * 5), then the longest possible path due to 28 * 5), then the longest possible path due to 4 is 2B.
29 * 29 *
30 * We shall indicate color with case, where b 30 * We shall indicate color with case, where black nodes are uppercase and red
31 * nodes will be lowercase. Unknown color nod 31 * nodes will be lowercase. Unknown color nodes shall be drawn as red within
32 * parentheses and have some accompanying tex 32 * parentheses and have some accompanying text comment.
33 */ 33 */
34 34
35 /* 35 /*
36 * Notes on lockless lookups: 36 * Notes on lockless lookups:
37 * 37 *
38 * All stores to the tree structure (rb_left a 38 * All stores to the tree structure (rb_left and rb_right) must be done using
39 * WRITE_ONCE(). And we must not inadvertently 39 * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
40 * tree structure as seen in program order. 40 * tree structure as seen in program order.
41 * 41 *
42 * These two requirements will allow lockless 42 * These two requirements will allow lockless iteration of the tree -- not
43 * correct iteration mind you, tree rotations 43 * correct iteration mind you, tree rotations are not atomic so a lookup might
44 * miss entire subtrees. 44 * miss entire subtrees.
45 * 45 *
46 * But they do guarantee that any such travers 46 * But they do guarantee that any such traversal will only see valid elements
47 * and that it will indeed complete -- does no 47 * and that it will indeed complete -- does not get stuck in a loop.
48 * 48 *
49 * It also guarantees that if the lookup retur 49 * It also guarantees that if the lookup returns an element it is the 'correct'
50 * one. But not returning an element does _NOT 50 * one. But not returning an element does _NOT_ mean it's not present.
51 * 51 *
52 * NOTE: 52 * NOTE:
53 * 53 *
54 * Stores to __rb_parent_color are not importa 54 * Stores to __rb_parent_color are not important for simple lookups so those
55 * are left undone as of now. Nor did I check 55 * are left undone as of now. Nor did I check for loops involving parent
56 * pointers. 56 * pointers.
57 */ 57 */
58 58
59 static inline void rb_set_black(struct rb_node 59 static inline void rb_set_black(struct rb_node *rb)
60 { 60 {
61 rb->__rb_parent_color += RB_BLACK; !! 61 rb->__rb_parent_color |= RB_BLACK;
62 } 62 }
63 63
64 static inline struct rb_node *rb_red_parent(st 64 static inline struct rb_node *rb_red_parent(struct rb_node *red)
65 { 65 {
66 return (struct rb_node *)red->__rb_par 66 return (struct rb_node *)red->__rb_parent_color;
67 } 67 }
68 68
69 /* 69 /*
70 * Helper function for rotations: 70 * Helper function for rotations:
71 * - old's parent and color get assigned to ne 71 * - old's parent and color get assigned to new
72 * - old gets assigned new as a parent and 'co 72 * - old gets assigned new as a parent and 'color' as a color.
73 */ 73 */
74 static inline void 74 static inline void
75 __rb_rotate_set_parents(struct rb_node *old, s 75 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
76 struct rb_root *root, 76 struct rb_root *root, int color)
77 { 77 {
78 struct rb_node *parent = rb_parent(old 78 struct rb_node *parent = rb_parent(old);
79 new->__rb_parent_color = old->__rb_par 79 new->__rb_parent_color = old->__rb_parent_color;
80 rb_set_parent_color(old, new, color); 80 rb_set_parent_color(old, new, color);
81 __rb_change_child(old, new, parent, ro 81 __rb_change_child(old, new, parent, root);
82 } 82 }
83 83
84 static __always_inline void 84 static __always_inline void
85 __rb_insert(struct rb_node *node, struct rb_ro 85 __rb_insert(struct rb_node *node, struct rb_root *root,
86 void (*augment_rotate)(struct rb_n 86 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
87 { 87 {
88 struct rb_node *parent = rb_red_parent 88 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
89 89
90 while (true) { 90 while (true) {
91 /* 91 /*
92 * Loop invariant: node is red 92 * Loop invariant: node is red.
93 */ 93 */
94 if (unlikely(!parent)) { 94 if (unlikely(!parent)) {
95 /* 95 /*
96 * The inserted node i 96 * The inserted node is root. Either this is the
97 * first node, or we r 97 * first node, or we recursed at Case 1 below and
98 * are no longer viola 98 * are no longer violating 4).
99 */ 99 */
100 rb_set_parent_color(no 100 rb_set_parent_color(node, NULL, RB_BLACK);
101 break; 101 break;
102 } 102 }
103 103
104 /* 104 /*
105 * If there is a black parent, 105 * If there is a black parent, we are done.
106 * Otherwise, take some correc 106 * Otherwise, take some corrective action as,
107 * per 4), we don't want a red 107 * per 4), we don't want a red root or two
108 * consecutive red nodes. 108 * consecutive red nodes.
109 */ 109 */
110 if(rb_is_black(parent)) 110 if(rb_is_black(parent))
111 break; 111 break;
112 112
113 gparent = rb_red_parent(parent 113 gparent = rb_red_parent(parent);
114 114
115 tmp = gparent->rb_right; 115 tmp = gparent->rb_right;
116 if (parent != tmp) { /* par 116 if (parent != tmp) { /* parent == gparent->rb_left */
117 if (tmp && rb_is_red(t 117 if (tmp && rb_is_red(tmp)) {
118 /* 118 /*
119 * Case 1 - no 119 * Case 1 - node's uncle is red (color flips).
120 * 120 *
121 * G 121 * G g
122 * / \ 122 * / \ / \
123 * p u 123 * p u --> P U
124 * / 124 * / /
125 * n 125 * n n
126 * 126 *
127 * However, si 127 * However, since g's parent might be red, and
128 * 4) does not 128 * 4) does not allow this, we need to recurse
129 * at g. 129 * at g.
130 */ 130 */
131 rb_set_parent_ 131 rb_set_parent_color(tmp, gparent, RB_BLACK);
132 rb_set_parent_ 132 rb_set_parent_color(parent, gparent, RB_BLACK);
133 node = gparent 133 node = gparent;
134 parent = rb_pa 134 parent = rb_parent(node);
135 rb_set_parent_ 135 rb_set_parent_color(node, parent, RB_RED);
136 continue; 136 continue;
137 } 137 }
138 138
139 tmp = parent->rb_right 139 tmp = parent->rb_right;
140 if (node == tmp) { 140 if (node == tmp) {
141 /* 141 /*
142 * Case 2 - no 142 * Case 2 - node's uncle is black and node is
143 * the parent' 143 * the parent's right child (left rotate at parent).
144 * 144 *
145 * G 145 * G G
146 * / \ 146 * / \ / \
147 * p U - 147 * p U --> n U
148 * \ 148 * \ /
149 * n 149 * n p
150 * 150 *
151 * This still 151 * This still leaves us in violation of 4), the
152 * continuatio 152 * continuation into Case 3 will fix that.
153 */ 153 */
154 tmp = node->rb 154 tmp = node->rb_left;
155 WRITE_ONCE(par 155 WRITE_ONCE(parent->rb_right, tmp);
156 WRITE_ONCE(nod 156 WRITE_ONCE(node->rb_left, parent);
157 if (tmp) 157 if (tmp)
158 rb_set 158 rb_set_parent_color(tmp, parent,
159 159 RB_BLACK);
160 rb_set_parent_ 160 rb_set_parent_color(parent, node, RB_RED);
161 augment_rotate 161 augment_rotate(parent, node);
162 parent = node; 162 parent = node;
163 tmp = node->rb 163 tmp = node->rb_right;
164 } 164 }
165 165
166 /* 166 /*
167 * Case 3 - node's unc 167 * Case 3 - node's uncle is black and node is
168 * the parent's left c 168 * the parent's left child (right rotate at gparent).
169 * 169 *
170 * G 170 * G P
171 * / \ / 171 * / \ / \
172 * p U --> n 172 * p U --> n g
173 * / 173 * / \
174 * n 174 * n U
175 */ 175 */
176 WRITE_ONCE(gparent->rb 176 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
177 WRITE_ONCE(parent->rb_ 177 WRITE_ONCE(parent->rb_right, gparent);
178 if (tmp) 178 if (tmp)
179 rb_set_parent_ 179 rb_set_parent_color(tmp, gparent, RB_BLACK);
180 __rb_rotate_set_parent 180 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
181 augment_rotate(gparent 181 augment_rotate(gparent, parent);
182 break; 182 break;
183 } else { 183 } else {
184 tmp = gparent->rb_left 184 tmp = gparent->rb_left;
185 if (tmp && rb_is_red(t 185 if (tmp && rb_is_red(tmp)) {
186 /* Case 1 - co 186 /* Case 1 - color flips */
187 rb_set_parent_ 187 rb_set_parent_color(tmp, gparent, RB_BLACK);
188 rb_set_parent_ 188 rb_set_parent_color(parent, gparent, RB_BLACK);
189 node = gparent 189 node = gparent;
190 parent = rb_pa 190 parent = rb_parent(node);
191 rb_set_parent_ 191 rb_set_parent_color(node, parent, RB_RED);
192 continue; 192 continue;
193 } 193 }
194 194
195 tmp = parent->rb_left; 195 tmp = parent->rb_left;
196 if (node == tmp) { 196 if (node == tmp) {
197 /* Case 2 - ri 197 /* Case 2 - right rotate at parent */
198 tmp = node->rb 198 tmp = node->rb_right;
199 WRITE_ONCE(par 199 WRITE_ONCE(parent->rb_left, tmp);
200 WRITE_ONCE(nod 200 WRITE_ONCE(node->rb_right, parent);
201 if (tmp) 201 if (tmp)
202 rb_set 202 rb_set_parent_color(tmp, parent,
203 203 RB_BLACK);
204 rb_set_parent_ 204 rb_set_parent_color(parent, node, RB_RED);
205 augment_rotate 205 augment_rotate(parent, node);
206 parent = node; 206 parent = node;
207 tmp = node->rb 207 tmp = node->rb_left;
208 } 208 }
209 209
210 /* Case 3 - left rotat 210 /* Case 3 - left rotate at gparent */
211 WRITE_ONCE(gparent->rb 211 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
212 WRITE_ONCE(parent->rb_ 212 WRITE_ONCE(parent->rb_left, gparent);
213 if (tmp) 213 if (tmp)
214 rb_set_parent_ 214 rb_set_parent_color(tmp, gparent, RB_BLACK);
215 __rb_rotate_set_parent 215 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
216 augment_rotate(gparent 216 augment_rotate(gparent, parent);
217 break; 217 break;
218 } 218 }
219 } 219 }
220 } 220 }
221 221
222 /* 222 /*
223 * Inline version for rb_erase() use - we want 223 * Inline version for rb_erase() use - we want to be able to inline
224 * and eliminate the dummy_rotate callback the 224 * and eliminate the dummy_rotate callback there
225 */ 225 */
226 static __always_inline void 226 static __always_inline void
227 ____rb_erase_color(struct rb_node *parent, str 227 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
228 void (*augment_rotate)(struct rb_node 228 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
229 { 229 {
230 struct rb_node *node = NULL, *sibling, 230 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
231 231
232 while (true) { 232 while (true) {
233 /* 233 /*
234 * Loop invariants: 234 * Loop invariants:
235 * - node is black (or NULL on 235 * - node is black (or NULL on first iteration)
236 * - node is not the root (par 236 * - node is not the root (parent is not NULL)
237 * - All leaf paths going thro 237 * - All leaf paths going through parent and node have a
238 * black node count that is 238 * black node count that is 1 lower than other leaf paths.
239 */ 239 */
240 sibling = parent->rb_right; 240 sibling = parent->rb_right;
241 if (node != sibling) { /* nod 241 if (node != sibling) { /* node == parent->rb_left */
242 if (rb_is_red(sibling) 242 if (rb_is_red(sibling)) {
243 /* 243 /*
244 * Case 1 - le 244 * Case 1 - left rotate at parent
245 * 245 *
246 * P 246 * P S
247 * / \ 247 * / \ / \
248 * N s 248 * N s --> p Sr
249 * / \ 249 * / \ / \
250 * Sl Sr 250 * Sl Sr N Sl
251 */ 251 */
252 tmp1 = sibling 252 tmp1 = sibling->rb_left;
253 WRITE_ONCE(par 253 WRITE_ONCE(parent->rb_right, tmp1);
254 WRITE_ONCE(sib 254 WRITE_ONCE(sibling->rb_left, parent);
255 rb_set_parent_ 255 rb_set_parent_color(tmp1, parent, RB_BLACK);
256 __rb_rotate_se 256 __rb_rotate_set_parents(parent, sibling, root,
257 257 RB_RED);
258 augment_rotate 258 augment_rotate(parent, sibling);
259 sibling = tmp1 259 sibling = tmp1;
260 } 260 }
261 tmp1 = sibling->rb_rig 261 tmp1 = sibling->rb_right;
262 if (!tmp1 || rb_is_bla 262 if (!tmp1 || rb_is_black(tmp1)) {
263 tmp2 = sibling 263 tmp2 = sibling->rb_left;
264 if (!tmp2 || r 264 if (!tmp2 || rb_is_black(tmp2)) {
265 /* 265 /*
266 * Cas 266 * Case 2 - sibling color flip
267 * (p 267 * (p could be either color here)
268 * 268 *
269 * 269 * (p) (p)
270 * 270 * / \ / \
271 * N 271 * N S --> N s
272 * 272 * / \ / \
273 * 273 * Sl Sr Sl Sr
274 * 274 *
275 * Thi 275 * This leaves us violating 5) which
276 * can 276 * can be fixed by flipping p to black
277 * if 277 * if it was red, or by recursing at p.
278 * p i 278 * p is red when coming from Case 1.
279 */ 279 */
280 rb_set 280 rb_set_parent_color(sibling, parent,
281 281 RB_RED);
282 if (rb 282 if (rb_is_red(parent))
283 283 rb_set_black(parent);
284 else { 284 else {
285 285 node = parent;
286 286 parent = rb_parent(node);
287 287 if (parent)
288 288 continue;
289 } 289 }
290 break; 290 break;
291 } 291 }
292 /* 292 /*
293 * Case 3 - ri 293 * Case 3 - right rotate at sibling
294 * (p could be 294 * (p could be either color here)
295 * 295 *
296 * (p) 296 * (p) (p)
297 * / \ 297 * / \ / \
298 * N S - 298 * N S --> N sl
299 * / \ 299 * / \ \
300 * sl sr !! 300 * sl Sr S
301 * 301 * \
302 * !! 302 * Sr
303 * 303 *
304 * Note: p mig 304 * Note: p might be red, and then both
305 * p and sl ar 305 * p and sl are red after rotation(which
306 * breaks prop 306 * breaks property 4). This is fixed in
307 * Case 4 (in 307 * Case 4 (in __rb_rotate_set_parents()
308 * whi 308 * which set sl the color of p
309 * and 309 * and set p RB_BLACK)
310 * 310 *
311 * (p) 311 * (p) (sl)
312 * / \ 312 * / \ / \
313 * N sl - 313 * N sl --> P S
314 * \ 314 * \ / \
315 * S !! 315 * S N Sr
316 * \ 316 * \
317 * sr !! 317 * Sr
318 */ 318 */
319 tmp1 = tmp2->r 319 tmp1 = tmp2->rb_right;
320 WRITE_ONCE(sib 320 WRITE_ONCE(sibling->rb_left, tmp1);
321 WRITE_ONCE(tmp 321 WRITE_ONCE(tmp2->rb_right, sibling);
322 WRITE_ONCE(par 322 WRITE_ONCE(parent->rb_right, tmp2);
323 if (tmp1) 323 if (tmp1)
324 rb_set 324 rb_set_parent_color(tmp1, sibling,
325 325 RB_BLACK);
326 augment_rotate 326 augment_rotate(sibling, tmp2);
327 tmp1 = sibling 327 tmp1 = sibling;
328 sibling = tmp2 328 sibling = tmp2;
329 } 329 }
330 /* 330 /*
331 * Case 4 - left rotat 331 * Case 4 - left rotate at parent + color flips
332 * (p and sl could be 332 * (p and sl could be either color here.
333 * After rotation, p 333 * After rotation, p becomes black, s acquires
334 * p's color, and sl 334 * p's color, and sl keeps its color)
335 * 335 *
336 * (p) 336 * (p) (s)
337 * / \ 337 * / \ / \
338 * N S --> 338 * N S --> P Sr
339 * / \ 339 * / \ / \
340 * (sl) sr N 340 * (sl) sr N (sl)
341 */ 341 */
342 tmp2 = sibling->rb_lef 342 tmp2 = sibling->rb_left;
343 WRITE_ONCE(parent->rb_ 343 WRITE_ONCE(parent->rb_right, tmp2);
344 WRITE_ONCE(sibling->rb 344 WRITE_ONCE(sibling->rb_left, parent);
345 rb_set_parent_color(tm 345 rb_set_parent_color(tmp1, sibling, RB_BLACK);
346 if (tmp2) 346 if (tmp2)
347 rb_set_parent( 347 rb_set_parent(tmp2, parent);
348 __rb_rotate_set_parent 348 __rb_rotate_set_parents(parent, sibling, root,
349 349 RB_BLACK);
350 augment_rotate(parent, 350 augment_rotate(parent, sibling);
351 break; 351 break;
352 } else { 352 } else {
353 sibling = parent->rb_l 353 sibling = parent->rb_left;
354 if (rb_is_red(sibling) 354 if (rb_is_red(sibling)) {
355 /* Case 1 - ri 355 /* Case 1 - right rotate at parent */
356 tmp1 = sibling 356 tmp1 = sibling->rb_right;
357 WRITE_ONCE(par 357 WRITE_ONCE(parent->rb_left, tmp1);
358 WRITE_ONCE(sib 358 WRITE_ONCE(sibling->rb_right, parent);
359 rb_set_parent_ 359 rb_set_parent_color(tmp1, parent, RB_BLACK);
360 __rb_rotate_se 360 __rb_rotate_set_parents(parent, sibling, root,
361 361 RB_RED);
362 augment_rotate 362 augment_rotate(parent, sibling);
363 sibling = tmp1 363 sibling = tmp1;
364 } 364 }
365 tmp1 = sibling->rb_lef 365 tmp1 = sibling->rb_left;
366 if (!tmp1 || rb_is_bla 366 if (!tmp1 || rb_is_black(tmp1)) {
367 tmp2 = sibling 367 tmp2 = sibling->rb_right;
368 if (!tmp2 || r 368 if (!tmp2 || rb_is_black(tmp2)) {
369 /* Cas 369 /* Case 2 - sibling color flip */
370 rb_set 370 rb_set_parent_color(sibling, parent,
371 371 RB_RED);
372 if (rb 372 if (rb_is_red(parent))
373 373 rb_set_black(parent);
374 else { 374 else {
375 375 node = parent;
376 376 parent = rb_parent(node);
377 377 if (parent)
378 378 continue;
379 } 379 }
380 break; 380 break;
381 } 381 }
382 /* Case 3 - le 382 /* Case 3 - left rotate at sibling */
383 tmp1 = tmp2->r 383 tmp1 = tmp2->rb_left;
384 WRITE_ONCE(sib 384 WRITE_ONCE(sibling->rb_right, tmp1);
385 WRITE_ONCE(tmp 385 WRITE_ONCE(tmp2->rb_left, sibling);
386 WRITE_ONCE(par 386 WRITE_ONCE(parent->rb_left, tmp2);
387 if (tmp1) 387 if (tmp1)
388 rb_set 388 rb_set_parent_color(tmp1, sibling,
389 389 RB_BLACK);
390 augment_rotate 390 augment_rotate(sibling, tmp2);
391 tmp1 = sibling 391 tmp1 = sibling;
392 sibling = tmp2 392 sibling = tmp2;
393 } 393 }
394 /* Case 4 - right rota 394 /* Case 4 - right rotate at parent + color flips */
395 tmp2 = sibling->rb_rig 395 tmp2 = sibling->rb_right;
396 WRITE_ONCE(parent->rb_ 396 WRITE_ONCE(parent->rb_left, tmp2);
397 WRITE_ONCE(sibling->rb 397 WRITE_ONCE(sibling->rb_right, parent);
398 rb_set_parent_color(tm 398 rb_set_parent_color(tmp1, sibling, RB_BLACK);
399 if (tmp2) 399 if (tmp2)
400 rb_set_parent( 400 rb_set_parent(tmp2, parent);
401 __rb_rotate_set_parent 401 __rb_rotate_set_parents(parent, sibling, root,
402 402 RB_BLACK);
403 augment_rotate(parent, 403 augment_rotate(parent, sibling);
404 break; 404 break;
405 } 405 }
406 } 406 }
407 } 407 }
408 408
409 /* Non-inline version for rb_erase_augmented() 409 /* Non-inline version for rb_erase_augmented() use */
410 void __rb_erase_color(struct rb_node *parent, 410 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
411 void (*augment_rotate)(struct rb_node 411 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
412 { 412 {
413 ____rb_erase_color(parent, root, augme 413 ____rb_erase_color(parent, root, augment_rotate);
414 } 414 }
415 EXPORT_SYMBOL(__rb_erase_color); 415 EXPORT_SYMBOL(__rb_erase_color);
416 416
417 /* 417 /*
418 * Non-augmented rbtree manipulation functions 418 * Non-augmented rbtree manipulation functions.
419 * 419 *
420 * We use dummy augmented callbacks here, and 420 * We use dummy augmented callbacks here, and have the compiler optimize them
421 * out of the rb_insert_color() and rb_erase() 421 * out of the rb_insert_color() and rb_erase() function definitions.
422 */ 422 */
423 423
424 static inline void dummy_propagate(struct rb_n 424 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
425 static inline void dummy_copy(struct rb_node * 425 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
426 static inline void dummy_rotate(struct rb_node 426 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
427 427
428 static const struct rb_augment_callbacks dummy 428 static const struct rb_augment_callbacks dummy_callbacks = {
429 .propagate = dummy_propagate, 429 .propagate = dummy_propagate,
430 .copy = dummy_copy, 430 .copy = dummy_copy,
431 .rotate = dummy_rotate 431 .rotate = dummy_rotate
432 }; 432 };
433 433
434 void rb_insert_color(struct rb_node *node, str 434 void rb_insert_color(struct rb_node *node, struct rb_root *root)
435 { 435 {
436 __rb_insert(node, root, dummy_rotate); 436 __rb_insert(node, root, dummy_rotate);
437 } 437 }
438 EXPORT_SYMBOL(rb_insert_color); 438 EXPORT_SYMBOL(rb_insert_color);
439 439
440 void rb_erase(struct rb_node *node, struct rb_ 440 void rb_erase(struct rb_node *node, struct rb_root *root)
441 { 441 {
442 struct rb_node *rebalance; 442 struct rb_node *rebalance;
443 rebalance = __rb_erase_augmented(node, 443 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
444 if (rebalance) 444 if (rebalance)
445 ____rb_erase_color(rebalance, 445 ____rb_erase_color(rebalance, root, dummy_rotate);
446 } 446 }
447 EXPORT_SYMBOL(rb_erase); 447 EXPORT_SYMBOL(rb_erase);
448 448
449 /* 449 /*
450 * Augmented rbtree manipulation functions. 450 * Augmented rbtree manipulation functions.
451 * 451 *
452 * This instantiates the same __always_inline 452 * This instantiates the same __always_inline functions as in the non-augmented
453 * case, but this time with user-defined callb 453 * case, but this time with user-defined callbacks.
454 */ 454 */
455 455
456 void __rb_insert_augmented(struct rb_node *nod 456 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
457 void (*augment_rotate)(struct rb_node 457 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
458 { 458 {
459 __rb_insert(node, root, augment_rotate 459 __rb_insert(node, root, augment_rotate);
460 } 460 }
461 EXPORT_SYMBOL(__rb_insert_augmented); 461 EXPORT_SYMBOL(__rb_insert_augmented);
462 462
463 /* 463 /*
464 * This function returns the first node (in so 464 * This function returns the first node (in sort order) of the tree.
465 */ 465 */
466 struct rb_node *rb_first(const struct rb_root 466 struct rb_node *rb_first(const struct rb_root *root)
467 { 467 {
468 struct rb_node *n; 468 struct rb_node *n;
469 469
470 n = root->rb_node; 470 n = root->rb_node;
471 if (!n) 471 if (!n)
472 return NULL; 472 return NULL;
473 while (n->rb_left) 473 while (n->rb_left)
474 n = n->rb_left; 474 n = n->rb_left;
475 return n; 475 return n;
476 } 476 }
477 EXPORT_SYMBOL(rb_first); 477 EXPORT_SYMBOL(rb_first);
478 478
479 struct rb_node *rb_last(const struct rb_root * 479 struct rb_node *rb_last(const struct rb_root *root)
480 { 480 {
481 struct rb_node *n; 481 struct rb_node *n;
482 482
483 n = root->rb_node; 483 n = root->rb_node;
484 if (!n) 484 if (!n)
485 return NULL; 485 return NULL;
486 while (n->rb_right) 486 while (n->rb_right)
487 n = n->rb_right; 487 n = n->rb_right;
488 return n; 488 return n;
489 } 489 }
490 EXPORT_SYMBOL(rb_last); 490 EXPORT_SYMBOL(rb_last);
491 491
492 struct rb_node *rb_next(const struct rb_node * 492 struct rb_node *rb_next(const struct rb_node *node)
493 { 493 {
494 struct rb_node *parent; 494 struct rb_node *parent;
495 495
496 if (RB_EMPTY_NODE(node)) 496 if (RB_EMPTY_NODE(node))
497 return NULL; 497 return NULL;
498 498
499 /* 499 /*
500 * If we have a right-hand child, go d 500 * If we have a right-hand child, go down and then left as far
501 * as we can. 501 * as we can.
502 */ 502 */
503 if (node->rb_right) { 503 if (node->rb_right) {
504 node = node->rb_right; 504 node = node->rb_right;
505 while (node->rb_left) 505 while (node->rb_left)
506 node = node->rb_left; !! 506 node=node->rb_left;
507 return (struct rb_node *)node; 507 return (struct rb_node *)node;
508 } 508 }
509 509
510 /* 510 /*
511 * No right-hand children. Everything 511 * No right-hand children. Everything down and left is smaller than us,
512 * so any 'next' node must be in the g 512 * so any 'next' node must be in the general direction of our parent.
513 * Go up the tree; any time the ancest 513 * Go up the tree; any time the ancestor is a right-hand child of its
514 * parent, keep going up. First time i 514 * parent, keep going up. First time it's a left-hand child of its
515 * parent, said parent is our 'next' n 515 * parent, said parent is our 'next' node.
516 */ 516 */
517 while ((parent = rb_parent(node)) && n 517 while ((parent = rb_parent(node)) && node == parent->rb_right)
518 node = parent; 518 node = parent;
519 519
520 return parent; 520 return parent;
521 } 521 }
522 EXPORT_SYMBOL(rb_next); 522 EXPORT_SYMBOL(rb_next);
523 523
524 struct rb_node *rb_prev(const struct rb_node * 524 struct rb_node *rb_prev(const struct rb_node *node)
525 { 525 {
526 struct rb_node *parent; 526 struct rb_node *parent;
527 527
528 if (RB_EMPTY_NODE(node)) 528 if (RB_EMPTY_NODE(node))
529 return NULL; 529 return NULL;
530 530
531 /* 531 /*
532 * If we have a left-hand child, go do 532 * If we have a left-hand child, go down and then right as far
533 * as we can. 533 * as we can.
534 */ 534 */
535 if (node->rb_left) { 535 if (node->rb_left) {
536 node = node->rb_left; 536 node = node->rb_left;
537 while (node->rb_right) 537 while (node->rb_right)
538 node = node->rb_right; !! 538 node=node->rb_right;
539 return (struct rb_node *)node; 539 return (struct rb_node *)node;
540 } 540 }
541 541
542 /* 542 /*
543 * No left-hand children. Go up till w 543 * No left-hand children. Go up till we find an ancestor which
544 * is a right-hand child of its parent 544 * is a right-hand child of its parent.
545 */ 545 */
546 while ((parent = rb_parent(node)) && n 546 while ((parent = rb_parent(node)) && node == parent->rb_left)
547 node = parent; 547 node = parent;
548 548
549 return parent; 549 return parent;
550 } 550 }
551 EXPORT_SYMBOL(rb_prev); 551 EXPORT_SYMBOL(rb_prev);
552 552
553 void rb_replace_node(struct rb_node *victim, s 553 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
554 struct rb_root *root) 554 struct rb_root *root)
555 { 555 {
556 struct rb_node *parent = rb_parent(vic 556 struct rb_node *parent = rb_parent(victim);
557 557
558 /* Copy the pointers/colour from the v 558 /* Copy the pointers/colour from the victim to the replacement */
559 *new = *victim; 559 *new = *victim;
560 560
561 /* Set the surrounding nodes to point 561 /* Set the surrounding nodes to point to the replacement */
562 if (victim->rb_left) 562 if (victim->rb_left)
563 rb_set_parent(victim->rb_left, 563 rb_set_parent(victim->rb_left, new);
564 if (victim->rb_right) 564 if (victim->rb_right)
565 rb_set_parent(victim->rb_right 565 rb_set_parent(victim->rb_right, new);
566 __rb_change_child(victim, new, parent, 566 __rb_change_child(victim, new, parent, root);
567 } 567 }
568 EXPORT_SYMBOL(rb_replace_node); 568 EXPORT_SYMBOL(rb_replace_node);
569 569
570 void rb_replace_node_rcu(struct rb_node *victi 570 void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
571 struct rb_root *root) 571 struct rb_root *root)
572 { 572 {
573 struct rb_node *parent = rb_parent(vic 573 struct rb_node *parent = rb_parent(victim);
574 574
575 /* Copy the pointers/colour from the v 575 /* Copy the pointers/colour from the victim to the replacement */
576 *new = *victim; 576 *new = *victim;
577 577
578 /* Set the surrounding nodes to point 578 /* Set the surrounding nodes to point to the replacement */
579 if (victim->rb_left) 579 if (victim->rb_left)
580 rb_set_parent(victim->rb_left, 580 rb_set_parent(victim->rb_left, new);
581 if (victim->rb_right) 581 if (victim->rb_right)
582 rb_set_parent(victim->rb_right 582 rb_set_parent(victim->rb_right, new);
583 583
584 /* Set the parent's pointer to the new 584 /* Set the parent's pointer to the new node last after an RCU barrier
585 * so that the pointers onwards are se 585 * so that the pointers onwards are seen to be set correctly when doing
586 * an RCU walk over the tree. 586 * an RCU walk over the tree.
587 */ 587 */
588 __rb_change_child_rcu(victim, new, par 588 __rb_change_child_rcu(victim, new, parent, root);
589 } 589 }
590 EXPORT_SYMBOL(rb_replace_node_rcu); 590 EXPORT_SYMBOL(rb_replace_node_rcu);
591 591
592 static struct rb_node *rb_left_deepest_node(co 592 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
593 { 593 {
594 for (;;) { 594 for (;;) {
595 if (node->rb_left) 595 if (node->rb_left)
596 node = node->rb_left; 596 node = node->rb_left;
597 else if (node->rb_right) 597 else if (node->rb_right)
598 node = node->rb_right; 598 node = node->rb_right;
599 else 599 else
600 return (struct rb_node 600 return (struct rb_node *)node;
601 } 601 }
602 } 602 }
603 603
604 struct rb_node *rb_next_postorder(const struct 604 struct rb_node *rb_next_postorder(const struct rb_node *node)
605 { 605 {
606 const struct rb_node *parent; 606 const struct rb_node *parent;
607 if (!node) 607 if (!node)
608 return NULL; 608 return NULL;
609 parent = rb_parent(node); 609 parent = rb_parent(node);
610 610
611 /* If we're sitting on node, we've alr 611 /* If we're sitting on node, we've already seen our children */
612 if (parent && node == parent->rb_left 612 if (parent && node == parent->rb_left && parent->rb_right) {
613 /* If we are the parent's left 613 /* If we are the parent's left node, go to the parent's right
614 * node then all the way down 614 * node then all the way down to the left */
615 return rb_left_deepest_node(pa 615 return rb_left_deepest_node(parent->rb_right);
616 } else 616 } else
617 /* Otherwise we are the parent 617 /* Otherwise we are the parent's right node, and the parent
618 * should be next */ 618 * should be next */
619 return (struct rb_node *)paren 619 return (struct rb_node *)parent;
620 } 620 }
621 EXPORT_SYMBOL(rb_next_postorder); 621 EXPORT_SYMBOL(rb_next_postorder);
622 622
623 struct rb_node *rb_first_postorder(const struc 623 struct rb_node *rb_first_postorder(const struct rb_root *root)
624 { 624 {
625 if (!root->rb_node) 625 if (!root->rb_node)
626 return NULL; 626 return NULL;
627 627
628 return rb_left_deepest_node(root->rb_n 628 return rb_left_deepest_node(root->rb_node);
629 } 629 }
630 EXPORT_SYMBOL(rb_first_postorder); 630 EXPORT_SYMBOL(rb_first_postorder);
631 631
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